Add LiDAR RTK hand-eye calibration workflow and results

.gitignore

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+__pycache__/
+*.pyc
+.venv/

CONSENSUS_SELECTION.md

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+# 最终推荐值补充说明
+
+两套后端各自结果均保留。最终推荐值又增加了一层不依赖外参X的交叉检查：只有同一运动对的Open3D B与small_gicp B相差不超过5 cm、0.5°时才进入最终求解；最终B数为39对。
+
+最终推荐：
+
+- 平移 `[1.297760, -0.000067, 0.720498] m`
+- RPY `[-0.785151, 1.202661, -0.835510] deg`
+- 第二批AX RMS：`0.07985 m / 0.96118°`
+- 第一批22对辅助复核：`0.06067 m / 1.00298°`
+
+完整结果见 `results/final_extrinsic_recommended.json`，选择摘要见 `results/final_summary.json`。执行完整 `run_all.ps1` 后，再执行 `run_consensus_finish.ps1` 可重建最终推荐结果。

PAIR_DIAGNOSTICS.md

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+# Pair 局部诊断与全局灵敏度扫描
+
+本说明补充主 README。所有变换均采用：
+
+```text
+X = T_body_lidar
+A_ij X = X B_ij
+B_ij = T_Li_Lj（把站点 j 点云变到站点 i）
+```
+
+模式 4 相对模式 3 的数值差定义为：
+
+```text
+Delta_ij = B_ij^-1 * (X^-1 * A_ij * X)
+```
+
+打印的平移 xyz 和旋转 RPY 是 `Delta_ij` 在站点 j 雷达局部坐标系中的分量，不是屏幕坐标。3D 相机视角会改变画面中的“横向”，所以不能仅凭屏幕左右判断车体系 Y 或 yaw。
+
+## Pair 0 当前诊断
+
+Open3D 精筛 Pair 0（station 0 <- 1）的当前结果为：
+
+```text
+translation xyz = [-1.2535, +1.4157, +7.7441] cm
+rotation RPY xyz = [-0.5355, -0.1093, +0.0247] deg
+norm = 7.9716 cm / 0.547109 deg
+```
+
+因此这对主要表现为 roll/pitch 相关姿态差和相对 Z 差，yaw 仅约 `0.025 deg`，不应优先调 yaw。
+
+## 可视化试验
+
+查看原结果：
+
+```powershell
+$Repo = "D:\Outdoor Ackerman Cart Sensor Adaptation\LiDAR_RTK_Calibration_Rigorous_20260721"
+powershell.exe -NoProfile -ExecutionPolicy Bypass -File "$Repo\run\view_open3d_result.ps1" -PairIndex 0
+```
+
+试验车体系左乘 pitch `+0.2 deg`：
+
+```powershell
+powershell.exe -NoProfile -ExecutionPolicy Bypass -File "$Repo\run\view_open3d_result.ps1" -PairIndex 0 -LeftPitchDeg 0.2
+```
+
+此时按键含义：`3` 为 GICP 的 B，`4` 为当前最终 X 预测，`5` 为试验修正后的 X 预测。试验使用：
+
+```text
+X_test = DeltaR_body * X
+```
+
+这是真正的车体系左乘，会同时旋转 X 的旋转部分和平移向量；小角度下才近似等价于直接给 JSON 的 pitch 加相同角度。
+
+## 全部运动对扫描
+
+运行：
+
+```powershell
+powershell.exe -NoProfile -ExecutionPolicy Bypass -File "$Repo\run\run_sensitivity_scan.ps1" -PairIndex 0
+```
+
+程序扫描：
+
+- pitch：`+0.1/+0.2/+0.3 deg`；
+- 在这些 pitch 及零 pitch 附近扫描 roll：`-0.2/-0.1/+0.1 deg`；
+- yaw `-0.2/+0.2 deg` 只作为低灵敏度对照；
+- Open3D 全部精筛对、small_gicp 全部精筛对、跨后端共识对分别计算；
+- 同时报告地面法向与高度残差；
+- 使用 `0.05 m / 0.5 deg` 作为透明的归一化尺度，统计全局 RMS、改善对数和恶化对数。
+
+输出位于 `results/diagnostics/`。JSON 保存逐对结果，CSV 便于横向比较。
+
+## 接受规则
+
+局部扫描只用于定位，程序不会覆盖 `final_extrinsic_recommended.json`。候选至少需要满足：
+
+1. 不能只改善 Pair 0；全部精筛对的归一化 RMS 应下降；
+2. 改善的运动对数量应多于恶化数量；
+3. Open3D、small_gicp 与共识集合应给出相同方向的趋势；
+4. 地面法向和高度约束不能明显恶化；
+5. 多个代表性运动对的模式 4/5 可视化应同步改善。
+
+如果只有 Pair 0 改善，应把它视为局部配准或场景问题，不修改全局 X。
+
+对于当前仅含 yaw 的 RTK A，车体系 Z 轴平移在 AX=XB 中不可观。扫描程序会用 `X.z + 0.10 m` 做数值检查，但不会扫描或修改 z；z 必须由地面高度约束或外部量测确定。

README.md

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+# 双天线 RTK—3D 激光雷达严谨手眼标定
+
+本仓库是当前建议提交和继续维护的正式版本。第二批 38 站高频 RTK 用于主要求解；第一批 38 站稀疏 RTK 只作辅助复核。Open3D GICP 和 small_gicp 分别生成雷达运动 (B)，两套独立结果及跨后端共识结果均保留。
+
+实际部署只读取 [`results/final_extrinsic_deployment.json`](results/final_extrinsic_deployment.json)。算法原始求解、残差、Bootstrap 和筛选记录保留在其他结果文件中，不应与部署文件混用。
+
+## 标定总体流程
+
+1. **准备静止站点数据**：每站车辆静止，保存一帧原始雷达点云和该站 RTK；程序只使用雷达传感器坐标系下的 `points_raw`。
+2. **由 RTK 生成车体运动 (A)**：将双天线 RTK 的位置、水平航向、杆臂和 heading offset 转为车体位姿 (T_{WB_i})，再计算
+   
+   \[
+   A_{ij}=T_{WB_i}^{-1}T_{WB_j}.
+   \]
+3. **由点云配准生成雷达运动 (B)**：Open3D GICP 和 small_gicp 分别把第 j 站点云配准到第 i 站，得到
+   
+   \[
+   B_{ij}=T_{L_iL_j}.
+   \]
+4. **先验证和筛选 B，再求 X**：使用对称留出点、重叠率、留出点 RMSE、海森矩阵、正反向一致性、多初值稳定性、旋转共轭不变量和闭环误差检查 B。这个阶段不读取待求外参 X，也不使用 AX 残差筛选 B。
+5. **建立跨后端共识 B**：只保留 Open3D 与 small_gicp 对同一运动对的 B 相差不超过 `0.05 m / 0.50°` 的边；最终使用 Open3D B，small_gicp 作为独立一致性门控。
+6. **求解手眼外参 X**：固定 A 和通过筛选的 B 后，求解
+   
+   \[
+   A_{ij}X=XB_{ij},\qquad X=T_{body\leftarrow lidar}.
+   \]
+   
+   使用 Huber 鲁棒最小二乘、12 个初值、地面平面约束和 100 次 Bootstrap。
+7. **结果复核**：第二批共识对用于主要求解和整体残差统计；第一批重新独立生成 B，只作为稀疏 RTK 辅助复核；3D 可视化分别比较模式 3 的 GICP B 与模式 4 的 (X^{-1}AX)。
+8. **形成部署结果**：第二批跨后端共识结果给出完整的 `[x,y,z,roll,pitch,yaw]`；部署 JSON 直接采用该算法结果。。
+
+### 验证逻辑
+
+顺序固定为：
+
+```text
+先生成 B
+  -> 用不依赖 X 的点云与几何指标筛 B
+  -> 用另一个 GICP 后端复核同一 B
+  -> 固定共识 B
+  -> 最后才求 X
+  -> AX 残差只用于结果评价，不反过来选择 B
+```
+
+代码证据：
+
+- [`code/refine_pairs.py`](code/refine_pairs.py) 不读取外参文件，只使用留出点、正反向和旋转共轭不变量等指标；
+- [`code/cross_backend_filter.py`](code/cross_backend_filter.py) 只比较两个后端的 B，不读取 X；
+- [`code/rigorous_calibration.py`](code/rigorous_calibration.py) 在 B 集合固定后才执行 `calibrate` 求 X；
+- 第一批辅助复核的 B 也重新独立生成，且不使用 AX 残差筛选。
+
+但这些检查仍不能把 B 变成绝对真值：重复结构、动态物体或错误局部最优仍可能让两个后端同时出错，所以必须结合模式 3 点云质量、留出集指标和多运动对整体统计判断。
+
+## 最终部署外参
+
+坐标变换定义：
+
+\[
+X=T_{body\leftarrow lidar}
+\]
+
+即将原始雷达点从雷达坐标系变换到以后轮轴中心为原点、X 前/Y 左/Z 上的车体坐标系。
+
+部署值：
+
+- 平移 `[x,y,z] = [1.297760, -0.000067, 0.720498] m`
+- RPY `[roll,pitch,yaw] = [-0.785151, 1.202661, -0.835510] deg`
+- 唯一部署文件：[`results/final_extrinsic_deployment.json`](results/final_extrinsic_deployment.json)
+
+该值来自第二批 39 对跨后端共识、完整地面平面约束和 Bootstrap 稳定性检查。
+
+算法在完整地面平面模型下的原始结果为：
+
+- 平移 `[1.297760, -0.000067, 0.720498] m`
+- RPY `[-0.785151, 1.202661, -0.835510] deg`
+- 文件：[`results/final_extrinsic_recommended.json`](results/final_extrinsic_recommended.json)
+
+`final_extrinsic_recommended.json` 保留完整求解、残差和 Bootstrap 记录，用于复现和审计；`final_extrinsic_deployment.json` 是唯一部署入口。
+
+共识结果统计：
+
+- 第二批 39 对 AX RMS：`0.07985 m / 0.96118°`
+- 第一批 22 对辅助复核：`0.06067 m / 1.00298°`
+- 结果摘要：[`results/final_summary.json`](results/final_summary.json)
+
+两套后端分别求得：
+
+| 后端 | 平移 `[x,y,z]` m | RPY deg | 第二批 AX RMS |
+|---|---|---|---|
+| Open3D GICP | `[1.297883,-0.003100,0.721789]` | `[-0.757207,1.146042,-0.879781]` | `0.1002 m / 1.0115°` |
+| small_gicp | `[1.299630,-0.003565,0.721886]` | `[-0.787156,1.141456,-0.935757]` | `0.1187 m / 1.1351°` |
+
+两后端单独求出的 X 相差 1.81 mm、0.063°。共识求解的 100 次 Bootstrap 标准差 `[x,y,z,roll,pitch,yaw]` 为：
+
+```text
+[0.00322 m, 0.00333 m, 0.00169 m, 0.0980°, 0.0746°, 0.1189°]
+```
+
+这里的 Z Bootstrap 只描述当前地面模型条件下的内部稳定性，不代表机械高度的绝对精度。
+
+重要限制：旋转 RMS 仍约 1°，所以这不是厘米级绝对精度认证。远距离点云仍可能看到角度错层；Bootstrap 也不包含 RTK 参考点、航向偏置或杆臂定义错误等系统误差。
+
+## 坐标与公式
+
+\[
+A_{ij}=T_{WB_i}^{-1}T_{WB_j},\qquad
+B_{ij}=T_{L_iL_j},\qquad
+A_{ij}X=XB_{ij}
+\]
+
+`B_ij` 把第 j 站雷达点变换到第 i 站雷达坐标系。程序只读取 `points_raw`，禁止使用已经变到车体坐标系的点。
+
+RTK 轨迹使用 `body_poses_rear_gga_raw_rear_to_front.csv`，对应后天线 GGA 位置和双天线后到前方向。
+
+地面约束采用完整平面变换：
+
+\[
+n_B=R_Xn_L,\qquad r_h=d_L-n_B^Tt_X-h_{body}
+\]
+
+不再使用旧近似式 `d_L-(t_z+h_body)`。
+
+## 详细求解流程
+
+1. 第二批高频 RTK 生成 A；第一批稀疏 RTK 不参与主要求解。
+2. 不使用手量外参作初值：生成 B 时 (X_0=I)，所以 (B_0=A)；求 X 也从单位变换和随机初值开始。
+3. 两后端均采用三级粗到细：体素 0.30/0.15/0.08 m，对应距离 1.20/0.50/0.25 m。
+4. 逐对检查对称留出点、海森矩阵、正反向一致性、多初值稳定性和 B 三角闭环。
+5. 使用重叠率、留出点 RMSE 和旋转共轭不变量筛选 B；不使用 AX 残差筛选。
+6. 两后端分别求 X；随后使用跨后端 B 一致性得到最终 39 对共识集合。
+7. 使用 Huber 鲁棒最小二乘、12 个随机初值、完整地面约束和 100 次 Bootstrap 求算法 X。
+8. 第一批重新独立生成 B，仅作辅助复核，不参与第二批求解。
+9. 使用共识算法完整解形成精简部署 JSON，不覆盖算法原始结果。
+
+## 目录
+
+```text
+code/
+  rigorous_calibration.py
+  refine_pairs.py
+  cross_backend_filter.py
+  summarize_results.py
+  finalize_consensus.py
+  scan_extrinsic_sensitivity.py
+  visualize_pair_3d.py
+run/
+  run_all.ps1
+  run_consensus_finish.ps1
+  run_sensitivity_scan.ps1
+  view_open3d_result.ps1
+  view_small_gicp_result.ps1
+results/
+  common/
+  open3d_gicp/
+  small_gicp/
+  consensus/
+  diagnostics/
+  final_extrinsic_deployment.json     # 实际部署只读取这个文件
+  final_extrinsic_recommended.json    # 算法原始结果及详细诊断
+  final_summary.json
+```
+
+## 安装与完整重跑
+
+```powershell
+$Repo = "D:\Outdoor Ackerman Cart Sensor Adaptation\LiDAR_RTK_Calibration_Rigorous_20260721"
+python -m pip install -r "$Repo\requirements.txt"
+powershell.exe -NoProfile -ExecutionPolicy Bypass -File "$Repo\run\run_all.ps1"
+powershell.exe -NoProfile -ExecutionPolicy Bypass -File "$Repo\run\run_consensus_finish.ps1"
+```
+
+如果 prepared 数据移动了：
+
+```powershell
+powershell.exe -NoProfile -ExecutionPolicy Bypass -File "$Repo\run\run_all.ps1" -Batch1Prepared "你的第一批prepared目录" -Batch2Prepared "你的第二批prepared目录"
+powershell.exe -NoProfile -ExecutionPolicy Bypass -File "$Repo\run\run_consensus_finish.ps1"
+```
+
+重跑 `run_consensus_finish.ps1` 会重新生成算法原始结果，但不会自动生成或覆盖已经人工确认的 `final_extrinsic_deployment.json`。
+
+## 3D 可视化
+
+Open3D 单后端结果：
+
+```powershell
+powershell.exe -NoProfile -ExecutionPolicy Bypass -File "$Repo\run\view_open3d_result.ps1" -PairIndex 0
+```
+
+small_gicp 单后端结果：
+
+```powershell
+powershell.exe -NoProfile -ExecutionPolicy Bypass -File "$Repo\run\view_small_gicp_result.ps1" -PairIndex 0
+```
+
+蓝色是目标站 i，橙色是源站 j。按键：`1` 原始；`2` RTK 初始 A；`3` GICP B；`4` 外参预测的 (X^{-1}AX)；指定左乘 RPY 试验量后，`5` 为试验结果。
+
+程序打印的差值为：
+
+\[
+B^{-1}(X^{-1}AX)
+\]
+
+其 xyz/RPY 分量位于站点 j 的雷达局部坐标系，不是屏幕坐标。模式 3 好而模式 4 差，说明 A/X 一致性不足；模式 3 本身差，说明该 B 不能用于判断外参。
+
+共识运动对可直接指定部署外参：
+
+```powershell
+python "$Repo\code\visualize_pair_3d.py" --frames "C:\Users\admin\Documents\Codex\2026-07-15\wo\outputs\calibration_data1_20260720\prepared\frames_all" --pairs "$Repo\results\consensus\B_batch2_consensus.npz" --extrinsic "$Repo\results\final_extrinsic_deployment.json" --pair-index 0
+```
+
+局部灵敏度扫描和判断规则见 [`PAIR_DIAGNOSTICS.md`](PAIR_DIAGNOSTICS.md)。
+
+## 关键质量文件
+
+- [`results/open3d_gicp/B_batch2_quality.json`](results/open3d_gicp/B_batch2_quality.json)：海森矩阵、留出点、正反向和多初值信息；
+- [`results/open3d_gicp/B_batch2_refined.refinement.json`](results/open3d_gicp/B_batch2_refined.refinement.json)：二级筛选原因；
+- [`results/consensus/B_batch2_consensus.consensus.json`](results/consensus/B_batch2_consensus.consensus.json)：跨后端一致性筛选；
+- [`results/consensus/batch1_auxiliary_check.json`](results/consensus/batch1_auxiliary_check.json)：第一批辅助复核；
+- [`results/final_summary.json`](results/final_summary.json)：算法结果摘要；
+- [`results/diagnostics/`](results/diagnostics/)：局部修正对单对及全体运动对的影响。
+
+## 必须外部确认的假设
+
+- `lat/lon/h` 确为后天线相位中心；
+- `rawHeading` 确为后天线指向前天线；
+- heading offset 数值和正负号正确；
+
+任何一项变化，都必须更新相应约束；RTK 定义变化时需要重新生成 A 并重跑。

code/cross_backend_filter.py

@@ -0,0 +1,81 @@
+#!/usr/bin/env python3
+"""Keep common A/B edges on which Open3D and small_gicp agree, without using X."""
+import argparse
+import json
+from pathlib import Path
+
+import numpy as np
+from scipy.spatial.transform import Rotation
+
+
+def key(meta):
+    return int(meta[0]), int(meta[1])
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--open3d-pairs", required=True)
+    parser.add_argument("--small-pairs", required=True)
+    parser.add_argument("--output", required=True)
+    parser.add_argument("--audit")
+    parser.add_argument("--max-translation", type=float, default=0.05)
+    parser.add_argument("--max-rotation", type=float, default=0.50)
+    parser.add_argument("--min-pairs", type=int, default=25)
+    args = parser.parse_args()
+
+    with np.load(args.open3d_pairs, allow_pickle=False) as source:
+        open_a = np.asarray(source["A"], float)
+        open_b = np.asarray(source["B"], float)
+        open_meta = np.asarray(source["meta"], float)
+        station_times = np.asarray(source["station_times"])
+        rtk_dt = np.asarray(source["rtk_nearest_dt_s"])
+    with np.load(args.small_pairs, allow_pickle=False) as source:
+        small = {key(meta): np.asarray(b, float)
+                 for meta, b in zip(source["meta"], source["B"])}
+
+    keep, audit = [], []
+    for meta, b_open in zip(open_meta, open_b):
+        edge = key(meta)
+        if edge not in small:
+            audit.append({"i": edge[0], "j": edge[1], "accepted": False,
+                          "reason": "not_in_small_gicp_refined"})
+            keep.append(False)
+            continue
+        delta = np.linalg.inv(b_open) @ small[edge]
+        translation = float(np.linalg.norm(delta[:3, 3]))
+        rotation = float(np.rad2deg(Rotation.from_matrix(delta[:3, :3]).magnitude()))
+        accepted = translation <= args.max_translation and rotation <= args.max_rotation
+        keep.append(accepted)
+        audit.append({
+            "i": edge[0], "j": edge[1],
+            "open3d_small_translation_m": translation,
+            "open3d_small_rotation_deg": rotation,
+            "accepted": accepted,
+            "reason": "" if accepted else "backend_disagreement",
+        })
+    keep = np.asarray(keep, bool)
+    output = Path(args.output)
+    output.parent.mkdir(parents=True, exist_ok=True)
+    np.savez_compressed(
+        output, A=open_a[keep], B=open_b[keep], meta=open_meta[keep],
+        station_times=station_times, rtk_nearest_dt_s=rtk_dt,
+        backend=np.asarray("open3d_gicp_cross_backend_consensus"),
+    )
+    audit_path = Path(args.audit or output.with_suffix(".consensus.json"))
+    audit_path.write_text(json.dumps({
+        "selection_is_X_independent": True,
+        "B_source": "Open3D; small_gicp is used only as an agreement gate",
+        "max_translation_m": args.max_translation,
+        "max_rotation_deg": args.max_rotation,
+        "input_open3d_pairs": len(open_b),
+        "accepted_pairs": int(np.count_nonzero(keep)),
+        "pairs": audit,
+    }, ensure_ascii=False, indent=2), encoding="utf-8")
+    if np.count_nonzero(keep) < args.min_pairs:
+        raise RuntimeError(f"only {np.count_nonzero(keep)} consensus pairs")
+    print(json.dumps({"accepted_pairs": int(np.count_nonzero(keep)),
+                      "output": str(output.resolve()), "audit": str(audit_path.resolve())}, indent=2))
+
+
+if __name__ == "__main__":
+    main()

code/finalize_consensus.py

@@ -0,0 +1,58 @@
+#!/usr/bin/env python3
+"""Publish the cross-backend-consensus result as the recommended deliverable."""
+import argparse
+import json
+from pathlib import Path
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--consensus-extrinsic", required=True)
+    parser.add_argument("--consensus-check", required=True)
+    parser.add_argument("--open3d-extrinsic", required=True)
+    parser.add_argument("--small-extrinsic", required=True)
+    parser.add_argument("--output", required=True)
+    parser.add_argument("--summary", required=True)
+    args = parser.parse_args()
+    consensus = json.loads(Path(args.consensus_extrinsic).read_text(encoding="utf-8-sig"))
+    check = json.loads(Path(args.consensus_check).read_text(encoding="utf-8-sig"))
+    open3d = json.loads(Path(args.open3d_extrinsic).read_text(encoding="utf-8-sig"))
+    small = json.loads(Path(args.small_extrinsic).read_text(encoding="utf-8-sig"))
+    summary = {
+        "recommended_method": "Open3D B gated by Open3D-small_gicp cross-backend agreement",
+        "selection_is_X_independent": True,
+        "second_batch_role": "estimation (dense RTK)",
+        "first_batch_role": "auxiliary check only (sparse RTK)",
+        "consensus": {
+            "translation_m": consensus["translation_m"],
+            "rotation_rpy_deg_xyz": consensus["rotation_rpy_deg_xyz"],
+            "estimation": consensus["estimation"]["residuals"],
+            "bootstrap_std": consensus["bootstrap"]["std"],
+            "batch1_auxiliary": check["metrics"],
+        },
+        "separate_backend_results": {
+            "open3d_gicp": {
+                "translation_m": open3d["translation_m"],
+                "rotation_rpy_deg_xyz": open3d["rotation_rpy_deg_xyz"],
+            },
+            "small_gicp": {
+                "translation_m": small["translation_m"],
+                "rotation_rpy_deg_xyz": small["rotation_rpy_deg_xyz"],
+            },
+        },
+        "warning": "AX rotation RMS remains about one degree; this is not centimetre-grade absolute certification.",
+    }
+    published = dict(consensus)
+    published["selection"] = {
+        "method": summary["recommended_method"],
+        "selection_is_X_independent": True,
+        "consensus_pair_threshold": "Open3D-small_gicp B delta <= 0.05 m and <= 0.50 deg",
+        "warning": summary["warning"],
+    }
+    Path(args.output).write_text(json.dumps(published, ensure_ascii=False, indent=2), encoding="utf-8")
+    Path(args.summary).write_text(json.dumps(summary, ensure_ascii=False, indent=2), encoding="utf-8")
+    print(json.dumps(summary, ensure_ascii=False, indent=2))
+
+
+if __name__ == "__main__":
+    main()

code/refine_pairs.py

@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+"""X-independent second-stage filter for stationary A/B pairs."""
+import argparse
+import json
+from pathlib import Path
+
+import numpy as np
+
+from rigorous_calibration import read_pairs, rotation_angle_deg
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--pairs", required=True)
+    parser.add_argument("--quality-json", required=True)
+    parser.add_argument("--output", required=True)
+    parser.add_argument("--audit")
+    parser.add_argument("--min-pairs", type=int, default=25)
+    parser.add_argument("--min-inlier-ratio", type=float, default=0.70)
+    parser.add_argument("--max-inlier-rmse", type=float, default=0.13)
+    parser.add_argument("--max-rotation-invariant-error", type=float, default=0.75)
+    parser.add_argument("--reverse-translation-tolerance", type=float, default=0.05)
+    parser.add_argument("--reverse-rotation-tolerance", type=float, default=0.50)
+    args = parser.parse_args()
+
+    a_array, b_array, meta, _ = read_pairs(args.pairs)
+    quality = json.loads(Path(args.quality_json).read_text(encoding="utf-8-sig"))
+    reports = {(int(item["i"]), int(item["j"])): item for item in quality["pairs"]}
+    keep, audit = [], []
+    for a_ij, b_ij, item_meta in zip(a_array, b_array, meta):
+        key = (int(item_meta[0]), int(item_meta[1]))
+        report = reports[key]
+        heldout = report["heldout_symmetric"]
+        reverse = report["forward_reverse"]
+        invariant = abs(rotation_angle_deg(a_ij[:3, :3]) - rotation_angle_deg(b_ij[:3, :3]))
+        reasons = []
+        if heldout["inlier_ratio"] < args.min_inlier_ratio:
+            reasons.append("overlap_ratio")
+        if heldout["inlier_rmse_m"] is None or heldout["inlier_rmse_m"] > args.max_inlier_rmse:
+            reasons.append("heldout_rmse")
+        if invariant > args.max_rotation_invariant_error:
+            reasons.append("rotation_conjugacy_invariant")
+        if reverse["translation_m"] > args.reverse_translation_tolerance:
+            reasons.append("forward_reverse_translation")
+        if reverse["rotation_deg"] > args.reverse_rotation_tolerance:
+            reasons.append("forward_reverse_rotation")
+        accepted = not reasons
+        keep.append(accepted)
+        audit.append({
+            "i": key[0], "j": key[1], "heldout_inlier_ratio": heldout["inlier_ratio"],
+            "heldout_inlier_rmse_m": heldout["inlier_rmse_m"],
+            "rotation_invariant_error_deg": invariant,
+            "reverse_translation_m": reverse["translation_m"],
+            "reverse_rotation_deg": reverse["rotation_deg"],
+            "accepted": accepted, "rejection_reasons": reasons,
+        })
+    keep = np.asarray(keep, bool)
+    output = Path(args.output)
+    output.parent.mkdir(parents=True, exist_ok=True)
+    with np.load(args.pairs, allow_pickle=False) as source:
+        np.savez_compressed(
+            output, A=a_array[keep], B=b_array[keep], meta=meta[keep],
+            station_times=np.asarray(source["station_times"]),
+            rtk_nearest_dt_s=np.asarray(source["rtk_nearest_dt_s"]),
+            backend=np.asarray(source["backend"]),
+        )
+    audit_path = Path(args.audit or output.with_suffix(".refinement.json"))
+    audit_path.write_text(json.dumps({
+        "selection_is_X_independent": True,
+        "criteria": {
+            "min_inlier_ratio": args.min_inlier_ratio,
+            "max_inlier_rmse_m": args.max_inlier_rmse,
+            "max_rotation_invariant_error_deg": args.max_rotation_invariant_error,
+            "reverse_translation_tolerance_m": args.reverse_translation_tolerance,
+            "reverse_rotation_tolerance_deg": args.reverse_rotation_tolerance,
+        },
+        "input_pairs": len(keep), "accepted_pairs": int(np.count_nonzero(keep)),
+        "pairs": audit,
+    }, ensure_ascii=False, indent=2), encoding="utf-8")
+    if np.count_nonzero(keep) < args.min_pairs:
+        raise RuntimeError(f"only {np.count_nonzero(keep)} refined pairs; need {args.min_pairs}")
+    print(json.dumps({"input_pairs": len(keep), "accepted_pairs": int(np.count_nonzero(keep)),
+                      "output": str(output.resolve()), "audit": str(audit_path.resolve())}, indent=2))
+
+
+if __name__ == "__main__":
+    main()

code/rigorous_calibration.py

@@ -0,0 +1,769 @@
+#!/usr/bin/env python3
+"""Rigorous stationary LiDAR / dual-antenna RTK hand-eye calibration.
+
+Convention: T_A_B maps points from frame B into frame A.
+X = T_body_lidar, A_ij = T_W_Bi^-1 T_W_Bj, B_ij = T_Li_Lj,
+therefore A_ij X = X B_ij. Raw sensor-frame points_raw are used.
+"""
+from __future__ import annotations
+
+import argparse
+import csv
+import json
+import math
+import time
+from dataclasses import dataclass
+from pathlib import Path
+
+import numpy as np
+from scipy.optimize import least_squares
+from scipy.spatial import cKDTree
+
+
+def skew(v):
+    x, y, z = v
+    return np.array([[0.0, -z, y], [z, 0.0, -x], [-y, x, 0.0]])
+
+
+def so3_exp(v):
+    angle = float(np.linalg.norm(v))
+    if angle < 1e-12:
+        return np.eye(3) + skew(v)
+    k = skew(np.asarray(v, float) / angle)
+    return np.eye(3) + math.sin(angle) * k + (1.0 - math.cos(angle)) * k @ k
+
+
+def so3_log(rotation):
+    cosine = float(np.clip((np.trace(rotation) - 1.0) / 2.0, -1.0, 1.0))
+    angle = math.acos(cosine)
+    vee = np.array([
+        rotation[2, 1] - rotation[1, 2],
+        rotation[0, 2] - rotation[2, 0],
+        rotation[1, 0] - rotation[0, 1],
+    ])
+    if angle < 1e-9:
+        return vee / 2.0
+    if abs(math.pi - angle) < 1e-5:
+        values, vectors = np.linalg.eigh((rotation + np.eye(3)) / 2.0)
+        return vectors[:, int(np.argmax(values))] * angle
+    return vee * angle / (2.0 * math.sin(angle))
+
+
+def quat_to_rotation(q):
+    x, y, z, w = np.asarray(q, float) / np.linalg.norm(q)
+    return np.array([
+        [1-2*(y*y+z*z), 2*(x*y-z*w), 2*(x*z+y*w)],
+        [2*(x*y+z*w), 1-2*(x*x+z*z), 2*(y*z-x*w)],
+        [2*(x*z-y*w), 2*(y*z+x*w), 1-2*(x*x+y*y)],
+    ])
+
+
+def rotation_to_quat(rotation):
+    from scipy.spatial.transform import Rotation
+    return Rotation.from_matrix(rotation).as_quat()
+
+
+def rpy_deg(rotation):
+    from scipy.spatial.transform import Rotation
+    return Rotation.from_matrix(rotation).as_euler("xyz", degrees=True).tolist()
+
+
+def make_transform(translation, rotation):
+    transform = np.eye(4)
+    transform[:3, :3] = rotation
+    transform[:3, 3] = translation
+    return transform
+
+
+def params_transform(params):
+    return make_transform(params[:3], so3_exp(params[3:]))
+
+
+def inverse_transform(transform):
+    answer = np.eye(4)
+    answer[:3, :3] = transform[:3, :3].T
+    answer[:3, 3] = -answer[:3, :3] @ transform[:3, 3]
+    return answer
+
+
+def transform_points(points, transform):
+    return points @ transform[:3, :3].T + transform[:3, 3]
+
+
+def rotation_angle_deg(rotation):
+    return math.degrees(np.linalg.norm(so3_log(rotation)))
+
+
+@dataclass
+class PoseSeries:
+    time: np.ndarray
+    transforms: np.ndarray
+
+
+def read_poses(path):
+    timestamps, transforms = [], []
+    with Path(path).open(encoding="utf-8-sig", newline="") as stream:
+        reader = csv.DictReader(stream)
+        required = ("time", "x", "y", "z", "qx", "qy", "qz", "qw")
+        missing = [key for key in required if key not in (reader.fieldnames or [])]
+        if missing:
+            raise ValueError(f"{path}: missing pose fields {missing}")
+        for row in reader:
+            timestamps.append(float(row["time"]))
+            translation = np.array([float(row[k]) for k in ("x", "y", "z")])
+            quaternion = np.array([float(row[k]) for k in ("qx", "qy", "qz", "qw")])
+            transforms.append(make_transform(translation, quat_to_rotation(quaternion)))
+    order = np.argsort(timestamps)
+    return PoseSeries(np.asarray(timestamps)[order], np.asarray(transforms)[order])
+
+
+def nearest_pose(series, timestamp):
+    index = int(np.argmin(np.abs(series.time - timestamp)))
+    return series.transforms[index], float(abs(series.time[index] - timestamp))
+
+
+def npz_files(root):
+    files = sorted(Path(root).rglob("*.npz"))
+    if not files:
+        raise FileNotFoundError(f"no NPZ files under {root}")
+    return files
+
+
+def load_npz_xyz(path, min_range=1.0, max_range=50.0):
+    with np.load(path, allow_pickle=False) as data:
+        if "points_raw" not in data:
+            raise ValueError(f"{path}: points_raw is required; cart-frame points are forbidden")
+        raw = np.asarray(data["points_raw"], dtype=np.float64)
+        timestamp = float(np.ravel(data["unix_time_ns"])[0]) / 1e9
+        counter = int(np.ravel(data["frame_counter"])[0])
+    distance = raw[:, 0] * 0.001
+    azimuth = np.deg2rad(raw[:, 1])
+    altitude = np.deg2rad(raw[:, 2])
+    valid = (
+        np.isfinite(distance + azimuth + altitude)
+        & (distance >= min_range)
+        & (distance <= max_range)
+    )
+    distance, azimuth, altitude = distance[valid], azimuth[valid], altitude[valid]
+    xyz = np.column_stack((
+        distance * np.cos(altitude) * np.cos(azimuth),
+        distance * np.cos(altitude) * np.sin(azimuth),
+        distance * np.sin(altitude),
+    ))
+    return timestamp, counter, xyz
+
+
+def load_stations(root, min_range, max_range, z_min=None, z_max=None):
+    stations = []
+    for path in npz_files(root):
+        timestamp, counter, xyz = load_npz_xyz(path, min_range, max_range)
+        if z_min is not None:
+            xyz = xyz[(xyz[:, 2] >= z_min) & (xyz[:, 2] <= z_max)]
+        stations.append((timestamp, counter, path, xyz))
+    stations.sort(key=lambda item: item[0])
+    return stations
+
+
+def split_holdout(points, fraction, phase):
+    stride = max(int(round(1.0 / fraction)), 2)
+    index = np.arange(len(points))
+    holdout = ((index + phase) % stride) == 0
+    return points[~holdout], points[holdout]
+
+
+def make_o3d_cloud(points, voxel):
+    import open3d as o3d
+    cloud = o3d.geometry.PointCloud()
+    cloud.points = o3d.utility.Vector3dVector(np.asarray(points, float))
+    return cloud.voxel_down_sample(voxel)
+
+
+def align_open3d(target, source, initial, voxels, correspondences, iterations):
+    import open3d as o3d
+    registration = o3d.pipelines.registration
+    estimate = registration.TransformationEstimationForGeneralizedICP()
+    criteria = registration.ICPConvergenceCriteria(max_iteration=iterations)
+    transform, stages = np.asarray(initial, float), []
+    final_target = final_source = final_answer = None
+    started = time.perf_counter()
+    for voxel, correspondence in zip(voxels, correspondences):
+        target_cloud = make_o3d_cloud(target, voxel)
+        source_cloud = make_o3d_cloud(source, voxel)
+        answer = registration.registration_generalized_icp(
+            source_cloud, target_cloud, correspondence, transform, estimate, criteria
+        )
+        transform = np.asarray(answer.transformation, float)
+        stages.append({
+            "voxel_m": voxel,
+            "max_correspondence_m": correspondence,
+            "fitness": float(answer.fitness),
+            "inlier_rmse_m": float(answer.inlier_rmse),
+            "target_points": len(target_cloud.points),
+            "source_points": len(source_cloud.points),
+        })
+        final_target, final_source, final_answer = target_cloud, source_cloud, answer
+    information = registration.get_information_matrix_from_point_clouds(
+        final_source, final_target, correspondences[-1], transform
+    )
+    inliers = int(round(float(final_answer.fitness) * len(final_source.points)))
+    return {
+        "transform": transform,
+        "hessian": np.asarray(information, float),
+        "converged": None,
+        "iterations": None,
+        "num_inliers": inliers,
+        "objective": float(final_answer.inlier_rmse ** 2 * max(inliers, 1)),
+        "elapsed_sec": time.perf_counter() - started,
+        "stages": stages,
+    }
+
+
+def align_small_gicp(target, source, initial, voxels, correspondences, iterations, threads):
+    import small_gicp
+    transform, stages, result = np.asarray(initial, float), [], None
+    started = time.perf_counter()
+    for voxel, correspondence in zip(voxels, correspondences):
+        result = small_gicp.align(
+            np.ascontiguousarray(target),
+            np.ascontiguousarray(source),
+            transform,
+            registration_type="GICP",
+            downsampling_resolution=voxel,
+            max_correspondence_distance=correspondence,
+            num_threads=threads,
+            max_iterations=iterations,
+            rotation_epsilon=math.radians(0.005),
+            translation_epsilon=0.0005,
+            verbose=False,
+        )
+        transform = np.asarray(result.T_target_source, float)
+        stages.append({
+            "voxel_m": voxel,
+            "max_correspondence_m": correspondence,
+            "converged": bool(result.converged),
+            "iterations": int(result.iterations),
+            "num_inliers": int(result.num_inliers),
+            "objective": float(result.error),
+        })
+    return {
+        "transform": transform,
+        "hessian": np.asarray(result.H, float),
+        "converged": bool(result.converged),
+        "iterations": int(result.iterations),
+        "num_inliers": int(result.num_inliers),
+        "objective": float(result.error),
+        "elapsed_sec": time.perf_counter() - started,
+        "stages": stages,
+    }
+
+
+def align_backend(backend, target, source, initial, args):
+    if backend == "open3d":
+        return align_open3d(
+            target, source, initial, args.voxels, args.correspondences, args.iterations
+        )
+    return align_small_gicp(
+        target, source, initial, args.voxels, args.correspondences,
+        args.iterations, args.threads
+    )
+
+
+def symmetric_heldout_metrics(target_fit, target_holdout, source_fit, source_holdout,
+                              transform, threshold):
+    transformed_source_fit = transform_points(source_fit, transform)
+    transformed_source_holdout = transform_points(source_holdout, transform)
+    forward = cKDTree(target_fit).query(transformed_source_holdout, workers=-1)[0]
+    reverse = cKDTree(transformed_source_fit).query(target_holdout, workers=-1)[0]
+    distances = np.concatenate((forward, reverse))
+    inliers = distances[distances <= threshold]
+    return {
+        "evaluated": int(len(distances)),
+        "inliers": int(len(inliers)),
+        "inlier_ratio": float(len(inliers) / max(len(distances), 1)),
+        "inlier_rmse_m": float(np.sqrt(np.mean(inliers**2))) if len(inliers) else None,
+        "median_m": float(np.median(distances)),
+        "p90_m": float(np.quantile(distances, 0.90)),
+        "p95_m": float(np.quantile(distances, 0.95)),
+    }
+
+
+def hessian_metrics(hessian, characteristic_length=10.0):
+    hessian = 0.5 * (np.asarray(hessian, float) + np.asarray(hessian, float).T)
+    scale = np.diag([1.0 / characteristic_length] * 3 + [1.0] * 3)
+    scaled = scale.T @ hessian @ scale
+    values, vectors = np.linalg.eigh(scaled)
+    largest = max(float(np.max(np.abs(values))), np.finfo(float).eps)
+    positive = values[values > largest * 1e-9]
+    condition = float(positive[-1] / positive[0]) if len(positive) else float("inf")
+    return {
+        "native_order": ["rx_rad", "ry_rad", "rz_rad", "tx_m", "ty_m", "tz_m"],
+        "scaled_eigenvalues": values.tolist(),
+        "effective_rank": int(len(positive)),
+        "scaled_condition_number": condition,
+        "weakest_scaled_direction": vectors[:, int(np.argmin(values))].tolist(),
+    }
+
+
+def transform_difference(reference, candidate):
+    delta = inverse_transform(reference) @ candidate
+    return {
+        "translation_m": float(np.linalg.norm(delta[:3, 3])),
+        "rotation_deg": rotation_angle_deg(delta[:3, :3]),
+    }
+
+
+def loop_metrics(transforms):
+    loops = []
+    for (i, j), b_ij in transforms.items():
+        for (j2, k), b_jk in transforms.items():
+            if j2 != j or (i, k) not in transforms:
+                continue
+            loops.append(transform_difference(transforms[(i, k)], b_ij @ b_jk))
+    if not loops:
+        return {"count": 0}
+    translation = np.array([item["translation_m"] for item in loops])
+    rotation = np.array([item["rotation_deg"] for item in loops])
+    return {
+        "count": len(loops),
+        "translation_rms_m": float(np.sqrt(np.mean(translation**2))),
+        "translation_p95_m": float(np.quantile(translation, 0.95)),
+        "rotation_rms_deg": float(np.sqrt(np.mean(rotation**2))),
+        "rotation_p95_deg": float(np.quantile(rotation, 0.95)),
+    }
+
+
+def cmd_ground(args):
+    stations = load_stations(args.frames, args.min_range, args.max_range)
+    rows = []
+    for timestamp, counter, _, xyz in stations:
+        roi = xyz[(xyz[:, 2] >= args.z_min) & (xyz[:, 2] <= args.z_max)]
+        if len(roi) < args.min_inliers:
+            continue
+        cloud = make_o3d_cloud(roi, args.voxel)
+        plane, indexes = cloud.segment_plane(
+            args.distance_threshold, 3, args.ransac_iterations
+        )
+        normal = np.asarray(plane[:3], float)
+        norm = np.linalg.norm(normal)
+        normal, distance = normal / norm, float(plane[3] / norm)
+        if distance < 0:
+            normal, distance = -normal, -distance
+        points = np.asarray(cloud.points)[indexes]
+        rms = float(np.sqrt(np.mean((points @ normal + distance) ** 2)))
+        if len(indexes) >= args.min_inliers and rms <= args.max_rms:
+            rows.append([timestamp, *normal, distance, len(indexes), rms, counter])
+    output = Path(args.output)
+    output.parent.mkdir(parents=True, exist_ok=True)
+    with output.open("w", encoding="utf-8", newline="") as stream:
+        writer = csv.writer(stream)
+        writer.writerow(["time", "nx", "ny", "nz", "d", "inliers", "rms_m", "frame_counter"])
+        writer.writerows(rows)
+    print(json.dumps({"planes": len(rows), "output": str(output.resolve())}, indent=2))
+
+
+def cmd_pairs(args):
+    if len(args.voxels) != len(args.correspondences):
+        raise ValueError("--voxels and --correspondences must have equal lengths")
+    stations = load_stations(
+        args.frames, args.min_range, args.max_range, args.z_min, args.z_max
+    )
+    body = read_poses(args.body)
+    if len(stations) < args.min_stations:
+        raise ValueError(f"need at least {args.min_stations} stations, got {len(stations)}")
+    body_poses, body_dt = [], []
+    for timestamp, _, _, xyz in stations:
+        if len(xyz) < args.min_roi_points:
+            raise ValueError(f"station at {timestamp} has only {len(xyz)} ROI points")
+        pose, dt = nearest_pose(body, timestamp + args.time_offset)
+        body_poses.append(pose)
+        body_dt.append(dt)
+    body_poses = np.asarray(body_poses)
+    split = [split_holdout(station[3], args.holdout_fraction, i)
+             for i, station in enumerate(stations)]
+    rng = np.random.default_rng(args.seed)
+    accepted_a, accepted_b, accepted_meta, reports = [], [], [], []
+    accepted_transforms = {}
+    for i in range(len(stations)):
+        for j in range(i + args.min_gap, min(len(stations), i + args.max_gap + 1)):
+            a_ij = inverse_transform(body_poses[i]) @ body_poses[j]
+            translation = float(np.linalg.norm(a_ij[:2, 3]))
+            rotation = rotation_angle_deg(a_ij[:3, :3])
+            if translation < args.min_translation and rotation < args.min_rotation:
+                continue
+            initial_b = a_ij.copy()  # X0=I; no measured extrinsic.
+            target_fit, target_holdout = split[i]
+            source_fit, source_holdout = split[j]
+            forward = align_backend(args.backend, target_fit, source_fit, initial_b, args)
+            heldout = symmetric_heldout_metrics(
+                target_fit, target_holdout, source_fit, source_holdout,
+                forward["transform"], args.evaluation_distance
+            )
+            hessian = hessian_metrics(forward["hessian"])
+            reverse_answer = align_backend(
+                args.backend, source_fit, target_fit, inverse_transform(initial_b), args
+            )
+            reverse = transform_difference(
+                forward["transform"], inverse_transform(reverse_answer["transform"])
+            )
+            multistart = []
+            for _ in range(args.multistart):
+                perturb = np.r_[
+                    rng.normal(0.0, args.multistart_translation_sigma, 3),
+                    np.deg2rad(rng.normal(0.0, args.multistart_rotation_sigma, 3)),
+                ]
+                candidate = align_backend(
+                    args.backend, target_fit, source_fit,
+                    params_transform(perturb) @ initial_b, args
+                )
+                multistart.append(transform_difference(forward["transform"], candidate["transform"]))
+            stable = [
+                item["translation_m"] <= args.multistart_translation_tolerance
+                and item["rotation_deg"] <= args.multistart_rotation_tolerance
+                for item in multistart
+            ]
+            success_rate = float(np.mean(stable)) if stable else 1.0
+            reasons = []
+            if forward["converged"] is False:
+                reasons.append("backend_not_converged")
+            if heldout["inlier_ratio"] < args.min_inlier_ratio:
+                reasons.append("heldout_inlier_ratio")
+            if heldout["inlier_rmse_m"] is None or heldout["inlier_rmse_m"] > args.max_inlier_rmse:
+                reasons.append("heldout_inlier_rmse")
+            if hessian["effective_rank"] < 6:
+                reasons.append("hessian_rank")
+            if hessian["scaled_condition_number"] > args.max_hessian_condition:
+                reasons.append("hessian_condition")
+            if reverse["translation_m"] > args.reverse_translation_tolerance:
+                reasons.append("forward_reverse_translation")
+            if reverse["rotation_deg"] > args.reverse_rotation_tolerance:
+                reasons.append("forward_reverse_rotation")
+            if success_rate < args.min_multistart_success:
+                reasons.append("multistart_instability")
+            accepted = not reasons
+            report = {
+                "i": i, "j": j,
+                "lidar_time_i": stations[i][0], "lidar_time_j": stations[j][0],
+                "frame_counter_i": stations[i][1], "frame_counter_j": stations[j][1],
+                "rtk_translation_m": translation, "rtk_rotation_deg": rotation,
+                "nearest_rtk_dt_i_s": body_dt[i], "nearest_rtk_dt_j_s": body_dt[j],
+                "initial_B_source": "X0=identity; B0=A (no measured extrinsic)",
+                "B_ij_4x4": forward["transform"].tolist(),
+                "backend": args.backend, "backend_converged": forward["converged"],
+                "backend_iterations": forward["iterations"],
+                "backend_num_inliers": forward["num_inliers"],
+                "backend_objective": forward["objective"],
+                "backend_elapsed_sec": forward["elapsed_sec"],
+                "multiscale_stages": forward["stages"],
+                "heldout_symmetric": heldout, "hessian": hessian,
+                "forward_reverse": reverse,
+                "multistart": {"runs": len(multistart), "success_rate": success_rate,
+                               "deltas": multistart},
+                "accepted": accepted, "rejection_reasons": reasons,
+            }
+            reports.append(report)
+            print(f"{args.backend} {i:02d}->{j:02d} rmse={heldout['inlier_rmse_m']} "
+                  f"ratio={heldout['inlier_ratio']:.3f} accepted={accepted}")
+            if accepted:
+                accepted_a.append(a_ij)
+                accepted_b.append(forward["transform"])
+                accepted_meta.append([i, j, stations[i][0], stations[j][0]])
+                accepted_transforms[(i, j)] = forward["transform"]
+    output = Path(args.output)
+    output.parent.mkdir(parents=True, exist_ok=True)
+    np.savez_compressed(
+        output, A=np.asarray(accepted_a), B=np.asarray(accepted_b),
+        meta=np.asarray(accepted_meta),
+        station_times=np.asarray([item[0] for item in stations]),
+        rtk_nearest_dt_s=np.asarray(body_dt), backend=np.asarray(args.backend),
+    )
+    quality = {
+        "schema_version": 2,
+        "backend": args.backend,
+        "transform_convention": "B_ij=T_Li_Lj maps station j points into station i",
+        "raw_point_field": "points_raw",
+        "measured_extrinsic_used_as_initial": False,
+        "stations": len(stations), "candidate_pairs": len(reports),
+        "accepted_pairs": len(accepted_a),
+        "parameters": vars(args),
+        "accepted_loop_closure": loop_metrics(accepted_transforms),
+        "pairs": reports,
+    }
+    quality["parameters"].pop("func", None)
+    quality_path = Path(args.quality_json or output.with_suffix(".quality.json"))
+    quality_path.write_text(json.dumps(quality, ensure_ascii=False, indent=2), encoding="utf-8")
+    csv_path = Path(args.quality_csv or output.with_suffix(".quality.csv"))
+    with csv_path.open("w", encoding="utf-8", newline="") as stream:
+        fields = ["i", "j", "rtk_translation_m", "rtk_rotation_deg",
+                  "heldout_inlier_ratio", "heldout_inlier_rmse_m",
+                  "hessian_rank", "hessian_condition", "reverse_translation_m",
+                  "reverse_rotation_deg", "multistart_success_rate", "accepted",
+                  "rejection_reasons"]
+        writer = csv.DictWriter(stream, fieldnames=fields)
+        writer.writeheader()
+        for item in reports:
+            writer.writerow({
+                "i": item["i"], "j": item["j"],
+                "rtk_translation_m": item["rtk_translation_m"],
+                "rtk_rotation_deg": item["rtk_rotation_deg"],
+                "heldout_inlier_ratio": item["heldout_symmetric"]["inlier_ratio"],
+                "heldout_inlier_rmse_m": item["heldout_symmetric"]["inlier_rmse_m"],
+                "hessian_rank": item["hessian"]["effective_rank"],
+                "hessian_condition": item["hessian"]["scaled_condition_number"],
+                "reverse_translation_m": item["forward_reverse"]["translation_m"],
+                "reverse_rotation_deg": item["forward_reverse"]["rotation_deg"],
+                "multistart_success_rate": item["multistart"]["success_rate"],
+                "accepted": item["accepted"],
+                "rejection_reasons": ";".join(item["rejection_reasons"]),
+            })
+    if len(accepted_a) < args.min_pairs:
+        raise RuntimeError(f"only {len(accepted_a)} accepted pairs; need {args.min_pairs}")
+    print(json.dumps({
+        "backend": args.backend, "stations": len(stations),
+        "candidate_pairs": len(reports), "accepted_pairs": len(accepted_a),
+        "output": str(output.resolve()), "quality_json": str(quality_path.resolve()),
+        "loop": quality["accepted_loop_closure"],
+    }, indent=2))
+
+
+def read_planes(path):
+    planes = []
+    with Path(path).open(encoding="utf-8-sig", newline="") as stream:
+        for row in csv.DictReader(stream):
+            normal = np.array([float(row[k]) for k in ("nx", "ny", "nz")])
+            norm = np.linalg.norm(normal)
+            normal, distance = normal / norm, float(row["d"]) / norm
+            if distance < 0:
+                normal, distance = -normal, -distance
+            planes.append([*normal, distance])
+    return np.asarray(planes)
+
+
+def read_pairs(path):
+    with np.load(path, allow_pickle=False) as data:
+        return (np.asarray(data["A"], float), np.asarray(data["B"], float),
+                np.asarray(data["meta"], float), len(data["station_times"]))
+
+
+def calibration_residual(params, a_array, b_array, planes, args):
+    x = params_transform(params)
+    values = []
+    for a_ij, b_ij in zip(a_array, b_array):
+        error = inverse_transform(a_ij @ x) @ x @ b_ij
+        values.extend((error[:3, 3] / args.translation_sigma).tolist())
+        values.extend((so3_log(error[:3, :3]) / math.radians(args.rotation_sigma)).tolist())
+    body_up = np.array([0.0, 0.0, 1.0])
+    for plane in planes:
+        normal_body = x[:3, :3] @ plane[:3]
+        values.extend((np.cross(normal_body, body_up) / args.plane_normal_sigma).tolist())
+        body_distance = plane[3] - float(normal_body @ x[:3, 3])
+        values.append((body_distance - args.body_height) / args.plane_height_sigma)
+    return np.asarray(values)
+
+
+def pair_metrics(a_array, b_array, x):
+    translation, rotation, rows = [], [], []
+    for index, (a_ij, b_ij) in enumerate(zip(a_array, b_array)):
+        predicted = inverse_transform(x) @ a_ij @ x
+        delta = inverse_transform(b_ij) @ predicted
+        t = float(np.linalg.norm(delta[:3, 3]))
+        r = rotation_angle_deg(delta[:3, :3])
+        translation.append(t); rotation.append(r)
+        rows.append({"pair_index": index, "translation_m": t, "rotation_deg": r})
+    translation, rotation = np.asarray(translation), np.asarray(rotation)
+    def stats(values):
+        return {
+            "rms": float(np.sqrt(np.mean(values**2))),
+            "median": float(np.median(values)),
+            "p90": float(np.quantile(values, 0.90)),
+            "p95": float(np.quantile(values, 0.95)),
+            "max": float(np.max(values)),
+        }
+    return {"pairs": len(rows), "translation_m": stats(translation),
+            "rotation_deg": stats(rotation), "per_pair": rows}
+
+
+def solve_extrinsic(a_array, b_array, planes, args):
+    rng = np.random.default_rng(args.seed)
+    starts = [np.zeros(6)]
+    for _ in range(args.solver_multistart - 1):
+        starts.append(np.r_[
+            rng.normal(0.0, args.start_translation_sigma, 3),
+            np.deg2rad(rng.normal(0.0, args.start_rotation_sigma, 3)),
+        ])
+    candidates = []
+    lower = np.r_[[-5.0] * 3, [-math.pi] * 3]
+    upper = np.r_[[5.0] * 3, [math.pi] * 3]
+    for start in starts:
+        answer = least_squares(
+            calibration_residual, np.clip(start, lower, upper),
+            args=(a_array, b_array, planes, args),
+            bounds=(lower, upper), loss="huber", f_scale=1.5,
+            x_scale="jac", max_nfev=args.max_nfev,
+        )
+        candidates.append(answer)
+    best = min(candidates, key=lambda item: item.cost)
+    return best, candidates
+
+
+def cmd_calibrate(args):
+    a_array, b_array, meta, stations = read_pairs(args.pairs)
+    planes = read_planes(args.ground_planes)
+    best, candidates = solve_extrinsic(a_array, b_array, planes, args)
+    x = params_transform(best.x)
+    residual = calibration_residual(best.x, a_array, b_array, planes, args)
+    absolute = np.abs(residual)
+    weights = np.ones_like(residual)
+    weights[absolute > 1.5] = 1.5 / absolute[absolute > 1.5]
+    weighted_jacobian = best.jac * np.sqrt(weights)[:, None]
+    singular = np.linalg.svd(weighted_jacobian, compute_uv=False)
+    condition = float(singular[0] / max(singular[-1], 1e-15))
+    dof = max(len(residual) - 6, 1)
+    covariance = np.linalg.pinv(weighted_jacobian.T @ weighted_jacobian) * float(
+        np.sum(weights * residual**2) / dof
+    )
+    sigma = np.sqrt(np.maximum(np.diag(covariance), 0.0))
+    candidate_summary = []
+    for item in candidates:
+        candidate_x = params_transform(item.x)
+        candidate_summary.append({
+            "cost": float(item.cost), "success": bool(item.success),
+            **transform_difference(x, candidate_x),
+        })
+    bootstrap = []
+    rng = np.random.default_rng(args.seed + 1)
+    for _ in range(args.bootstrap):
+        indexes = rng.integers(0, len(a_array), len(a_array))
+        answer = least_squares(
+            calibration_residual, best.x,
+            args=(a_array[indexes], b_array[indexes], planes, args),
+            loss="huber", f_scale=1.5, x_scale="jac", max_nfev=args.max_nfev,
+        )
+        bootstrap.append(np.r_[answer.x[:3], rpy_deg(so3_exp(answer.x[3:]))])
+    bootstrap = np.asarray(bootstrap)
+    result = {
+        "schema_version": 2,
+        "success": bool(best.success),
+        "message": best.message,
+        "convention": "T_body_lidar maps raw LiDAR points into rear-axle body frame",
+        "equation": "A_ij X = X B_ij",
+        "measured_extrinsic_used_as_initial": False,
+        "translation_m": x[:3, 3].tolist(),
+        "rotation_rpy_deg_xyz": rpy_deg(x[:3, :3]),
+        "quaternion_xyzw": rotation_to_quat(x[:3, :3]).tolist(),
+        "matrix_4x4": x.tolist(),
+        "estimation": {"stations": stations, "pairs": len(a_array),
+                       "residuals": pair_metrics(a_array, b_array, x)},
+        "ground": {
+            "planes": len(planes),
+            "body_origin_height_above_ground_m": args.body_height,
+            "formula": "d_lidar - (R_X n_lidar)^T t_X - body_height",
+        },
+        "linearized_one_sigma": {
+            "translation_m": sigma[:3].tolist(),
+            "rotation_deg": np.rad2deg(sigma[3:]).tolist(),
+            "warning": "conditional local estimate; bootstrap is the primary stability check",
+        },
+        "weighted_jacobian_condition_number": condition,
+        "solver_multistart": {
+            "runs": len(candidates), "candidates_relative_to_best": candidate_summary,
+        },
+        "bootstrap": {
+            "runs": len(bootstrap),
+            "order": ["x_m", "y_m", "z_m", "roll_deg", "pitch_deg", "yaw_deg"],
+            "std": np.std(bootstrap, axis=0, ddof=1).tolist() if len(bootstrap) > 1 else None,
+            "p025": np.quantile(bootstrap, 0.025, axis=0).tolist() if len(bootstrap) else None,
+            "p975": np.quantile(bootstrap, 0.975, axis=0).tolist() if len(bootstrap) else None,
+        },
+    }
+    output = Path(args.output)
+    output.parent.mkdir(parents=True, exist_ok=True)
+    output.write_text(json.dumps(result, ensure_ascii=False, indent=2), encoding="utf-8")
+    print(json.dumps(result, ensure_ascii=False, indent=2))
+
+
+def cmd_validate(args):
+    result = json.loads(Path(args.extrinsic).read_text(encoding="utf-8-sig"))
+    x = np.asarray(result["matrix_4x4"], float)
+    a_array, b_array, meta, stations = read_pairs(args.pairs)
+    metrics = pair_metrics(a_array, b_array, x)
+    for row, pair_meta in zip(metrics["per_pair"], meta):
+        row.update({"i": int(pair_meta[0]), "j": int(pair_meta[1])})
+    report = {
+        "role": "auxiliary check only; first-batch RTK is sparse",
+        "blind_with_respect_to_X": True,
+        "note": "No AX residual was used to select these pairs",
+        "stations": stations, "metrics": metrics,
+    }
+    output = Path(args.output)
+    output.parent.mkdir(parents=True, exist_ok=True)
+    output.write_text(json.dumps(report, ensure_ascii=False, indent=2), encoding="utf-8")
+    print(json.dumps(report, ensure_ascii=False, indent=2))
+
+
+def build_parser():
+    parser = argparse.ArgumentParser(description=__doc__)
+    commands = parser.add_subparsers(dest="command", required=True)
+    ground = commands.add_parser("ground")
+    ground.add_argument("--frames", required=True); ground.add_argument("--output", required=True)
+    ground.add_argument("--min-range", type=float, default=1.0); ground.add_argument("--max-range", type=float, default=30.0)
+    ground.add_argument("--z-min", type=float, default=-1.4); ground.add_argument("--z-max", type=float, default=-0.4)
+    ground.add_argument("--voxel", type=float, default=0.08); ground.add_argument("--distance-threshold", type=float, default=0.025)
+    ground.add_argument("--ransac-iterations", type=int, default=500); ground.add_argument("--min-inliers", type=int, default=500)
+    ground.add_argument("--max-rms", type=float, default=0.025); ground.set_defaults(func=cmd_ground)
+
+    pairs = commands.add_parser("pairs")
+    pairs.add_argument("--backend", choices=["open3d", "small_gicp"], required=True)
+    pairs.add_argument("--frames", required=True); pairs.add_argument("--body", required=True)
+    pairs.add_argument("--output", required=True); pairs.add_argument("--quality-json"); pairs.add_argument("--quality-csv")
+    pairs.add_argument("--time-offset", type=float, default=0.0)
+    pairs.add_argument("--min-stations", type=int, default=30); pairs.add_argument("--min-pairs", type=int, default=25)
+    pairs.add_argument("--min-gap", type=int, default=1); pairs.add_argument("--max-gap", type=int, default=5)
+    pairs.add_argument("--min-translation", type=float, default=0.5); pairs.add_argument("--min-rotation", type=float, default=3.0)
+    pairs.add_argument("--min-range", type=float, default=2.0); pairs.add_argument("--max-range", type=float, default=50.0)
+    pairs.add_argument("--z-min", type=float, default=-0.60); pairs.add_argument("--z-max", type=float, default=5.0)
+    pairs.add_argument("--min-roi-points", type=int, default=1000)
+    pairs.add_argument("--holdout-fraction", type=float, default=0.20)
+    pairs.add_argument("--voxels", nargs="+", type=float, default=[0.30, 0.15, 0.08])
+    pairs.add_argument("--correspondences", nargs="+", type=float, default=[1.20, 0.50, 0.25])
+    pairs.add_argument("--iterations", type=int, default=60); pairs.add_argument("--threads", type=int, default=8)
+    pairs.add_argument("--evaluation-distance", type=float, default=0.25)
+    pairs.add_argument("--min-inlier-ratio", type=float, default=0.35); pairs.add_argument("--max-inlier-rmse", type=float, default=0.16)
+    pairs.add_argument("--max-hessian-condition", type=float, default=1e8)
+    pairs.add_argument("--reverse-translation-tolerance", type=float, default=0.08)
+    pairs.add_argument("--reverse-rotation-tolerance", type=float, default=0.50)
+    pairs.add_argument("--multistart", type=int, default=2)
+    pairs.add_argument("--multistart-translation-sigma", type=float, default=0.30)
+    pairs.add_argument("--multistart-rotation-sigma", type=float, default=3.0)
+    pairs.add_argument("--multistart-translation-tolerance", type=float, default=0.08)
+    pairs.add_argument("--multistart-rotation-tolerance", type=float, default=0.50)
+    pairs.add_argument("--min-multistart-success", type=float, default=0.50)
+    pairs.add_argument("--seed", type=int, default=20260721); pairs.set_defaults(func=cmd_pairs)
+
+    calibrate = commands.add_parser("calibrate")
+    calibrate.add_argument("--pairs", required=True); calibrate.add_argument("--ground-planes", required=True)
+    calibrate.add_argument("--output", required=True)
+    calibrate.add_argument("--translation-sigma", type=float, default=0.05)
+    calibrate.add_argument("--rotation-sigma", type=float, default=0.5)
+    calibrate.add_argument("--plane-normal-sigma", type=float, default=0.02)
+    calibrate.add_argument("--plane-height-sigma", type=float, default=0.03)
+    calibrate.add_argument("--body-height", type=float, default=0.2335)
+    calibrate.add_argument("--solver-multistart", type=int, default=12)
+    calibrate.add_argument("--start-translation-sigma", type=float, default=1.0)
+    calibrate.add_argument("--start-rotation-sigma", type=float, default=20.0)
+    calibrate.add_argument("--bootstrap", type=int, default=100)
+    calibrate.add_argument("--max-nfev", type=int, default=1000)
+    calibrate.add_argument("--seed", type=int, default=20260721); calibrate.set_defaults(func=cmd_calibrate)
+
+    validate = commands.add_parser("validate")
+    validate.add_argument("--pairs", required=True); validate.add_argument("--extrinsic", required=True)
+    validate.add_argument("--output", required=True); validate.set_defaults(func=cmd_validate)
+    return parser
+
+
+def main():
+    args = build_parser().parse_args()
+    args.func(args)
+
+
+if __name__ == "__main__":
+    main()

code/scan_extrinsic_sensitivity.py

@@ -0,0 +1,311 @@
+#!/usr/bin/env python3
+"""Scan body-left RPY corrections locally and validate them over every B pair.
+
+This command is diagnostic only.  It never writes or replaces an extrinsic JSON.
+"""
+from __future__ import annotations
+
+import argparse
+import csv
+import json
+import math
+from pathlib import Path
+
+import numpy as np
+from scipy.spatial.transform import Rotation
+
+from rigorous_calibration import (
+    inverse_transform, read_pairs, read_planes, rotation_angle_deg, rpy_deg,
+)
+
+
+def statistics(values):
+    values = np.asarray(values, float)
+    return {
+        "rms": float(np.sqrt(np.mean(values ** 2))),
+        "median": float(np.median(values)),
+        "p90": float(np.quantile(values, 0.90)),
+        "p95": float(np.quantile(values, 0.95)),
+        "max": float(np.max(values)),
+    }
+
+
+def body_left_rpy(x, rpy_correction_deg):
+    correction = np.eye(4)
+    correction[:3, :3] = Rotation.from_euler(
+        "xyz", np.asarray(rpy_correction_deg, float), degrees=True
+    ).as_matrix()
+    return correction @ x
+
+
+def pair_delta(a_ij, b_ij, x):
+    predicted = inverse_transform(x) @ a_ij @ x
+    delta = inverse_transform(b_ij) @ predicted
+    translation = np.asarray(delta[:3, 3], float)
+    return {
+        "translation_xyz_m": translation.tolist(),
+        "translation_xyz_cm": (100.0 * translation).tolist(),
+        "translation_norm_m": float(np.linalg.norm(translation)),
+        "rotation_rpy_deg_xyz": rpy_deg(delta[:3, :3]),
+        "rotation_angle_deg": rotation_angle_deg(delta[:3, :3]),
+    }
+
+
+def ground_metrics(planes, x, body_height):
+    if len(planes) == 0:
+        return None
+    up = np.array([0.0, 0.0, 1.0])
+    tilt_deg, height_m = [], []
+    for plane in planes:
+        normal_body = x[:3, :3] @ plane[:3]
+        normal_body /= np.linalg.norm(normal_body)
+        tilt_deg.append(math.degrees(math.atan2(
+            np.linalg.norm(np.cross(normal_body, up)),
+            float(np.clip(normal_body @ up, -1.0, 1.0)),
+        )))
+        height_m.append(
+            float(plane[3] - normal_body @ x[:3, 3] - body_height)
+        )
+    return {
+        "normal_tilt_deg": statistics(tilt_deg),
+        "height_residual_m": statistics(height_m),
+    }
+
+
+def evaluate(label, correction, a_array, b_array, meta, x, pair_index,
+             translation_scale, rotation_scale, planes, body_height):
+    candidate_x = body_left_rpy(x, correction)
+    per_pair = []
+    translation, rotation, normalized = [], [], []
+    for index, (a_ij, b_ij, pair_meta) in enumerate(zip(a_array, b_array, meta)):
+        item = pair_delta(a_ij, b_ij, candidate_x)
+        item.update({
+            "pair_index": index,
+            "i": int(pair_meta[0]),
+            "j": int(pair_meta[1]),
+        })
+        t = item["translation_norm_m"]
+        r = item["rotation_angle_deg"]
+        translation.append(t)
+        rotation.append(r)
+        normalized.append(math.hypot(t / translation_scale, r / rotation_scale))
+        per_pair.append(item)
+    return {
+        "label": label,
+        "body_left_rpy_correction_deg_xyz": list(map(float, correction)),
+        "candidate_extrinsic": {
+            "translation_m": candidate_x[:3, 3].tolist(),
+            "rotation_rpy_deg_xyz": rpy_deg(candidate_x[:3, :3]),
+        },
+        "all_pairs": {
+            "count": len(per_pair),
+            "translation_m": statistics(translation),
+            "rotation_deg": statistics(rotation),
+            "normalized_pair_score": statistics(normalized),
+            "normalized_global_rms": float(np.sqrt(np.mean(np.asarray(normalized) ** 2))),
+        },
+        "selected_pair": per_pair[pair_index],
+        "ground": ground_metrics(planes, candidate_x, body_height),
+        "per_pair": per_pair,
+    }
+
+
+def candidate_grid(pitch_values, roll_values, yaw_values):
+    answer = [("baseline", (0.0, 0.0, 0.0))]
+    for pitch in pitch_values:
+        answer.append((f"pitch_{pitch:+.3f}", (0.0, pitch, 0.0)))
+    for pitch in (0.0, *pitch_values):
+        for roll in roll_values:
+            answer.append((
+                f"pitch_{pitch:+.3f}_roll_{roll:+.3f}",
+                (roll, pitch, 0.0),
+            ))
+    for yaw in yaw_values:
+        answer.append((f"yaw_{yaw:+.3f}_diagnostic", (0.0, 0.0, yaw)))
+    unique = []
+    seen = set()
+    for label, values in answer:
+        key = tuple(round(float(value), 12) for value in values)
+        if key not in seen:
+            seen.add(key)
+            unique.append((label, values))
+    return unique
+
+
+def z_observability(a_array, x, test_shift_m):
+    shift = np.eye(4)
+    shift[2, 3] = test_shift_m
+    shifted_x = shift @ x
+    effects = []
+    for a_ij in a_array:
+        before = inverse_transform(x) @ a_ij @ x
+        after = inverse_transform(shifted_x) @ a_ij @ shifted_x
+        delta = inverse_transform(before) @ after
+        effects.append((
+            float(np.linalg.norm(delta[:3, 3])),
+            rotation_angle_deg(delta[:3, :3]),
+        ))
+    effects = np.asarray(effects, float)
+    maximum = np.max(effects, axis=0)
+    return {
+        "body_left_z_test_shift_m": test_shift_m,
+        "max_predicted_motion_change_translation_m": float(maximum[0]),
+        "max_predicted_motion_change_rotation_deg": float(maximum[1]),
+        "numerically_unobservable": bool(maximum[0] < 1e-10 and maximum[1] < 1e-10),
+        "note": "AX pairs cannot determine X.z when every A rotation preserves body Z; use ground/external height constraints.",
+    }
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--pairs", required=True)
+    parser.add_argument("--extrinsic", required=True)
+    parser.add_argument("--output", required=True)
+    parser.add_argument("--csv")
+    parser.add_argument("--ground-planes")
+    parser.add_argument("--pair-index", type=int, default=0)
+    parser.add_argument("--pitch-values", nargs="+", type=float, default=[0.1, 0.2, 0.3])
+    parser.add_argument("--roll-values", nargs="+", type=float, default=[-0.2, -0.1, 0.1])
+    parser.add_argument("--yaw-values", nargs="+", type=float, default=[-0.2, 0.2])
+    parser.add_argument("--translation-scale", type=float, default=0.05)
+    parser.add_argument("--rotation-scale", type=float, default=0.5)
+    parser.add_argument("--body-height", type=float, default=0.2335)
+    args = parser.parse_args()
+
+    a_array, b_array, meta, stations = read_pairs(args.pairs)
+    if not 0 <= args.pair_index < len(a_array):
+        raise IndexError(f"pair-index {args.pair_index} outside [0,{len(a_array)-1}]")
+    with Path(args.extrinsic).open(encoding="utf-8-sig") as stream:
+        x = np.asarray(json.load(stream)["matrix_4x4"], float)
+    planes = read_planes(args.ground_planes) if args.ground_planes else np.empty((0, 4))
+
+    candidates = [
+        evaluate(
+            label, correction, a_array, b_array, meta, x, args.pair_index,
+            args.translation_scale, args.rotation_scale, planes, args.body_height,
+        )
+        for label, correction in candidate_grid(
+            args.pitch_values, args.roll_values, args.yaw_values
+        )
+    ]
+    baseline = candidates[0]
+    baseline_scores = np.asarray([
+        math.hypot(
+            item["translation_norm_m"] / args.translation_scale,
+            item["rotation_angle_deg"] / args.rotation_scale,
+        )
+        for item in baseline["per_pair"]
+    ])
+    base_global = baseline["all_pairs"]["normalized_global_rms"]
+    for candidate in candidates:
+        scores = np.asarray([
+            math.hypot(
+                item["translation_norm_m"] / args.translation_scale,
+                item["rotation_angle_deg"] / args.rotation_scale,
+            )
+            for item in candidate["per_pair"]
+        ])
+        delta = scores - baseline_scores
+        candidate["comparison_to_baseline"] = {
+            "normalized_global_rms_change": float(
+                candidate["all_pairs"]["normalized_global_rms"] - base_global
+            ),
+            "improved_pairs": int(np.sum(delta < -1e-12)),
+            "worsened_pairs": int(np.sum(delta > 1e-12)),
+            "unchanged_pairs": int(np.sum(np.abs(delta) <= 1e-12)),
+            "median_per_pair_score_change": float(np.median(delta)),
+            "global_consistency_signal": bool(
+                candidate["all_pairs"]["normalized_global_rms"] < base_global
+                and np.sum(delta < -1e-12) > np.sum(delta > 1e-12)
+            ),
+        }
+
+    ranking = sorted(
+        candidates,
+        key=lambda item: item["all_pairs"]["normalized_global_rms"],
+    )
+    report = {
+        "schema_version": 1,
+        "diagnostic_only": True,
+        "extrinsic_was_modified": False,
+        "equation": "delta_ij = B_ij^-1 * (X^-1 * A_ij * X)",
+        "correction_convention": "X_test = DeltaR_body * X; DeltaR uses fixed body xyz RPY axes",
+        "component_frame": "delta translation/RPY components are in station-j LiDAR coordinates, not screen axes",
+        "selection_rule": (
+            "Never accept a correction from selected_pair alone. Require improvement over all "
+            "refined pairs, directional consistency across pairs, acceptable ground constraints, "
+            "and independent visual review. This script never overwrites X."
+        ),
+        "pairs_file": str(Path(args.pairs).resolve()),
+        "extrinsic_file": str(Path(args.extrinsic).resolve()),
+        "stations": stations,
+        "pairs": len(a_array),
+        "selected_pair_index": args.pair_index,
+        "selected_pair_stations": [int(meta[args.pair_index, 0]), int(meta[args.pair_index, 1])],
+        "normalization": {
+            "translation_scale_m": args.translation_scale,
+            "rotation_scale_deg": args.rotation_scale,
+        },
+        "z_observability": z_observability(a_array, x, 0.10),
+        "ranking_by_all_pair_normalized_rms": [
+            {
+                "rank": rank,
+                "label": item["label"],
+                "body_left_rpy_correction_deg_xyz": item["body_left_rpy_correction_deg_xyz"],
+                "normalized_global_rms": item["all_pairs"]["normalized_global_rms"],
+                **item["comparison_to_baseline"],
+            }
+            for rank, item in enumerate(ranking, 1)
+        ],
+        "candidates": candidates,
+    }
+
+    output = Path(args.output)
+    output.parent.mkdir(parents=True, exist_ok=True)
+    output.write_text(json.dumps(report, ensure_ascii=False, indent=2), encoding="utf-8")
+    csv_path = Path(args.csv) if args.csv else output.with_suffix(".csv")
+    with csv_path.open("w", encoding="utf-8", newline="") as stream:
+        fields = [
+            "label", "roll_correction_deg", "pitch_correction_deg", "yaw_correction_deg",
+            "selected_pair_translation_cm", "selected_pair_rotation_deg",
+            "all_pair_translation_rms_m", "all_pair_rotation_rms_deg",
+            "normalized_global_rms", "normalized_global_rms_change",
+            "improved_pairs", "worsened_pairs", "global_consistency_signal",
+            "ground_normal_tilt_rms_deg", "ground_height_rms_m",
+        ]
+        writer = csv.DictWriter(stream, fieldnames=fields)
+        writer.writeheader()
+        for item in candidates:
+            correction = item["body_left_rpy_correction_deg_xyz"]
+            ground = item["ground"]
+            comparison = item["comparison_to_baseline"]
+            writer.writerow({
+                "label": item["label"],
+                "roll_correction_deg": correction[0],
+                "pitch_correction_deg": correction[1],
+                "yaw_correction_deg": correction[2],
+                "selected_pair_translation_cm": item["selected_pair"]["translation_norm_m"] * 100.0,
+                "selected_pair_rotation_deg": item["selected_pair"]["rotation_angle_deg"],
+                "all_pair_translation_rms_m": item["all_pairs"]["translation_m"]["rms"],
+                "all_pair_rotation_rms_deg": item["all_pairs"]["rotation_deg"]["rms"],
+                "normalized_global_rms": item["all_pairs"]["normalized_global_rms"],
+                "normalized_global_rms_change": comparison["normalized_global_rms_change"],
+                "improved_pairs": comparison["improved_pairs"],
+                "worsened_pairs": comparison["worsened_pairs"],
+                "global_consistency_signal": comparison["global_consistency_signal"],
+                "ground_normal_tilt_rms_deg": None if ground is None else ground["normal_tilt_deg"]["rms"],
+                "ground_height_rms_m": None if ground is None else ground["height_residual_m"]["rms"],
+            })
+
+    print(json.dumps({
+        "diagnostic_only": True,
+        "selected_pair": baseline["selected_pair"],
+        "z_observability": report["z_observability"],
+        "top_all_pair_candidates": report["ranking_by_all_pair_normalized_rms"][:8],
+        "output": str(output.resolve()),
+        "csv": str(csv_path.resolve()),
+    }, ensure_ascii=False, indent=2))
+
+
+if __name__ == "__main__":
+    main()

code/summarize_results.py

@@ -0,0 +1,87 @@
+#!/usr/bin/env python3
+"""Build a concise backend comparison and select the recommended result."""
+import argparse
+import json
+from pathlib import Path
+
+import numpy as np
+from scipy.spatial.transform import Rotation
+
+
+def main():
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--open3d", required=True)
+    parser.add_argument("--small", required=True)
+    parser.add_argument("--open3d-quality", required=True)
+    parser.add_argument("--small-quality", required=True)
+    parser.add_argument("--open3d-check", required=True)
+    parser.add_argument("--small-check", required=True)
+    parser.add_argument("--output", required=True)
+    parser.add_argument("--recommended-output", required=True)
+    args = parser.parse_args()
+
+    open_result = json.loads(Path(args.open3d).read_text(encoding="utf-8-sig"))
+    small_result = json.loads(Path(args.small).read_text(encoding="utf-8-sig"))
+    open_quality = json.loads(Path(args.open3d_quality).read_text(encoding="utf-8-sig"))
+    small_quality = json.loads(Path(args.small_quality).read_text(encoding="utf-8-sig"))
+    open_check = json.loads(Path(args.open3d_check).read_text(encoding="utf-8-sig"))
+    small_check = json.loads(Path(args.small_check).read_text(encoding="utf-8-sig"))
+    x_open = np.asarray(open_result["matrix_4x4"], float)
+    x_small = np.asarray(small_result["matrix_4x4"], float)
+    delta = np.linalg.inv(x_open) @ x_small
+
+    def compact(result, quality, check):
+        estimate = result["estimation"]["residuals"]
+        auxiliary = check["metrics"]
+        return {
+            "translation_m": result["translation_m"],
+            "rotation_rpy_deg_xyz": result["rotation_rpy_deg_xyz"],
+            "estimation_pairs": estimate["pairs"],
+            "estimation_translation_rms_m": estimate["translation_m"]["rms"],
+            "estimation_rotation_rms_deg": estimate["rotation_deg"]["rms"],
+            "bootstrap_std": result["bootstrap"]["std"],
+            "initial_B_loop_closure": quality["accepted_loop_closure"],
+            "batch1_auxiliary_pairs": auxiliary["pairs"],
+            "batch1_auxiliary_translation_rms_m": auxiliary["translation_m"]["rms"],
+            "batch1_auxiliary_rotation_rms_deg": auxiliary["rotation_deg"]["rms"],
+        }
+
+    summary = {
+        "recommended_backend": "open3d_gicp",
+        "selection_reason": (
+            "The two X estimates agree closely; Open3D has lower second-batch AX residual, "
+            "better B loop closure, and lower first-batch auxiliary residual."
+        ),
+        "coordinate_convention": "T_body_lidar maps raw LiDAR points into rear-axle body frame",
+        "measured_extrinsic_used_as_initial": False,
+        "second_batch_role": "estimation (dense RTK)",
+        "first_batch_role": "auxiliary check only (sparse RTK)",
+        "backend_difference": {
+            "translation_m": float(np.linalg.norm(delta[:3, 3])),
+            "rotation_deg": float(np.rad2deg(Rotation.from_matrix(delta[:3, :3]).magnitude())),
+        },
+        "open3d_gicp": compact(open_result, open_quality, open_check),
+        "small_gicp": compact(small_result, small_quality, small_check),
+        "important_limit": (
+            "Backend agreement is strong, but AX rotation RMS remains about one degree. "
+            "This is not a centimetre-grade absolute certification."
+        ),
+    }
+    output = Path(args.output)
+    output.parent.mkdir(parents=True, exist_ok=True)
+    output.write_text(json.dumps(summary, ensure_ascii=False, indent=2), encoding="utf-8")
+    recommended = dict(open_result)
+    recommended["selection"] = {
+        "recommended_backend": "open3d_gicp",
+        "comparison_summary": str(output.name),
+        "backend_difference": summary["backend_difference"],
+        "warning": summary["important_limit"],
+    }
+    Path(args.recommended_output).write_text(
+        json.dumps(recommended, ensure_ascii=False, indent=2), encoding="utf-8"
+    )
+    print(json.dumps(summary, ensure_ascii=False, indent=2))
+
+
+if __name__ == "__main__":
+    main()

code/visualize_pair_3d.py

@@ -0,0 +1,169 @@
+#!/usr/bin/env python3
+"""Interactive 3D comparison of raw, RTK, GICP and hand-eye-predicted motion."""
+import argparse
+import json
+
+import numpy as np
+from scipy.spatial.transform import Rotation
+
+from rigorous_calibration import (
+    inverse_transform, load_stations, rotation_angle_deg, rpy_deg, transform_points,
+)
+
+
+COLORS = {
+    "target": [0.10, 0.65, 1.00],
+    "source": [1.00, 0.35, 0.05],
+}
+
+
+def cloud(o3d, points, color, voxel):
+    item = o3d.geometry.PointCloud()
+    item.points = o3d.utility.Vector3dVector(points)
+    item = item.voxel_down_sample(voxel)
+    item.paint_uniform_color(color)
+    return item
+
+
+def delta_components(reference, candidate):
+    """Components of reference^-1*candidate, plus coordinate-invariant norms."""
+    delta = inverse_transform(reference) @ candidate
+    translation = np.asarray(delta[:3, 3], float)
+    return {
+        "translation_xyz_cm": (translation * 100.0).tolist(),
+        "translation_norm_cm": float(np.linalg.norm(translation) * 100.0),
+        "rotation_rpy_deg_xyz": rpy_deg(delta[:3, :3]),
+        "rotation_angle_deg": rotation_angle_deg(delta[:3, :3]),
+    }
+
+
+def body_left_rpy(x, rpy_correction_deg):
+    correction = np.eye(4)
+    correction[:3, :3] = Rotation.from_euler(
+        "xyz", np.asarray(rpy_correction_deg, float), degrees=True
+    ).as_matrix()
+    return correction @ x
+
+
+def print_delta(name, reference, candidate):
+    item = delta_components(reference, candidate)
+    tx, ty, tz = item["translation_xyz_cm"]
+    roll, pitch, yaw = item["rotation_rpy_deg_xyz"]
+    print(
+        f"{name}: B^-1*motion translation xyz = "
+        f"[{tx:+.4f}, {ty:+.4f}, {tz:+.4f}] cm; "
+        f"rpy xyz = [{roll:+.4f}, {pitch:+.4f}, {yaw:+.4f}] deg; "
+        f"norm = {item['translation_norm_cm']:.4f} cm / "
+        f"{item['rotation_angle_deg']:.6f} deg"
+    )
+    return item
+
+
+def main():
+    import open3d as o3d
+
+    parser = argparse.ArgumentParser(description=__doc__)
+    parser.add_argument("--frames", required=True)
+    parser.add_argument("--pairs", required=True)
+    parser.add_argument("--extrinsic", required=True)
+    parser.add_argument("--pair-index", type=int, default=0)
+    parser.add_argument("--voxel", type=float, default=0.10)
+    parser.add_argument(
+        "--left-rpy-deg", nargs=3, type=float, default=[0.0, 0.0, 0.0],
+        metavar=("ROLL", "PITCH", "YAW"),
+        help="optional body-frame left correction applied as DeltaR_body * X",
+    )
+    args = parser.parse_args()
+
+    stations = load_stations(args.frames, 1.0, 60.0)
+    with np.load(args.pairs, allow_pickle=False) as data:
+        if len(stations) != len(data["station_times"]):
+            raise ValueError(
+                f"frames contain {len(stations)} stations but pair file records "
+                f"{len(data['station_times'])}"
+            )
+        if not 0 <= args.pair_index < len(data["A"]):
+            raise IndexError(
+                f"pair-index {args.pair_index} outside [0,{len(data['A']) - 1}]"
+            )
+        a_ij = np.asarray(data["A"][args.pair_index], float)
+        b_gicp = np.asarray(data["B"][args.pair_index], float)
+        i, j = np.asarray(data["meta"][args.pair_index, :2], int)
+
+    with open(args.extrinsic, encoding="utf-8-sig") as stream:
+        result = json.load(stream)
+    x = np.asarray(result["matrix_4x4"], float)
+    b_calibrated = inverse_transform(x) @ a_ij @ x
+
+    transforms = {
+        "1 raw": np.eye(4),
+        "2 RTK initial (X0=I)": a_ij,
+        "3 GICP B": b_gicp,
+        "4 calibrated X^-1 A X": b_calibrated,
+    }
+    correction = np.asarray(args.left_rpy_deg, float)
+    if np.any(np.abs(correction) > 0.0):
+        x_test = body_left_rpy(x, correction)
+        transforms[
+            f"5 test body-left RPY {correction.tolist()} deg"
+        ] = inverse_transform(x_test) @ a_ij @ x_test
+
+    target = stations[i][3]
+    source = stations[j][3]
+    print(f"pair_index={args.pair_index}, station {i} <- {j}")
+    print("blue = target station i; orange = source station j after selected transform")
+    print("keys: 1 raw | 2 RTK initial | 3 GICP | 4 calibrated | 5 test correction | Q/Esc exit")
+    print(
+        "IMPORTANT: delta xyz/rpy are components of B^-1*(X^-1*A*X), expressed "
+        "in station-j LiDAR coordinates; screen-left/right depends on the 3D camera view."
+    )
+    baseline = print_delta("mode 4 minus mode 3", b_gicp, b_calibrated)
+    roll, pitch, yaw = np.abs(baseline["rotation_rpy_deg_xyz"])
+    if max(roll, pitch) > max(0.10, 2.0 * yaw):
+        print("diagnosis: roll/pitch components dominate yaw; do not prioritize yaw tuning for this pair.")
+    tx, ty, tz = np.abs(baseline["translation_xyz_cm"])
+    if tz > max(tx, ty):
+        print("diagnosis: the largest translation component is relative Z, not lateral XY.")
+    body_up = np.array([0.0, 0.0, 1.0])
+    if np.linalg.norm(a_ij[:3, :3] @ body_up - body_up) < 1e-8:
+        print(
+            "observability: this A preserves the body Z axis, so body-left X.z "
+            "translation is unobservable from this pair; use ground/external height constraints."
+        )
+    if "5 test body-left RPY " + str(correction.tolist()) + " deg" in transforms:
+        print_delta("mode 5 minus mode 3", b_gicp, list(transforms.values())[-1])
+
+    viewer = o3d.visualization.VisualizerWithKeyCallback()
+    viewer.create_window("Rigorous LiDAR registration inspection - 3D", 1400, 900)
+    target_cloud = cloud(o3d, target, COLORS["target"], args.voxel)
+    source_cloud = cloud(o3d, source, COLORS["source"], args.voxel)
+    viewer.add_geometry(target_cloud)
+    viewer.add_geometry(source_cloud)
+    axes = o3d.geometry.TriangleMesh.create_coordinate_frame(size=1.0)
+    viewer.add_geometry(axes)
+    current = np.eye(4)
+
+    def select(name):
+        def callback(vis):
+            nonlocal current
+            desired = transforms[name]
+            source_cloud.transform(desired @ inverse_transform(current))
+            current = desired
+            vis.update_geometry(source_cloud)
+            if name == "3 GICP B":
+                print(f"{name}: reference registration B; delta = 0")
+            else:
+                print_delta(name + " minus mode 3", b_gicp, desired)
+            return False
+        return callback
+
+    for key, name in zip((ord("1"), ord("2"), ord("3"), ord("4"), ord("5")), transforms):
+        viewer.register_key_callback(key, select(name))
+    viewer.get_render_option().background_color = np.array([0.02, 0.02, 0.02])
+    viewer.get_render_option().point_size = 2.0
+    viewer.run()
+    viewer.destroy_window()
+
+
+if __name__ == "__main__":
+    main()

requirements.txt

@@ -0,0 +1,4 @@
+numpy>=1.26
+scipy>=1.11
+open3d>=0.18
+small-gicp==1.0.1

results/README.md

@@ -0,0 +1,60 @@
+# 标定结果索引
+
+本目录保存本次双天线 RTK—3D LiDAR 手眼标定的可复现结果。坐标约定统一为：
+
+```text
+X = T_body_lidar
+```
+
+即外参将**原始 LiDAR 点**变换到以**后轮轴中心**为原点、X 前/Y 左/Z 上的车体系。
+
+## 部署时只使用这一个文件
+
+[`final_extrinsic_deployment.json`](final_extrinsic_deployment.json) 是唯一用于部署的外参文件：
+
+```text
+translation [m] = [ 1.297759692, -0.000067331, 0.720497835 ]
+RPY xyz [deg]  = [ -0.785151146, 1.202660822, -0.835510053 ]
+```
+
+## 顶层汇总文件
+
+| 文件 | 用途 | 是否用于部署 |
+|---|---|---|
+| [`final_extrinsic_deployment.json`](final_extrinsic_deployment.json) | 精简、固定的最终外参；含平移、RPY、四元数和 4×4 矩阵。 | **是，唯一入口** |
+| [`final_extrinsic_recommended.json`](final_extrinsic_recommended.json) | 同一算法外参的完整求解记录、残差、地面约束、条件数和 Bootstrap。 | 否；用于审计/复现。 |
+| [`final_summary.json`](final_summary.json) | 共识结果的摘要。 | 否；用于查看指标。 |
+| [`comparison_summary.json`](comparison_summary.json) | Open3D GICP、small_gicp 与共识解的对比。 | 否；用于方法对比。 |
+
+`final_extrinsic_deployment.json` 与 `final_extrinsic_recommended.json` 的外参数值相同；前者只是删除了求解过程字段，供上游程序稳定读取。
+
+## 子目录
+
+| 目录 | 内容 | 用途 |
+|---|---|---|
+| [`common/`](common/) | 第二批每个静止站点拟合得到的地面平面。 | 地面约束检查。 |
+| [`open3d_gicp/`](open3d_gicp/) | Open3D GICP 生成的 LiDAR 相对运动 B、质量指标、精筛记录和对应外参。 | 后端一的独立结果。 |
+| [`small_gicp/`](small_gicp/) | small_gicp 生成的 LiDAR 相对运动 B、质量指标、精筛记录和对应外参。 | 后端二的独立结果。 |
+| [`consensus/`](consensus/) | 两后端一致性筛选后的共识 B，共识外参和第一批辅助复核。 | 主要求解依据。 |
+| [`diagnostics/`](diagnostics/) | 单运动对 roll/pitch/yaw 局部灵敏度扫描。 | 仅诊断，不可直接当外参。 |
+
+## 如何识别 B 文件
+
+每个 `.npz` 都是 LiDAR 相对运动集合 `B_ij = T_Li_Lj`，把第 j 个静止站点的点云变换到第 i 个站点 LiDAR 坐标系。它们不是车体—雷达外参，不能直接写入部署配置。
+
+- `B_batch2_*`：第二批 38 站高频 RTK 数据，主要求解使用。
+- `B_batch1_*`：第一批 38 站稀疏 RTK 数据，仅作辅助复核。
+- `*_estimation.npz`：点云配准的初始候选集合。
+- `*_refined.npz`：经过点云质量门限后的集合。
+- `consensus/B_batch2_consensus.npz`：Open3D 与 small_gicp 对同一运动对的 B 差异不超过 `0.05 m / 0.50°` 后保留的 39 对；它是最终主求解输入。
+
+同名的 `.quality.json/.csv` 记录配准质量，`.refinement.json` 记录精筛过程，`.consensus.json` 记录跨后端一致性筛选。它们都用于追溯，不用于部署。
+
+## 结果使用边界
+
+- 主结果由第二批数据求解；第一批只作为独立辅助检查，不参与主结果拟合。
+- B 的筛选先于 X 的求解，并且不读取待求外参 X，不用 AX 残差反过来选择 B。
+- 第二批共识集的 AX RMS 为 `0.07985 m / 0.96118°`；旋转残差约 1°，因此不是厘米级绝对精度认证。
+- 当前 RTK 轨迹只有位置和 yaw，没有 roll/pitch。AX 残差对 Z 不可观；Z 必须结合地面约束和独立机械量测确认。
+
+更多流程、运行命令和可视化说明见仓库根目录的 [`README.md`](../README.md)。

results/common/ground_planes_batch2.csv

@@ -0,0 +1,39 @@
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results/comparison_summary.json

@@ -0,0 +1,79 @@
+{
+  "recommended_backend": "open3d_gicp",
+  "selection_reason": "The two X estimates agree closely; Open3D has lower second-batch AX residual, better B loop closure, and lower first-batch auxiliary residual.",
+  "coordinate_convention": "T_body_lidar maps raw LiDAR points into rear-axle body frame",
+  "measured_extrinsic_used_as_initial": false,
+  "second_batch_role": "estimation (dense RTK)",
+  "first_batch_role": "auxiliary check only (sparse RTK)",
+  "backend_difference": {
+    "translation_m": 0.00181035475331947,
+    "rotation_deg": 0.06312194455789993
+  },
+  "open3d_gicp": {
+    "translation_m": [
+      1.2978831677200011,
+      -0.0030997734098957433,
+      0.7217892226151688
+    ],
+    "rotation_rpy_deg_xyz": [
+      -0.7572070226288585,
+      1.1460424368859559,
+      -0.8797812288284186
+    ],
+    "estimation_pairs": 66,
+    "estimation_translation_rms_m": 0.10017183831403174,
+    "estimation_rotation_rms_deg": 1.011529772202344,
+    "bootstrap_std": [
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+      0.002063603632322515,
+      0.001427746471392659,
+      0.07576290622767821,
+      0.06304875844333606,
+      0.07843172452171372
+    ],
+    "initial_B_loop_closure": {
+      "count": 106,
+      "translation_rms_m": 0.020350848901853437,
+      "translation_p95_m": 0.04464367942375473,
+      "rotation_rms_deg": 0.2674546762953808,
+      "rotation_p95_deg": 0.5761692075739222
+    },
+    "batch1_auxiliary_pairs": 41,
+    "batch1_auxiliary_translation_rms_m": 0.06627076507951374,
+    "batch1_auxiliary_rotation_rms_deg": 1.0783402768758907
+  },
+  "small_gicp": {
+    "translation_m": [
+      1.2996301155160686,
+      -0.0035647011612625953,
+      0.7218861757826791
+    ],
+    "rotation_rpy_deg_xyz": [
+      -0.7871563544979889,
+      1.1414557494228486,
+      -0.9357571721886107
+    ],
+    "estimation_pairs": 80,
+    "estimation_translation_rms_m": 0.11870623426762615,
+    "estimation_rotation_rms_deg": 1.135091439337232,
+    "bootstrap_std": [
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+      0.0019214288447692426,
+      0.0013180801706094514,
+      0.06849719260762097,
+      0.05792635838163369,
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+    "initial_B_loop_closure": {
+      "count": 252,
+      "translation_rms_m": 0.06356464456110195,
+      "translation_p95_m": 0.12253135158224471,
+      "rotation_rms_deg": 0.7286536542725655,
+      "rotation_p95_deg": 1.4911215410143956
+    },
+    "batch1_auxiliary_pairs": 36,
+    "batch1_auxiliary_translation_rms_m": 0.07402020402512643,
+    "batch1_auxiliary_rotation_rms_deg": 1.1492603033421918
+  },
+  "important_limit": "Backend agreement is strong, but AX rotation RMS remains about one degree. This is not a centimetre-grade absolute certification."
+}

results/consensus/B_batch1_consensus.consensus.json

@@ -0,0 +1,328 @@
+{
+  "selection_is_X_independent": true,
+  "B_source": "Open3D; small_gicp is used only as an agreement gate",
+  "max_translation_m": 0.05,
+  "max_rotation_deg": 0.5,
+  "input_open3d_pairs": 41,
+  "accepted_pairs": 22,
+  "pairs": [
+    {
+      "i": 0,
+      "j": 1,
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+      "accepted": false,
+      "reason": "backend_disagreement"
+    },
+    {
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+      "j": 3,
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+      "open3d_small_rotation_deg": 0.14377171116926005,
+      "accepted": true,
+      "reason": ""
+    },
+    {
+      "i": 1,
+      "j": 2,
+      "open3d_small_translation_m": 0.012040931709501762,
+      "open3d_small_rotation_deg": 0.09198739647809913,
+      "accepted": true,
+      "reason": ""
+    },
+    {
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+      "j": 3,
+      "open3d_small_translation_m": 0.020167802344555865,
+      "open3d_small_rotation_deg": 0.10088741778579047,
+      "accepted": true,
+      "reason": ""
+    },
+    {
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+      "j": 5,
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+      "accepted": false,
+      "reason": "backend_disagreement"
+    },
+    {
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+      "j": 4,
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+    {
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+    {
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+      "open3d_small_rotation_deg": 0.18948013657322885,
+      "accepted": true,
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+    {
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+    {
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+    {
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+      "accepted": false,
+      "reason": "backend_disagreement"
+    },
+    {
+      "i": 16,
+      "j": 18,
+      "accepted": false,
+      "reason": "not_in_small_gicp_refined"
+    },
+    {
+      "i": 17,
+      "j": 18,
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+      "open3d_small_rotation_deg": 0.49818041971185584,
+      "accepted": true,
+      "reason": ""
+    },
+    {
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+      "j": 19,
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+      "open3d_small_rotation_deg": 0.6456312776257432,
+      "accepted": false,
+      "reason": "backend_disagreement"
+    },
+    {
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+      "j": 20,
+      "accepted": false,
+      "reason": "not_in_small_gicp_refined"
+    },
+    {
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+      "j": 21,
+      "open3d_small_translation_m": 0.06690824468510452,
+      "open3d_small_rotation_deg": 0.5787554058174607,
+      "accepted": false,
+      "reason": "backend_disagreement"
+    },
+    {
+      "i": 19,
+      "j": 20,
+      "accepted": false,
+      "reason": "not_in_small_gicp_refined"
+    },
+    {
+      "i": 20,
+      "j": 21,
+      "open3d_small_translation_m": 0.02975935281075696,
+      "open3d_small_rotation_deg": 0.36957453812106744,
+      "accepted": true,
+      "reason": ""
+    },
+    {
+      "i": 20,
+      "j": 22,
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+}

results/consensus/B_batch2_consensus.consensus.json

@@ -0,0 +1,530 @@
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+}

results/consensus/batch1_auxiliary_check.json

@@ -0,0 +1,179 @@
+{
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results/consensus/extrinsic_batch2_consensus.json

@@ -0,0 +1,399 @@
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+}

results/diagnostics/consensus_pair0_left_rpy_scan.csv

@@ -0,0 +1,19 @@
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results/diagnostics/open3d_refined_pair0_left_rpy_scan.csv

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results/diagnostics/small_gicp_refined_pair0_left_rpy_scan.csv

@@ -0,0 +1,19 @@
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results/final_extrinsic_deployment.json

@@ -0,0 +1,45 @@
+{
+    "convention":  "T_body_lidar maps raw LiDAR points into rear-axle body frame",
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+}

results/final_extrinsic_recommended.json

@@ -0,0 +1,405 @@
+{
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+  "message": "`ftol` termination condition is satisfied.",
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+  }
+}

results/final_summary.json

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+  },
+  "warning": "AX rotation RMS remains about one degree; this is not centimetre-grade absolute certification."
+}

results/open3d_gicp/B_batch1_quality.csv

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results/open3d_gicp/batch1_auxiliary_check.json

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results/open3d_gicp/extrinsic_batch2.json

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results/open3d_gicp/extrinsic_batch2_refined.json

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results/small_gicp/batch1_auxiliary_check.json

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results/small_gicp/extrinsic_batch2.json

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results/small_gicp/extrinsic_batch2_refined.json

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+          "pair_index": 74,
+          "translation_m": 0.04383537712573055,
+          "rotation_deg": 0.5600272304118834
+        },
+        {
+          "pair_index": 75,
+          "translation_m": 0.0849604176628602,
+          "rotation_deg": 1.2304564930488662
+        },
+        {
+          "pair_index": 76,
+          "translation_m": 0.010862365758746927,
+          "rotation_deg": 0.38357205151967033
+        },
+        {
+          "pair_index": 77,
+          "translation_m": 0.053059282511333926,
+          "rotation_deg": 0.9610287581424943
+        },
+        {
+          "pair_index": 78,
+          "translation_m": 0.04551226086388418,
+          "rotation_deg": 1.1597952394623392
+        },
+        {
+          "pair_index": 79,
+          "translation_m": 0.016850631999927004,
+          "rotation_deg": 0.7568718165305058
+        }
+      ]
+    }
+  },
+  "ground": {
+    "planes": 38,
+    "body_origin_height_above_ground_m": 0.2335,
+    "formula": "d_lidar - (R_X n_lidar)^T t_X - body_height"
+  },
+  "linearized_one_sigma": {
+    "translation_m": [
+      0.004217873072423743,
+      0.004428061325180952,
+      0.004921296107038976
+    ],
+    "rotation_deg": [
+      0.04989765234702571,
+      0.04568528000305764,
+      0.12720936620845405
+    ],
+    "warning": "conditional local estimate; bootstrap is the primary stability check"
+  },
+  "weighted_jacobian_condition_number": 6.329566115808833,
+  "solver_multistart": {
+    "runs": 12,
+    "candidates_relative_to_best": [
+      {
+        "cost": 354.634716588624,
+        "success": true,
+        "translation_m": 3.20226506801652e-10,
+        "rotation_deg": 2.202963019076451e-08
+      },
+      {
+        "cost": 354.6347165886241,
+        "success": true,
+        "translation_m": 7.896781546182907e-10,
+        "rotation_deg": 1.0169266187599847e-07
+      },
+      {
+        "cost": 354.6347165886238,
+        "success": true,
+        "translation_m": 8.217931179403876e-10,
+        "rotation_deg": 6.93412504585164e-08
+      },
+      {
+        "cost": 354.6347165886237,
+        "success": true,
+        "translation_m": 3.469446951953614e-18,
+        "rotation_deg": 0.0
+      },
+      {
+        "cost": 354.6347165886238,
+        "success": true,
+        "translation_m": 1.3034248658026153e-10,
+        "rotation_deg": 2.7806728416619943e-08
+      },
+      {
+        "cost": 354.6347165886238,
+        "success": true,
+        "translation_m": 2.260359361733417e-10,
+        "rotation_deg": 2.6418689746833837e-08
+      },
+      {
+        "cost": 354.634716588624,
+        "success": true,
+        "translation_m": 7.589395457725227e-10,
+        "rotation_deg": 4.91609016107675e-08
+      },
+      {
+        "cost": 354.6347165886238,
+        "success": true,
+        "translation_m": 1.2750789560311927e-10,
+        "rotation_deg": 7.759775984980414e-10
+      },
+      {
+        "cost": 354.634716588624,
+        "success": true,
+        "translation_m": 7.805526908313695e-10,
+        "rotation_deg": 6.684488070039544e-08
+      },
+      {
+        "cost": 354.634716588624,
+        "success": true,
+        "translation_m": 7.763945275712574e-10,
+        "rotation_deg": 8.931061588988946e-08
+      },
+      {
+        "cost": 354.6347165886244,
+        "success": true,
+        "translation_m": 9.383630927674663e-10,
+        "rotation_deg": 1.3000921411943172e-07
+      },
+      {
+        "cost": 354.634716588624,
+        "success": true,
+        "translation_m": 6.944401937454179e-10,
+        "rotation_deg": 7.954648404736881e-08
+      }
+    ]
+  },
+  "bootstrap": {
+    "runs": 100,
+    "order": [
+      "x_m",
+      "y_m",
+      "z_m",
+      "roll_deg",
+      "pitch_deg",
+      "yaw_deg"
+    ],
+    "std": [
+      0.0017068433472663032,
+      0.0019214288447692426,
+      0.0013180801706094514,
+      0.06849719260762097,
+      0.05792635838163369,
+      0.062093058432709465
+    ],
+    "p025": [
+      1.2968099294514637,
+      -0.006751632579940086,
+      0.7193267956198541,
+      -0.9300082754299475,
+      1.0287033540941326,
+      -1.0774039892205403
+    ],
+    "p975": [
+      1.302479553931627,
+      -0.0001961195897526885,
+      0.7244258625906532,
+      -0.6646157463265417,
+      1.254120304082275,
+      -0.8275267997610058
+    ]
+  }
+}

run/run_all.ps1

@@ -0,0 +1,32 @@
+param(
+    [string]$Batch1Prepared = "C:\Users\admin\Documents\Codex\2026-07-15\wo\outputs\calibration_20260717\prepared",
+    [string]$Batch2Prepared = "C:\Users\admin\Documents\Codex\2026-07-15\wo\outputs\calibration_data1_20260720\prepared"
+)
+$ErrorActionPreference = "Stop"
+$Repo = Split-Path -Parent $PSScriptRoot
+$Code = Join-Path $Repo "code\rigorous_calibration.py"
+$Refine = Join-Path $Repo "code\refine_pairs.py"
+$Summary = Join-Path $Repo "code\summarize_results.py"
+$R = Join-Path $Repo "results"
+$B1Frames = Join-Path $Batch1Prepared "frames_all"
+$B2Frames = Join-Path $Batch2Prepared "frames_all"
+$B1Body = Join-Path $Batch1Prepared "body_poses_rear_gga_raw_rear_to_front.csv"
+$B2Body = Join-Path $Batch2Prepared "body_poses_rear_gga_raw_rear_to_front.csv"
+
+python $Code ground --frames $B2Frames --output "$R\common\ground_planes_batch2.csv"
+
+python $Code pairs --backend small_gicp --frames $B2Frames --body $B2Body --output "$R\small_gicp\B_batch2_estimation.npz" --quality-json "$R\small_gicp\B_batch2_quality.json" --quality-csv "$R\small_gicp\B_batch2_quality.csv"
+python $Code pairs --backend open3d --frames $B2Frames --body $B2Body --output "$R\open3d_gicp\B_batch2_estimation.npz" --quality-json "$R\open3d_gicp\B_batch2_quality.json" --quality-csv "$R\open3d_gicp\B_batch2_quality.csv" --max-gap 3 --multistart 1 --iterations 40
+python $Refine --pairs "$R\small_gicp\B_batch2_estimation.npz" --quality-json "$R\small_gicp\B_batch2_quality.json" --output "$R\small_gicp\B_batch2_refined.npz"
+python $Refine --pairs "$R\open3d_gicp\B_batch2_estimation.npz" --quality-json "$R\open3d_gicp\B_batch2_quality.json" --output "$R\open3d_gicp\B_batch2_refined.npz"
+python $Code calibrate --pairs "$R\small_gicp\B_batch2_refined.npz" --ground-planes "$R\common\ground_planes_batch2.csv" --output "$R\small_gicp\extrinsic_batch2_refined.json"
+python $Code calibrate --pairs "$R\open3d_gicp\B_batch2_refined.npz" --ground-planes "$R\common\ground_planes_batch2.csv" --output "$R\open3d_gicp\extrinsic_batch2_refined.json"
+
+python $Code pairs --backend small_gicp --frames $B1Frames --body $B1Body --output "$R\small_gicp\B_batch1_auxiliary.npz" --quality-json "$R\small_gicp\B_batch1_quality.json" --quality-csv "$R\small_gicp\B_batch1_quality.csv" --max-gap 3 --multistart 1 --iterations 40
+python $Code pairs --backend open3d --frames $B1Frames --body $B1Body --output "$R\open3d_gicp\B_batch1_auxiliary.npz" --quality-json "$R\open3d_gicp\B_batch1_quality.json" --quality-csv "$R\open3d_gicp\B_batch1_quality.csv" --max-gap 3 --multistart 1 --iterations 40
+python $Refine --pairs "$R\small_gicp\B_batch1_auxiliary.npz" --quality-json "$R\small_gicp\B_batch1_quality.json" --output "$R\small_gicp\B_batch1_auxiliary_refined.npz"
+python $Refine --pairs "$R\open3d_gicp\B_batch1_auxiliary.npz" --quality-json "$R\open3d_gicp\B_batch1_quality.json" --output "$R\open3d_gicp\B_batch1_auxiliary_refined.npz"
+python $Code validate --pairs "$R\small_gicp\B_batch1_auxiliary_refined.npz" --extrinsic "$R\small_gicp\extrinsic_batch2_refined.json" --output "$R\small_gicp\batch1_auxiliary_check.json"
+python $Code validate --pairs "$R\open3d_gicp\B_batch1_auxiliary_refined.npz" --extrinsic "$R\open3d_gicp\extrinsic_batch2_refined.json" --output "$R\open3d_gicp\batch1_auxiliary_check.json"
+
+python $Summary --open3d "$R\open3d_gicp\extrinsic_batch2_refined.json" --small "$R\small_gicp\extrinsic_batch2_refined.json" --open3d-quality "$R\open3d_gicp\B_batch2_quality.json" --small-quality "$R\small_gicp\B_batch2_quality.json" --open3d-check "$R\open3d_gicp\batch1_auxiliary_check.json" --small-check "$R\small_gicp\batch1_auxiliary_check.json" --output "$R\comparison_summary.json" --recommended-output "$R\final_extrinsic_recommended.json"

run/run_consensus_finish.ps1

@@ -0,0 +1,12 @@
+$ErrorActionPreference = "Stop"
+$Repo = Split-Path -Parent $PSScriptRoot
+$Code = Join-Path $Repo "code\rigorous_calibration.py"
+$Filter = Join-Path $Repo "code\cross_backend_filter.py"
+$Finalize = Join-Path $Repo "code\finalize_consensus.py"
+$R = Join-Path $Repo "results"
+
+python $Filter --open3d-pairs "$R\open3d_gicp\B_batch2_refined.npz" --small-pairs "$R\small_gicp\B_batch2_refined.npz" --output "$R\consensus\B_batch2_consensus.npz"
+python $Filter --open3d-pairs "$R\open3d_gicp\B_batch1_auxiliary_refined.npz" --small-pairs "$R\small_gicp\B_batch1_auxiliary_refined.npz" --output "$R\consensus\B_batch1_consensus.npz" --min-pairs 15
+python $Code calibrate --pairs "$R\consensus\B_batch2_consensus.npz" --ground-planes "$R\common\ground_planes_batch2.csv" --output "$R\consensus\extrinsic_batch2_consensus.json"
+python $Code validate --pairs "$R\consensus\B_batch1_consensus.npz" --extrinsic "$R\consensus\extrinsic_batch2_consensus.json" --output "$R\consensus\batch1_auxiliary_check.json"
+python $Finalize --consensus-extrinsic "$R\consensus\extrinsic_batch2_consensus.json" --consensus-check "$R\consensus\batch1_auxiliary_check.json" --open3d-extrinsic "$R\open3d_gicp\extrinsic_batch2_refined.json" --small-extrinsic "$R\small_gicp\extrinsic_batch2_refined.json" --output "$R\final_extrinsic_recommended.json" --summary "$R\final_summary.json"

run/run_sensitivity_scan.ps1

@@ -0,0 +1,15 @@
+param([int]$PairIndex = 0)
+$Repo = Split-Path -Parent $PSScriptRoot
+$Code = "$Repo\code\scan_extrinsic_sensitivity.py"
+$X = "$Repo\results\final_extrinsic_recommended.json"
+$Ground = "$Repo\results\common\ground_planes_batch2.csv"
+$Out = "$Repo\results\diagnostics"
+
+python $Code --pairs "$Repo\results\open3d_gicp\B_batch2_refined.npz" --extrinsic $X --ground-planes $Ground --pair-index $PairIndex --output "$Out\open3d_refined_pair${PairIndex}_left_rpy_scan.json"
+if ($LASTEXITCODE -ne 0) { exit $LASTEXITCODE }
+
+python $Code --pairs "$Repo\results\small_gicp\B_batch2_refined.npz" --extrinsic $X --ground-planes $Ground --pair-index $PairIndex --output "$Out\small_gicp_refined_pair${PairIndex}_left_rpy_scan.json"
+if ($LASTEXITCODE -ne 0) { exit $LASTEXITCODE }
+
+python $Code --pairs "$Repo\results\consensus\B_batch2_consensus.npz" --extrinsic $X --ground-planes $Ground --pair-index $PairIndex --output "$Out\consensus_pair${PairIndex}_left_rpy_scan.json"
+exit $LASTEXITCODE

run/view_open3d_result.ps1

@@ -0,0 +1,14 @@
+param(
+    [int]$PairIndex = 0,
+    [string]$Frames = "C:\Users\admin\Documents\Codex\2026-07-15\wo\outputs\calibration_data1_20260720\prepared\frames_all",
+    [double]$LeftRollDeg = 0.0,
+    [double]$LeftPitchDeg = 0.0,
+    [double]$LeftYawDeg = 0.0
+)
+$Repo = Split-Path -Parent $PSScriptRoot
+python "$Repo\code\visualize_pair_3d.py" `
+    --frames $Frames `
+    --pairs "$Repo\results\open3d_gicp\B_batch2_refined.npz" `
+    --extrinsic "$Repo\results\final_extrinsic_recommended.json" `
+    --pair-index $PairIndex `
+    --left-rpy-deg $LeftRollDeg $LeftPitchDeg $LeftYawDeg

run/view_small_gicp_result.ps1

@@ -0,0 +1,18 @@
+param(
+    [int]$PairIndex = 0,
+    [string]$Frames = "C:\Users\admin\Documents\Codex\2026-07-15\wo\outputs\calibration_data1_20260720\prepared\frames_all",
+    [string]$Extrinsic = "",
+    [double]$LeftRollDeg = 0.0,
+    [double]$LeftPitchDeg = 0.0,
+    [double]$LeftYawDeg = 0.0
+)
+$Repo = Split-Path -Parent $PSScriptRoot
+if ([string]::IsNullOrWhiteSpace($Extrinsic)) {
+    $Extrinsic = "$Repo\results\small_gicp\extrinsic_batch2_refined.json"
+}
+python "$Repo\code\visualize_pair_3d.py" `
+    --frames $Frames `
+    --pairs "$Repo\results\small_gicp\B_batch2_refined.npz" `
+    --extrinsic $Extrinsic `
+    --pair-index $PairIndex `
+    --left-rpy-deg $LeftRollDeg $LeftPitchDeg $LeftYawDeg