【M-LOAM学习】

M-LOAM(INITIALIZATION)

Article Analysis

Scan-Based Motion Estimation

通过在consecutive frame (each LiDAR)（因为omp parallel）中寻找correspondences然后通过最小化所有考虑feature之间residual error的transformation between frame to frame
针对于一个LASER在Kframe的相邻两次scan，分别考虑planar feature 以及 corner feature
planar feature

其点到平面的距离公式通过点的坐标和法向量表示为：

具体分析如下：

最终构建的edge residual 如下：

请添加图片描述

M-LOAM在initialization的outstanding feature为：提供了状态的额外约束，同时残差表示为向量，能够✖协方差阵
最终的函数构造为：

在获取增量运动的点云后，选择使用将点转换到最后一帧数据来对点云进行畸变校正，也就是在[t_k-1,t_k]获得的增量点云数据，如果进行畸变校正需要转移到t_k-1时刻进行畸变校正，这也就需要从current time到t_k-1time的rotation matrix 以及translation 这里针对于[t_k-1,t_k]，采用线性插值插值处于该时段每个时刻出现的t_i

在这里插入图片描述

Calibration of Multi-LiDAR System
初始化外部参数通过对齐两个传感器的运动序列进行外参初始化。
在外参校准的过程中使用手眼标定方法手眼标定
手眼标定选择两部法实现这里(t_l_i^b与R_l_i^b是待求的)
旋转初始化(Rotation Initialization):
通过运用quaternion四元数重写上式。转成线性方程是为了更好的实现多个时间段四元数线性叠加的过程
(需要足够的运动激励)这里如果运动约束充分那么对应的3-DoF的rotation是可观测的，那么对应的Q_k的0空间对应的秩为1，因为3DoF可以观测所以对应的能观性矩阵的秩数为3(如果存在多轴退化的情况那么导致多个维度的运动信息不可观测那么就会出现Q_k秩大于1的情况(多维度不可观测))
零空间对应着维度的不可观测性
运动退化导致维度不可观测

多轴的位姿退化使得Q_k的零空间代表的不可观测性维度增加，导致Q_k的秩大于1
平移初始化(Translation Initialization):
通过rotational calibration校正完成，根据手眼标定基于已经标定的旋转矩阵来标定平移变量(translation)。本文中因为仅仅考虑二维平面所以在z方向的平移t_z不可观测(在后续精化标定中涉及)

INITIALIZATION代码分析

初始化步骤的开始：void Estimator::process()
根据在Measurement Processing阶段得到的feature set实现初始化
首先判断if(ESTIMATE_EXTRINSIC == 2)（2 Have no prior about extrinsic parameters. We will initialize and optimize around them）
按照论文中的方式：实现手眼标定实现参数初始化
这里巧妙的运用了**#pragma omp parallel for num_threads(NUM_OF_LASER)通过为每个laser数据处理标定分配多线程独立实现EXTRINSIC初始估计。
通过函数trackCloud**实现点云追踪
第一步：提取上一帧经过校正的点云插入到kdtree方便寻找最近邻点

    PointICloudPtr corner_points_last = boost::make_shared<PointICloud>(prev_cloud_feature.find("corner_points_less_sharp")->second);PointICloudPtr surf_points_last = boost::make_shared<PointICloud>(prev_cloud_feature.find("surf_points_less_flat")->second);kdtree_corner_last->setInputCloud(corner_points_last);kdtree_surf_last->setInputCloud(surf_points_last);

第二步：获取当前current time的特征点对应的点云数据

 PointICloudPtr corner_points_sharp = boost::make_shared<PointICloud>(cur_cloud_feature.find("corner_points_sharp")->second);PointICloudPtr surf_points_flat = boost::make_shared<PointICloud>(cur_cloud_feature.find("surf_points_flat")->second);

第三步：通过非线性最小二乘通过最小化planar facto and corner factor实现initial motion estimation (state)(帧到帧的姿态估计)

f_extract_.matchCornerFromScan(kdtree_corner_last, *corner_points_last, *corner_points_sharp, pose_local, corner_scan_features);

实现基于scan扫描线的corner feature matching
matchCornerFromScan用来从扫描线中匹配角点特征

流程：将corner_points_sharp(current time)的角点特征通过TransformToStart函数，转换到t_k-1帧坐标系中，与corner_points_last上一帧经过校正的角点特征存放如kdtree_corner_from_scan中(这里在trackCloud函数里面已经实现了将prev_cloud_feature存放入kdtree_corner_last)，然后通过nearestKSearch函数寻找投影点point_sel的最近邻点因为是edge factor 所以最终需要找到两个nearest factor,通过判断** if (min_point_ind2 >= 0) 如果存在两个nearest point 那么存储两个点的系数到coeff**，保存feature(idx_，point_，coeffs_)三类信息。

void FeatureExtract::matchCornerFromScan(const typename pcl::KdTreeFLANN<PointType>::Ptr &kdtree_corner_from_scan,const typename pcl::PointCloud<PointType> &cloud_scan,const typename pcl::PointCloud<PointType> &cloud_data,const Pose &pose_local,std::vector<PointPlaneFeature> &features)
{if (!pcl::traits::has_field<PointType, pcl::fields::intensity>::value){std::cerr << "[FeatureExtract] Point does not have intensity field!" << std::endl;exit(EXIT_FAILURE);}
/*f_extract_.matchCornerFromScan(kdtree_corner_last, *corner_points_last, *corner_points_sharp, pose_local, corner_scan_features); */size_t cloud_size = cloud_data.points.size();/*corner feature size */features.resize(cloud_size);size_t cloud_cnt = 0;PointType point_sel;std::vector<int> point_search_ind;std::vector<float> point_search_sqdis;for (size_t i = 0; i < cloud_data.points.size(); i++){// not consider distortion/*转换到tk-1 frame to search the corrected cloud point*/TransformToStart(cloud_data.points[i], point_sel, pose_local, false, SCAN_PERIOD);/*from last corner set to find the nearest correspondent for the corner projection*/kdtree_corner_from_scan->nearestKSearch(point_sel, 1, point_search_ind, point_search_sqdis);int closest_point_ind = -1, min_point_ind2 = -1;if (point_search_sqdis[0] < DISTANCE_SQ_THRESHOLD)/*通过DISTANCE_SQ_THRESHOLD判断最近邻是否满足距离要求限制*/{closest_point_ind = point_search_ind[0];/*最近扫描点的索引*/int closest_point_scan_id = int(cloud_scan.points[closest_point_ind].intensity);/*找对应的投影点的最近邻点的最近点 形成edge feature*/float min_point_sqdis2 = DISTANCE_SQ_THRESHOLD;// search in the direction of increasing scan linefor (int j = closest_point_ind + 1; j < (int)cloud_scan.points.size(); j++){// if in the same scan line, continueif (int(cloud_scan.points[j].intensity) <= closest_point_scan_id)continue;// if not in nearby scans, end the loopif (int(cloud_scan.points[j].intensity) > (closest_point_scan_id + NEARBY_SCAN))break;float point_sqdis = sqrSum(cloud_scan.points[j].x - point_sel.x,cloud_scan.points[j].y - point_sel.y,cloud_scan.points[j].z - point_sel.z);if (point_sqdis < min_point_sqdis2){// find nearer pointmin_point_sqdis2 = point_sqdis;min_point_ind2 = j;}}// search in the direction of decreasing scan linefor (int j = closest_point_ind - 1; j >= 0; j--){// if in the same scan line, continueif (int(cloud_scan.points[j].intensity) >= closest_point_scan_id)continue;// if not in nearby scans, end the loopif (int(cloud_scan.points[j].intensity) < (closest_point_scan_id - NEARBY_SCAN))break;float point_sqdis = sqrSum(cloud_scan.points[j].x - point_sel.x,cloud_scan.points[j].y - point_sel.y,cloud_scan.points[j].z - point_sel.z);if (point_sqdis < min_point_sqdis2){// find nearer pointmin_point_sqdis2 = point_sqdis;min_point_ind2 = j;}}}if (min_point_ind2 >= 0) // both closest_point_ind and min_point_ind2 is valid{Eigen::Matrix<double, 6, 1> coeff;coeff(0) = cloud_scan.points[closest_point_ind].x,coeff(1) = cloud_scan.points[closest_point_ind].y,coeff(2) = cloud_scan.points[closest_point_ind].z;coeff(3) = cloud_scan.points[min_point_ind2].x,coeff(4) = cloud_scan.points[min_point_ind2].y,coeff(5) = cloud_scan.points[min_point_ind2].z;PointPlaneFeature feature;feature.idx_ = i;feature.point_ = Eigen::Vector3d{cloud_data.points[i].x, cloud_data.points[i].y, cloud_data.points[i].z};feature.coeffs_ = coeff;/*corner feature 对应的corner correspondent point {x,y,z}*/features[cloud_cnt] = feature;cloud_cnt++;}}features.resize(cloud_cnt);
}

通过**f_extract_.matchSurfFromScan(kdtree_surf_last, *surf_points_last, *surf_points_flat, pose_local, surf_scan_features);**提取面特征(surf feature from scan)

void FeatureExtract::matchSurfFromScan(const typename pcl::KdTreeFLANN<PointType>::Ptr &kdtree_surf_from_scan,const typename pcl::PointCloud<PointType> &cloud_scan,const typename pcl::PointCloud<PointType> &cloud_data,const Pose &pose_local,std::vector<PointPlaneFeature> &features)
{if (!pcl::traits::has_field<PointType, pcl::fields::intensity>::value){std::cerr << "[FeatureExtract] Point does not have intensity field!" << std::endl;exit(EXIT_FAILURE);}features.clear();PointType point_sel;std::vector<int> point_search_ind;std::vector<float> point_search_sqdis;for (size_t i = 0; i < cloud_data.points.size(); i++){// not consider distortion/*线投影到初始坐标系*/TransformToStart(cloud_data.points[i], point_sel, pose_local, false, SCAN_PERIOD);/*然后通过最近邻搜索具有corner feature 最近邻的cloud point*/kdtree_surf_from_scan->nearestKSearch(point_sel, 1, point_search_ind, point_search_sqdis);/*因为是surf point 所以选择3个不共线的点 作为 平面点来分析*//*规定 min_point_ind3 在相邻的扫描线上 而min_point_ind2 与closest_point_ind要么在同扫描线要么在相邻扫描线上*/int closest_point_ind = -1, min_point_ind2 = -1, min_point_ind3 = -1;if (point_search_sqdis[0] < DISTANCE_SQ_THRESHOLD){closest_point_ind = point_search_ind[0];/*最近点的id*/// get closest point's scan IDint closest_point_scan_id = int(cloud_scan.points[closest_point_ind].intensity);float min_point_sqdis2 = DISTANCE_SQ_THRESHOLD, min_point_sqdis3 = DISTANCE_SQ_THRESHOLD;
#pragma region 在最近点的扫描线增加以及减少的方向上搜索该closest_point_ind的相邻点// search in the direction of increasing scan linefor (int j = closest_point_ind + 1; j < (int)cloud_scan.points.size(); j++){// if not in nearby scans, end the loopif (int(cloud_scan.points[j].intensity) > (closest_point_scan_id + NEARBY_SCAN))break;float point_sqdis = sqrSum(cloud_scan.points[j].x - point_sel.x,cloud_scan.points[j].y - point_sel.y,cloud_scan.points[j].z - point_sel.z);// if in the same or lower scan lineif (int(cloud_scan.points[j].intensity) <= closest_point_scan_id && point_sqdis < min_point_sqdis2){min_point_sqdis2 = point_sqdis;min_point_ind2 = j;}// if in the higher scan lineelse if (int(cloud_scan.points[j].intensity) > closest_point_scan_id && point_sqdis < min_point_sqdis3){min_point_sqdis3 = point_sqdis;min_point_ind3 = j;}}// search in the direction of decreasing scan linefor (int j = closest_point_ind - 1; j >= 0; j--){// if not in nearby scans, end the loopif (int(cloud_scan.points[j].intensity) < (closest_point_scan_id - NEARBY_SCAN))break;float point_sqdis = sqrSum(cloud_scan.points[j].x - point_sel.x,cloud_scan.points[j].y - point_sel.y,cloud_scan.points[j].z - point_sel.z);// if in the same or higher scan lineif (int(cloud_scan.points[j].intensity) >= closest_point_scan_id && point_sqdis < min_point_sqdis2){min_point_sqdis2 = point_sqdis;min_point_ind2 = j;}else if (int(cloud_scan.points[j].intensity) < closest_point_scan_id && point_sqdis < min_point_sqdis3){// find nearer pointmin_point_sqdis3 = point_sqdis;min_point_ind3 = j;}}
#pragma endregionif (min_point_ind2 >= 0 && min_point_ind3 >= 0){Eigen::Vector3f last_point_j(cloud_scan.points[closest_point_ind].x,cloud_scan.points[closest_point_ind].y,cloud_scan.points[closest_point_ind].z);Eigen::Vector3f last_point_l(cloud_scan.points[min_point_ind2].x,cloud_scan.points[min_point_ind2].y,cloud_scan.points[min_point_ind2].z);Eigen::Vector3f last_point_m(cloud_scan.points[min_point_ind3].x,cloud_scan.points[min_point_ind3].y,cloud_scan.points[min_point_ind3].z);Eigen::Vector3f w = (last_point_j - last_point_l).cross(last_point_j - last_point_m);/*平面的法向量*/w.normalize();/*法向量变成单位向量*/float negative_OA_dot_norm = -w.dot(last_point_j);/*D的normalize值*/float pd2 = -(w.x() * point_sel.x + w.y() * point_sel.y + w.z() * point_sel.z + negative_OA_dot_norm); // distance float s = 1 - 0.9f * fabs(pd2) / sqrt(sqrSum(point_sel.x, point_sel.y, point_sel.z));Eigen::Vector4d coeff(w.x(), w.y(), w.z(), negative_OA_dot_norm);PointPlaneFeature feature;feature.idx_ = i;feature.point_ = Eigen::Vector3d{cloud_data.points[i].x, cloud_data.points[i].y, cloud_data.points[i].z};feature.coeffs_ = coeff;feature.type_ = 's';features.push_back(feature);}}}
}

判断线特征以及面特征的数量总和是否满足大于10个特征数量
如果特征数量总和大于10 那么通过LidarScanPlaneNormFactor创建plane feature
通过LidarScanEdgeFactorVector创建corner_scan_features的corner feature

对于planefeature的AddResidualBlock其通过重载Ealuate实现(自己实现计算jacobians矩阵)

    bool Evaluate(double const *const *param, double *residuals, double **jacobians) const{Eigen::Quaterniond q_last_curr(param[0][6], param[0][3], param[0][4], param[0][5]);Eigen::Vector3d t_last_curr(param[0][0], param[0][1], param[0][2]);/*插值*/q_last_curr = Eigen::Quaterniond::Identity().slerp(s_, q_last_curr);/*四元数相对姿态的球面插值*/t_last_curr = s_ * t_last_curr;/*在matchCornerFromScan中计算的feature向量*/Eigen::Vector3d w(coeff_(0), coeff_(1), coeff_(2));double d = coeff_(3);double a = w.dot(q_last_curr * point_ + t_last_curr) + d;/*对应点到面的距离*/residuals[0] = a;/*残差*/if (jacobians){Eigen::Matrix3d R = q_last_curr.toRotationMatrix();if (jacobians[0]){Eigen::Map<Eigen::Matrix<double, 1, 7, Eigen::RowMajor>> jacobian_pose(jacobians[0]);Eigen::Matrix<double, 1, 6> jaco; // [dy/dt, dy/dR, 1]jaco.setZero();jaco.leftCols<3>() = w.transpose();jaco.rightCols<3>() = -w.transpose() * R * Utility::skewSymmetric(point_);jacobian_pose.setZero();jacobian_pose.leftCols<6>() = jaco;}}return true;}

对于EdgeFactor加入重载evaluate构建残差最终 在论文中明确了edge residual 不再充当scalars标量而是represented as a vector 能够allowing us to multiply a 3*3 covariance matrix 但是貌似代码中并没有类似的实例列举？？

    bool Evaluate(double const *const *param, double *residuals, double **jacobians) const{/*set q_last_curr and t_last_curr as the states*/Eigen::Quaterniond q_last_curr(param[0][6], param[0][3], param[0][4], param[0][5]);Eigen::Vector3d t_last_curr(param[0][0], param[0][1], param[0][2]);/*数据插值*/q_last_curr = Eigen::Quaterniond::Identity().slerp(s_, q_last_curr);t_last_curr = s_ * t_last_curr;/*last point a and last point b and last point (projection to the tk-1)*/Eigen::Vector3d lpa(coeff_(0), coeff_(1), coeff_(2));Eigen::Vector3d lpb(coeff_(3), coeff_(4), coeff_(5));Eigen::Vector3d lp = q_last_curr * point_ + t_last_curr;Eigen::Vector3d nu = (lp - lpa).cross(lp - lpb);/*四边形面积*/Eigen::Vector3d de = lpa - lpb;/*四边形底边长*/residuals[0] = nu.x() / de.norm();/*高对应的向量(距离的投影)*/residuals[1] = nu.y() / de.norm();residuals[2] = nu.z() / de.norm();/*edge residual represented as vectors allowing us to multiply a 3*3 covariance matrix*/// residuals[0] = nu.norm / de.norm();if (jacobians){Eigen::Matrix3d R = q_last_curr.toRotationMatrix();if (jacobians[0]){Eigen::Map<Eigen::Matrix<double, 3, 7, Eigen::RowMajor>> jacobian_pose(jacobians[0]);Eigen::Matrix<double, 3, 6> jaco; // [dy/dt, dy/dq, 1]double  eta = 1.0 / de.norm();jaco.leftCols<3>() = -eta * Utility::skewSymmetric(lpa - lpb);jaco.rightCols<3>() = eta * Utility::skewSymmetric(lpa - lpb) * R * Utility::skewSymmetric(point_);jacobian_pose.setZero();jacobian_pose.leftCols<6>() = jaco;}}return true;}

**摄制完成相应的edge factor 以及 surf factor后执行optimization **

       // step 3: optimizationTicToc t_solver;ceres::Solver::Options options;options.linear_solver_type = ceres::DENSE_SCHUR;options.max_num_iterations = 4;// options.max_solver_time_in_seconds = 0.005;options.minimizer_progress_to_stdout = false;// options.check_gradients = false;// options.gradient_check_relative_precision = 1e-4;ceres::Solver::Summary summary;ceres::Solve(options, &problem, &summary);// std::cout << summary.BriefReport() << std::endl;// std::cout << summary.FullReport() << std::endl;// printf("solver time %f ms \n", t_solver.toc());

至此：pose_laser_cur_对于帧与帧之间的特征匹配优化实现完成
然后通过pose_prev_cur获取优化后的位姿然后返回帧与帧之间匹配的优化位姿。
（达到当前增量位姿优化更新的目的）更新的是增量位姿

 Pose pose_prev_cur(Eigen::Quaterniond(para_pose[6], para_pose[3], para_pose[4], para_pose[5]), Eigen::Vector3d(para_pose[0], para_pose[1], para_pose[2]));return pose_prev_cur;

通过pose_laser_cur_将IDX_REF；主雷达的quaternion以及 transformation的优化增量姿态传递给Qs_与Ts_，
经过帧与帧之间的特征匹配实现的增量位姿优化

    Qs_[cir_buf_cnt_] = pose_laser_cur_[IDX_REF].q_;Ts_[cir_buf_cnt_] = pose_laser_cur_[IDX_REF].t_;Header_[cir_buf_cnt_].stamp = ros::Time(cur_feature_.first);

针对于当前帧的特征实现体素滤波器对滤波进行降采样

for (size_t n = 0; n < NUM_OF_LASER; n++){/*针对于corner point feature 实现down size 降采样 */PointICloud &corner_points = cur_feature_.second[n]["corner_points_less_sharp"];down_size_filter_corner_.setInputCloud(boost::make_shared<PointICloud>(corner_points));down_size_filter_corner_.filter(corner_points_stack_[n][cir_buf_cnt_]);corner_points_stack_size_[n][cir_buf_cnt_] = corner_points_stack_[n][cir_buf_cnt_].size();/*第N个雷达点云的corner point size */
/*同理 对surf point 面点实现降采样*/PointICloud &surf_points = cur_feature_.second[n]["surf_points_less_flat"];/*surf feature*/down_size_filter_surf_.setInputCloud(boost::make_shared<PointICloud>(surf_points));/*input cloud feature*/down_size_filter_surf_.filter(surf_points_stack_[n][cir_buf_cnt_]);/*down size filter 降采样*/surf_points_stack_size_[n][cir_buf_cnt_] = surf_points_stack_[n][cir_buf_cnt_].size();/**/}

因为需要自动标定外参所以 solver_flag_一直设置为初始化执行case:INITIAL,通过slideWindow()函数不断的将基于帧与帧之间的优化位姿通过滑动窗口实现数据存入

case INITIAL:/*set initial*/{printf("[INITIAL]\n");/*将Q T surf_point corner_point push into the */slideWindow();/*是不是实现了两次连续的插入first*/if (cir_buf_cnt_ < WINDOW_SIZE){cir_buf_cnt_++;if (cir_buf_cnt_ == WINDOW_SIZE){slideWindow(); /*等到窗口尺寸的时候 仍然进行一次滑动窗口 将第一个重复的数据进行剔除*/}}

然后根据雷达的数量执行针对于当前优化位姿的特征点信息降采样，然后通过判断solver_flag_实现对于当前帧对应的特征数据作为下一个帧的特征数据的输入实现插入，通过滑动窗口，存入corner feature ,surf feature 以及Qs_和Ts_的增量优化位姿后在对帧到帧匹配用到的弱面点以及弱角点信息进行存储这些信息来自于未被降采样的cur_feature_数据存储器

    prev_time_ = cur_time_;prev_feature_.first = prev_time_;prev_feature_.second.clear();prev_feature_.second.resize(NUM_OF_LASER);for (size_t n = 0; n < NUM_OF_LASER; n++){prev_feature_.second[n].insert(make_pair("corner_points_less_sharp", cur_feature_.second[n].find("corner_points_less_sharp")->second));prev_feature_.second[n].insert(make_pair("surf_points_less_flat", cur_feature_.second[n].find("surf_points_less_flat")->second));}

对于经过一系列运动后==cloud point已经存在由于LiDAR旋转切片扫描而引入的运动畸变，对应的处理策略是：在解算完成增量运动信息后，我们将这些cloud point 信息transforming into the last frame 然后进行correct **

这里实现为：
首先通过pose_laser_cur存储获取当前的rotation quaternion以及trasformation information 然后pose_undist用来存储经过帧与帧之间的优化位姿匹配得到的增量位姿信息**通过pose_undist[IDX_REF] = pose_laser_prev_.inverse() * pose_laser_cur;将增量位姿从body对应的坐标系转换到主雷达对应的laser坐标系，下面的for 循环同样实现将每个雷达测量得到的incremental motion信息转换到主雷达对应的坐标系中的增量然后到主雷达坐标系中的投影==，最后通过**undistortMeasurements(pose_undist);将当前帧对应的cloud point 点云信息 transform成为[t_k-1,t_k]对应的last (start time t_k-1)**最终实现畸变校正

/*如果存在运动畸变*/if (DISTORTION){/*对应当前点的位姿*/Pose pose_laser_cur = Pose(Qs_[cir_buf_cnt_ - 1], Ts_[cir_buf_cnt_ - 1]);/*当前的pose*/std::vector<Pose> pose_undist = pose_rlt_;/*pose_rlt_存储优化后的增量雷达信息*/pose_undist[IDX_REF] = pose_laser_prev_.inverse() * pose_laser_cur;for (size_t n = 0; n < NUM_OF_LASER; n++){/*body 2 laser frame*/Pose pose_ext(qbl_[n], tbl_[n]);/*pose extrinsic parameter*//*pose_ext.inverse() -> laser 2 body frame* pose_rlt_ in body frame* pose_ext -> body 2 laser frame* finally :pose_undist is in laser frame* */pose_undist[n] = pose_ext.inverse() * pose_rlt_[IDX_REF] * pose_ext;/*转变为在雷达坐标系表示的运动增量(incremental motion)在laser 坐标系的投影(in laser projection)*/}undistortMeasurements(pose_undist);pose_laser_prev_ = pose_laser_cur;}

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首先在每次执行完成motion estimation and obtain the optimized incremental motion information基于帧到帧的匹配后通过initial_extrinsics_.addPose(pose_rlt_) 向initial_extrinsics_中增加外部运动信息直到满足所需要的足够的运动movement后执行calibrating extrinsic param
执行的addPose函数主要是：通过调用checkScrewMotion函数检查主雷达与辅雷达之间运动存在的点云运动畸变，返回满足小于rotation 以及 transformation 畸变阈值的优化pose state通过pq_pose_.push()将满足条件的增量pose state 数据存储到pq_pose_中
这里设置有一个小技巧：pq_pose_.size()来代表插入的满足条件的增量点云pose_laser的索引
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同样，只有在满足if (initial_extrinsics_.addPose(pose_rlt_) && (cir_buf_cnt_ == WINDOW_SIZE))的时候，这保证了在具有sufficient optimized relative movement 实现 calibrating extrinsic parameter
下面对于达到sufficient movement后进行calibrating extrinsic param(外参校正基于手眼标定，对应Artical Analysis的第二部分 2. Calibration of Multi-LiDAR System)
针对于每一个辅助雷达基于手眼标定进行外部参数标定返回标定结果到calib_result
并输出标定后的外参矩阵QBL[n] = calib_result.q_; TBL[n] = calib_result.t_;

                for (size_t n = 0; n < NUM_OF_LASER; n++){if (initial_extrinsics_.cov_rot_state_[n]) continue;Pose calib_result;/*calibrate the rotation*/if (initial_extrinsics_.calibExRotation(IDX_REF, n, calib_result)){/*calibrate the translation*/if (initial_extrinsics_.calibExTranslation(IDX_REF, n, calib_result)){/*输出多个传感器雷达校正完成后的初始参数(initial extrinsic of laser)* 其中包括* quaternion body to laser* translation body to laser** */std::cout << common::YELLOW << "Initial extrinsic of laser_" << n << ": " << calib_result << common::RESET << std::endl;qbl_[n] = calib_result.q_;tbl_[n] = calib_result.t_;// tdbl_[n] = calib_result.td_;QBL[n] = calib_result.q_;TBL[n] = calib_result.t_;// TDBL[n] = calib_result.td_;}}}

最后判断是否所有的雷达全部完成了rotation以及translation的外参估计如果全部完成那么
最终将ESTIMATE_EXTRINSIC改成1

if ((initial_extrinsics_.full_cov_rot_state_) && (initial_extrinsics_.full_cov_pos_state_)){std::cout << common::YELLOW << "All initial extrinsic rotation calib success" << common::RESET << std::endl;ESTIMATE_EXTRINSIC = 1;initial_extrinsics_.saveStatistics();}