我拿港科技沈老師的VINS中的BA優化來闡述ceres-solver怎么做邊緣化和稀疏化.

代碼如下：

void Estimator::optimization() {ceres::Problem problem;ceres::LossFunction *loss_function;//loss_function = new ceres::HuberLoss(1.0);loss_function = new ceres::CauchyLoss(1.0); //添加需要優化的變量（camera的pose，imu的biases）for (int i = 0; i < WINDOW_SIZE + 1; i++){ceres::LocalParameterization *local_parameterization = new PoseLocalParameterization();problem.AddParameterBlock(para_Pose[i], SIZE_POSE, local_parameterization);problem.AddParameterBlock(para_SpeedBias[i], SIZE_SPEEDBIAS);} //添加camera和IMU的坐標變換的變量for (int i = 0; i < NUM_OF_CAM; i++){ceres::LocalParameterization *local_parameterization = new PoseLocalParameterization();problem.AddParameterBlock(para_Ex_Pose[i], SIZE_POSE, local_parameterization);if (!ESTIMATE_EXTRINSIC){ROS_DEBUG("fix extinsic param");problem.SetParameterBlockConstant(para_Ex_Pose[i]);}elseROS_DEBUG("estimate extinsic param");}TicToc t_whole, t_prepare; //把要優化的變量轉成數組的形式vector2double(); //添加上一次邊緣化的parameter blocksif (last_marginalization_info){// construct new marginlization_factorMarginalizationFactor *marginalization_factor = new MarginalizationFactor(last_marginalization_info);problem.AddResidualBlock(marginalization_factor, NULL,last_marginalization_parameter_blocks);} //添加當前sliding window中的優化變量for (int i = 0; i < WINDOW_SIZE; i++){int j = i + 1;if (pre_integrations[j]->sum_dt > 10.0)continue;IMUFactor* imu_factor = new IMUFactor(pre_integrations[j]);problem.AddResidualBlock(imu_factor, NULL, para_Pose[i], para_SpeedBias[i], para_Pose[j], para_SpeedBias[j]);}int f_m_cnt = 0;int feature_index = -1;for (auto &it_per_id : f_manager.feature)//遍歷sliding window的幀數{it_per_id.used_num = it_per_id.feature_per_frame.size();//每一幀圖像feature的個數if (!(it_per_id.used_num >= 2 && it_per_id.start_frame < WINDOW_SIZE - 2))continue;++feature_index;int imu_i = it_per_id.start_frame, imu_j = imu_i - 1;Vector3d pts_i = it_per_id.feature_per_frame[0].point;for (auto &it_per_frame : it_per_id.feature_per_frame)//遍歷每一幀圖像所有features{imu_j++;if (imu_i == imu_j){continue;}Vector3d pts_j = it_per_frame.point;ProjectionFactor *f = new ProjectionFactor(pts_i, pts_j);problem.AddResidualBlock(f, loss_function, para_Pose[imu_i], para_Pose[imu_j], para_Ex_Pose[0], para_Feature[feature_index]);f_m_cnt++;}}relocalize = false;//loop close factor//閉環檢測，閉環這里就不說了if(LOOP_CLOSURE){int loop_constraint_num = 0;for (int k = 0; k < (int)retrive_data_vector.size(); k++){ for(int i = 0; i < WINDOW_SIZE; i++){if(retrive_data_vector[k].header == Headers[i].stamp.toSec()){relocalize = true;ceres::LocalParameterization *local_parameterization = new PoseLocalParameterization();problem.AddParameterBlock(retrive_data_vector[k].loop_pose, SIZE_POSE, local_parameterization);loop_window_index = i;loop_constraint_num++;int retrive_feature_index = 0;int feature_index = -1;for (auto &it_per_id : f_manager.feature){it_per_id.used_num = it_per_id.feature_per_frame.size();if (!(it_per_id.used_num >= 2 && it_per_id.start_frame < WINDOW_SIZE - 2))continue;++feature_index;int start = it_per_id.start_frame;if(start <= i){ while(retrive_data_vector[k].features_ids[retrive_feature_index] < it_per_id.feature_id){retrive_feature_index++;}if(retrive_data_vector[k].features_ids[retrive_feature_index] == it_per_id.feature_id){Vector3d pts_j = Vector3d(retrive_data_vector[k].measurements[retrive_feature_index].x, retrive_data_vector[k].measurements[retrive_feature_index].y, 1.0);Vector3d pts_i = it_per_id.feature_per_frame[0].point;ProjectionFactor *f = new ProjectionFactor(pts_i, pts_j);problem.AddResidualBlock(f, loss_function, para_Pose[start], retrive_data_vector[k].loop_pose, para_Ex_Pose[0], para_Feature[feature_index]);retrive_feature_index++;} }}}}}ROS_DEBUG("loop constraint num: %d", loop_constraint_num);}ROS_DEBUG("visual measurement count: %d", f_m_cnt);ROS_DEBUG("prepare for ceres: %f", t_prepare.toc());ceres::Solver::Options options;options.linear_solver_type = ceres::DENSE_SCHUR;//線性求解類型 為什么是Dense schur？//options.num_threads = 2;options.trust_region_strategy_type = ceres::DOGLEG;//信頼域類型options.max_num_iterations = NUM_ITERATIONS;//options.use_explicit_schur_complement = true;//選擇schur//options.minimizer_progress_to_stdout = true;//options.use_nonmonotonic_steps = true;if (marginalization_flag == MARGIN_OLD)options.max_solver_time_in_seconds = SOLVER_TIME * 4.0 / 5.0;elseoptions.max_solver_time_in_seconds = SOLVER_TIME;TicToc t_solver;ceres::Solver::Summary summary;ceres::Solve(options, &problem, &summary);//cout << summary.BriefReport() << endl;ROS_DEBUG("Iterations : %d", static_cast<int>(summary.iterations.size()));ROS_DEBUG("solver costs: %f", t_solver.toc());// relative info between two loop frame if(LOOP_CLOSURE && relocalize)//計算閉環后的相對位姿{ for (int k = 0; k < (int)retrive_data_vector.size(); k++){for(int i = 0; i< WINDOW_SIZE; i++){if(retrive_data_vector[k].header == Headers[i].stamp.toSec()){retrive_data_vector[k].relative_pose = true;Matrix3d Rs_i = Quaterniond(para_Pose[i][6], para_Pose[i][3], para_Pose[i][4], para_Pose[i][5]).normalized().toRotationMatrix();Vector3d Ps_i = Vector3d(para_Pose[i][0], para_Pose[i][1], para_Pose[i][2]);Quaterniond Qs_loop;Qs_loop = Quaterniond(retrive_data_vector[k].loop_pose[6], retrive_data_vector[k].loop_pose[3], retrive_data_vector[k].loop_pose[4], retrive_data_vector[k].loop_pose[5]).normalized().toRotationMatrix();Matrix3d Rs_loop = Qs_loop.toRotationMatrix();Vector3d Ps_loop = Vector3d( retrive_data_vector[k].loop_pose[0], retrive_data_vector[k].loop_pose[1], retrive_data_vector[k].loop_pose[2]);retrive_data_vector[k].relative_t = Rs_loop.transpose() * (Ps_i - Ps_loop);retrive_data_vector[k].relative_q = Rs_loop.transpose() * Rs_i;retrive_data_vector[k].relative_yaw = Utility::normalizeAngle(Utility::R2ypr(Rs_i).x() - Utility::R2ypr(Rs_loop).x());if (abs(retrive_data_vector[k].relative_yaw) > 30.0 || retrive_data_vector[k].relative_t.norm() > 20.0)retrive_data_vector[k].relative_pose = false;}} } }double2vector(); //邊緣化操作TicToc t_whole_marginalization; //沈老師這里邊緣化有兩個策略，如果在sliding window中第二近的frame是關鍵幀則丟棄sliding window中最老的幀、否則丟棄該幀。無論丟棄哪一幀，都需要邊緣化。if (marginalization_flag == MARGIN_OLD)//丟棄老的一幀。{MarginalizationInfo *marginalization_info = new MarginalizationInfo();vector2double();if (last_marginalization_info){vector<int> drop_set;for (int i = 0; i < static_cast<int>(last_marginalization_parameter_blocks.size()); i++){if (last_marginalization_parameter_blocks[i] == para_Pose[0] ||last_marginalization_parameter_blocks[i] == para_SpeedBias[0])drop_set.push_back(i);}// construct new marginlization_factorMarginalizationFactor *marginalization_factor = new MarginalizationFactor(last_marginalization_info);ResidualBlockInfo *residual_block_info = new ResidualBlockInfo(marginalization_factor, NULL,last_marginalization_parameter_blocks,drop_set);marginalization_info->addResidualBlockInfo(residual_block_info);//添加上一次邊緣化的變量}{if (pre_integrations[1]->sum_dt < 10.0){IMUFactor* imu_factor = new IMUFactor(pre_integrations[1]);ResidualBlockInfo *residual_block_info = new ResidualBlockInfo(imu_factor, NULL,vector<double *>{para_Pose[0], para_SpeedBias[0], para_Pose[1], para_SpeedBias[1]},vector<int>{0, 1});marginalization_info->addResidualBlockInfo(residual_block_info);//添加優化變量}}{int feature_index = -1;for (auto &it_per_id : f_manager.feature){it_per_id.used_num = it_per_id.feature_per_frame.size();if (!(it_per_id.used_num >= 2 && it_per_id.start_frame < WINDOW_SIZE - 2))continue;++feature_index;int imu_i = it_per_id.start_frame, imu_j = imu_i - 1;if (imu_i != 0)continue;Vector3d pts_i = it_per_id.feature_per_frame[0].point;for (auto &it_per_frame : it_per_id.feature_per_frame){imu_j++;if (imu_i == imu_j)continue;Vector3d pts_j = it_per_frame.point;ProjectionFactor *f = new ProjectionFactor(pts_i, pts_j);ResidualBlockInfo *residual_block_info = new ResidualBlockInfo(f, loss_function,vector<double *>{para_Pose[imu_i], para_Pose[imu_j], para_Ex_Pose[0], para_Feature[feature_index]},vector<int>{0, 3});marginalization_info->addResidualBlockInfo(residual_block_info);//添加優化變量}}}TicToc t_pre_margin;marginalization_info->preMarginalize();ROS_DEBUG("pre marginalization %f ms", t_pre_margin.toc());TicToc t_margin;marginalization_info->marginalize();ROS_DEBUG("marginalization %f ms", t_margin.toc());std::unordered_map<long, double *> addr_shift;for (int i = 1; i <= WINDOW_SIZE; i++){addr_shift[reinterpret_cast<long>(para_Pose[i])] = para_Pose[i - 1];addr_shift[reinterpret_cast<long>(para_SpeedBias[i])] = para_SpeedBias[i - 1];}for (int i = 0; i < NUM_OF_CAM; i++)addr_shift[reinterpret_cast<long>(para_Ex_Pose[i])] = para_Ex_Pose[i];vector<double *> parameter_blocks = marginalization_info->getParameterBlocks(addr_shift);if (last_marginalization_info)delete last_marginalization_info;last_marginalization_info = marginalization_info;last_marginalization_parameter_blocks = parameter_blocks;}else{if (last_marginalization_info &&std::count(std::begin(last_marginalization_parameter_blocks), std::end(last_marginalization_parameter_blocks), para_Pose[WINDOW_SIZE - 1])){MarginalizationInfo *marginalization_info = new MarginalizationInfo();vector2double();if (last_marginalization_info){vector<int> drop_set;for (int i = 0; i < static_cast<int>(last_marginalization_parameter_blocks.size()); i++){ROS_ASSERT(last_marginalization_parameter_blocks[i] != para_SpeedBias[WINDOW_SIZE - 1]);if (last_marginalization_parameter_blocks[i] == para_Pose[WINDOW_SIZE - 1])drop_set.push_back(i);}// construct new marginlization_factorMarginalizationFactor *marginalization_factor = new MarginalizationFactor(last_marginalization_info);ResidualBlockInfo *residual_block_info = new ResidualBlockInfo(marginalization_factor, NULL,last_marginalization_parameter_blocks,drop_set);marginalization_info->addResidualBlockInfo(residual_block_info);}TicToc t_pre_margin;ROS_DEBUG("begin marginalization");marginalization_info->preMarginalize();ROS_DEBUG("end pre marginalization, %f ms", t_pre_margin.toc());TicToc t_margin;ROS_DEBUG("begin marginalization");marginalization_info->marginalize();ROS_DEBUG("end marginalization, %f ms", t_margin.toc());std::unordered_map<long, double *> addr_shift;for (int i = 0; i <= WINDOW_SIZE; i++){if (i == WINDOW_SIZE - 1)continue;else if (i == WINDOW_SIZE){addr_shift[reinterpret_cast<long>(para_Pose[i])] = para_Pose[i - 1];addr_shift[reinterpret_cast<long>(para_SpeedBias[i])] = para_SpeedBias[i - 1];}else{addr_shift[reinterpret_cast<long>(para_Pose[i])] = para_Pose[i];addr_shift[reinterpret_cast<long>(para_SpeedBias[i])] = para_SpeedBias[i];}}for (int i = 0; i < NUM_OF_CAM; i++)addr_shift[reinterpret_cast<long>(para_Ex_Pose[i])] = para_Ex_Pose[i];vector<double *> parameter_blocks = marginalization_info->getParameterBlocks(addr_shift);if (last_marginalization_info)delete last_marginalization_info;last_marginalization_info = marginalization_info;last_marginalization_parameter_blocks = parameter_blocks;}}ROS_DEBUG("whole marginalization costs: %f", t_whole_marginalization.toc());ROS_DEBUG("whole time for ceres: %f", t_whole.toc()); }

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