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预积分相关处理文件：integration_base.h class IntegrationBase IntegrationBase( const Eigen::Vector3d &_acc_0, const Eigen::Vector3d &_gyr_0, const Eigen::Vector3d &_linearized_ba, const Eigen::Vector3d &_linearized_bg )//_acc_0：初始时刻加速度；//_gyr_0：初始时刻角加速度；//_linearized_ba：加速度计临偏；//_linearized_bg：陀螺仪临偏；
: acc_0{_acc_0}, gyr_0{_gyr_0}, linearized_acc{_acc_0}, linearized_gyr{_gyr_0},linearized_ba{_linearized_ba}, linearized_bg{_linearized_bg},jacobian{Eigen::Matrix<double, 15, 15>::Identity()}, covariance{Eigen::Matrix<double, 15, 15>::Zero()},sum_dt{0.0}, delta_p{Eigen::Vector3d::Zero()}, delta_q{Eigen::Quaterniond::Identity()}, delta_v{Eigen::Vector3d::Zero()}
//jacobian：雅可比矩阵，初始化为单位矩阵，15 x 15//covariance：协方差矩阵，初始化为零矩阵，15 x 15//delta_p：对应于预积分量α，初始化为0向量，3 x 1//delta_q：对应于预积分量γ，初始化为单位四元数, ，3 x 1//delta_v：对应于预积分量β，初始化为零向量，3 x 1
//Δx{k+1} = FΔx{k }+ Gn{k}//P{k+1}=FP{K}F^T + GvG^T;//P和v分别是Δx和n的协方差矩阵//噪声；k时刻加速度计噪声和陀螺仪噪声、k+1时刻加速度计噪声和陀螺仪噪声、两个临偏的随机游走，即18 x 1;//noise：此处noise指噪声的协方差矩阵v，18 x 18；//初始化时，各变量仅与自身有关//参考eigen中block的使用noise = Eigen::Matrix<double, 18, 18>::Zero();noise.block<3, 3>(0, 0) = (ACC_N * ACC_N) * Eigen::Matrix3d::Identity();noise.block<3, 3>(3, 3) = (GYR_N * GYR_N) * Eigen::Matrix3d::Identity();noise.block<3, 3>(6, 6) = (ACC_N * ACC_N) * Eigen::Matrix3d::Identity();noise.block<3, 3>(9, 9) = (GYR_N * GYR_N) * Eigen::Matrix3d::Identity();noise.block<3, 3>(12, 12) = (ACC_W * ACC_W) * Eigen::Matrix3d::Identity();noise.block<3, 3>(15, 15) = (GYR_W * GYR_W) * Eigen::Matrix3d::Identity();
函数作用： IntegrationBase类的接口，每来一个imu数据，调用该接口将参数存入对应buf，并通过函数propagate()进行处理； 函数声明： void push_back( double dt, const Eigen::Vector3d &acc, const Eigen::Vector3d &gyr ) 函数参数 // dt ：时间戳 // acc：该时间戳加速度计值 // gyr：该时间戳陀螺仪值 propagate(dt, acc, gyr);//调用propagate函数进行中值积分 函数作用： 进行中值积分，然后更新上一时刻状态量； 函数声明： void propagate( double _dt, const Eigen::Vector3d &_acc_1, const Eigen::Vector3d &_gyr_1 ) 函数参数 // _dt ：时间戳 // _acc_1：该时间戳加速度计值 // _gyr_1：该时间戳陀螺仪值 midPointIntegration( _dt, acc_0, gyr_0, _acc_1, _gyr_1, //时间戳i时刻加速度计值和陀螺仪值、i+1时刻加速度计值和陀螺仪值 delta_p, delta_q, delta_v, //i时候预积分α、β、γ linearized_ba, linearized_bg, //加速度计和陀螺仪临偏 result_delta_p, result_delta_q, result_delta_v, //求得i+1时刻预积分α、β、γ result_linearized_ba, result_linearized_bg, 1 //求得加速度计和陀螺仪临偏 ); //将当前时刻更新为上一时刻delta_p = result_delta_p;delta_q = result_delta_q;delta_v = result_delta_v;linearized_ba = result_linearized_ba;linearized_bg = result_linearized_bg;delta_q.normalize();sum_dt += dt;acc_0 = acc_1;gyr_0 = gyr_1;
void midPointIntegration( double _dt, const Eigen::Vector3d &_acc_0, const Eigen::Vector3d &_gyr_0, const Eigen::Vector3d &_acc_1, const Eigen::Vector3d &_gyr_1, const Eigen::Vector3d &delta_p, const Eigen::Quaterniond &delta_q, const Eigen::Vector3d &delta_v, const Eigen::Vector3d &linearized_ba, const Eigen::Vector3d &linearized_bg, Eigen::Vector3d &result_delta_p, Eigen::Quaterniond &result_delta_q, Eigen::Vector3d &result_delta_v, Eigen::Vector3d &result_linearized_ba, Eigen::Vector3d &result_linearized_bg, bool update_jacobian)
函数参数
//_dt：时间戳 //_acc_0：i时刻加速度计值 //_gyr_0,：i时刻陀螺仪值 //_acc_1：i+1时刻加速度计值 //_gyr_1：i+1时刻陀螺仪值 //delta_p：i时刻预积分α //delta_q：i时刻预积分γ，即Rki:第i帧IMU变换到第k帧图像的旋转 //delta_v,：i时刻预积分β //linearized_ba：i时刻加速度计临偏 //linearized_bg,：i时刻陀螺仪临偏 //result_delta_p：出参，i+1时刻预积分α //result_delta_q：出参，i+1时刻预积分γ //result_delta_v,：出参，i+1时刻预积分β //result_linearized_ba：出参，i+1时刻加速度计临偏 //result_linearized_bg：出参，i+1时刻陀螺仪临偏 //update_jacobian：是否更新雅可比矩阵 第一步：更新中值积分中的状态量 Vector3d un_acc_0 = delta_q * (_acc_0 - linearized_ba); // a{k}=R{ki}*(a{i}-b{a})，将第i帧imu加速度计值转换到第k帧图像中；
Vector3d un_gyr = 0.5 * (_gyr_0 + _gyr_1) - linearized_bg; //中值积分，用i和i+1时刻陀螺仪均值表示整段时间
result_delta_q = delta_q * Quaterniond(1, un_gyr(0) * _dt / 2, un_gyr(1) * _dt / 2, un_gyr(2) * _dt / 2);//i+1时刻imu到第k帧图像的旋转=i时刻imu到第k帧旋转*第i时刻imu到第i+1时刻imu的旋转//[cos(theta/2) n*sin(theta/2)]，当角度趋近于0，[1 n*theta/2]=[1 w*dt/2]，w是陀螺仪值；//R{k<i+1}=R{ki}*R{i+1<-i}
Vector3d un_acc_1 = result_delta_q * (_acc_1 - linearized_ba);// a{k}=R{ki+1}*(a{i}-ba)，将第i+1帧imu加速度计值转换到第k帧图像中；
Vector3d un_acc = 0.5 * (un_acc_0 + un_acc_1);//中值积分，用i和i+1时刻加速度计均值表示整段时间
result_delta_p = delta_p + delta_v * _dt + 0.5 * un_acc * _dt * _dt;result_delta_v = delta_v + un_acc * _dt;//根据速度、加速度、位移物理运动关系
result_linearized_ba = linearized_ba;result_linearized_bg = linearized_bg; //临差默认为不变；
计算若干中间量，推出相应反对称矩阵，便于更新F矩阵 Vector3d w_x = 0.5 * (_gyr_0 + _gyr_1) - linearized_bg; //(w{k}+w{k+1})/2-b{wk},对应上面绿色框Vector3d a_0_x = _acc_0 - linearized_ba; //a{k}-b{ak}，对应上面红色框Vector3d a_1_x = _acc_1 - linearized_ba; //a{k+1}-b{ak}，对应上面黄色框Matrix3d R_w_x, R_a_0_x, R_a_1_x; //存储上面三个中间量的反对称矩阵
R_w_x<<0, -w_x(2), w_x(1), w_x(2), 0, -w_x(0), -w_x(1), w_x(0), 0;R_a_0_x<<0, -a_0_x(2), a_0_x(1), a_0_x(2), 0, -a_0_x(0), -a_0_x(1), a_0_x(0), 0;R_a_1_x<<0, -a_1_x(2), a_1_x(1),a_1_x(2), 0, -a_1_x(0),-a_1_x(1), a_1_x(0), 0;//计算反对称矩阵
//开始更新F矩阵MatrixXd F = MatrixXd::Zero(15, 15);F.block<3, 3>(0, 0) = Matrix3d::Identity(); F.block<3, 3>(0, 3) = -0.25 * delta_q.toRotationMatrix() * R_a_0_x * _dt * _dt + -0.25 * result_delta_q.toRotationMatrix() * R_a_1_x * (Matrix3d::Identity() - R_w_x * _dt) * _dt * _dt;F.block<3, 3>(0, 6) = MatrixXd::Identity(3,3) * _dt;F.block<3, 3>(0, 9) = -0.25 * (delta_q.toRotationMatrix() + result_delta_q.toRotationMatrix()) * _dt * _dt;F.block<3, 3>(0, 12) = -0.25 * result_delta_q.toRotationMatrix() * R_a_1_x * _dt * _dt * -_dt;F.block<3, 3>(3, 3) = Matrix3d::Identity() - R_w_x * _dt;F.block<3, 3>(3, 12) = -1.0 * MatrixXd::Identity(3,3) * _dt;F.block<3, 3>(6, 3) = -0.5 * delta_q.toRotationMatrix() * R_a_0_x * _dt + -0.5 * result_delta_q.toRotationMatrix() * R_a_1_x * (Matrix3d::Identity() - R_w_x * _dt) * _dt;F.block<3, 3>(6, 6) = Matrix3d::Identity();F.block<3, 3>(6, 9) = -0.5 * (delta_q.toRotationMatrix() + result_delta_q.toRotationMatrix()) * _dt;F.block<3, 3>(6, 12) = -0.5 * result_delta_q.toRotationMatrix() * R_a_1_x * _dt * -_dt;F.block<3, 3>(9, 9) = Matrix3d::Identity();F.block<3, 3>(12, 12) = Matrix3d::Identity();
//更新V矩阵
MatrixXd V = MatrixXd::Zero(15,18);V.block<3, 3>(0, 0) = 0.25 * delta_q.toRotationMatrix() * _dt * _dt;V.block<3, 3>(0, 3) = 0.25 * -result_delta_q.toRotationMatrix() * R_a_1_x * _dt * _dt * 0.5 * _dt;V.block<3, 3>(0, 6) = 0.25 * result_delta_q.toRotationMatrix() * _dt * _dt;V.block<3, 3>(0, 9) = V.block<3, 3>(0, 3);V.block<3, 3>(3, 3) = 0.5 * MatrixXd::Identity(3,3) * _dt;V.block<3, 3>(3, 9) = 0.5 * MatrixXd::Identity(3,3) * _dt;V.block<3, 3>(6, 0) = 0.5 * delta_q.toRotationMatrix() * _dt;V.block<3, 3>(6, 3) = 0.5 * -result_delta_q.toRotationMatrix() * R_a_1_x * _dt * 0.5 * _dt;V.block<3, 3>(6, 6) = 0.5 * result_delta_q.toRotationMatrix() * _dt;V.block<3, 3>(6, 9) = V.block<3, 3>(6, 3);V.block<3, 3>(9, 12) = MatrixXd::Identity(3,3) * _dt;V.block<3, 3>(12, 15) = MatrixXd::Identity(3,3) * _dt;
//更新雅可比矩阵和协方差矩阵jacobian = F * jacobian;covariance = F * covariance * F.transpose() + V * noise * V.transpose();
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