IMU与GPS传感器ESKF融合定位

分别在两个终端下运行命令：

rosbag play utbm_robocar_dataset_20180502_noimage1.bag
roslaunch imu_gps_localization imu_gps_localization.launch

1、代码整体框架说明

代码具体结构框架如下图所示：

cpp文件	文件具体实现作用	备注
localization_node.cpp	主函数文件，实现初始化ros，初始化LocalizationWrapper类
localization_wrapper.h	LocalizationWrapper类定义，主要声明构造函数、析构函数以及imu回调函数、gps回调函数、打印状态、打印gps数据，把状态格式数据转换成ros话题机制
localization_wrapper.cpp	构造函数中主要是加载参数，保存数据到文件夹下，订阅imu和gps的话题然后发布融合后的轨迹；析构函数主要是释放空间；imu回调函数主要是读取imu数据，然后对数据进行处理，转变状态发布成ros话题，打印状态；gps回调函数主要是实现读取数据，然后进行处理，最后打印。
imu_gps_localizer.cpp	ProcessImuData()函数初始化imu数据，对imu数据进行预测，从ENU坐标系转换到GPS坐标系，发布融合后的状态；ProcessGpsPositionData()函数主要实现初始化数据以及位置的更新。
imu_gps_localizer.h	ImuGpsLocalizer类构造函数，声明ProcessImuData()函数，声明ProcessGpsPositionData()函数
initializer.h	初始化类，主要是构造函数，添加imu数据，添加gps数据，计算imu数据到gps数据的旋转矩阵这里参考的是openvins
imu_processor.cpp	滤波融合的预测部分Predict()函数具体实现
imu_processor.h	ImuProcessor类主要是滤波融合的预测部分Predict()函数声明
gps_processor.h	GpsProcessor类通过GPS位置更新系统的状态UpdateStateByGpsPosition()以及计算残差以及雅可比矩阵和把得到的误差更新状态
base_type.h	主要是imu数据、GPS数据以及系统状态的数据结构
utils.h	主要包括弧度和角度之间的相互转换、ENU坐标系与LLA坐标系的转换以及得到反对称矩阵

2、主要函数介绍

2.1 LocalizationWrapper构造函数

LocalizationWrapper构造函数主要实现加载参数、添加数据保存位置、订阅话题和发布话题

LocalizationWrapper::LocalizationWrapper(ros::NodeHandle& nh) {
    // Load configs.
    double acc_noise, gyro_noise, acc_bias_noise, gyro_bias_noise;
    nh.param("acc_noise",       acc_noise, 1e-2);
    nh.param("gyro_noise",      gyro_noise, 1e-4);
    nh.param("acc_bias_noise",  acc_bias_noise, 1e-6);
    nh.param("gyro_bias_noise", gyro_bias_noise, 1e-8);

    double x, y, z;
    nh.param("I_p_Gps_x", x, 0.);
    nh.param("I_p_Gps_y", y, 0.);
    nh.param("I_p_Gps_z", z, 0.);
    const Eigen::Vector3d I_p_Gps(x, y, z);

    std::string log_folder
        = "/home/sunshine/catkin_imu_gps_localization/src/imu_gps_localization";
    ros::param::get("log_folder", log_folder);

    // Log.
    file_state_.open(log_folder + "/state.csv");
    file_gps_.open(log_folder +"/gps.csv");

    // Initialization imu gps localizer.
    imu_gps_localizer_ptr_ = 
        std::make_unique<ImuGpsLocalization::ImuGpsLocalizer>(acc_noise, gyro_noise,
                                                              acc_bias_noise, gyro_bias_noise,
                                                              I_p_Gps);

    // Subscribe topics.
    imu_sub_ = nh.subscribe("/imu/data", 10,  &LocalizationWrapper::ImuCallback, this);
    //TODO 运行数据集需要修改的地方： gps的话题为/fix
    gps_position_sub_ = nh.subscribe("/fix", 10,  &LocalizationWrapper::GpsPositionCallback, this);
    
    //发布融合后的轨迹
    state_pub_ = nh.advertise<nav_msgs::Path>("fused_path", 10);
}

2.2 滤波算法进行预测

void ImuProcessor::Predict(const ImuDataPtr last_imu, const ImuDataPtr cur_imu, State* state) {
    // Time.
    const double delta_t = cur_imu->timestamp - last_imu->timestamp;
    const double delta_t2 = delta_t * delta_t;

    // Set last state.
    State last_state = *state;
    // mid_point integration methods
    // Acc and gyro.
    const Eigen::Vector3d acc_unbias = 0.5 * (last_imu->acc + cur_imu->acc) - last_state.acc_bias;
    const Eigen::Vector3d gyro_unbias = 0.5 * (last_imu->gyro + cur_imu->gyro) - last_state.gyro_bias;

    // Normal state. 
    // Using P58. of "Quaternion kinematics for the error-state Kalman Filter".
    state->G_p_I = last_state.G_p_I + last_state.G_v_I * delta_t + 
                   0.5 * (last_state.G_R_I * acc_unbias + gravity_) * delta_t2;
    state->G_v_I = last_state.G_v_I + (last_state.G_R_I * acc_unbias + gravity_) * delta_t;
    const Eigen::Vector3d delta_angle_axis = gyro_unbias * delta_t;
    if (delta_angle_axis.norm() > 1e-12) {
        // std::cout << "norm" << delta_angle_axis.norm() << "normlized"
        //           << delta_angle_axis.normalized() << std::endl;
        state->G_R_I = last_state.G_R_I
            * Eigen::AngleAxisd(delta_angle_axis.norm(),
                                delta_angle_axis.normalized())
                  .toRotationMatrix();
    }
    // Error-state. Not needed.

    // Covariance of the error-state.   
    Eigen::Matrix<double, 15, 15> Fx = Eigen::Matrix<double, 15, 15>::Identity();
    Fx.block<3, 3>(0, 3)   = Eigen::Matrix3d::Identity() * delta_t;
    Fx.block<3, 3>(3, 6)   = - state->G_R_I * GetSkewMatrix(acc_unbias) * delta_t;
    Fx.block<3, 3>(3, 9)   = - state->G_R_I * delta_t;
    if (delta_angle_axis.norm() > 1e-12) {
        Fx.block<3, 3>(6, 6) = Eigen::AngleAxisd(delta_angle_axis.norm(), delta_angle_axis.normalized()).toRotationMatrix().transpose();
    } else {
        Fx.block<3, 3>(6, 6).setIdentity();
    }
    Fx.block<3, 3>(6, 12)  = - Eigen::Matrix3d::Identity() * delta_t;

    Eigen::Matrix<double, 15, 12> Fi = Eigen::Matrix<double, 15, 12>::Zero();
    Fi.block<12, 12>(3, 0) = Eigen::Matrix<double, 12, 12>::Identity();

    Eigen::Matrix<double, 12, 12> Qi = Eigen::Matrix<double, 12, 12>::Zero();
    Qi.block<3, 3>(0, 0) = delta_t2 * acc_noise_ * Eigen::Matrix3d::Identity();
    Qi.block<3, 3>(3, 3) = delta_t2 * gyro_noise_ * Eigen::Matrix3d::Identity();
    Qi.block<3, 3>(6, 6) = delta_t * acc_bias_noise_ * Eigen::Matrix3d::Identity();
    Qi.block<3, 3>(9, 9) = delta_t * gyro_bias_noise_ * Eigen::Matrix3d::Identity();
    //协方差预测
    state->cov = Fx * last_state.cov * Fx.transpose() + Fi * Qi * Fi.transpose();

    // Time and imu.
    state->timestamp = cur_imu->timestamp;
    state->imu_data_ptr = cur_imu;
}

2.3 通过GPS位置测量数据更新系统的状态

bool GpsProcessor::UpdateStateByGpsPosition(const Eigen::Vector3d& init_lla, const GpsPositionDataPtr gps_data_ptr, State* state) {
    Eigen::Matrix<double, 3, 15> H;
    Eigen::Vector3d residual;
    ComputeJacobianAndResidual(init_lla, gps_data_ptr, *state, &H, &residual);
    const Eigen::Matrix3d& V = gps_data_ptr->cov;

    // EKF.
    const Eigen::MatrixXd& P = state->cov;
    //P：状态的协方差矩阵；V：gps数据的协方差矩阵；H：误差状态的雅可比矩阵
    const Eigen::MatrixXd K = P * H.transpose() * (H * P * H.transpose() + V).inverse();
    const Eigen::VectorXd delta_x = K * residual;

    // Add delta_x to state.
    AddDeltaToState(delta_x, state);

    // Covarance.
    const Eigen::MatrixXd I_KH = Eigen::Matrix<double, 15, 15>::Identity() - K * H;
    state->cov = I_KH * P * I_KH.transpose() + K * V * K.transpose();
}
//计算雅克比矩阵以及残差项 P61 Quaternion kinematics for the error-state Kalman filter
void GpsProcessor::ComputeJacobianAndResidual(const Eigen::Vector3d& init_lla,  
                                              const GpsPositionDataPtr gps_data, 
                                              const State& state,
                                              Eigen::Matrix<double, 3, 15>* jacobian,
                                              Eigen::Vector3d* residual) {
    const Eigen::Vector3d& G_p_I   = state.G_p_I;
    const Eigen::Matrix3d& G_R_I   = state.G_R_I;

    // Convert wgs84 to ENU frame.
    Eigen::Vector3d G_p_Gps;
    ConvertLLAToENU(init_lla, gps_data->lla, &G_p_Gps);

    // Compute residual.
    *residual = G_p_Gps - (G_p_I + G_R_I * I_p_Gps_);

    // Compute jacobian.？？？对哪一项求导？
    jacobian->setZero();
    jacobian->block<3, 3>(0, 0)  = Eigen::Matrix3d::Identity();
    jacobian->block<3, 3>(0, 6)  = - G_R_I * GetSkewMatrix(I_p_Gps_);
}
//添加误差项到状态
void AddDeltaToState(const Eigen::Matrix<double, 15, 1>& delta_x, State* state) {
    state->G_p_I     += delta_x.block<3, 1>(0, 0);
    state->G_v_I     += delta_x.block<3, 1>(3, 0);
    state->acc_bias  += delta_x.block<3, 1>(9, 0);
    state->gyro_bias += delta_x.block<3, 1>(12, 0);

    if (delta_x.block<3, 1>(6, 0).norm() > 1e-12) {
        state->G_R_I *= Eigen::AngleAxisd(delta_x.block<3, 1>(6, 0).norm(), delta_x.block<3, 1>(6, 0).normalized()).toRotationMatrix();
    }
}

3. 结果评价

参考文献：

IMU & GPS定位 Quaternion kinematics for ESKF[part 3]

EU Long-term Dataset with Multiple Sensors for Autonomous Driving

Quaternion kinematics for the error-state Kalman filter

Woosik Lee, Intermittent GPS-aided VIO: Online Initialization and Calibration.

A General Optimization-based Framework for Global Pose Estimation with Multiple Sensors

A General Optimization-based Framework for Local Odometry Estimation with Multiple Sensors