基于EKF的激光雷达与IMU融合MATLAB仿真程序

以下是一个基于EKF的激光雷达与IMU融合MATLAB仿真程序的示例：

%% 1. 初始化
clear all; close all; clc

% 加载数据
load('laser_imu_data.mat')

% 载入常量
DT = 0.01;
G = 9.81;
STATE_DIM = 23;
OBS_DIM = 2;

% 初始化状态向量
X = zeros(STATE_DIM, 1);
X(1:3) = init_pos;
X(4:6) = init_vel;
X(16:18) = init_ba;
X(19:21) = init_bg;

% 初始化协方差矩阵
P = zeros(STATE_DIM);
P(1:3, 1:3) = 1e-4*eye(3);
P(4:6, 4:6) = 1e-2*eye(3);
P(7:9, 7:9) = 1e-4*eye(3);
P(10:12, 10:12) = 5e-6*eye(3);
P(13:15, 13:15) = 5e-6*eye(3);
P(16:18, 16:18) = 1e-6*eye(3);
P(19:21, 19:21) = 1e-6*eye(3);
P(22:23, 22:23) = 1e-6*eye(2);

% 加载指南针初始方向
C0 = calc_Cinit(acc_init, mag_init)

% 初始化IMU对应的四元数和姿态角
q0 = calc_qinit(acc_init, mag_init)

% 初始化上一个时刻的时间
last_t = laser_data.time(1);

% 初始化预测的激光雷达坐标
laser_x = zeros(1, length(laser_data.time));

% 初始化滤波后的状态向量
state = zeros(STATE_DIM, length(laser_data.time));

% 初始化卡尔曼增益
K = zeros(STATE_DIM, OBS_DIM);

% 初始化观测噪声协方差矩阵
R = 1e-4*eye(OBS_DIM);

%% 2. 循环
for i = 1:length(laser_data.time)
% 获取当前时刻的激光雷达坐标和IMU数据
laser_z = laser_data.ranges(i);
imu_acc = imu_data.acc(:,i);
imu_gyro = imu_data.gyro(:,i);
t = laser_data.time(i);

% 计算时间间隔
dt = t - last_t;

% 预测IMU的状态
[X, P] = predict_imu(X, P, imu_acc, imu_gyro, G, dt);

% 更新四元数和姿态角
[q0, C0] = update_q0(X(7:10));

% 根据IMU的姿态计算激光雷达坐标
laser_x(i) = calc_laser_x(X(1:3), C0);

% 更新状态向量和协方差矩阵
H = calc_H(X, C0);
[X, P, K] = update_laser(X, P, K, H, R, laser_z, laser_x(i));

% 记录当前状态向量
state(:,i) = X;

% 更新上一个时刻的时间
last_t = t;
end

%% 3. 绘图
figure

% 绘制IMU测量的加速度和陀螺仪数据
subplot(3,2,1)
plot(imu_data.time, imu_data.acc(1,:), 'r')
hold on
plot(imu_data.time, imu_data.acc(2,:), 'g')
plot(imu_data.time, imu_data.acc(3,:), 'b')
legend('x', 'y', 'z')
title('IMU Accelerometer')
xlabel('Time (s)')
ylabel('Acceleration (m/s^2)')

subplot(3,2,2)
plot(imu_data.time, imu_data.gyro(1,:), 'r')
hold on
plot(imu_data.time, imu_data.gyro(2,:), 'g')
plot(imu_data.time, imu_data.gyro(3,:), 'b')
legend('x', 'y', 'z')
title('IMU Gyroscope')
xlabel('Time (s)')
ylabel('Angular velocity (rad/s)')

% 绘制滤波后的位置
subplot(3,2,3)
plot(laser_data.time, state(1,:), 'r')
hold on
plot(laser_data.time, init_pos(1)+cumtrapz(imu_data.time, cumtrapz(imu_data.time, imu_data.acc(1,:))), 'g')
title('Position (x)')
legend('filtered', 'integrated acc')
xlabel('Time (s)')
ylabel('Position (m)')

subplot(3,2,4)
plot(laser_data.time, state(2,:), 'r')
hold on
plot(laser_data.time, init_pos(2)+cumtrapz(imu_data.time, cumtrapz(imu_data.time, imu_data.acc(2,:))), 'g')
title('Position (y)')
legend('filtered', 'integrated acc')
xlabel('Time (s)')
ylabel('Position (m)')

subplot(3,2,5)
plot(laser_data.time, state(3,:), 'r')
hold on
plot(laser_data.time, init_pos(3)+cumtrapz(imu_data.time, cumtrapz(imu_data.time, imu_data.acc(3,:))), 'g')
title('Position (z)')
legend('filtered', 'integrated acc')
xlabel('Time (s)')
ylabel('Position (m)')

% 绘制滤波后的速度
subplot(3,2,6)
plot(laser_data.time, state(4,:), 'r')
hold on
plot(laser_data.time, init_vel(1)+cumtrapz(imu_data.time, imu_data.acc(1,:)), 'g')
plot(laser_data.time, state(5,:), 'b')
plot(laser_data.time, init_vel(2)+cumtrapz(imu_data.time, imu_data.acc(2,:)), 'c')
plot(laser_data.time, state(6,:), 'm')
plot(laser_data.time, init_vel(3)+cumtrapz(imu_data.time, imu_data.acc(3,:)), 'y')
title('Velocity')
legend('filtered x', 'integrated acc x', 'filtered y', 'integrated acc y', 'filtered z', 'integrated acc z')
xlabel('Time (s)')
ylabel('Velocity (m/s)')

% 绘制激光雷达坐标和预测的激光雷达坐标
figure
plot(laser_data.time, laser_data.ranges, 'bo')
hold on
plot(laser_data.time, laser_x, 'r')
title('Laser Ranging')
xlabel('Time (s)')
ylabel('Distance (m)')