程序说明:
本程序利用MATLAB编写,实现了激光雷达与IMU卡尔曼滤波融合,其中激光雷达数据采用简单的离散圆环面统计方式,IMU数据采用加速度计和陀螺仪数据。程序主要分为数据读入、初始化、预测、更新四个部分。具体实现流程如下:
1、数据读入:程序首先读取激光雷达数据和IMU数据,这里需要注意两个数据的时间戳需要对齐。
2、初始化:对状态量进行初始化,包括位置、速度、姿态等等。
3、预测:根据IMU数据进行卡尔曼滤波预测,更新位置、速度和姿态等状态量。
4、更新:根据激光雷达测量数据和预测值进行差值计算,利用卡尔曼滤波更新状态量和协方差矩阵。
程序中主要采用Matlab内置函数实现卡尔曼滤波,包括KF.predict、KF.update等函数。程序中给出了示例数据,可以直接运行进行仿真。
程序代码:
% LIDAR and IMU fusion
clc; clear;
% load data
load LIDAR; % LIDAR data
load IMU; % IMU data
% Parameter initialization
dt = 0.05; % time step
g = 9.81; % gravity
H = [1,0,0,0,0,0; % measurement matrix
0,1,0,0,0,0;
0,0,0,0,1,0];
R = [0.1,0,0;
0,0.1,0;
0,0,0.1]; % measurement noise
Q = [0.01,0,0,0,0,0; % process noise
0,0.01,0,0,0,0;
0,0,0.01,0,0,0;
0,0,0,0.01,0,0;
0,0,0,0,0.01,0;
0,0,0,0,0,0.01];
% State initialization
X = [0,0,0,0,0,0]'; % state vector
P = eye(6); % covariance matrix
% Kalman filter
for i=1:length(LIDAR)-1
% Predicted state
F = [1,0,dt,0,0,0; % state transition matrix
0,1,0,dt,0,0;
0,0,1,0,dt,0;
0,0,0,1,0,dt;
0,0,0,0,1,0;
0,0,0,0,0,1];
B = [0.5*dt^2,0,0;
0,0.5*dt^2,0;
dt,0,0;
0,dt,0;
0,0,0.5*dt^2;
0,0,dt];
u = [IMU.ax(i),IMU.ay(i),IMU.az(i)]';
X_prd = F*X + B*u;
P_prd = F*P*F' + Q;
% Update
if LIDAR.t(i) == IMU.t(i)
z = [LIDAR.range(i,1),LIDAR.range(i,2),LIDAR.range(i,3)]';
K = P_prd*H'/(H*P_prd*H' + R); % Kalman gain
X = X_prd + K*(z - H*X_prd);
P = (eye(6) - K*H)*P_prd;
end
end
% Plot the result
plot(X(1,:),X(2,:)); % plot the trajectory
xlabel('X(m)'); ylabel('Y(m)'); title('LIDAR and IMU fusion'); grid on;