编一段惯导和里程计组合导航MATLAB仿真代码

以下是一个简单的惯导和里程计组合导航MATLAB仿真代码：

% 设定初始状态
x0 = [0; 0; 0; 0; 0; 0]; % [x位置，y位置，航向角，速度，加速度，角速度]

% 定义时间步长和仿真时间
dt = 0.1; % 时间步长
T = 10; % 仿真时间
N = T / dt; % 时间步数

% 定义惯导测量噪声和里程计测量噪声的标准差
sigma_gyro = 0.01; % 角速度测量噪声标准差
sigma_accel = 0.1; % 加速度测量噪声标准差
sigma_rng = 1; % 里程计距离测量噪声标准差
sigma_brg = 0.01; % 里程计方位角测量噪声标准差

% 生成真实轨迹和传感器测量数据
x_true = zeros(6, N);
x_sense = zeros(4, N);
x_true(:,1) = x0;
x_sense(:,1) = [0; 0; 0; 0];
for k = 2:N
x_true(:,k) = update_true_state(x_true(:,k-1), dt);
x_sense(:,k) = sense_state(x_true(:,k), sigma_gyro, sigma_accel, sigma_rng, sigma_brg);
end

% 利用惯导和里程计组合导航估计轨迹
x_est = zeros(6, N);
x_est(:,1) = x0;
P = diag([0.01^2, 0.01^2, 0.01^2, 0.1^2, 0.1^2, 0.1^2]);
for k = 2:N
% 预测步：利用上一个时刻的状态和动态方程进行状态预测
[F, G] = calc_jacobians(x_est(:,k-1), dt);
x_pred = F * x_est(:,k-1) + G * [x_sense(1,k); x_sense(2,k); x_sense(3,k)];
P_pred = F * P * F' + G * diag([sigma_gyro^2, sigma_gyro^2, sigma_accel^2]) * G';

% 更新步：利用当前时刻的测量值和观测方程进行状态更新
[H, R] = calc_jacobians(x_pred, x_sense(:,k), sigma_rng, sigma_brg);
K = P_pred * H' / (H * P_pred * H' + R);
x_est(:,k) = x_pred + K * (x_sense(:,k) - sense_state(x_pred, 0, 0, sigma_rng, sigma_brg));
P = (eye(6) - K * H) * P_pred;
end

% 绘制真实轨迹和估计轨迹
figure;
hold on;
plot(x_true(1,:), x_true(2,:), 'b-', 'LineWidth', 1);
plot(x_est(1,:), x_est(2,:), 'r-', 'LineWidth', 1);
xlabel('x位置');
ylabel('y位置');
legend('真实轨迹', '估计轨迹');
title('惯导和里程计组合导航仿真结果');

% 动态方程
function x_new = update_true_state(x_old, dt)
x_new = zeros(6,1);
x_new(1) = x_old(1) + x_old(4) * cos(x_old(3)) * dt;
x_new(2) = x_old(2) + x_old(4) * sin(x_old(3)) * dt;
x_new(3) = x_old(3) + x_old(6) * dt;
x_new(4) = x_old(4) + x_old(5) * dt;
x_new(5) = x_old(5);
x_new(6) = x_old(6);
end

% 观测方程
function y = sense_state(x, sigma_gyro, sigma_accel, sigma_rng, sigma_brg)
y = zeros(4,1);
y(1) = x(4);
y(2) = sigma_gyro * randn();
y(3) = sigma_accel * randn();
y(4) = [sqrt(x(1)^2 + x(2)^2) + sigma_rng * randn(); atan2(x(2), x(1)) + x(3) + sigma_brg * randn()];
end

% 计算状态转移矩阵和控制矩阵的雅可比矩阵
function [F, G] = calc_jacobians(x, dt)
F = [1, 0, -x(4)*sin(x(3))*dt, cos(x(3))*dt, 0, 0;
0, 1, x(4)*cos(x(3))*dt, sin(x(3))*dt, 0, 0;
0, 0, 1, 0, 0, x(4)*dt;
0, 0, 0, 1, dt, 0;
0, 0, 0, 0, 1, 0;
0, 0, 0, 0, 0, 1];
G = [cos(x(3))*dt, 0, 0;
sin(x(3))*dt, 0, 0;
0, dt, 0;
0, 0, dt;
0, 0, 0;
0, 0, 0];
end

% 计算观测矩阵和观测噪声协方差的雅可比矩阵
function [H, R] = calc_jacobians(x, y, sigma_rng, sigma_brg)
H = [0, 0, 0, 1, 0, 0;
0, 0, 0, 0, 1, 0;
0, 0, 0, 0, 0, 1;
x(1)/sqrt(x(1)^2+x(2)^2), x(2)/sqrt(x(1)^2+x(2)^2), 0, 0, 0, 0;
-x(2)/(x(1)^2+x(2)^2), x(1)/(x(1)^2+x(2)^2), 0, 0, 0, 1];
R = [sigma_rng^2, 0; 0, sigma_brg^2];
end