给我一个扩展卡尔曼滤波算法的matlab代码
时间: 2023-07-25 17:20:02 浏览: 47
以下是一个简单的扩展卡尔曼滤波(EKF)的matlab代码示例:
```
% EKF algorithm for a 2D robot localization problem
% State variables
x = [0; 0; 0]; % x,y,theta
P = eye(3); % covariance matrix
% Measurement noise
R = diag([0.1; 0.1]);
% Process noise
Q = diag([0.01; 0.01; 0.01]);
% Time step
dt = 0.1;
% Control inputs
u = [1; 0.1];
% Simulation time
T = 10;
% Preallocate memory for results
x_est = zeros(3, T/dt);
% EKF loop
for t=1:T/dt
% Simulate robot motion
x = [x(1) + u(1)*cos(x(3))*dt;
x(2) + u(1)*sin(x(3))*dt;
x(3) + u(2)*dt];
% Compute Jacobian of motion model
F = [1 0 -u(1)*sin(x(3))*dt;
0 1 u(1)*cos(x(3))*dt;
0 0 1];
% Update covariance matrix
P = F*P*F' + Q;
% Simulate measurement
z = [x(1) + randn()*sqrt(R(1,1));
x(2) + randn()*sqrt(R(2,2))];
% Compute Jacobian of measurement model
H = [1 0 0;
0 1 0];
% Compute Kalman gain
K = P*H'*inv(H*P*H' + R);
% Update state estimate
x = x + K*(z - H*x);
% Update covariance matrix
P = (eye(3) - K*H)*P;
% Save estimate
x_est(:,t) = x;
end
% Plot results
figure;
hold on;
plot(x_est(1,:), x_est(2,:), 'b');
plot(x(1), x(2), 'ro');
xlabel('x');
ylabel('y');
legend('EKF estimate', 'True position');
```
这个示例演示了一个简单的2D机器人定位问题,其中机器人沿着一条直线行驶,并且每个时间步骤都会接收到来自距离传感器的测量。该算法使用EKF来估计机器人的位置和方向,并且通过将估计值与真实值进行比较来评估算法的性能。