write matlab code of square root information filter
时间: 2024-01-21 09:18:21 浏览: 26
Here's an example code for the Square Root Information Filter (SRIF) in MATLAB:
```
function [x_est, P_est] = srif(A, B, C, Q, R, y, x0, P0)
% A: state transition matrix
% B: input matrix
% C: measurement matrix
% Q: process noise covariance matrix
% R: measurement noise covariance matrix
% y: measurement vector
% x0: initial state estimate
% P0: initial state covariance matrix
n = size(A, 1); % number of states
m = size(B, 2); % number of inputs
p = size(C, 1); % number of measurements
% Initialize state and covariance estimates
x = x0;
P = P0;
% Compute square root of covariance matrix
S = chol(P, 'lower');
% Time update
x = A * x;
S = [S, zeros(n, p); zeros(p, n), eye(p)];
S = S * [chol(A*P*A' + Q, 'lower'), zeros(n, p); zeros(p, n), eye(p)];
S = triu(S);
P = S * S';
% Measurement update
K = P*C'/(C*P*C' + R);
e = y - C*x;
x = x + K*e;
P = (eye(n) - K*C)*P;
% Compute square root of covariance matrix
S = chol(P, 'lower');
% Output estimates
x_est = x;
P_est = P;
end
```
You can call this function by passing in the necessary parameters:
```
x_est = zeros(n, 1); % initial state estimate
P_est = eye(n); % initial state covariance
for k = 1:N % loop over time steps
% Time update
[x_est, P_est] = srif(A, B, C, Q, R, y(:,k), x_est, P_est);
end
```
Note that this code assumes that the initial state estimate and covariance are known. If they are not known, you can use a different algorithm (such as the Kalman filter) to estimate them before using the SRIF.