create an extended kalman filter in matlab

To create an Extended Kalman Filter (EKF) in MATLAB, you can follow these general steps:

1. Define the system dynamics: The EKF requires a model of the system dynamics, which can be nonlinear. You can either create a function file that calculates the state transition matrix and input matrix, or write the equations directly in the main script.

2. Define the measurement model: You need to define the relationship between the sensor measurements and the states of the system. The EKF assumes that this relationship is also nonlinear. Again, you can either create a function file or write the equations directly.

3. Initialize the filter: Set the initial state estimate and covariance matrix.

4. Measure and update: Measure the system using the available sensors, then update the state estimate and covariance matrix using the Kalman filter equations.

5. Repeat: Perform steps 4-5 for each time step.

Here's some sample MATLAB code that illustrates these steps:

main.m
% Define system dynamics
dt = 0.1; % time step
A = [1 dt; 0 1]; % state transition matrix
B = [dt^2/2; dt]; % input matrix
u = 1; % input (optional)
f = @(x) A*x + B*u; % state equations

% Define measurement model
H = [1 0]; % measurement matrix
z = 0; % dummy measurement (optional)
h = @(x) H*x + z; % measurement equations

% Initialize filter
x = [0; 0]; % initial state estimate
P = eye(2); % initial covariance matrix

% Simulate system and measure
N = 100; % number of time steps
x_true = zeros(2,N); % true state
z_meas = zeros(1,N); % measured output
for k = 1:N
    % Simulate true system
    x_true(:,k+1) = f(x_true(:,k));
    
    % Measure system
    z_meas(k) = h(x_true(:,k+1)) + randn(1)*0.1;
    
    % Update filter
    [x,P] = ekf(x,P,z_meas(k),f,h,A,B,H); % function call
end

% Plot results
t = 0:dt:(N*dt);
figure;
plot(t,x_true(1,:),t,x(1,:),t,z_meas);
legend('True state','Estimated state','Measured output');
936 chars
37 lines

In this example, the ekf function is a separate file that contains the Kalman filter equations for the EKF. You can find many examples of EKF implementations in MATLAB online, as well as more advanced variations such as the Unscented Kalman Filter (UKF) and Particle Filter (PF).