create a multivariate kalman filter without using functions in matlab

To create a multivariate Kalman filter without using built-in MATLAB functions, you can implement the algorithm manually. Here is a step-by-step process to create a multivariate Kalman filter:

1. Define the system matrices:

   • State transition matrix (A)
   • Control input matrix (B)
   • Measurement matrix (C)
   • State covariance matrix (P)
   • Measurement covariance matrix (R)
   • Control input matrix (U)

2. Initialize the initial state estimate (x) and the initial state covariance matrix (P).

3. For each time step, perform the following steps:

   • Predict the next state estimate and covariance:

     main.m
     x = A * x + B * U
     P = A * P * A' + Q
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   • Compute the Kalman gain:

     main.m
     K = P * C' * inv(C * P * C' + R)
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   • Update the state estimate and covariance:

     main.m
     x = x + K * (measurement - C * x)
     P = (eye(size(x, 1)) - K * C) * P
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4. Repeat step 3 for each time step.

Here's an example implementation for a 2-dimensional state Kalman filter:

main.m
% System matrices
A = [1 0; 0 1];
B = eye(2);
C = eye(2);
Q = eye(2); % Process noise covariance matrix
R = eye(2); % Measurement noise covariance matrix
U = [0; 0]; % Control input

% Initial state estimate and covariance
x = [0; 0];
P = eye(2);

% Measurements
measurements = [1 1; 2 2; 3 3];

% Kalman filter loop
for t = 1:size(measurements, 1)
    % Predict
    x = A * x + B * U;
    P = A * P * A' + Q;

    % Update
    K = P * C' * inv(C * P * C' + R);
    x = x + K * (measurements(t, :)' - C * x);
    P = (eye(size(x, 1)) - K * C) * P;
end

% Final state estimate
x
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Note that this is a basic implementation and may require additional adjustments and error handling based on your specific use case.