If you have ever wondered how a GPS knows exactly where you are even when the signal is noisy, or how a robot balances itself, the answer is likely the Kalman Filter.
for i = 2:length(t) % Predict the state x_pred = A*x_est(i-1); P_pred = A*P_est(i-1)*A' + Q;Mistake: Using inv() in the Kalman gain formula.
Fix: Use the backslash operator or pinv(). MATLAB’s K = P_pred * H' / S is numerically stable. The Kalman Filter for Beginners: A MATLAB Tutorial
The Kalman filter works in two steps:
Kalman filtering provides an efficient, recursive estimator for linear Gaussian systems. MATLAB makes it straightforward to prototype filters; extend to nonlinear problems with EKF/UKF as needed. MATLAB’s K = P_pred * H' / S is numerically stable
The difference between a perfect filter and a useless one is tuning Q and R. MATLAB makes it straightforward to prototype filters; extend
T = 100; pos_true = zeros(1,T); pos_meas = zeros(1,T); pos_est = zeros(1,T);