Kalman Filter For Beginners With Matlab Examples Download Top ◆ < AUTHENTIC >

% State: [position; velocity]
x_est = [0; 1];          % initial guess
P_est = eye(2);          % initial uncertainty
% Matrices
A = [1 dt; 0 1];         % position = pos + vel*dt, velocity constant
H = [1 0];               % we measure only position
Q = [0.01 0; 0 0.01];    % small process noise
R = measurement_noise^2; % measurement noise variance

Before a single line of math, let’s build intuition with a simple story. % State: [position; velocity] x_est = [0; 1];

Scenario: You are in a dark room trying to track the position of a toy car moving at constant velocity. Your only tool? A noisy camera that takes a picture every second.

The Kalman Filter asks: How much do I trust my prediction vs. my measurement? Before a single line of math, let’s build

It calculates a Kalman Gain—a dynamic weight. If the measurement is very noisy (camera blurry), the gain is low, and we trust the prediction more. If the model is uncertain (the car might have hit a wall), the gain is high, and we trust the camera more.

The result? A smooth, precise, and real-time estimate. The Kalman Filter asks: How much do I

filtered_positions = zeros(size(t));
for k = 1:length(t)
% --- Predict ---
x_pred = A * x_est;
P_pred = A * P_est * A' + Q;
% --- Update using measurement ---
z = measurements(k);
K = P_pred * H' / (H * P_pred * H' + R);
x_est = x_pred + K * (z - H * x_pred);
P_est = (eye(2) - K * H) * P_pred;
% Store filtered position
filtered_positions(k) = x_est(1);

end

We take a sensor measurement. We compare it to our prediction.