--- Kalman Filter For Beginners With Matlab Examples Best -

%% Run Kalman Filter for k = 1:N % --- PREDICT STEP --- x_pred = F * x_est; P_pred = F * P * F' + Q;

% Store results est_pos(k) = x_est(1); est_vel(k) = x_est(2); end --- Kalman Filter For Beginners With MATLAB Examples BEST

subplot(2,1,2); plot(t, true_vel, 'g-', 'LineWidth', 2); hold on; plot(t, est_vel, 'b-', 'LineWidth', 1.5); xlabel('Time (s)'); ylabel('Velocity (m/s)'); title('Velocity Estimate'); legend('True', 'Kalman Estimate'); grid on; %% Run Kalman Filter for k = 1:N

figure; subplot(2,1,1); plot(1:50, K_history, 'b-', 'LineWidth', 2); xlabel('Time Step'); ylabel('Kalman Gain (Position)'); title('Kalman Gain Convergence'); grid on; Example 2: Visualizing the Kalman Gain This example

K_history(k) = K(1); P_history(k) = P(1,1); end

subplot(2,1,2); plot(1:50, P_history, 'r-', 'LineWidth', 2); xlabel('Time Step'); ylabel('Position Uncertainty (P)'); title('Uncertainty Decrease Over Time'); grid on;

The filter starts with an initial guess (0 m position, 10 m/s velocity). As each noisy GPS reading arrives, the Kalman filter computes the optimal blend between the model prediction and the measurement. Notice how the position estimate (blue line) is much smoother than the noisy measurements (red dots), and the velocity converges to the true value (10 m/s). Example 2: Visualizing the Kalman Gain This example shows how the filter becomes more confident over time.