--- Kalman Filter For Beginners With Matlab Examples Best <Authentic · 2024>

K_history = zeros(50, 1); P_history = zeros(50, 1);

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;

% Storage for results est_pos = zeros(1, N); est_vel = zeros(1, N); --- Kalman Filter For Beginners With MATLAB Examples BEST

% True system: constant velocity of 10 m/s true_pos = 0:dt 10:T 10; % Starting at 0, moving at 10 m/s true_vel = 10 * ones(size(t));

x_est = x_pred + K * y; P = (eye(2) - K * H) * P_pred; K_history = zeros(50, 1); P_history = zeros(50, 1);

x_est = [0; 0]; P = [100 0; 0 100]; % High initial uncertainty

%% Run Kalman Filter for k = 1:N % --- PREDICT STEP --- x_pred = F * x_est; P_pred = F * P * F' + Q; K_history = zeros(50

%% Initialize Kalman Filter % State vector: [position; velocity] x_est = [0; 10]; % Initial guess (position, velocity) P = [1 0; 0 1]; % Initial uncertainty covariance

% Update (using a dummy measurement) S = H * P_pred * H' + R; K = P_pred * H' / S; P = (eye(2) - K * H) * P_pred;

% Store results est_pos(k) = x_est(1); est_vel(k) = x_est(2); end

subplot(2,1,1); plot(t, true_pos, 'g-', 'LineWidth', 2); hold on; plot(t, measurements, 'r.', 'MarkerSize', 8); plot(t, est_pos, 'b-', 'LineWidth', 1.5); xlabel('Time (s)'); ylabel('Position (m)'); title('Kalman Filter: Position Tracking'); legend('True', 'Noisy Measurements', 'Kalman Estimate'); grid on;