Kalman Filter For Beginners With Matlab Examples Download File

Now let’s track a car moving at constant velocity. The state vector is:

x = [position; velocity]

👉 Download Link:
kalman_filter_for_beginners_matlab_examples.zip – Click to Download

(File includes all .m scripts and a brief PDF cheat sheet of the equations.)

Here's a complete mini-tutorial you can save and use:

%% Kalman Filter for Beginners - 1D Example
% Tracking a moving object with noisy measurements
clear; clc; close all;
% --- System Definition ---
% State: x = [position; velocity]
% Model: x(k) = A * x(k-1) + B * u(k) + w(k) kalman filter for beginners with matlab examples download
dt = 0.1;          % Time step (seconds)
A = [1 dt; 0 1];   % State transition matrix
B = [dt^2/2; dt];  % Control input matrix (for acceleration)
H = [1 0];         % Measurement matrix (we measure position only)
% --- Noise Covariances ---
Q = [0.01 0; 0 0.01];  % Process noise covariance
R = 1;                  % Measurement noise covariance (position noise)
% --- Initial Estimates ---
x_est = [0; 0];        % Initial state estimate [position; velocity]
P = [1 0; 0 1];        % Initial estimation error covariance
% --- Generate True Data and Measurements ---
t = 0:dt:10;
N = length(t);
u = 0.5 * ones(1, N);  % Constant acceleration input
% True state (for comparison)
x_true = zeros(2, N);
x_true(:,1) = [0; 0];
for k = 2:N
x_true(:,k) = A * x_true(:,k-1) + B * u(k-1);
end Now let’s track a car moving at constant velocity
% Measurements: true position + noise
measurements = x_true(1,:) + sqrt(R) * randn(1, N);
% --- Kalman Filter Loop ---
x_hist = zeros(2, N);  % Store estimates
P_hist = zeros(2, 2, N);
for k = 1:N
% --- Prediction Step ---
x_pred = A * x_est + B * u(k);
P_pred = A * P * A' + Q;
% --- Update Step (if measurement available)---
K = P_pred * H' / (H * P_pred * H' + R);  % Kalman Gain
y = measurements(k) - H * x_pred;         % Innovation
x_est = x_pred + K * y;
P = (eye(2) - K * H) * P_pred;
% Store results
x_hist(:,k) = x_est;
P_hist(:,:,k) = P;

end
% --- Visualization ---
figure('Position', [100 100 800 600]); end % --- Visualization --- figure('Position', [100 100
subplot(3,1,1);
plot(t, x_true(1,:), 'g-', 'LineWidth', 1.5); hold on;
plot(t, measurements, 'rx', 'MarkerSize', 4);
plot(t, x_hist(1,:), 'b-', 'LineWidth', 1.5);
legend('True Position', 'Measurements', 'Kalman Estimate');
ylabel('Position (m)'); title('Kalman Filter Tracking');
grid on;
subplot(3,1,2);
plot(t, x_true(2,:), 'g-', 'LineWidth', 1.5); hold on;
plot(t, x_hist(2,:), 'b-', 'LineWidth', 1.5);
legend('True Velocity', 'Kalman Estimate');
ylabel('Velocity (m/s)'); grid on;
subplot(3,1,3);
innovation = measurements - x_hist(1,:);
plot(t, innovation, 'k-');
ylabel('Innovation'); xlabel('Time (s)');
title('Measurement Innovation (should be zero-mean)');
grid on;
% --- Calculate RMS Error ---
pos_error_kf = sqrt(mean((x_hist(1,:) - x_true(1,:)).^2));
pos_error_meas = sqrt(mean((measurements - x_true(1,:)).^2));
fprintf('RMS Position Error:\n');
fprintf('  Raw Measurements: %.3f m\n', pos_error_meas);
fprintf('  Kalman Filter:    %.3f m\n', pos_error_kf);
fprintf('Improvement: %.1f%%\n', (1 - pos_error_kf/pos_error_meas)*100);

x_new = x_pred + K * (measurement - x_pred)