%% Initialize Kalman Filter % State vector: [position; velocity] x_est = [0; 10]; % Initial guess (position, velocity) P = [1 0; 0 1]; % Initial uncertainty covariance
% --- UPDATE STEP (using measurement)--- z = measurements(k); y = z - H * x_pred; % Innovation (residual) S = H * P_pred * H' + R; % Innovation covariance K = P_pred * H' / S; % Kalman Gain
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;
% Process noise covariance Q (small for constant velocity model) Q = [0.01 0; 0 0.01]; --- Kalman Filter For Beginners With MATLAB Examples BEST
K_history(k) = K(1); P_history(k) = P(1,1); end
% Store results est_pos(k) = x_est(1); est_vel(k) = x_est(2); end
With MATLAB, you can start simple—tracking a position in 1D—and gradually move to 2D tracking, then to EKF for a mobile robot. The examples provided give you a working foundation. Experiment by changing noise levels, initial conditions, and tuning parameters. The Kalman filter is not just a tool; it's a way of thinking about fusing information in the presence of uncertainty. %% Initialize Kalman Filter % State vector: [position;
x_est = x_pred + K * y; P = (eye(2) - K * H) * P_pred;
% Measurement: noisy GPS (standard deviation = 3 meters) measurement_noise = 3; measurements = true_pos + measurement_noise * randn(size(t));
Introduction Imagine trying to track the exact position of a moving car using a noisy GPS signal. The GPS might tell you the car is at one location, but your intuition says it should be further along the road. Which do you trust? This fundamental problem of blending noisy measurements with a mathematical model is where the Kalman Filter (KF) excels. The Kalman filter is not just a tool;
K_history = zeros(50, 1); P_history = zeros(50, 1);
Developed by Rudolf E. Kálmán in 1960, the Kalman filter is a recursive algorithm that estimates the state of a dynamic system from a series of incomplete and noisy measurements. It is widely used in robotics, navigation, economics, and signal processing. For beginners, the math can seem daunting, but the core idea is simple:
for k = 1:50 % Predict x_pred = F * x_est; P_pred = F * P * F' + Q;
%% Kalman Filter for 1D Position Tracking clear; clc; close all; % Simulation parameters dt = 0.1; % Time step (seconds) T = 10; % Total time (seconds) t = 0:dt:T; % Time vector N = length(t); % Number of steps
