% 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));
%% 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
for k = 1:50 % Predict x_pred = F * x_est; P_pred = F * P * F' + Q; --- Kalman Filter For Beginners With MATLAB Examples BEST
%% Plot results figure('Position', [100 100 800 600]);
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: % True system: constant velocity of 10 m/s
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.
K_history(k) = K(1); P_history(k) = P(1,1); end For beginners, the math can seem daunting, but
% Measurement noise covariance R R = measurement_noise^2;
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.
% Measurement matrix H (we only measure position) H = [1 0];
% Update (using a dummy measurement) S = H * P_pred * H' + R; K = P_pred * H' / S; P = (eye(2) - K * H) * P_pred;