Kalman Filter is an optimal estimation algorithm that provides the "best guess" of a system's state by combining noisy sensor measurements with a mathematical model . It operates in a continuous Predict-Correct loop to minimize the variance of the estimate over time Core Concept: The Predict-Correct Loop

% Define the system matrices
A = [1 1; 0 1];  % state transition matrix
H = [1 0];  % measurement matrix
Q = [0.001 0; 0 0.001];  % process noise covariance
R = [1];  % measurement noise covariance
Book Review: Kalman Filter for Beginners: with MATLAB Examples
Authors: Phil Kim, Lynn Huh
Publisher: A-Jin Publishing
Target Audience: Engineering students, hobbyists, and professionals needing a practical introduction to estimation.
Let's consider a simple example where we want to estimate the position and velocity of an object from noisy measurements of its position.
7. Download the Code

ZIP file contents:
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;