Kalman Filter For Beginners: With Matlab Examples Download !full! Top

This guide provides a comprehensive introduction to the Kalman Filter, explains why it is one of the "top" tools in engineering, and provides a complete, runnable MATLAB example.

Since I cannot provide a direct file download link, I have provided the complete source code below. You can copy and paste this directly into a MATLAB script file (.m) to run it immediately.

Step 3: Expected Output

When you run this script, you will see:

  • Top Plot: Green (true), Red dots (noisy sensor), Blue (Kalman estimate). The blue line smoothly follows the green line, ignoring most of the red noise.
  • Bottom Plot: The Kalman filter quickly learns the velocity (slope) and converges to the true velocity of 1 m/s.
  • Command Window: You’ll see something like: 
    RMSE of Raw Measurements: 4.98 meters
RMSE of Kalman Filter: 1.52 meters
    The error is reduced by more than 60%!

The "Tuning" (Matrices Q and R)

This is where the "magic" happens.

  • R (Measurement Noise): If your sensor is very cheap and jittery, make R large. The filter will trust the physics model more than the sensor.
  • Q (Process Noise): If you are tracking a car that might brake or accelerate randomly, make Q larger. The filter will realize that "physics prediction might be wrong" and react faster to changes.

5. MATLAB Example – Tracking a Moving Object

Let’s implement a 1D Kalman Filter to track a car moving at constant velocity.

The MATLAB Code

You can copy and paste this directly into a MATLAB script (e.g., kf_demo.m).

%% Kalman Filter Beginner Demo
% Tracking a falling object (1D motion) with noisy measurements.

clc; clear; close all;


%% 1. Initialization and Parameters
dt = 0.1;            % Time step (seconds)
t = 0:dt:10;         % Time vector
g = 9.8;             % Gravity This guide provides a comprehensive introduction to the


% --- The "Truth" (Simulation of reality) ---
true_position = 100 - 0.5 * g * t.^2; % Falling from 100m
true_velocity = -g * t;


% --- The Sensor (Noisy Measurements) ---
% We only measure position, with a variance of 25 (std dev = 5m)
measurement_noise = randn(size(t)) * 5;
measured_position = true_position + measurement_noise;


%% 2. Kalman Filter Setup


% State Vector: x = [position; velocity]
x = [0; 0]; % Initial guess (we assume it starts at 0,0 - this is wrong on purpose to test the filter)


% Covariance Matrix: How unsure are we about our initial guess?
P = [1 0; 0 1];


% State Transition Matrix (Physics: F)
% Position_new = Position_old + Velocity*dt
% Velocity_new = Velocity_old (assuming no drag for simplicity)
F = [1 dt; 0 1];


% Control Input Matrix (External force: Gravity)
% We know gravity pulls it down, so we account for it.
B = [0.5*dt^2; dt];
u = g; % Input magnitude (acceleration) Step 3: Expected Output When you run this


% Measurement Matrix (We can only see position)
H = [1 0];


% Process Noise (Uncertainty in the model physics)
Q = [0.1 0; 0 0.1];


% Measurement Noise (Uncertainty of the sensor)
R = 25;


% Pre-allocate memory for plotting
est_position = zeros(size(t));
est_velocity = zeros(size(t));


%% 3. The Kalman Filter Loop


for i = 1:length(t)


% --- A. PREDICT STEP ---
% 1. Predict State (x_pred = F*x + B*u)
x = F * x + B * u;
% 2. Predict Covariance (P_pred = F*P*F' + Q)
P = F * P * F' + Q;
% --- B. UPDATE STEP ---
% 1. Calculate Kalman Gain (K)
% K = P * H' * inv(H * P * H' + R)
K = P * H' * inv(H * P * H' + R);
% 2. Update State with Measurement (z)
z = measured_position(i); % The sensor reading
x = x + K * (z - H * x);
% 3. Update Covariance
P = (eye(2) - K * H) * P;
% Store data for plotting
est_position(i) = x(1);
est_velocity(i) = x(2);



end


%% 4. Visualization
figure('Name', 'Kalman Filter Demo', 'Color', 'w');


% Position Plot
subplot(2, 1, 1);
plot(t, true_position, 'g', 'LineWidth', 2); hold on;
plot(t, measured_position, 'r.');
plot(t, est_position, 'b-', 'LineWidth', 2);
legend('True Position', 'Noisy Measurement', 'Kalman Estimate');
xlabel('Time (s)'); ylabel('Position (m)');
title('Kalman Filter Tracking a Falling Object');
grid on;


% Velocity Plot
subplot(2, 1, 2);
plot(t, true_velocity, 'g', 'LineWidth', 2); hold on;
plot(t, est_velocity, 'b-', 'LineWidth', 2);
legend('True Velocity', 'Kalman Estimate');
xlabel('Time (s)'); ylabel('Velocity (m/s)');
title('Velocity

The "Physics" (Matrix F)

We defined F = [1 dt; 0 1]. This matrix tells the filter how the object moves based on high-school physics:

  • New Position = Old Position + (Velocity × Time).
  • New Velocity = Old Velocity.

Step 3: Run the Filter

filtered_positions = zeros(size(t));

for k = 1:length(t)
% --- Predict ---
x_pred = A * x_est;
P_pred = A * P_est * A' + Q;


% --- Update using measurement ---
z = measurements(k);
K = P_pred * H' / (H * P_pred * H' + R);
x_est = x_pred + K * (z - H * x_pred);
P_est = (eye(2) - K * H) * P_pred;
% Store filtered position
filtered_positions(k) = x_est(1);



end

1. The “Learn by Example” Toolkit (1D, 2D, and 3D)

  • What: A ZIP file containing three MATLAB scripts: KF_1D_ConstantVelocity.m, KF_2D_FallingObject.m, KF_3D_AircraftTracking.m
  • Why download: Each script includes extensive comments and plotting functions.
  • How to get: (In a real article, link here. Search GitHub: “Kalman Filter MATLAB beginner” or use File Exchange ID: 53770)

Step 1: Define the Problem

  • Real State: Object starts at position 0, velocity 1 m/s.
  • Measurement: Noisy sensor reports position with standard deviation of 5 meters.
  • Goal: Recover the true position from the noise.