Kalman Filter For Beginners With Matlab Examples Download Top 【Edge】

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

For a beginner, the Kalman Filter is simply two alternating steps:

The difference between a perfect filter and a useless one is tuning Q and R. Let’s implement a 1D Kalman Filter to track

Beginner’s rule of thumb: Start with R as the variance of your sensor’s noise (measure it). Start with Q as a small diagonal matrix. Then tweak. % True system: car moves with velocity 1 m/s dt = 0

% True system: car moves with velocity 1 m/s
dt = 0.1;                % time step (seconds)
t = 0:dt:10;             % time vector
true_position = t;       % true position (no noise)
% Simulate noisy measurements (e.g., GPS error)
measurement_noise = 0.5;
measurements = true_position + measurement_noise * randn(size(t));

This is a self-contained script. It simulates a moving object, creates noisy measurements, and uses a Kalman Filter to smooth the data.

Instructions:

%% Kalman Filter for Beginners - 1D Position Tracking
% This example simulates an object moving at a constant velocity.
% We will track it using a Kalman Filter.
clc; clear; close all;
%% 1. Simulation Parameters
dt = 1;              % Time step (1 second)
n_iter = 50;         % Number of iterations
% True State (What actually happens)
true_velocity = 2;   % Moving 2 meters per second
initial_position = 0;
% Generate True Data
true_positions = initial_position + (0:n_iter-1) * true_velocity;
% Generate Noisy Measurements (Simulating a Sensor)
measurement_noise = 10; % Variance of the sensor noise
measurements = true_positions + sqrt(measurement_noise) * randn(1, n_iter);
%% 2. Kalman Filter Initialization
% State Vector [x; v] -> [Position; Velocity]
% We assume the object starts at 0 with 0 velocity.
x = [0; 0];
% State Transition Matrix (The Physics Model)
% x_new = x_old + v_old * dt
% v_new = v_old
F = [1 dt; 
     0  1];
% Measurement Matrix (We only measure Position)
% z = [1 0] * [x; v]
H = [1 0];
% Process Noise Covariance (Q)
% How much uncertainty is in the physical model?
% Small Q = We trust the physics model perfectly.
% Large Q = We expect the object to move unpredictably (acceleration).
Q = [0.1 0; 
     0 0.1];
% Measurement Noise Covariance (R)
% This comes from the sensor specs. We defined noise variance as 10 above.
R = measurement_noise;
% State Covariance Matrix (P)
% Initial uncertainty about our guess.
P = [1 0; 
     0 1];
%% 3. The Kalman Filter Loop
% Arrays to store results for plotting
x_est = zeros(2, n_iter);
for k = 1:n_iter
% --- STEP 1: PREDICT ---
    % Predict the state ahead
    x = F * x;
% Predict the error covariance ahead
    P = F * P * F' + Q;
% --- STEP 2: UPDATE (MEASUREMENT) ---
    % Compute the Kalman Gain
    % This determines how much we trust the measurement vs the prediction
    K = P * H' / (H * P * H' + R);
% Update the estimate with the measurement
    % z(k) is the current sensor reading
    x = x + K * (measurements(k) - H * x);
% Update the error covariance
    P = (eye(2) - K * H) * P;
% Store result
    x_est(:, k) = x;
end
%% 4. Plotting Results
figure('Name', 'Kalman Filter Demo', 'Color', 'w');
hold on;
% Plot True Path
plot(true_positions, 'g-', 'LineWidth', 2, 'DisplayName', 'True Position');
% Plot Noisy Measurements
plot(measurements, 'r.', 'MarkerSize', 10, 'DisplayName', 'Measurements (Noisy)');
% Plot Kalman Filter Estimate
plot(x_est(1, :), 'b-', 'LineWidth', 2, 'DisplayName', 'Kalman Estimate');
title('Kalman Filter Tracking: 1D Motion');
xlabel('Time (s)');
ylabel('Position (m)');
legend('Location', 'NorthWest');
grid on;
hold off;

Consider a discrete linear time‑invariant system: x_k = A x_k-1 + B u_k-1 + w_k-1 z_k = H x_k + v_k where x_k is the state, u_k control input, z_k measurement, w_k process noise ~ N(0,Q), v_k measurement noise ~ N(0,R).

Goal: estimate x_k given measurements z_1..z_k. This is a self-contained script