Kalman Filter For Beginners With Matlab Examples Download Direct

Output figure: Smoother curve than raw measurements

% Kalman Filter for Beginners - Temperature Tracking Example
clear; clc; close all;
% True state (constant temperature)
true_temp = 25;
% Simulation parameters
dt = 1;      % time step (seconds)
T = 50;      % total time steps
% Noise parameters
process_noise_std = 0.5;   % uncertainty in model (e.g., window opens)
measurement_noise_std = 2; % sensor noise kalman filter for beginners with matlab examples download
% Initial guess
x_est = 20;   % initial estimate (wrong on purpose)
P_est = 5;    % initial uncertainty (high)
% Storage
x_history = zeros(1,T);
meas_history = zeros(1,T); Output figure : Smoother curve than raw measurements
for k = 1:T
% --- Simulate measurement (with noise) ---
z = true_temp + measurement_noise_std * randn;
meas_history(k) = z;
% --- Prediction step ---
% For constant temperature, prediction = previous estimate
x_pred = x_est;
P_pred = P_est + process_noise_std^2;
% --- Kalman gain ---
K = P_pred / (P_pred + measurement_noise_std^2);
% --- Update step ---
x_est = x_pred + K * (z - x_pred);
P_est = (1 - K) * P_pred;
x_history(k) = x_est;

end
% Plot results
time = 1:T;
plot(time, true_temp*ones(1,T), 'k--', 'LineWidth', 2); hold on;
plot(time, meas_history, 'ro', 'MarkerSize', 4);
plot(time, x_history, 'b-', 'LineWidth', 1.5);
legend('True Temp', 'Noisy Measurements', 'Kalman Filter Estimate');
xlabel('Time step'); ylabel('Temperature (°C)');
title('Kalman Filter for Beginners: Temperature Tracking');
grid on;

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