% 1D Kalman Filter Example: Temperature Tracking clear; clc; close all; % Simulation Parameters true_temp = 72; % The actual constant temperature num_steps = 100; % Number of iterations sensor_noise_sigma = 2; % Standard deviation of measurement noise % Generate noisy measurements rng(42); % Seed for reproducibility measurements = true_temp + sensor_noise_sigma * randn(1, num_steps); % Initialize Kalman Filter Variables estimated_temp = zeros(1, num_steps); P = 10; % Initial estimation error covariance Q = 0.001; % Process noise covariance (highly stable system) R = sensor_noise_sigma^2; % Measurement noise covariance x_hat = 65; % Initial guess % Kalman Filter Loop for k = 1:num_steps % 1. Predict Step x_hat_minus = x_hat; % State prediction (static system) P_minus = P + Q; % Error covariance prediction % 2. Update Step K = P_minus / (P_minus + R); % Calculate Kalman Gain x_hat = x_hat_minus + K * (measurements(k) - x_hat_minus); % Update estimate P = (1 - K) * P_minus; % Update error covariance % Store the result estimated_temp(k) = x_hat; end % Plotting Results figure; plot(1:num_steps, true_temp * ones(1, num_steps), 'g-', 'LineWidth', 2); hold on; plot(1:num_steps, measurements, 'r.', 'MarkerSize', 10); plot(1:num_steps, estimated_temp, 'b-', 'LineWidth', 2); xlabel('Time Step'); ylabel('Temperature (°F)'); title('1D Kalman Filter: Temperature Estimation'); legend('True Value', 'Noisy Measurement', 'Kalman Estimate', 'Location', 'Best'); grid on; Use code with caution. 2D Kalman Filter MATLAB Example (Position and Velocity)

This code demonstrates the core logic: predict, compute the gain, update the estimate, and update the covariance. After running it, you'll see the estimate dramatically smooth out the noisy measurement data to converge on the true value.

Uncertainty: The "Error Covariance" increases because we are guessing. 2. The Correction (Measurement Update)

% ---- Update Step (when a new measurement is available) ---- % 1. Compute the Kalman Gain K = P_pred * H' / (H * P_pred * H' + R);

The best way to learn is by doing. MATLAB is the perfect environment for this because of its intuitive matrix operations and built-in visualization tools.

end

1. Kalman filter by VPS Naidu (MATLAB Central File Exchange)

The Kalman filter is beautifully represented by a set of equations. For a beginner, it's most helpful to think of these in terms of their function rather than their derivation.

Based on our current understanding of the system's physics (e.g., velocity, acceleration), we predict where the system should be in the next moment. B. The Update Step ("Measurement Update")

Copy and paste this code directly into your MATLAB editor to execute the simulation.