% Simple 1D Kalman Filter Example clear all; % 1. Simulation Parameters Nsamples = 100; % Number of data samples TrueValue = 14.4; % The actual true value we want to find SensorNoise = 2.0; % Standard deviation of the sensor noise % Generate fake noisy sensor data MeasurementData = TrueValue + SensorNoise * randn(Nsamples, 1); % 2. Initialize Kalman Filter Variables X_estimate = 10.0; % Initial guess of the state P_error = 1.0; % Initial estimation error variance Q_process_noise = 0.001; % Process noise (how much the true value drifts) R_sensor_noise = 4.0; % Measurement noise variance (SensorNoise squared) % Memory allocation for plotting Saved_Estimates = zeros(Nsamples, 1); % 3. The Kalman Filter Loop for k = 1:Nsamples % --- PREDICT STEP --- % Since the true value is mostly constant, our predicted next state % is just our previous estimated state. X_predict = X_estimate; P_predict = P_error + Q_process_noise; % --- UPDATE STEP --- % Calculate the Kalman Gain KalmanGain = P_predict / (P_predict + R_sensor_noise); % Get current measurement Z_measure = MeasurementData(k); % Correct the prediction with the new measurement X_estimate = X_predict + KalmanGain * (Z_measure - X_predict); % Update the error covariance for the next iteration P_error = (1 - KalmanGain) * P_predict; % Save the result Saved_Estimates(k) = X_estimate; end % 4. Plot the Results figure; plot(1:Nsamples, MeasurementData, 'r.', 'MarkerSize', 8); hold on; plot(1:Nsamples, Saved_Estimates, 'b-', 'LineWidth', 2); plot(1:Nsamples, repmat(TrueValue, Nsamples, 1), 'g--', 'LineWidth', 1.5); xlabel('Time Step'); ylabel('Value'); title('1D Kalman Filter Performance'); legend('Noisy Measurements', 'Kalman Filter Estimate', 'True Value'); grid on; Use code with caution. What Happens When You Run This Code?
It starts with the basics, like the Average Filter and Moving Average Filter , to get you used to the idea of updating estimates in real-time.
Projects the current state and error covariance forward in time to find the a priori estimate for the next time step. % Simple 1D Kalman Filter Example clear all; % 1
Imagine you are driving a car through a long, dark tunnel. Your GPS loses its satellite connection, so it cannot tell you exactly where you are. You look at your speedometer, but it has a slight delay and is not 100% accurate. How do you guess your exact position? You use two things:
: Noisy readings collected from physical sensors. The Kalman Filter Loop for k = 1:Nsamples
The Kalman Filter mathematically balances these two sources, weights them by their respective uncertainties (variances), and calculates the most statistically probable state. The Four Essential Filters in the Book
Are you trying to solve a (like smoothing sensor noise or predicting a moving target)? What Happens When You Run This Code
% Store result estimates(k) = x_est;
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If P (prediction error) is high, K is high → Trust the measurement.
: Adjusts the prediction using the sensor data weighted by the Kalman Gain.