% --- Noise Covariances --- Q = [0.01 0; 0 0.01]; % Process noise covariance R = 1; % Measurement noise covariance (position noise)
The "Kalman Gain" determines how much to trust the measurement versus the prediction.
% Plot the results plot(t, x_true, 'b', t, x_est(1, :), 'r'); xlabel('Time'); ylabel('Position'); legend('True', 'Estimated');
👉 [kalman_filter_for_beginners.m] (Save the file above as kalman_filter_for_beginners.m ) kalman filter for beginners with matlab examples download
x̂k=x̂k−+K(zk−x̂k−)x hat sub k equals x hat sub k raised to the negative power plus cap K open paren z sub k minus x hat sub k raised to the negative power close paren
% Generate some measurements t = 0:dt:10; x_true = sin(t); v_true = cos(t); y = [x_true; v_true] + 0.1*randn(2, size(t));
Copy the code above into a .m file in MATLAB and watch how the blue line (the filter) ignores the red dots (the noise) to follow the truth! % --- Noise Covariances --- Q = [0
Here's a you can save and use:
% Kalman Filter Simple 1D Example clear; clc; % 1. Parameters duration = 50; % total time steps true_velocity = 0.5; % actual speed (m/s) process_noise = 0.01; % how much the "model" drifts sensor_noise = 2.0; % how "shaky" the GPS is % 2. Initialize Variables true_pos = 0; estimated_pos = 0; % initial guess P = 1; % initial error covariance (uncertainty) A = 1; % state transition model H = 1; % measurement model Q = process_noise; % process noise covariance R = sensor_noise; % measurement noise covariance % Pre-allocate for plotting history_true = zeros(duration, 1); history_measured = zeros(duration, 1); history_estimated = zeros(duration, 1); % 3. The Kalman Loop for t = 1:duration % --- Real World --- true_pos = true_pos + true_velocity + randn*sqrt(Q); measurement = true_pos + randn*sqrt(R); % --- Kalman Filter Step 1: Predict --- pos_pred = A * estimated_pos + true_velocity; P_pred = A * P * A' + Q; % --- Kalman Filter Step 2: Update --- K = P_pred * H' / (H * P_pred * H' + R); % Kalman Gain estimated_pos = pos_pred + K * (measurement - H * pos_pred); P = (1 - K * H) * P_pred; % Save data history_true(t) = true_pos; history_measured(t) = measurement; history_estimated(t) = estimated_pos; end % 4. Visualize Results plot(1:duration, history_measured, 'r.', 'DisplayName', 'Noisy Measurement'); hold on; plot(1:duration, history_true, 'k-', 'LineWidth', 2, 'DisplayName', 'True Path'); plot(1:duration, history_estimated, 'b-', 'LineWidth', 2, 'DisplayName', 'Kalman Filter Estimate'); legend; xlabel('Time'); ylabel('Position'); title('Kalman Filter: Smooth Estimates from Noisy Data'); Use code with caution. Why Use MATLAB for Kalman Filters?
The Kalman filter is a recursive algorithm that uses a combination of prediction and measurement updates to estimate the state of a system. It's based on the following assumptions: Parameters duration = 50; % total time steps
The Kalman filter works by combining the predictions from a dynamic model with noisy measurements to produce an optimal estimate of the state. The algorithm consists of two main steps:
The journey starts with a single line of MATLAB code. Download an example today, run it, and see for yourself the power of this incredible algorithm.