% --- Plot Results --- figure; subplot(2,1,1); hold on; plot(0:dt:T, true_state(1,:), 'k--', 'LineWidth', 2); plot(0:dt:T, measurements, 'rx', 'MarkerSize', 3); plot(0:dt:T, estimated_states(1,:), 'b-', 'LineWidth', 1.5); ylabel('Position (meters)'); legend('True','Measured','KF Estimate','Location','best'); title('Kalman Filter for Train Tracking');
fprintf('RMSE of Raw Measurements: %.2f meters\n', rmse_before); fprintf('RMSE of Kalman Filter: %.2f meters\n', rmse_after);
% Define the process noise covariance matrix Q and measurement noise covariance matrix R Q = [0.001 0; 0 0.001]; R = [1];
Knowing these details will allow me to provide a tailored version of the code. % --- Plot Results --- figure; subplot(2,1,1); hold
In practice, your primary task as a beginner is often to correctly tune the two key trust parameters, Q and R . Q reflects the trust in your model (a higher Q means you trust your model less), and R reflects the trust in your sensor measurements (a higher R means you trust the measurements less). Getting these right is the key to a successful filter.
This advanced example tracks an object moving along a 1D track with a constant velocity. The state vector tracks both position and velocity simultaneously.
%% Simulation parameters dt = 0.01; % 10 ms time step t_end = 2; % 2 seconds of fall t = 0:dt:t_end; N = length(t); g = -9.81; % Gravity (m/s^2) Getting these right is the key to a successful filter
The filter uses a mathematical model of the physical system to project the current state forward in time.
Based on your query, here is a summary for a popular book that matches that description:
: Refines the prediction using a new, noisy measurement to find the "best" estimate. Universität Stuttgart 2. Simple MATLAB Code Example %% Simulation parameters dt = 0
A Kalman filter combines your mathematical prediction and your noisy GPS measurements. It calculates the mathematically optimal middle ground, giving you a far more accurate position than either source could provide alone. Why Use a Kalman Filter?
x_hat = x_hat_pred + K * (measurements(k) - x_hat_pred); % Update estimate P = (1 - K) * P_pred; % Update error covariance
Your relies on dead reckoning: you know your starting point, your speed, and your direction. However, wind and currents introduce drift error over time.