Most tutorials jump into matrix algebra and covariance propagation without context. Here, we will start with a (e.g., tracking the temperature of a room) before moving to a 2D motion example in MATLAB.
Estimating hidden market volatility and tracking fast-moving macroeconomic indicators.
% Storage x_history = zeros(1,T); meas_history = zeros(1,T);
% Preallocate storage for results x_history = zeros(1, num_samples);
This code implements a simple Kalman filter for a sine wave with additive white Gaussian noise.
When you run this code, you’ll see that even though the individual measurements are scattered around the true value, the Kalman filter quickly converges and provides a smooth, stable estimate. This simple example demonstrates the core concept: optimal fusion of model and measurement.
(Measurement Matrix): Maps the true state space to the sensor measurements. Since our sensor only measures position, it extracts the position value and ignores velocity. MATLAB Code: 2D Object Tracking
If the noise is Gaussian, the Kalman filter provides the best possible estimate.
% Generate noisy measurements true_voltage = 14.2; % True constant voltage num_samples = 50; measurements = true_voltage + sqrt(R)*randn(num_samples, 1);