Kalman Filtering through Online Estimating the Power Spectral Density of Brownian Motion Process Noise for Target Tracking

For linear state estimation problems involving Brownian motion process noise, this paper proposes a novel adaptive Kalman filter that leverages online assessment of the power spectral density (PSD) for continuous-time dynamic noise. Unlike existing adaptive filters that estimate the entire noise covariance matrix, this work proposes to directly evaluate the noise PSD according to a analytical derivation for process noise covariance. As the key innovation, the proposed adaption scheme significantly reduces the number of scalar unknowns and results in enhanced accuracy for estimating the PSD of Brownian motion noise. As the resulted advantage, the new adaptive Kalman filter mitigates the crucial reliance on noise statistics without extra computation. Numerical examples of target tracking demonstrate the new adaptive Kalman filter's filtering adaptability, accuracy, and simplicity.