The Process Noise Model of Kalman Filter for Chirp Radar

Abstract

This paper provides a process noise model of a two-state Kalman filter for tracking with linear frequency modulated (LFM) waveforms. The steady-state gains and error covariance of this Kalman filter with process noise model are derived. The derived steady-state gains are such that sensor-noise only (SNO) covariance matrix of $\alpha\beta$-filter with these steady-state gains equals an estimate covariance matrix of a first-degree fixed-memory smoothing algorithm. Thus, the Kalman filter with proposed process noise model approximates the fixed-memory polynomial filter in terms of tracking accuracies. The first-degree fixed-memory smoothing algorithm is a first-degree fixedmemory polynomial filter based on least-squares estimation. Also the range and range rate lag error expressions are derived for the fixed-memory polynomial filter.