Kalman Filter Derivation and Comparison to MUltiple SIgnal Classification (MUSIC)

Abstract

MUltiple SIgnal Classification (MUSIC) is a standard technique utilizing multiple-element antenna covariance information to estimate wavefront angle of arrival (AoA). This paper outlines and compares a Kalman Filter implementation of the wavefront AoA estimation which utilizes the same MUSIC-related covariance matrix. Both algorithms exploit the relative phases derived by the covariance matrix; unlike MUSIC, the Kalman Filter implementation allows for the AoA estimate to filter through time- history measurement updates. The relative phases are a function of the AoA of the wavefront impinging on a generic array and are used as measurement updates to an extended Kalman filter (EKF) which estimates the AoA of the dominant signal source. In this paper, the relative phases are derived, the techniques used to generate relative phase measurements from the signal covariance are detailed, and the corresponding measurement model of the EKF is presented. Additionally, a simple phase matching technique that minimizes the difference between the measured and expected relative phases is presented. The EKF and phase matching techniques are tested against simple signal simulations with varying signal-to-noise ratios (SNRs). These simulations are detailed and results comparing the estimation techniques to the MUSIC technique are presented. The estimation techniques that utilize relative phase measurements produce accurate results comparable to the MUSIC technique at high SNRs and the EKF provides filtered estimates at low SNRs.