Analysis of the widely linear complex Kalman filter
Dahir H. Dini, Danilo P. Mandic · 2010
Abstract — Recently, a class of widely linear (augmented) complex-valued Kalman filters (KFs), that make use of aug-mented complex statistics, have been proposed for sequential state space estimation of the generality of complex signals. This was achieved in the context of neural network training, and has allowed for a unified treatment of both second-order circular and noncircular signals, that is, both those with rotation invariant and rotation-dependent distributions. In this paper, we revisit the augmented complex KF, augmented complex extended KF, and augmented complex unscented KF in a more general context, and analyze their performances for different degrees of noncircularity of input and the state and measurement noises. For rigor, a theoretical bound for the performance advantage of widely linear KFs over their strictly linear counterparts is provided. The analysis also addresses the duality with bivariate real-valued KFs, together with several issues of implementation. Simulations using both synthetic and real world proper and improper signals support the analysis. Index Terms — Augmented complex Kalman filter, complex circularity, complex Kalman filter, extended Kalman filter,