The Augmented Complex Particle Filter

Complex Gaussian signals in engineering applications are typically noncircular, that is, they have rotation dependent distributions. However, current complex valued particle filters (PFs) have assumed (implicitly or explicitly) circular signal distributions, which for noncircular signals leads to suboptimal performance. In this correspondence, we employ a recent development in the so-called augmented complex statistics and propose the augmented complex PF (ACPF) and the augmented complex Gaussian PF (ACGPF) for the sequential estimation of complex states in both circular and noncircular noise. The analysis and simulations illuminate theoretical and practical advantages for the proposed solutions.