Sequential Bayesian Algorithms for Identification and Blind Equalization of Unit-Norm Channels

In many estimation problems of interest, the unknown parameters reside on spherical manifolds. As most common filtering algorithms assume that parameters have Gaussian prior distributions, their application to such problems leads to suboptimal performance. In this letter, we propose a model in which the unknown unit-norm parameter vectors have Fisher-Bingham (F-B) prior distributions. We show that if the observations relate to the parameters via Gaussian likelihoods, the F-B priors form a conjugate model that yields closed-form, recursive estimators that naturally take into account the restrictions on the unknowns. We apply this model to a communication setup with multiple gain-controlled FIR frequency-selective channels, deriving a novel maximum a posteriori (MAP) channel parameter estimator and a blind equalizer based on Rao-Blackwellized particle filters. As we verify via Monte Carlo numerical simulations, the F-B model leads to superior performance compared to previous algorithms that adopt mismatched Gaussian prior models.