Summary

In this paper we have considered incorporation of knowledge of prior distributions on both primary location and nuisance signal amplitude parameters into the conditional maximum likelihood source location estimation framework. We have focused on using prior distributions on the signal amplitude parameters to marginalize over them. Under the assumption of additive Gaussian noise, we have introduced an EM algorithmic approach to solving the resulting optimization problem, which is in general intractable to solve directly.

We have derived specific EM algorithms for two cases: the temporally independent Gaussian signal amplitude case; and the time dependent signal amplitude case where temporal dependence is modeled as Gauss-Markov. These algorithms are computationally simple in that the E-step computations are straightforward, and the M-step optimization problem is comparable to that of CML source localization. For the temporally independent Gaussian signal amplitude case, we have provided simulations which establish the efficacy of the proposed EM algorithmic approach, illustrate the performance advantage of marginalization compared to joint estimation, and demonstrate the effect of mismatch between the actual and prior nuisance parameter distributions.