  Multi-sensor state space models underpin fusion applications in networks of
sensors. Estimation of latent parameters in these models has the potential to
provide highly desirable capabilities such as network self-calibration.
Conventional solutions to the problem pose difficulties in scaling with the
number of sensors due to the joint multi-sensor filtering involved when
evaluating the parameter likelihood. In this article, we propose a separable
pseudo-likelihood which is a more accurate approximation compared to a
previously proposed alternative under typical operating conditions. In
addition, we consider using separable likelihoods in the presence of many
objects and ambiguity in associating measurements with objects that originated
them. To this end, we use a state space model with a hypothesis based
parameterisation, and, develop an empirical Bayesian perspective in order to
evaluate separable likelihoods on this model using local filtering. Bayesian
inference with this likelihood is carried out using belief propagation on the
associated pairwise Markov random field. We specify a particle algorithm for
latent parameter estimation in a linear Gaussian state space model and
demonstrate its efficacy for network self-calibration using measurements from
non-cooperative targets in comparison with alternatives.
