Multi-sensor state space models underpin fusion applications in networks ofsensors. Estimation of latent parameters in these models has the potential toprovide highly desirable capabilities such as network self-calibration.Conventional solutions to the problem pose difficulties in scaling with thenumber of sensors due to the joint multi-sensor filtering involved whenevaluating the parameter likelihood. In this article, we propose a separablepseudo-likelihood which is a more accurate approximation compared to apreviously proposed alternative under typical operating conditions. Inaddition, we consider using separable likelihoods in the presence of manyobjects and ambiguity in associating measurements with objects that originatedthem. To this end, we use a state space model with a hypothesis basedparameterisation, and, develop an empirical Bayesian perspective in order toevaluate separable likelihoods on this model using local filtering. Bayesianinference with this likelihood is carried out using belief propagation on theassociated pairwise Markov random field. We specify a particle algorithm forlatent parameter estimation in a linear Gaussian state space model anddemonstrate its efficacy for network self-calibration using measurements fromnon-cooperative targets in comparison with alternatives.
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