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We consider a class of filtering problems for large populations where eachindividual is modeled by the same hidden Markov model (HMM). In this paper, wefocus on aggregate inference problems in HMMs with discrete state space andcontinuous observation space. The continuous observations are aggregated in away such that the individuals are indistinguishable from measurements. Wepropose an aggregate inference algorithm called continuous observationcollective forward-backward algorithm. It extends the recently proposedcollective forward-backward algorithm for aggregate inference in HMMs withdiscrete observations to the case of continuous observations. The efficacy ofthis algorithm is illustrated through several numerical experiments.

Filtering for Aggregate Hidden Markov Models with Continuous Observations