  We consider a class of filtering problems for large populations where each
individual is modeled by the same hidden Markov model (HMM). In this paper, we
focus on aggregate inference problems in HMMs with discrete state space and
continuous observation space. The continuous observations are aggregated in a
way such that the individuals are indistinguishable from measurements. We
propose an aggregate inference algorithm called continuous observation
collective forward-backward algorithm. It extends the recently proposed
collective forward-backward algorithm for aggregate inference in HMMs with
discrete observations to the case of continuous observations. The efficacy of
this algorithm is illustrated through several numerical experiments.
