Feedback particle filter for collective inference

<p style='text-indent:20px;'>The purpose of this paper is to describe the feedback particle filter algorithm for problems where there are a large number (<inline-formula><tex-math id="M1">\begin{document}$ M $\end{document}</tex-math></inline-formula>) non-interacting agents (targets) with id="M2">\begin{document}$ non-agent specific observations (measurements) that originate from these agents. In its basic form, problem characterized by data association uncertainty whereby between and must be deduced in addition agent state. paper, large-<inline-formula><tex-math id="M3">\begin{document}$ $\end{document}</tex-math></inline-formula> limit interpreted as collective inference. This viewpoint used derive equation empirical distribution hidden states. A (FPF) presented illustrated via numerical simulations. Results Euclidean finite state-space cases, both continuous-time settings. The classical FPF shown special case (with <inline-formula><tex-math id="M4">\begin{document}$ = 1 more general results. simulations help show well approximates states id="M5">\begin{document}$ $\end{document}</tex-math></inline-formula>.</p>