Bayesian filtering for multi-object systems with independently generated observations

TL;DR

This paper develops a Bayesian filtering framework for multi-object systems where each object independently generates observations, utilizing variational calculus and generating functionals to derive general update formulas.

Contribution

It introduces a novel variational calculus-based approach for Bayesian filtering in multi-object systems with independent observations, extending existing methods.

Findings

Derived general formulas for the updated generating functional

Applied variational calculus to multi-object Bayesian filtering

Extended Bayes' rule to multi-object systems

Abstract

A general approach for Bayesian filtering of multi-object systems is studied, with particular emphasis on the model where each object generates observations independently of other objects. The approach is based on variational calculus applied to generating functionals, using the general version of Faa di Bruno's formula for Gateaux differentials. This result enables us to determine some general formulae for the updated generating functional after the application of a multi-object analogue of Bayes' rule.