# Multiple Bayesian Filtering as Message Passing

## TL;DR

This paper introduces a general message passing framework for interconnected Bayesian filters, enabling the development of new filtering algorithms that improve complexity-accuracy tradeoffs in dynamic systems.

## Contribution

It proposes a novel method to derive interconnected Bayesian filtering algorithms using graphical models and message passing, exemplified by combining particle and Kalman filters.

## Key findings

- New filtering algorithms outperform marginalized and multiple particle filters in complexity-accuracy tradeoff.
- The method effectively integrates different Bayesian filters for complex systems.
- Numerical results demonstrate improved efficiency in specific dynamic systems.

## Abstract

In this manuscript, a general method for deriving filtering algorithms that involve a network of interconnected Bayesian filters is proposed. This method is based on the idea that the processing accomplished inside each of the Bayesian filters and the interactions between them can be represented as message passing algorithms over a proper graphical model. The usefulness of our method is exemplified by developing new filtering techniques, based on the interconnection of a particle filter and an extended Kalman filter, for conditionally linear Gaussian systems. Numerical results for two specific dynamic systems evidence that the devised algorithms can achieve a better complexity-accuracy tradeoff than marginalized particle filtering and multiple particle filtering.