# Double Bayesian Smoothing as Message Passing

## TL;DR

This paper introduces double Bayesian smoothing, a new method that enhances filtering and smoothing in dynamic systems by combining two Bayesian filters and two backward information filters, improving accuracy and efficiency.

## Contribution

The paper extends the double Bayesian filtering concept to smoothing, deriving algorithms for conditionally linear Gaussian systems and demonstrating improved performance over existing methods.

## Key findings

- Achieves better complexity-accuracy tradeoff.
- Enhances tracking capability in dynamic systems.
- Outperforms recent smoothing techniques.

## Abstract

Recently, a novel method for developing filtering algorithms, based on the interconnection of two Bayesian filters and called double Bayesian filtering, has been proposed. In this manuscript we show that the same conceptual approach can be exploited to devise a new smoothing method, called double Bayesian smoothing. A double Bayesian smoother combines a double Bayesian filter, employed in its forward pass, with the interconnection of two backward information filters used in its backward pass. As a specific application of our general method, a detailed derivation of double Bayesian smoothing algorithms for conditionally linear Gaussian systems is illustrated. Numerical results for two specific dynamic systems evidence that these algorithms can achieve a better complexity-accuracy tradeoff and tracking capability than other smoothing techniques recently appeared in the literature.