# A New Smoothing Technique based on the Parallel Concatenation of Forward/Backward Bayesian Filters: Turbo Smoothing

## TL;DR

This paper introduces turbo smoothing, a new method combining forward and backward Bayesian filters via parallel concatenation, improving complexity-accuracy tradeoff in smoothing for linear Gaussian systems.

## Contribution

It extends turbo filtering concepts to smoothing, proposing algorithms that outperform recent methods in complexity and accuracy for certain systems.

## Key findings

- Achieves better complexity-accuracy tradeoff
- Demonstrates improved performance over recent smoothing techniques
- Validates algorithms with numerical results on linear Gaussian systems

## Abstract

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