# Damped Posterior Linearization Filter

## TL;DR

This paper introduces a double-loop version of the iterated posterior linearization filter (IPLF) that improves convergence and maintains high accuracy in Bayesian state estimation by incorporating an optimization algorithm in the inner loop.

## Contribution

The paper proposes a novel double-loop IPLF that enhances convergence properties by integrating an optimization step for the posterior mean.

## Key findings

- The double-loop IPLF converges better than the original IPLF.
- The proposed method achieves accuracy comparable or superior to existing algorithms.
- Simulation results validate improved convergence and performance.

## Abstract

The iterated posterior linearization filter (IPLF) is an algorithm for Bayesian state estimation that performs the measurement update using iterative statistical regression. The main result behind IPLF is that the posterior approximation is more accurate when the statistical regression of measurement function is done in the posterior instead of the prior as is done in non-iterative Kalman filter extensions. In IPLF, each iteration in principle gives a better posterior estimate to obtain a better statistical regression and more accurate posterior estimate in the next iteration. However, IPLF may diverge. IPLF's fixed- points are not described as solutions to an optimization problem, which makes it challenging to improve its convergence properties. In this letter, we introduce a double-loop version of IPLF, where the inner loop computes the posterior mean using an optimization algorithm. Simulation results are presented to show that the proposed algorithm has better convergence than IPLF and its accuracy is similar to or better than other state-of-the-art algorithms.