Recursive state estimation via approximate modal paths

TL;DR

This paper introduces a recursive method for approximate modal path estimation using a combined two-filter approach with quadratic approximation, improving filtering and smoothing in state estimation tasks.

Contribution

It develops a novel recursive formulation for modal paths with a quadratic approximation, enabling effective filtering and smoothing in state estimation.

Findings

Method performs on par or better than existing algorithms

Quadratic approximation effectively handles intractable value functions

Combined two-filter approach enhances recursive estimation

Abstract

In this paper, a method for recursively computing approximate modal paths is developed. A recursive formulation of the modal path can be obtained either by backward or forward dynamic programming. By combining both methods, a ``two-filter'' formula is demonstrated. Both method involves a recursion over a so-called value function, which is intractable in general. This problem is overcome by quadratic approximation of the value function in the forward dynamic programming paradigm, resulting in both a filtering and smoothing method. The merit of the approach is verified in a simulation experiments, where it is shown to be on par or better than other modern algorithms.