Stochastic filtering under model ambiguity

TL;DR

This paper addresses non-linear filtering under model uncertainty by transforming the problem into a weighted control problem and establishing the existence and uniqueness of the ambiguity filter.

Contribution

It introduces a novel approach to handle model ambiguity in non-linear filtering through a mini-max theorem and control problem formulation.

Findings

Converted uncertain filtering to a weighted control problem

Proved the existence and uniqueness of the ambiguity filter

Provided a characterization of the ambiguity filter

Abstract

In this paper, we study a non-linear filtering problem in the presence of signal model uncertainty. The model ambiguity is characterized by a class of probability measures from which the true one is taken. After interchanging the order of extremum problems by using the mini-max theorem, we find that the uncertain filtering problem can be converted to a weighted conditional mean-field optimal control problem. Further, we characterize the ambiguity filter and prove its unique existence.