On the convergence of a Risk Sensitive like Filter

TL;DR

This paper investigates the convergence properties of a risk-sensitive filter with a time-varying risk parameter, demonstrating convergence to a fixed point using contraction analysis techniques.

Contribution

It introduces a convergence analysis for a risk-sensitive filter with a dynamic risk parameter, extending understanding of its stability and fixed point behavior.

Findings

The Riccati-like iteration converges to a fixed point.

Contraction analysis proves the convergence.

The filter maintains stability with a time-varying risk parameter.

Abstract

In this paper, we analyze the convergence of a risk sensitive like filter where the risk sensitivity parameter is time varying. Such filter has a Kalman like structure and its gain matrix is updated according to a Riccati like iteration. We show that the iteration converges to a fixed point by using the contraction analysis.