Simultaneous Mode, Input and State Estimation for Switched Linear Stochastic Systems

TL;DR

This paper introduces a filtering algorithm for simultaneously estimating the mode, input, and state of switched linear stochastic systems, using a multiple-model approach and a generalized innovation property, with proven convergence conditions.

Contribution

The paper presents a novel multiple-model filtering algorithm that estimates mode, input, and state simultaneously in switched linear stochastic systems, with theoretical convergence guarantees.

Findings

Algorithm accurately estimates mode, input, and state in simulations.

Generalized innovation is shown to be Gaussian white noise.

Convergence conditions are established for the proposed method.

Abstract

In this paper, we propose a filtering algorithm for simultaneously estimating the mode, input and state of hidden mode switched linear stochastic systems with unknown inputs. Using a multiple-model approach with a bank of linear input and state filters for each mode, our algorithm relies on the ability to find the most probable model as a mode estimate, which we show is possible with input and state filters by identifying a key property, that a particular residual signal we call generalized innovation is a Gaussian white noise. We also provide an asymptotic analysis for the proposed algorithm and provide sufficient conditions for asymptotically achieving convergence to the true model (consistency), or to the 'closest' model according to an information-theoretic measure (convergence). A simulation example of intention-aware vehicles at an intersection is given to demonstrate the effectiveness of our approach.