Joint State and Sparse Input Estimation in Linear Dynamical Systems

TL;DR

This paper introduces a Bayesian framework for jointly estimating states and sparse inputs in linear dynamical systems from low-dimensional measurements, outperforming existing methods in accuracy and efficiency.

Contribution

It proposes novel Bayesian and regularizer-based methods for joint state and sparse input estimation, addressing low-dimensional measurement challenges.

Findings

Outperforms state-of-the-art methods in accuracy

Reduces computational time and memory usage

Effective in low-dimensional measurement regimes

Abstract

Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we consider the problem of jointly estimating the states and sparse inputs of such systems from low-dimensional (compressive) measurements. Due to the low-dimensional measurements, conventional Kalman filtering and smoothing algorithms fail to accurately estimate the states and inputs. We present a Bayesian approach that exploits the input sparsity to significantly improve estimation accuracy. Sparsity in the input estimates is promoted by using different prior distributions on the input. We investigate two main approaches: regularizer-based MAP, and {Bayesian learning-based estimation}. We also extend the approaches to handle control inputs with common support and analyze the time and memory complexities of the presented algorithms. Finally, using numerical simulations, we show that our algorithms outperform the state-of-the-art methods in terms of accuracy and time/memory complexities, especially in the low-dimensional measurement regime.