Joint State and Input Estimation of Agent Based on Recursive Kalman Filter Given Prior Knowledge

TL;DR

This paper presents a unified recursive Kalman filter approach for joint state and input estimation in autonomous systems, incorporating prior knowledge to improve accuracy and decision-making under noise and disturbances.

Contribution

It introduces a combined continuous and discrete input estimation framework using the EM algorithm with prior knowledge constraints, enhancing estimation accuracy and robustness.

Findings

81% variance reduction over KF in continuous space

47% variance reduction over RKF in continuous space

Significant improvement in decision-making accuracy in discrete space

Abstract

Modern autonomous systems are purposed for many challenging scenarios, where agents will face unexpected events and complicated tasks. The presence of disturbance noise with control command and unknown inputs can negatively impact robot performance. Previous research of joint input and state estimation separately studied the continuous and discrete cases without any prior information. This paper combines the continuous and discrete input cases into a unified theory based on the Expectation-Maximum (EM) algorithm. By introducing prior knowledge of events as the constraint, inequality optimization problems are formulated to determine a gain matrix or dynamic weights to realize an optimal input estimation with lower variance and more accurate decision-making. Finally, statistical results from experiments show that our algorithm owns 81\% improvement of the variance than KF and 47\% improvement than RKF in continuous space; a remarkable improvement of right decision-making probability of our input estimator in discrete space, identification ability is also analyzed by experiments.