An Online Exploratory Maximum Likelihood Estimation Approach to Adaptive Kalman Filtering | IEEE Journals & Magazine | IEEE Xplore

An Online Exploratory Maximum Likelihood Estimation Approach to Adaptive Kalman Filtering


Abstract:

Over the past few decades, numerous adaptive Kalman filters (AKFs) have been proposed. However, achieving online estimation with both high estimation accuracy and fast co...Show More

Abstract:

Over the past few decades, numerous adaptive Kalman filters (AKFs) have been proposed. However, achieving online estimation with both high estimation accuracy and fast convergence speed is challenging, especially when both the process noise and measurement noise covariance matrices are relatively inaccurate. Maximum likelihood estimation (MLE) possesses the potential to achieve this goal, since its theoretical accuracy is guaranteed by asymptotic optimality and the convergence speed is fast due to weak dependence on accurate state estimation. Unfortunately, the maximum likelihood cost function is so intricate that the existing MLE methods can only simply ignore all historical measurement information to achieve online estimation, which cannot adequately realize the potential of MLE. In order to design online MLE-based AKFs with high estimation accuracy and fast convergence speed, an online exploratory MLE approach is proposed, based on which a mini-batch coordinate descent noise covariance matrix estimation framework is developed. In this framework, the maximum likelihood cost function is simplified for online estimation with fewer and simpler terms which are selected in a mini-batch and calculated with a backtracking method. This maximum likelihood cost function is sidestepped and solved by exploring possible estimated noise covariance matrices adaptively while the historical measurement information is adequately utilized. Furthermore, four specific algorithms are derived under this framework to meet different practical requirements in terms of convergence speed, estimation accuracy, and calculation load. Abundant simulations and experiments are carried out to verify the validity and superiority of the proposed algorithms as compared with existing state-of-the-art AKFs.
Published in: IEEE/CAA Journal of Automatica Sinica ( Volume: 12, Issue: 1, January 2025)
Page(s): 228 - 254
Date of Publication: 24 December 2024

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I. Introduction

The Kalman filter (KF) [1] has been well-known for its ability to achieve optimal state estimation under linear Gaussian conditions [2], and it has been widely used in numerous fields such as target tracking [3], navigation positioning [4], [5], human-robot interaction [6], data service [7], [8], and industrial robot calibration [9], [10]. The performance of the KF depends largely on the setting accuracy of noise covariance matrices (NCMs), and the inaccurate selections of the process noise covariance matrix (PNCM) and measurement noise covariance matrix (MNCM) will signifi-cantly reduce state estimation accuracy or even lead to filtering divergence [11]. Unfortunately, it is difficult to obtain accurate NCMs in many practical application scenarios. For example, in a swarm robotic system, the presence of numerous sensors renders the precise acquisitions of all NCMs a cumbersome and intricate endeavor [12]. Motivated by this problem, several AKFs have been proposed, which aim to estimate unknown/inaccurate NCMs adaptively for improving state estimation accuracy. Such AKFs based on online estimation of NCMs are favored in extensive real-time tasks due to their advantages of feeding back real-time measurements into the filters. This paper therefore focuses on proposing an improved online estimation framework for NCMs, from which some novel AKFs will be developed.

References

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