A Novel Adaptive Kalman Filter With Inaccurate Process and Measurement Noise Covariance Matrices

Yulong Huang,Yonggang Zhang,Ning Li,Jonathon Chambers,Zhemin Wu

doi:10.1109/tac.2017.2730480

Abstract

In this paper, a novel variational Bayesian (VB)-based adaptive Kalman filter (VBAKF) for linear Gaussian state-space models with inaccurate process and measurement noise covariance matrices is proposed. By choosing inverse Wishart priors, the state together with the predicted error and measurement noise covariance matrices are inferred based on the VB approach. Simulation results for a target tracking example illustrate that the proposed VBAKF has better robustness to resist the uncertainties of process and measurement noise covariance matrices than existing state-of-the-art filters.

Highlights

T HE Kalman filter is an optimal state estimator for linear Gaussian state-space models, and it has been widely used in many applications, such as navigation, target tracking and control
The Sage-Husa adaptive Kalman filter (AKF) (SHAKF) is a covariance matching method, which estimates the noise statistics recursively based on the maximum a posterior criterion [5], [6]
The convergence to the right noise covariance matrices is not guaranteed with SHAKF, which may lead to filtering divergence [1]

Summary

Introduction

T HE Kalman filter is an optimal state estimator for linear Gaussian state-space models, and it has been widely used in many applications, such as navigation, target tracking and control. In many applications, such as Global Positioning System (GPS) and Inertial Navigation System (INS) based integrated navigation systems, their noise statistics may be unknown and time-varying [2], [3], [4]. The Sage-Husa AKF (SHAKF) is a covariance matching method, which estimates the noise statistics recursively based on the maximum a posterior criterion [5], [6]. The convergence to the right noise covariance matrices is not guaranteed with SHAKF, which may lead to filtering divergence [1]. The Innovation-based AKF (IAKF) is a maximum likelihood method, which estimates the noise covariance matrices based on the fact that the innovation sequence of the Kalman filter is a white process [2].

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Results

Conclusion