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.