Abstract
Strong tracking filtering (STF) is a popular adaptive estimation method to effectively deal with state estimation for linear and nonlinear dynamic systems with inaccurate models or sudden change of state. The key of the STF is to use a time-variant fading factor, which can be evaluated based on the current measurement innovation in real time, to forcefully correct one step state prediction error covariance. The strong tracking filtering technology has been extensively applied in many practical systems, but the theoretical analysis is highly lacking. In an effort to better understand STF, a novel analysis framework is developed for the strong tracking filtering and some new problems are discussed for the first time. For this, we propose a new perspective that correcting the state prediction error covariance by using the fading factor can be thought of directly modifying the state model by correcting the covariance of the process noise. Based on this proposed point of view, the conditions for the STF function to be effective are deeply analyzed in a certain linear dynamic system. Meanwhile, issues of false alarm and alarm failure are also briefly discussed for the strong tracking filtering function. Some numerical simulation examples are demonstrated to validate the results.
Highlights
State estimation is an important topic in many fields such as signal processing, target tracking, information fusion, and fault diagnosis [1,2,3]
The Kalman filter (KF) presented by Kalman (1960) is a strong and popular tool to estimate system state for linear systems and it is optimal in the sense of linear minimum mean square error (LMMSE) when the parameters of estimation models are accurate [4, 5]
Aiming at this problem mentioned above, a strong tracking filter (STF) was firstly presented in fault diagnosis field to deal with nonlinear state estimation with inaccurate models and the original purpose is only to overcome the shortcomings existing in the extended Kalman filter (EKF) for nonlinear systems [6,7,8,9]
Summary
State estimation is an important topic in many fields such as signal processing, target tracking, information fusion, and fault diagnosis [1,2,3]. As a result of the linearization, the models used in the EKF algorithm mismatch the practical ones, which deteriorates the estimation and convergence performance of the EKF To resolve this issue, the strong tracking filter, which is one of the adaptive filters, uses a time-variant fading factor based on the current measurement innovation to adjust dynamically the prediction error covariance matrix. It is necessary to discuss condition under which the strong tracking filtering function is activated and analyze range of its effectiveness It is an interesting and innovative issue to perfect the strong tracking filtering theory. It should be noted that the linear dynamic system is considered for simplicity in this paper In this view, the effect of the strong tracking fading factor is equivalently thought to modify the state model (or the covariance of process noise) in real time based on the current measurement innovation. The analysis process and some discussions on the condition of the active strong tracking function are presented to explain our view and some numerical simulation examples are demonstrated to validate the results presented in this paper
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