Abstract
Censored measurements frequently occur in network systems involving censored sensors or saturated sensors. In addition, unreliable network characteristics can produce random measurement delays during signal transmission. In this paper, we investigate the state estimation problem for network systems with the simultaneous appearance of the aforementioned two measurement uncertainties. The occurrences of two random measurement phenomena are described by two Bernoulli random variables in which the censored variable is dependent on the delay variable. The probability of the process signal being uncensored is calculated by the local approximations using a priori and a posteriori of the state estimation. Then, a novel measurement model that incorporates both the censoring random matrix and the signal delay is established. Based on this model, an optimal recursive estimation method is proposed for systems with specified two uncertainties by making use of an innovation analysis approach and a weighted conditional expectation formula. The superior performance of our proposed method is verified through a typical oscillator simulation example.
Highlights
In the last few decades, the problem of state estimation for discrete-time linear systems has been extensively studied by researchers owing to its important applications in various fields such as target tracking, navigation and parameter estimation [1]–[10]
Censoring has the form of a piecewise linear transform, with a zero slope in the censored region, causing significant challenges to the general nonlinear estimators, such as the unscented Kalman filter (UKF) and extended Kalman filter (EKF) [19]
The measurement noise is non-Gaussian near the censoring region, a novel Tobit Kalman filter (TKF) was developed based on the formulation of the Kalman filter [20], which was a computationally efficient, unbiased recursive estimator for this special dynamic system with censored measurements
Summary
In the last few decades, the problem of state estimation for discrete-time linear systems has been extensively studied by researchers owing to its important applications in various fields such as target tracking, navigation and parameter estimation [1]–[10]. Tobit measurement censoring is a common uncertainty that occurs in many engineering applications such as i) biochemical measurements with limit-of-detection saturation, ii)inexpensive sensors with saturation censoring, and iii) lineof-sight tracking with occlusion. Tobit censoring is referred to as clipped measurement or limit-of-detection. Censoring has the form of a piecewise linear transform, with a zero slope in the censored region, causing significant challenges to the general nonlinear estimators, such as the unscented Kalman filter (UKF) and extended Kalman filter (EKF) [19]. The measurement noise is non-Gaussian near the censoring region, a novel Tobit Kalman filter (TKF) was developed based on the formulation of the Kalman filter [20], which was a computationally efficient, unbiased recursive estimator for this special dynamic system with censored measurements. In the literature [19], it was shown that the TKF has more accurate state estimates and state error covariance with censored measurement data, while both EKF and UKF provide unreliable estimates in censored data conditions
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