Observable Degree Analysis to Match Estimation Performance for Wireless Tracking Networks

Abstract

State estimation suffers some new challenging problems when wireless sensor networks (WSNs) are used in mobile target tracking systems. An important problem among them is low observability, which makes it necessary to further study performance of tracking estimators from an observable degree point of view. This paper studies observable degree analysis (ODA) to formulate the estimator performance for a kind of wireless tracking filter. For a kind of time-varying Kalman estimator, an improved ODA method is proposed by using weighted least square, Cauchy Schwarz inequality and normalization processing. The main contributions are that the relation is firstly analytically established between the observable degree and the estimation performance, and finally the observable degree is normalized in [0,1]. Meanwhile, observable degrees are both given for local state components and the global state. Thereby, we have the conclusion that higher observable degree corresponds to better estimation performance of the Kalman filter. Accordingly, it is potentially hopeful to achieve an effective function to study estimation performance of tracking estimators by directly using the observable degree. Simulation is provided to verify the results on real-time and generality, completeness and consistency/matching of the proposed observable degree analysis.

Cramer-Rao lower bound-based observable degree analysis

“…In particular, observability is closely related to state estimation ability [2][3][4]. The indicator called observable degree (OD) has been used to quantitatively measure the degree of observability [5][6][7]. However, limited by slow progress of the observability theory, observable degree analysis (ODA) faces many difficulties in theory and applications.…”

“…In general, there are two methods through which OD can be analyzed. One is based on the observability matrix, whereas the other uses estimation error covariance, which is a performance measurement index [5][6][7]. Intuitively, the two methods should be closely related; however, the corresponding study was very incomplete.…”

“…Intuitively, the two methods should be closely related; however, the corresponding study was very incomplete. In one of our previous studies [7], we attempted to explore this issue. In particular, a novel ODA method based on an estimation performance measure (ODAEPM) was presented.…”

“…Afterwards, the relation between the observable degree and the performance index of the KF is clearly disclosed. However, the following shortcomings still remain [7]:…”

“…Motivated by these limitations, in this study, we try to extend the result without process noise in [7] by using the Cramer-Rao lower bound (CRLB), which is a basic concept a strong tool in state estimation; it is generally used to measure the availability of the unbiased estimator [8,9]. The main contribution of this study is to demonstrate the consistency between the ODA in [7] and the CRLB theory by obtaining the relation between the Fisher information matrix and the OD's discriminant matrix. Namely, this study shows that there is a natural relation between the two approaches.…”