Abstract
This paper addresses the localization of a timing signal source based on the time of arrival (TOA) measurements that are collected from nearby sensors that are position known and synchronized to each other. Generally speaking, for such TOA-based source localization, the corresponding observation equations contain nonlinear relationship between measurements and unknown parameters, which normally results in the nonexistence of any efficient unbiased estimator that attains the Cramer-Rao lower bound (CRLB). In this paper, we devise a new approach that utilizes linearization and adopts suitable coordinate system translation to eliminate nonlinearity from the converted observation equations. The performance analysis and simulation study conducted show that our proposed algorithm can achieve the CRLB when the zero-mean Gaussian and independent measurement errors are sufficiently small.
Highlights
Wireless sensor networks have the potential to play a very important role in various location-aware applications [1], for example event/target monitoring [2, 3]. One of such applications is the monitoring of a timing signal source, where the task is to localize the source based on the time of arrival (TOA) measurements that are collected from nearby sensors that are position known and synchronized to each other [4, 5]
For such TOA-based source localization the corresponding observation equations contain nonlinear relationship between measurements and unknown parameters. Such nonlinearity normally results in the nonexistence of any efficient unbiased estimator that attains the Cramer-Rao lower bound (CRLB) [6]
In the presence of sufficiently small zero-mean Gaussian and independent measurement errors, the above m.s. localization error is lower bounded by the CRLB, which can be derived based on the probability density function of all TOA measurements given all unknowns and all sensors’ positions [5]
Summary
Wireless sensor networks have the potential to play a very important role in various location-aware applications [1], for example event/target monitoring [2, 3] One of such applications is the monitoring of a timing signal source, where the task is to localize the source based on the time of arrival (TOA) measurements that are collected from nearby sensors that are position known and synchronized to each other [4, 5]. Speaking, for such TOA-based source localization the corresponding observation equations contain nonlinear relationship between measurements and unknown parameters (i.e., the position and transmit time of the source).
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