Abstract
Performance analysis of connectivity-based geolocation in ultra-dense networks (UDNs) is a very important task. Although several performance analyses have been presented for range-free localization, determining the best achievable positioning accuracy of range-free localization remains an open problem. In this paper, we first derive the Cramer-Rao lower bound (CRLB) for the performance evaluation of range-free localization. All the current performance analyses in the literature for range-free localization are used to evaluate the real performance of a given algorithm, whereas the proposed CRLB provides a benchmark to evaluate the performance of any unbiased range-free location algorithm and determines the physical impossibility of the variance of an unbiased estimator being less than the bound. To the best of our knowledge, this is the first time in the literature that the CRLB for range-free localization has been derived. Second, the theoretical variance of centroid-based localization (CL) with an arbitrary node distribution is derived in this paper. In contrast to the existing theoretical variance of CL for uniform node distribution, the proposed theoretical variance can be used to evaluate the performance of CL in the case of an arbitrary node distribution. Additionally, characteristics of the proposed CRLB and theoretical variance are given in this paper. Finally, an optimal estimator based on a maximum likelihood estimator (MLE) is proposed to improve positioning accuracy. Since both prior information on the spatial node distribution and the connectivity property are effectively utilized in our algorithm, the proposed method performs better than the CL method and can asymptotically attain the CRLB.
Highlights
With the increasing number of networked devices, location estimation of a blind node (BN) in ultra-dense network (UDN) systems has gained considerable attention in recent years [1]
The proposed Cramer-Rao lower bound (CRLB) provides a benchmark to evaluate the performance of any unbiased range-free location algorithm, and the real performance of centroid-based localization (CL) with an arbitrary node distribution can be evaluated by the proposed theoretical variance
Theoretical analysis shows that CRLB is inversely correlated with the density of the UDN
Summary
With the increasing number of networked devices, location estimation of a blind node (BN) in ultra-dense network (UDN) systems has gained considerable attention in recent years [1]. Localization and tracking methods [27], [30], [31] that consider the connectivity information and motion model of a BN were designed for mobility-assisted WSNs. In addition to the above location schemes, some theoretical analyses for performance evaluation on range-free localization were presented in [26], [27], [31]. (3) An optimal estimator based on an MLE is proposed to improve positioning accuracy Since both the prior information on spatial node distribution and the connectivity property are effectively utilized in our algorithm, the proposed method performs better than the CL method and can asymptotically attain the CRLB.
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