Connectivity-Based Localization in Ultra-Dense Networks: CRLB, Theoretical Variance, and MLE

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. INDEX TERMS Connectivity-based localization, Cramer-Rao lower bound (CRLB), theoretical variance, maximum likelihood estimator (MLE), centroid-based localization (CL).

Mobile Location in Wireless Sensor Networks Based on Multi Spot Measurements Model

“…Many localization methods are presented in the literature [ 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ]. There are two ways to locate a sensor in WSNs: (1) range-based and (2) range-free methods.…”

“…Compared with those on range-based techniques, relatively fewer studies [ 26 , 27 , 28 , 29 , 30 , 31 , 32 ] have been reported for range-free location techniques. Among range-free methods, Centroid-based localization (CL) is the most famous; it functions by determining the BN’s position as the centroid of RNs.…”

“…Although many studies are reported for both range-based and range-free location methods [ 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 ], they are all based on a one-spot measurement model, as shown in Figure 1 . Since the existing location methods have been widely studied, it is difficult to improve their positioning accuracy further.…”

Determination of CRLB and Minimum Variance Unbiased Estimator of a DC Signal in AWGN Using Laplace Transform

“…This lower bound can easily help select the best estimator for a given problem in hand based on the minimum variance it can attain. On the other language, the bound tells how best one can achieve during a given estimation problem (Alslaimy and Smith, 2019;Huang et al, 2020;Hung et al, 2020;Kay, 1993;Khorasani et al, 2020;Li et al, 2021;Mao et al, 2020;Tian et al, 2020).…”

Determination of Cramer-Rao Lower Bound (CRLB) and Minimum Variance Unbiased Estimator of a DC Signal in AWGN Using Laplace Transform

“…This lower bound can easily help select the best estimator for a given problem in hand based on the minimum variance it can attain. On the other language, the bound tells how best one can achieve during a given estimation problem (Alslaimy and Smith 2019, Huang et al 2020, Hung et al 2020, Kay 1993, Khorasani et al 2020, Li et al 2021, Mao et al 2020, Tian et al 2020.…”