Nodes localization with inaccurate anchors via EM algorithm in wireless sensor networks

Abstract

Due to the inevitable errors introduced by means of observations and estimation algorithms, anchors' locations are usually not accurate in practical applications. This paper proposes an Expectation-Maximization (EM)-based localization algorithm with inaccurate anchors and noisy range measurements in wireless sensor networks. A circularly symmetric Gaussian distribution is used to approximate the a posteriori distribution of anchor's position uncertainty by minimizing the Kullback-Leibler (KL) divergence, building on which, we are able to derive a close-form expression of the expectation step (Estep). Then, a gradient method is followed in the maximization step (M-step) to find the solution which maximizes the E-step. Simulation results show that the EM estimator for localization can mitigate the impact of the anchors' position uncertainties and outperforms the approximated Maximum Likelihood (ML) estimator which ignores the anchors' position uncertainties.

Variational Inference-Based Positioning with Nondeterministic Measurement Accuracies and Reference Location Errors

“…Thirdly, Scenario C in TABLE 2 (where RSS, TOA and AOA measurement data are considered respectively) is simulated to compare the proposed VIP algorithm with other localization algorithms, including importance samplingbased positioning (ISP) [20], mulihop-aided particle swarm optimization (PSO)-based localization [51], weighted least square-based positioning (WLSP) [52], expectationmaximisation-based positioning (EMP) [21], second-order cone programming (SOCP) method [53], semi-definite programming (SDP)-based approach [54], adaptive simulated annealing (ASA)-assisted maximum likelihood localization [55], auxiliary variables-assisted total least square-based positioning (TLSP) [56].…”

“…In this part, the proposed VIP algorithm is compared with several existing localization methods, e.g., ISP [20], ESP [21], PSO [51], WLSP [52], SOCP [53], SDP [54], ASA [55] and TLSP [56] in Scenario C, where RSS, TOA and AOA data are considered, to demonstrate its localization accuracy.…”

“…A multitude of localization schemes have been proposed with different measurement data (e.g., node connectivity [6], multihop number [15], [16], AOA [12], TOA [8], [9], [10], [11], time difference of arrival [17], frequency difference of arrival [18], gain ratios of arrival and range differences of arrival [19]), under various constraints (e.g., the reference node location errors [20], [21] and radio wave measurement [6]) in different scenarios (e.g., underwater [22], indoor [23], outdoor [24], dynamic tracking [25] and acoustic environment [26]). For example, the reference node location error was studied in [20] and [21], where the importance sampling and expectation-maximization-based positioning methods were proposed respectively to deal with the anchor node location errors.…”

“…For example, the reference node location error was studied in [20] and [21], where the importance sampling and expectation-maximization-based positioning methods were proposed respectively to deal with the anchor node location errors. The corresponding Cramer-Rao lower bound (CRLB) was derived in [20] to quantify the impact of reference node location errors.…”

Gaussian message-based cooperative localization on factor graph in wireless sensor networks

“…Location awareness have become an essential feature in wireless sensor networks [1]- [5]. Information collected by a sensor network is usually meaningful only combined with the location, such as monitoring, tracking, logistics.…”