In this paper, we investigate the performance of positioning algorithms in wireless cellular networks based on time difference of arrival (TDoA) measurements provided by the base stations. The localization process of the mobile station results in a non-linear least squares estimation problem which cannot be solved analytically. Therefore, we use iterative algorithms to determine an estimate of the mobile station position. The well-known Gauss-Newton method fails to converge for certain geometric constellations, and thus, it is not suitable for a general solution in cellular networks. Another algorithm is the steepest descent method which has a slow convergence in the final iteration steps. Hence, we apply the Levenberg-Marquardt algorithm as a new approach in the cellular network localization framework. We show that this method meets the best trade-off between accuracy and computational complexity
"Given the range-difference measurements, various methods have been proposed in the literature to compute a location estimate. Iterative methods—such as Taylor series expansion , Gauss-Newton, steepest descent, or Levenberg-Marquardt algorithm —require an accurate initial position estimate (which is often not available) and are computationally expensive. Therefore, closed-form solutions (based, for instance, on the least squares principle) have been proposed , including the spherical intersection and interpolation methods  and the approximate maximum likelihood and two-stage maximum likelihood (TSML) methods  . "
[Show abstract][Hide abstract] ABSTRACT: In this paper, we consider the problem of locating a target node (TN) moving along a corridor in a large industrial environment by means of ultrawide band signaling from fixed anchor nodes (ANs) uniformly positioned at the same height on both sides of the corridor. For a representative geometry of a large indoor (industrial) scenario, we formulate an analytical approach to the optimized placement (in terms of internode distance) of ANs using the criterion of minimizing the average mean square error (MSE) in the time-difference-of-arrival-based estimated positions of the TN. Under the assumption of a fixed variance of the range estimation error, we derive a simple closed-form expression for the optimal inter-AN distance in terms of the corridor width and the height of the ANs. The effectiveness of the analytical approach is confirmed by simulations. We also show that the proposed approach allows the MSE in the TN position estimates to reach the Cramer Rao lower bound.
IEEE Transactions on Aerospace and Electronic Systems 04/2015; 51(2):987-999. DOI:10.1109/TAES.2014.130722 · 1.76 Impact Factor
"In this work, we investigate self-localization in UWB networks. Among the wide variety of location estimation techniques which have been proposed in the literature, it is worth recalling iterative methods, such as those based on Taylor series expansion  or the steepest-descent algorithm , graph-based methods , or methods based on metaheuristics . To overcome some limitations of these methods, closed-form algorithms have been studied, such as the plane intersection (PI) method  and the Two-stage maximum-likelihood (TSML) method . "
[Show abstract][Hide abstract] ABSTRACT: In this paper, we address the problem of localizing sensor nodes in a static network, given that the positions of a few of them (denoted as “beacons“) are a priori known. We refer to this problem as “auto-localization.” Three localization techniques are considered: the two-stage maximum-likelihood (TSML) method; the plane intersection (PI) method; and the particle swarm optimization (PSO) algorithm. While the first two techniques come from the communication-theoretic “world,” the last one comes from the soft computing “world.” The performance of the considered localization techniques is investigated, in a comparative way, taking into account (i) the number of beacons and (ii) the distances between beacons and nodes. Since our simulation results show that a PSO-based approach allows obtaining more accurate position estimates, in the second part of the paper we focus on this technique proposing a novel hybrid version of the PSO algorithm with improved performance. In particular, we investigate, for various population sizes, the number of iterations which are needed to achieve a given error tolerance. According to our simulation results, the hybrid PSO algorithm guarantees faster convergence at a reduced computational complexity, making it attractive for dynamic localization. In more general terms, our results show that the application of soft computing techniques to communication-theoretic problems leads to interesting research perspectives.
"Besides the FP method, to achieve higher accuracy in localization of mobile nodes, many conventional iterative methods like Gauss-Newton, Steepest Descent, Levenberg-Marquardt have been proposed in conjunction with TOA or TDOA methods for mitigating NLOS errors. Among them, the Steepest Descent algorithm shows the slowest convergence in the final iteration steps, but for maintaining higher accuracy and low complexity the Levenberg-Marquardt method is the most suitable one to estimate a node location among the iterative methods . Moreover, these iterative methods require initial positioning guesses. "
[Show abstract][Hide abstract] ABSTRACT: Recently, Impulse Radio Ultra Wideband (IR-UWB) signaling has become popular for providing precise location accuracy for mobile and wireless sensor node localization in the indoor environment due to its large bandwidth and high time resolution while providing ultra-high transmission capacity. However, the Non-line-of-sight (NLOS) error mitigation has considerable importance in localization of wireless nodes. In order to mitigate NLOS errors in indoor localization this paper proposes and investigates a novel approach which creates a hybrid combination of channel impulse response (CIR)-based fingerprinting (FP) positioning and an iterative Time of Arrival (TOA) real time positioning method using Ultra Wideband (UWB) signaling. Besides, to reduce the calculation complexities in FP method, this paper also introduces a unique idea for the arrangement of reference nodes (or tags) to create a fingerprinting database. The simulation results confirm that the proposed hybrid method yields better positioning accuracies and is much more robust in NLOS error mitigation than TOA only and FP only and a conventional iterative positioning method.
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