Joint synchronization and localization using TOAs: A linearization based WLS solution
01 Sep 2010-IEEE Journal on Selected Areas in Communications (Newcastle University)-Vol. 28, Iss: 7, pp 1016-1025
TL;DR: A low-complexity algorithm is proposed, which is based on the linearized equations from TOA measurements and applies a weighted least square (WLS) criterion in a computationally efficient way to closely approach the LS solution in estimation performance.
Abstract: Joint synchronization and localization using time of arrival (TOA) measurements is a very important research topic for many wireless ad hoc sensor network applications. For such TOA based joint synchronization and localization, the least square (LS) criterion and its corresponding solution have been shown to exhibit optimum estimation performance but generally at a very high computational complexity. Due to its importance and difficulty, in this paper we consider the issue how to approach the estimation performance of such LS solution at low computational complexity: We propose a low-complexity algorithm, which is based on the linearized equations from TOA measurements and applies a weighted least square (WLS) criterion in a computationally efficient way to closely approach the LS solution in estimation performance; Via analyzing and simulating its estimation performance we evidently demonstrate the proposed algorithm of its superior trade-off between estimation performance and computational complexity. The proposed algorithm is also applicable to similar application areas involving TOA base joint timing and positioning.
Citations
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TL;DR: This paper proposes robust time-based localization strategies to locate a target node with the help of anchors (nodes with known positions) in asynchronous networks, and counter the uncertainties caused by the target node by ignoring the timestamps from this node.
Abstract: Time-based localization approaches attract a lot of interest due to their high accuracy and potentially low cost for wireless sensor networks (WSNs). However, time-based localization is tightly coupled with clock synchronization. Thus, the reliability of timestamps in time-based localization becomes an important yet challenging task to deal with. In this paper, we propose robust time-based localization strategies to locate a target node with the help of anchors (nodes with known positions) in asynchronous networks. Two kinds of asynchronous networks are considered: one only with clock offsets, labeled quasi-synchronous networks, whereas the other with not only clock offsets but also clock skews, labeled fully asynchronous networks. A novel ranging protocol is developed for both networks, namely asymmetric trip ranging (ATR), to reduce the communication load and explore the broadcast property of WSNs. Regardless of the reliability of the timestamp report from the target node, closed-form least-squares (LS) estimators are derived to accurately estimate the target node position. As a result, we counter the uncertainties caused by the target node by ignoring the timestamps from this node. Furthermore, in order to simplify the estimator in fully asynchronous networks, localization and synchronization are decoupled. A simple yet efficient method is proposed to first Calibrate the Clock Skews of the anchors, and then Estimate the Node Position (CCS-ENP). Finally, Cramer-Rao bounds (CRBs) and simulation results corroborate the efficiency of our localization schemes.
109 citations
TL;DR: A state dimension reduction method is proposed to overcome the particle degeneracy problem of particle filter which is used to fusion GNSS and 5G D2D measurements and shows that the proposed integrated methodology outperforms the nonintegrated one.
Abstract: Global navigation satellite system (GNSS) is not suitable for the dense urban or indoor environments as the satellite signals are very weak. Meanwhile, positioning is an important application of the fifth-generation (5G) communication system. GNSS/5G integrated positioning system becomes a promising research topic with the development of 5G standard. This paper focuses on the integrated methodology of GNSS and device to device (D2D) measurements in 5G communication system. We analyze the characteristics of this type of integrated system and propose a high-efficiency D2D positioning measure protocol, named crossover multiple-way ranging, which consumes less communication resources. Then, to deal with the high-dimensional state space in the integrated system, a state dimension reduction method is proposed to overcome the particle degeneracy problem of particle filter which is used to fusion GNSS and 5G D2D measurements. Three integrated algorithms in different scenarios have been proposed: the first one is the integrated algorithm when the range measurements can be measured directly. The second one is the integrated algorithm with unknown time skew and offset of each mobile terminal. The third one is the integrated algorithm in GNSS-denied environment which is prevalent in urban and indoor applications. The simulation and experimental results show that our proposed integrated methodology outperforms the nonintegrated one.
65 citations
Cites methods from "Joint synchronization and localizat..."
...Unlike using either a least squares based estimator or a factor graph to find the position and time uncertainties [25], [26], we use an orthogonal projection operator...
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...A joint time synchronization and localization method was proposed in [25] which considers the synchronization problem and positioning problem in a unique framework....
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TL;DR: In this article, the authors presented a factor graph representation of the joint localization and time synchronization problem based on TOA measurements, in which the non-line-of-sight measurements are also taken into consideration.
Abstract: Localization and synchronization are very important in many wireless applications such as monitoring and vehicle tracking. Utilizing the same time of arrival (TOA) measurements for simultaneous localization and synchronization is challenging. In this paper, we present a factor graph (FG) representation of the joint localization and time synchronization problem based on TOA measurements, in which the non-line-of-sight measurements are also taken into consideration. On this FG, belief propagation (BP) message passing and variational message passing (VMP) are applied to derive two fully distributed cooperative algorithms with low computational requirements. Due to the nonlinearity in the observation function, it is intractable to compute the messages in closed form and most existing solutions rely on Monte Carlo methods, e.g., particle filtering. We linearize a specific nonlinear term in the expressions of messages, which enables us to use a Gaussian representation for all messages. Accordingly, only the mean and variance have to be updated and transmitted between neighboring nodes, which significantly reduces the communication overhead and computational complexity. A message passing schedule scheme is proposed to trade off between estimation performance and communication overhead. Simulation results show that the proposed algorithms perform very close to particle-based methods with much lower complexity especially in densely connected networks.
64 citations
TL;DR: This work develops a distributed (decentralized) belief propagation algorithm for CoSLAS in the practically important case of an affine clock model and asymmetric time stamping and combines particle implementations with parametric message representations and takes advantage of a conditional independence property.
Abstract: Cooperative localization in agent networks based on interagent time-of-flight measurements is closely related to synchronization. To leverage this relation, we propose a Bayesian factor graph framework for cooperative simultaneous localization and synchronization (CoSLAS). This framework is suited to mobile agents and time-varying local clock parameters. Building on the CoSLAS factor graph, we develop a distributed (decentralized) belief propagation algorithm for CoSLAS in the practically important case of an affine clock model and asymmetric time stamping. Our algorithm is compatible with real-time operation and a time-varying network connectivity. To achieve high accuracy at reduced complexity and communication cost, the algorithm combines particle implementations with parametric message representations and takes advantage of a conditional independence property. Simulation results demonstrate the good performance of the proposed algorithm in a challenging scenario with time-varying network connectivity.
64 citations
Cites background from "Joint synchronization and localizat..."
...Estimation of static clock and location parameter s is considered (i) for a single agent in [6]–[9], (ii) for multip le agents with centralized computation in [10]–[12], and (iii ) for multiple agents with distributed computation in [12]–[16] ....
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References
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TL;DR: Using the models, the authors have shown the calculation of a Cramer-Rao bound (CRB) on the location estimation precision possible for a given set of measurements in wireless sensor networks.
Abstract: Accurate and low-cost sensor localization is a critical requirement for the deployment of wireless sensor networks in a wide variety of applications. In cooperative localization, sensors work together in a peer-to-peer manner to make measurements and then forms a map of the network. Various application requirements influence the design of sensor localization systems. In this article, the authors describe the measurement-based statistical models useful to describe time-of-arrival (TOA), angle-of-arrival (AOA), and received-signal-strength (RSS) measurements in wireless sensor networks. Wideband and ultra-wideband (UWB) measurements, and RF and acoustic media are also discussed. Using the models, the authors have shown the calculation of a Cramer-Rao bound (CRB) on the location estimation precision possible for a given set of measurements. The article briefly surveys a large and growing body of sensor localization algorithms. This article is intended to emphasize the basic statistical signal processing background necessary to understand the state-of-the-art and to make progress in the new and largely open areas of sensor network localization research.
3,080 citations
"Joint synchronization and localizat..." refers background in this paper
...INTRODUCTION MANY wireless ad hoc sensor network applications request the involved sensors to be synchronized and localized with respect to each other, sensor synchronization and localization thus attract more and more attentions recently [1]....
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TL;DR: An effective technique in locating a source based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors is proposed and is shown to attain the Cramer-Rao lower bound near the small error region.
Abstract: An effective technique in locating a source based on intersections of hyperbolic curves defined by the time differences of arrival of a signal received at a number of sensors is proposed. The approach is noniterative and gives an explicit solution. It is an approximate realization of the maximum-likelihood estimator and is shown to attain the Cramer-Rao lower bound near the small error region. Comparisons of performance with existing techniques of beamformer, spherical-interpolation, divide and conquer, and iterative Taylor-series methods are made. The proposed technique performs significantly better than spherical-interpolation, and has a higher noise threshold than divide and conquer before performance breaks away from the Cramer-Rao lower bound. It provides an explicit solution form that is not available in the beamforming and Taylor-series methods. Computational complexity is comparable to spherical-interpolation but substantially less than the Taylor-series method. >
2,202 citations
"Joint synchronization and localizat..." refers methods in this paper
...For TOA based joint synchronization and localization three linearization based algorithms with closed form solutions are straightforward directly from the counterparts for the TDOA or TOA based localization, see [5][10] and the references therein: One algorithm is achieved by regarding the linearizationcaused extra variable as a totally irrelevant variable, i....
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TL;DR: Three noniterative techniques are presented for localizing a single source given a set of noisy range-difference measurements, and in one case the maximum likelihood bearing estimate is approached.
Abstract: Three noniterative techniques are presented for localizing a single source given a set of noisy range-difference measurements. The localization formulas are derived from linear least-squares "equation error" minimization, and in one case the maximum likelihood bearing estimate is approached. Geometric interpretations of the equation error norms minimized by the three methods are given, and the statistical performances of the three methods are compared via computer simulation.
724 citations
"Joint synchronization and localizat..." refers background in this paper
...However, so far Bancroft’s algorithm has not yet been explored to its potential: It has not yet been extended to the case with more anchors as well as noisy TOA measurements, although there are a few extensions in literature to the time difference of arrival (TDOA) or TOA based positioning [3][12]....
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TL;DR: It is shown that the CWLS estimator yields better performance than the LS method and achieves both the Crame/spl acute/r-Rao lower bound and the optimal circular error probability at sufficiently high signal-to-noise ratio conditions.
Abstract: Localization of mobile phones is of considerable interest in wireless communications. In this correspondence, two algorithms are developed for accurate mobile location using the time-of-arrival measurements of the signal from the mobile station received at three or more base stations. The first algorithm is an unconstrained least squares (LS) estimator that has implementation simplicity. The second algorithm solves a nonconvex constrained weighted least squares (CWLS) problem for improving estimation accuracy. It is shown that the CWLS estimator yields better performance than the LS method and achieves both the Crame/spl acute/r-Rao lower bound and the optimal circular error probability at sufficiently high signal-to-noise ratio conditions.
531 citations
TL;DR: In this paper, it is shown that if the additional information is the navigator altitude, or the range difference to a fourth station, the computation of the navigation fix is reduced to finding the roots of a quadratic.
Abstract: Navigation fixed from range differences to three stations and an additional piece of information are investigated. It is shown that if the additional information is the navigator altitude, or the range difference to a fourth station, the computation of the navigation fix is reduced to finding the roots of a quadratic. If the additional information is the range to another station, or that the navigator is on the Earth ellipsoid, the fix can be obtained by solving a quartic. By emphasizing the underlying geometric interpretations, these fixes and their simple solutions are made clear. The derivations also show that the same solution algorithms are applicable if the basic navigation measurements are range sums instead of range differences. >
477 citations