Source Localization: Algorithms and Analysis
01 Jan 2012-pp 25-66
TL;DR: This chapter contains sections titled: Introduction Measurement Models and Principles for source Localization Algorithms for Source Localization Performance Analysis for LocalizationAlgorithms and Conclusion.
Abstract: Time of arrival (TOA), time difference of arrival (TDOA), time sum of arrival (TSOA), received signal strength (RSS), and direction of arrival (DOA) of the emitted signal are commonly used measurements for source localization. This chapter introduces two categories of positioning algorithms based on TOA, TDOA, TSOA, RSS, and DOA measurements. The first category works on the nonlinear equations directly obtained from the nonlinear relationships between the source and measurements. Corresponding examples, namely, nonlinear least squares (NLS) and maximum likelihood (ML) estimators, are presented. The second category attempts to convert the equations to linear. The chapter discusses the linear least squares, weighted linear least squares (WLLS), and subspace approaches. It develops the mean and variance expressions for any positioning method which can be formulated as an unconstrained optimization problem. The Cramer‐Rao lower bound (CRLB), which is a lower bound on the variance attainable by any unbiased location estimator using the same data, is also discussed.
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TL;DR: Improved methods for estimating the time-of-arrival of transmissions at receivers and transmitter location estimation algorithms may be applied across a range of applications and technologies such as radar, sonar, the Global positioning system, wireless sensor networks, underwater animal tracking, mobile communications, and multimedia.
Abstract: Locating the position of fixed or mobile sources (i.e., transmitters) based on measurements obtained from sensors (i.e., receivers) is an important research area that is attracting much interest. In this paper, we review several representative localization algorithms that use time of arrivals (TOAs) and time difference of arrivals (TDOAs) to achieve high signal source position estimation accuracy when a transmitter is in the line-of-sight of a receiver. Circular (TOA) and hyperbolic (TDOA) position estimation approaches both use nonlinear equations that relate the known locations of receivers and unknown locations of transmitters. Estimation of the location of transmitters using the standard nonlinear equations may not be very accurate because of receiver location errors, receiver measurement errors, and computational efficiency challenges that result in high computational burdens. Least squares and maximum likelihood based algorithms have become the most popular computational approaches to transmitter location estimation. In this paper, we summarize the computational characteristics and position estimation accuracies of various positioning algorithms. By improving methods for estimating the time-of-arrival of transmissions at receivers and transmitter location estimation algorithms, transmitter location estimation may be applied across a range of applications and technologies such as radar, sonar, the Global Positioning System, wireless sensor networks, underwater animal tracking, mobile communications, and multimedia.
123 citations
TL;DR: Numerical results verify that the ℓp-MUSIC methodology outperforms the standard MUSIC scheme and several existing outlier-resistant DOA estimation approaches in terms of resolution capability and estimation accuracy.
Abstract: A family of algorithms, named lp-MUSIC, for direction-of-arrival (DOA) estimation in impulsive noise is proposed. The lp-MUSIC estimator adopts the lp-norm (1 ≤ p 2) of the residual fitting error matrix as the objective function for subspace decomposition, rather than the Frobenius norm that is used in the conventional MUSIC method. Although the matrix lp-norm minimization based subspace decomposition will lead to a nonconvex optimization problem, two iterative algorithms are designed for achieving efficient solutions. The first algorithm is the iteratively reweighted singular value decomposition (IR-SVD), where the SVD of a reweighted data matrix is performed in each iteration. The second algorithm solves the nonconvex matrix lp-norm minimization by alternating convex optimization. Two complex-valued Newton's methods with optimal step size in each iteration are devised to solve the resulting convex problem. The convergence of the iterative procedure is also proved. Numerical results verify that the lp-MUSIC methodology outperforms the standard MUSIC scheme and several existing outlier-resistant DOA estimation approaches in terms of resolution capability and estimation accuracy.
121 citations
Cites background from "Source Localization: Algorithms and..."
...D IRECTION-OF-ARRIVAL (DOA) estimation of multiple emitting sources is an important issue in array processing and has various applications in radar, sonar, wireless communications and source localization [1]–[3]....
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TL;DR: A new CWLS estimator is proposed to separate the source coordinates and the additional variable to different sides of the linear equations where the latter is first solved via a quadratic equation.
99 citations
Cites background from "Source Localization: Algorithms and..."
...Time-difference-of-arrival (TDOA), which is the difference in arrival times between signals received at spatially separated receivers, is one of the commonly used measurements for source localization [4]....
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TL;DR: An overview of the emerging field of massive MIMO localization is provided, which can be used to meet the requirements of 5G, by exploiting different spatial signatures of users.
97 citations
Cites background from "Source Localization: Algorithms and..."
...time-difference-of-arrival (TDOA) and angle-of-arrival (AOA) of the emitted signal [1, 2]....
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TL;DR: A quadratically constrained quadratic program (QCQP) for target localization is formulated and is proved to be an unbiased position estimate whose variance equals the Cramer-Rao lower bound.
97 citations
References
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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
TL;DR: In this article, a derivation of the principal algorithms and an analysis of the performance of the two most important passive location systems for stationary transmitters, hyperbolic location systems and directionfinding location systems, are presented.
Abstract: A derivation of the principal algorithms and an analysis of the performance of the two most important passive location systems for stationary transmitters, hyperbolic location systems and directionfinding location systems, are presented. The concentration ellipse, the circular error probability, and the geometric dilution of precision are defined and related to the location-system and received-signal characteristics. Doppler and other passive location systems are briefly discussed.
1,208 citations
16 Mar 2009
TL;DR: This paper describes several cooperative localization algorithms and quantify their performance, based on realistic UWB ranging models developed through an extensive measurement campaign using FCC-compliant UWB radios, and presents a powerful localization algorithm that is fully distributed, can cope with a wide variety of scenarios, and requires little communication overhead.
Abstract: Location-aware technologies will revolutionize many aspects of commercial, public service, and military sectors, and are expected to spawn numerous unforeseen applications. A new era of highly accurate ubiquitous location-awareness is on the horizon, enabled by a paradigm of cooperation between nodes. In this paper, we give an overview of cooperative localization approaches and apply them to ultrawide bandwidth (UWB) wireless networks. UWB transmission technology is particularly attractive for short- to medium-range localization, especially in GPS-denied environments: wide transmission bandwidths enable robust communication in dense multipath scenarios, and the ability to resolve subnanosecond delays results in centimeter-level distance resolution. We will describe several cooperative localization algorithms and quantify their performance, based on realistic UWB ranging models developed through an extensive measurement campaign using FCC-compliant UWB radios. We will also present a powerful localization algorithm by mapping a graphical model for statistical inference onto the network topology, which results in a net-factor graph, and by developing a suitable net-message passing schedule. The resulting algorithm (SPAWN) is fully distributed, can cope with a wide variety of scenarios, and requires little communication overhead to achieve accurate and robust localization.
1,028 citations
TL;DR: The proposed maximum-likelihood location estimator for wideband sources in the near field of the sensor array is derived and is shown to yield superior performance over other suboptimal techniques, including the wideband MUSIC and the two-step least-squares methods.
Abstract: In this paper, we derive the maximum-likelihood (ML) location estimator for wideband sources in the near field of the sensor array. The ML estimator is optimized in a single step, as opposed to other estimators that are optimized separately in relative time-delay and source location estimations. For the multisource case, we propose and demonstrate an efficient alternating projection procedure based on sequential iterative search on single-source parameters. The proposed algorithm is shown to yield superior performance over other suboptimal techniques, including the wideband MUSIC and the two-step least-squares methods, and is efficient with respect to the derived Cramer-Rao bound (CRB). From the CRB analysis, we find that better source location estimates can be obtained for high-frequency signals than low-frequency signals. In addition, large range estimation error results when the source signal is unknown, but such unknown parameter does not have much impact on angle estimation. In some applications, the locations of some sensors may be unknown and must be estimated. The proposed method is extended to estimate the range from a source to an unknown sensor location. After a number of source-location frames, the location of the uncalibrated sensor can be determined based on a least-squares unknown sensor location estimator.
545 citations
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