A Survey on Wireless Position Estimation <s> Statistical Techniques <s> The authors present an exact solution to the problem of maximum-likelihood time-delay estimation over arbitrary observation time T. That is, the standard assumption T>> tau /sub c/+d/sub max/ made in the derivation of the asymptotic maximum-likelihood (AML) estimator, where t/sub c/ is the correlation time of the various processes involved and d/sub max/ the maximum permissible delay, is relaxed. The exact maximum-likelihood (EML) processor is shown to consist of a special finite-time beamformer, followed by a scalar postprocessor based on the eigenvalues and eigenfunctions of a certain integral equation. The solution of this integral equation is obtained for the case of stationary signals with rational power spectral densities (PSD). The performance of EML and AML are compared by means of computer simulations for a first-order low-pass PSD. The results show that EML can lead to a significant improvement in performances (bias, variance, large errors) when the condition T>> tau /sub c/+d/sub max/ is not satisfied. > <s> BIB001 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> Preface I. Introduction II. Elements of Hypothesis Testing III. Signal Detection in Discrete Time IV. Elements of Parameter Estimation V. Elements of Signal Estimation VI. Signal Detection in Continuous Time VII. Signal Estimation in Continuous Time References Index <s> BIB002 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> Applications for the location of subscribers of wireless services continue to expand. Consequently, location techniques for wireless technologies are being investigated. With code-division multiple access (CDMA) being deployed by a variety of cellular and PCS providers, developing an approach for location in CDMA networks is imperative. This article discusses the applications of location technology, the methods available for its implementation in CDMA networks, and the problems that are encountered when using CDMA networks for positioning. <s> BIB003 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> Subscriber radio location techniques are investigated for code-division multiple-access (CDMA) cellular networks. Two methods are considered for radio location: measured times of arrival (ToA) and angles of arrival (AoA). The ToA measurements are obtained from the code tracking loop in the CDMA receiver, and the AoA measurements at a base station (BS) are assumed to be made with an antenna array. The performance of the two methods is evaluated for both ranging and two-dimensional (2-D) location, while varying the propagation conditions and the number of BS's used for the location estimate. <s> BIB004 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> This paper presents the problem of identifying whether a received signal at a base station is due to a line-of-sight (LOS) transmission or not (NLOS). This is a first step towards estimating the mobile station's location. We formulate the NLOS identification problem as a binary hypothesis test where the range measurements are modeled as being corrupted by additive noise, with different probability distributions depending on the hypothesis. We solve the binary hypothesis test under several assumptions, proposing appropriate decision criteria. <s> BIB005 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> From the Publisher: ::: Wireless Location in CDMA Cellular Radio Systems investigates methods for wireless location in CDMA networks and analyzes their performances. Techniques for measuring location parameters (AoAs, ToAs, etc.) are presented along with algorithms for calculating position from those parameters. Several impairments to accurate location are covered and analyzed including multipath propagation, non-line-of-sight propagation, and multiple-access interference. Many of the topics in this book are also applicable to FDMA- and TDMA-based communication networks. <s> BIB006 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> A major concern of cellular and PCS-based wireless location systems is the effect of the harsh propagation environment, particularly non-line-of-sight (NLOS) propagation. In order to improve location accuracy under such conditions, this paper proposes a novel location technique that estimates the true, or line-of-sight (LOS), ranges based on NLOS range measurements. The algorithms, designed for NLOS environments, make use of well-known multipath scattering models (ring/disk of scatterers and Gaussian distributed scatterers) in order to incorporate the effects of NLOS propagation. From PDFs of the TOAs derived using the models, maximum likelihood expectation-maximization and Bayesian estimators are applied to multipath TOA measurements at each BS to estimate the LOS distance between the MS and the BS. Simulated results show that the algorithms provide considerable improvement over traditional location algorithms. <s> BIB007 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> We present a novel approach for reducing the effect of non-line-of-sight (NLOS) error that inhibits accurate location of wireless mobile stations (MSs). The location algorithm is developed based on the distribution of times of arrival (TOAs) generated from multipath scattering models that have been published in the literature. By matching the statistics of the measured TOAs of several multipath arrivals with those produced by the scattering models, estimates of the line-of-sight (LOS) TOAs between each base station (BS) and the MS are obtained. The LOS TOAs can then be used in any traditional TOA location algorithm. The algorithm shows a significant improvement in location accuracy for a TOA system in NLOS environment. <s> BIB008 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> This paper proposes a mobile user location scheme for wideband code-division multiple-access (CDMA) wireless communication systems. To achieve high location accuracy and low cost of the mobile receiver, the location scheme combines the time difference of arrival (TDOA) measurements from the forward link pilot signals with the angle of arrival (AOA) measurement from the reverse link pilot signal. High chip rates in wideband CDMA systems facilitate accurate TDOA measurements, and a smart antenna used at the home base station (BS) can provide accurate AOA measurement in a macrocell environment. A two-step least square location estimator is developed based on a linear form of the AOA equation in the small error region. Numerical results demonstrate that the proposed hybrid TDOA/AOA location scheme gives a much higher location accuracy than TDOA only location, when the number of base stations is small and/or when the TDOA measurements have a relatively poor accuracy. <s> BIB009 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> One of the major challenges to finding accurate mobile terminal location is the non-line-of-sight (NLOS) propagation caused by the blocking of the signal's direct path by obstacles. Traditional location algorithms perform poorly in NLOS environments and this has made it necessary to develop techniques to identify NLOS transmissions and then employ suitable error mitigation techniques. It is extremely difficult to characterize NLOS error because it varies with time and is location specific. We present statistical based techniques to distinguish LOS and NLOS propagation for various scenarios and present simulation results to validate them. <s> BIB010 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> A time-of-arrival (ToA)-based ranging scheme using an ultra-wideband (UWB) radio link is proposed. This ranging scheme implements a search algorithm for the detection of a direct path signal in the presence of dense multipath, utilizing generalized maximum-likelihood (GML) estimation. Models for critical parameters in the algorithm are based on statistical analysis of propagation data and the algorithm is tested on another independent set of propagation measurements. The proposed UWB ranging system uses a correlator and a parallel sampler with a high-speed measurement capability in each transceiver to accomplish two-way ranging between them in the absence of a common clock. <s> BIB011 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> Ultra-wideband (UWB) radio is gaining increasing attention thanks to its attractive features that include low-power low-complexity baseband operation and ample multipath diversity. Realization of its potential, however, faces the challenge of low-complexity high-performance timing acquisition. In this paper, we develop a blind timing acquisition algorithm for frame-level synchronization. Relying on simple integrate-and-dump operations over one symbol duration, our algorithm exploits the rich multipath diversity enabled by UWB transmissions. It outperforms existing blind algorithms and has comparable performance to data-aided ones. Equally attractive is its applicability to UWB links with or without time hopping (TH), over frequency-flat or multipath channels. It is also worth stressing that our "dirty" template based scheme is able to achieve timing synchronization at any desirable resolution and is readily applicable to non-UWB systems, so long as intersymbol interference is absent. <s> BIB012 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> Commercial applications for the location of subscribers of wireless services continue to expand. Consequently, finding the Cramer-Rao lower bound (CRLB), which serves as an optimality criterion for the location estimation problem, is of interest. In this paper, we derive the deterministic CRLBs for the estimation of the specular multipath parameters and the positions of the mobiles in an asynchronous direct sequence code division multiple access (DS-CDMA) system operating over specular multipath fading channels. We assume a multilateral radio location system where the location estimates are obtained from some or all of the estimated signal parameters at different clusters of antennas of arbitrary geometry. Extension for unilateral and composite radio location techniques is also discussed. As an application example, we use numerical simulations to investigate the effects of specular multipath and multiple access interference (MAI) on the positioning accuracy for different radio location techniques. <s> BIB013 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> Indoor localization systems are undoubtedly of interest in many application fields. Like outdoor systems, they suffer from nonline-of-sight (NLOS) errors which hinder their robustness and accuracy. Though many ad hoc techniques have been developed to deal with this problem, unfortunately most of them are not applicable indoors due to the high variability of the environment (movement of furniture and of people, etc.). In this paper, we describe the use of robust regression techniques to detect and reject NLOS measures in a location estimation using multilateration. We show how the least-median-of-squares technique can be used to overcome the effects of NLOS errors, even in environments with little infrastructure, and validate its suitability by comparing it to other methods described in the bibliography. We obtained remarkable results when using it in a real indoor positioning system that works with Bluetooth and ultrasound (BLUPS), even when nearly half the measures suffered from NLOS or other coarse errors. <s> BIB014 </s> A Survey on Wireless Position Estimation <s> Statistical Techniques <s> This paper presents a new position-determination estimator for trilateration location. The proposed estimator takes the measurement bias into consideration and improves the location accuracy of a mobile location system. In case that a mobile station (MS) utilizes signals from a set of base stations for its location, the computed location is largely affected by nonline-of-sight (NLOS) error in signal propagation. A constrained optimization method in a three-stage estimation structure is proposed to estimate and eliminate the measurement bias contained in each pseudorange and mainly caused by the NLOS error. A linear observation model of the bias is formulated, and the interior-point optimization technique optimally estimates the bias by introducing a feasible range of the measurement bias. It is demonstrated that the new three-stage estimator successfully computes an accurate location of an MS in a realistic environment setting. The location accuracy of the proposed estimator is analyzed and compared with the existing methods through mathematical formulations and simulations. The proposed estimator efficiently mitigates the effect of a measurement bias and shows that the iterated least square (ILS) accuracy of 118 m [67% distance root-mean-square (DRMS)] can be improved to about 17 m in a typical urban environment <s> BIB015
Unlike the geometric techniques, the statistical approach presents a theoretical framework for position estimation in the presence of multiple position related parameter estimates with or without noise. In order to formulate this generic framework, consider the following model for the parameters estimated in the first step of a two-step positioning algorithm where N m is the number of parameter estimates, η i is the noise at the ith estimation, and f i (x, y) is the true value of the ith signal parameter, which is a function of the position of the target, (x, y). Note that N m is equal to the number of reference nodes for RSS, AOA and TOA based positioning, whereas it is one less than the number of reference nodes for TDOA based positioning as each TDOA parameter is estimated with respect to one reference node. For various positioning systems, f i (x, y) in (17) can be expressed as where (x i , y i ) is the position of the ith reference node and (x 0 , y 0 ) is the reference node, relative to which the TDOA parameters are estimated. In vector notations, the model in (17) can be expressed as where T . Depending on the available information related to the noise term η in BIB012 , parametric or nonparametric approaches can be followed. In the case that the probability density function of the noise η is known except for a set of parameters, denoted by λ, parametric approaches, such as Bayesian and maximum likelihood (ML) estimation, can be employed. In the absence of information about the form of the probability density function of η, nonparametric techniques need to be used. Note that the k-NN, SVR and neural networks approaches studied in Section 3.1 are examples of non-parametric estimators since they do not assume any form for the probability density function of the noise. However, they utilize a training database. Although the form of the density function is unknown in the nonparametric case, there can still be some generic information about some of its parameters  , such as its variance and symmetry properties, which can be used to design non-parametric estimation rules, such as the least median of squares technique in BIB014 , the residual weighting algorithm in  and the variance weighted least squares technique in BIB003 . For the remainder of this section, the parametric approaches are studied in detail. Let the vector of unknown parameters be represented by θ, which consists of the position of the target node, as well as the unknown parameters of the noise distribution 11 ; i.e., θ = x y λ T T . Depending on the availability of prior information on θ, Bayesian or ML estimation techniques can be applied BIB007 . In the presence of prior information on θ, which is represented as a prior probability distribution π(θ), the Bayesian approach can be used to obtain an estimate of θ that minimizes a specific cost function BIB002 . Two common Bayesian estimators are the MMSE and the MAP estimators, which estimate θ asθ where E {θ| z} is the conditional expectation of θ given z, and p(z|θ) represents the probability density function of z conditioned on θ. In the absence of prior information on θ, the ML estimation is commonly employed, which calculates the value of θ that maximizes the likelihood function; i.e.,θ Note that since f (x, y) is a deterministic function, the likelihood function can be expressed as where p η (· | θ) represents the conditional probability density function of the noise vector conditioned on θ. Depending on the properties of the noise vector, various scenarios can be considered. Case-1: Independent Noise Components: For independent noise components, the likelihood function in (23) can be expressed as where p ηi (· | θ) represents the conditional probability density function for the ith noise component given θ. The independent noise assumption is usually valid for TOA, RSS and AOA estimation. However, for TDOA estimation, the noise components are correlated, as all TDOAs are computed with respect to the same reference node. Therefore, TDOA based systems can be studied through the generic expression in BIB004 , or by using a correlated Gaussian model under certain conditions, as will be investigated later. For TOA, RSS and AOA based systems in LOS conditions, the parameters of the noise can be assumed to be known, since the noise is mainly due to thermal (background) noise in an LOS scenario. Then, the unknown parameter vector reduces to θ = [x y] T . Also, it is possible to (approximately) model each noise component by a zero mean Gaussian random variable in the LOS case  ; that is, Then, the likelihood function in (24) can be expressed as From (26), the ML estimator in BIB013 can be obtained aŝ which is the well-known non-linear least-squares (NLS) estimator BIB006 . Note that the weights are inversely proportional to the noise variances since a larger variance means a less reliable estimate. Common techniques for solving (27) include gradient descent algorithms and linearization techniques via the Taylor series expansion BIB006 , BIB015 . In the presence of NLOS propagation between the target node and some reference nodes, the noise model can be significantly different for the parameter estimates at those reference nodes compared to the ones at the LOS nodes. If the positions of the reference nodes are sufficiently separated, the conditional independence assumption in (24) can still hold. Therefore, the ML position estimator can be obtained using BIB013 and (24) by using appropriate noise distributions for LOS and NLOS reference nodes  . The noise distribution in the NLOS case is commonly modeled as the sum of two noise terms, one related to the background noise, and the other related to the NLOS error. In this case, the noise distribution is usually considerably different than the Gaussian model in BIB001 13 . Some common models for the NLOS error include Gamma distribution  and distributions based on certain scattering models BIB008 . In many cases, the errors due to NLOS propagation dominate the estimation errors due to background noise. Case-2: Correlated Gaussian Noise Components: For a noise vector modeled as a multivariate Gaussian random variable with mean µ and covariance matrix Σ, the likelihood function is given by Then, the ML position estimation can be calculated aŝ where θ consists of the position of the target node and the unknown parameters related to µ and Σ. For a noise distribution with zero mean and a known covariance matrix, (29) simplifies tô which is called the weighted LS (WLS) solution BIB006 . Although the independent noise model in Case-1 is not well-suited for TDOA based positioning systems, the correlated Gaussian noise model in BIB009 can represent such systems quite accurately for sufficiently large SNRs. As an example, consider TDOA estimation via difference of TOA estimates. If the estimates of range differences (equivalently, TDOA estimates) are modeled as 12 It is assumed to be known which nodes are LOS and which are NLOS. Such an information can be obtained using NLOS detection algorithms BIB005 , BIB010 ,  . BIB011 The error due to NLOS propagation can also be considered as a fixed unknown bias term. However, it is shown in  that in the absence of statistical information about NLOS errors, the parameter estimates from NLOS nodes can be discarded as they do not contribute to the positioning accuracy. where  where  In other words, the noise is Gaussian with correlated components (since the correlation matrix is not diagonal) in this case. In the case of NLOS propagation between the target node and a number of reference nodes, the Gaussian model in (28) may not be very accurate. Therefore, the generic ML estimation in BIB013 and (23) should be performed for TDOA estimation in NLOS scenarios.