On Data Fusion for Wireless Localization

1 1On data Fusion for Wireless LocalizationRobin Wentao Ouyang, Albert Kai-Sun Wong, Mung ChiangAbstract This paper presents a data Fusion framework forwireless Localization via the weighted least square estimator(WLSE). Three types of Fusion schemes are presented: mea-surement Fusion , estimate Fusion and mixed Fusion . Theoreticalperformance comparison among these schemes in terms of theestimation error covariance matrix is conducted. We show that, ifthe raw measurement vectors are correlated, then measurementfusion achieves the best performance, followed by mixed fusionand estimate Fusion is the worst. If the raw measurement vectorsare uncorrelated, then they can achieve the same benefits that can be earned from data Fusion are alsoinvestigated and numerical case studies are presented to validateour theoretical Terms Wireless Localization , data Fusion , weighted leastsquare estimator (WLSE), Cramer-Rao lower bound (CRLB).

2 I. INTRODUCTIONW ireless Localization has attracted great attention over thepast decade [1] [3]. Currently used Localization systems aremainly in four categories: satellite-based, cellular network(CN)-based, Wireless local area network (WLAN)-based andwireless sensor network (WSN)-based. Satellite-based local-ization system, , the Global Positioning System (GPS) [4],utilizes pseudo time-of-arrival (TOA), code phase or Dopplershift measurements to estimate the mobile station (MS) lo-cation. The location-pertaining measurements the other threekinds of systems utilized are TOA, time-difference-of-arrival(TDOA), round trip time (RTT), time advance (TA), angle-of-arrival (AOA), received signal strength (RSS), received signallevel (RXLEV, actually quantized RSS) and so forth.

3 Thelocalization problem is to estimate the MS location basedon location-pertaining measurements with respect to a set ofreference stations (RSs). For analytical purposes, we consideronly the parametric model based Localization techniques in techniques based on different types of mea-surements have their own advantages and disadvantages. Incertain scenarios, the techniques based on single type ofmeasurement may not be satisfactory. Hybrid methods (datafusion) which seek performance gain by fusing data fromdifferent types of measurements and/or multiple localizationsystems are thus resorted to. We classify data Fusion meth-ods as three types: measurement Fusion , estimate Fusion andmixed Fusion .

4 In measurement Fusion , only the raw location-pertaining measurements are fused. In estimate Fusion , only thelocal estimates (already an estimate of the MS location, , aGPS location fix) are fused. In mixed Fusion , combinations ofraw measurements and local estimates are fused. Here, weuse mixed Fusion to distinguish from so called hybrid methods used in the existing literature concerning data fusionin Wireless Localization . Most of the hybrid methods proposedare actually measurement Fusion since they fuse only differenttypes of raw measurements, while our defined mixed fusionfuses both raw measurements and local measurement Fusion , [5] proposes an AOAassisted TOA positioning system and [6] propose hybridTOA/AOA techniques for non-line-of-sight (NLOS) [7] miti-gation.

5 A hybrid TDOA/AOA technique is proposed in [8] forwideband code division multiple access (WCDMA) cellularsystems. [9] explores the combination of TDOA and RSS forcellular network positioning. [10] resorts to a triplet hybridscheme using TOA, time sum of arrival (TSOA) and TDOAto reduce the NLOS errors. [11] proposes hybrid pseudoTOA/TA/RXLEV methods between GPS and a CN-basedlocalization system to achieve enhanced accuracy. Besidesmeasurement Fusion , estimate Fusion is used in [12] to fuse twolocation estimates from TOA and TDOA estimators. Recently,[13] uses mixed Fusion to improve the initial GPS locationfix accuracy by making use of terrestrial TOA and , there does not exist a general framework for allthese types of Fusion schemes and the performance comparisonamong these Fusion schemes is also unaddressed.

6 Therefore,in this paper, we propose a unified data Fusion frameworkbased on the weighted least square estimator (WLSE) [15]for Wireless Localization where the MS location is treated asa deterministic unknown vector. The proposed data fusionframework can effectively fuse all the available raw measure-ments and/or local estimates. We also analyze and comparethe theoretical performance of these Fusion schemes in termsof the estimation error covariance matrix. Assuming that allthe estimates (local estimates and data Fusion ) are done viathe WLSE, we show that1)Property 1: If the raw measurement vectors are uncor-related, then the three Fusion schemes achieve the )Property 2.

7 If the raw measurement vectors are corre-lated, then measurement Fusion achieves the best per-formance, followed by mixed Fusion and lastly 1tells us if the raw measurement vectors are un-correlated, then there is no performance degradation in theraw measurements local estimates estimate Fusion ormixed Fusion processes compared with measurement fusionwhich directly fuse all the raw measurements. Therefore,providing only local estimates is equivalent to providing allthe raw measurements. While the former offers privacy sincethe information about the RSs used does not need to 2tells us if some raw measurement vectorsare correlated, to obtain good performance, it is better to fusethem together to generate a local estimate, rather than produceseparate local estimates based on individual raw measurement2vectors and then fuse these local estimates together.

8 ForGaussian measurement errors, the WLSE is equivalent tothe maximum likelihood estimator (MLE) and the estimationerror covariance matrix then attains the corresponding Cramer-Rao lower bound (CRLB), which sets a lower bound on thecovariance matrix of any unbiased estimator for deterministicunknowns. In consequence, the corresponding estimation meansquare error (MSE) then becomes the minimum from data Fusion and the pros and cons of the threefusion schemes are also investigated. For example, data fusioncan bring lowered estimation error, improved resilience to badgeometric layouts, enhanced Localization availability, improveddata usage, easy cooperation among different localizationsystems with maintained privacy, distributed implementationwith retained performance and so remainder of this paper is organized as follows.

9 SectionII introduces the WLSE and the data models used in wirelesslocation. Section III presents the data Fusion framework,derives the estimation error covariance matrices and discussesthe relationship among the three Fusion schemes. Section IVinvestigates the benefits from data Fusion and the pros and consof respective Fusion methods. Section V provides numericalcase studies in comparing the performance among measure-ment Fusion , estimate Fusion and mixed Fusion . Finally, SectionVI concludes the PRELIMINARIESIn this section, we first introduce the definition and prop-erties of the WLSE. Then, we present the data models forfour kinds of commonly used raw measurements, followed bythe data model for a local estimate.

10 Throughout this paper, weassume that all the covariance matrices are invertible, and thuspositive definite [14]. We denote a positive definite matrixAasA 0and a positive semidefinite matrixBasB WLSEG iven data that modeled asz=s( ) +n(s( )is a knownfunction of ;nhas zero mean and known covariance matrixCn;z,s( )andnare allN 1vectors), to estimate theunknown parameter ( is treated as a deterministicp 1vector), the WLSE [15] is to minimize the following penaltyfunction = arg min (z s( ))TC 1n(z s( )).(1)1) Case I:s( )is linear in , ,s( ) =H (His aknownN pmatrix). The data model becomesz=H + this case, has closed-form expression = (HTC 1nH) 1 HTC 1nz.(2)with covariance matrixC= (HTC 1nH) 1.