a systems engineering approach to improving the accuracy of mobile station location estimation

14 IEEE SYSTEMS JOURNAL, VOL. 8, NO. 1, MARCH 2014

A Systems Engineering Approach to Improving theAccuracy of Mobile Station Location Estimation

Reza Rahdar, Member, IEEE, Jerrell T. Stracener, and Eli V. Olinick

Abstract—Enhanced 911 is a first line of assistance for prac-tically every emergency situation, and many cell phone userstoday expect the same results from an emergency call no matterwhere they are—whether on the side of the road, in the woods,or in a building. It is a vital part of our nation’s emergencyresponse and disaster preparedness system. In the context of911 service, demand for providing reliable and accurate mobilestation (MS) location estimation has become a high priority andhas gained momentum in recent years. A major challenge inmobile station location estimation is locating an emergency callerwithin desired accuracy in an adverse environment where non-line-of-site (NLOS) propagation exists. This paper develops amethodology to improve the accuracy of mobile station locationestimation in an NLOS environment. A unique feature of thismethodology development, compared to other approaches in theliterature, is the application of the systems engineering process.While there are many definitions, systems engineering as appliedhere is an approach and process for developing the preferredsolution to a set of requirements. The methodology consists oftwo stages. In the first stage, a series of time-of-arrival rangemeasurements are made from each base station (BS) to theMS. Binary hypothesis testing on the standard deviation of therange measurements at a given BS is used to determine if themeasures are taken under NLOS conditions. Then, if possible,any BS deemed to be NLOS is eliminated from the estimationin the second stage, in which the selected time measurementsof several BSs are combined through least squares to estimatethe location of the mobile station. Based on a simulation study,the methodology appears to have the potential to significantlyimprove the accuracy of location estimates in certain situations.

Index Terms—Constrained least squares, least squares, line-of-site (LOS), mobile station location estimation, non-line-of-site(NLOS), root mean square error, systems engineering, vee model.

I. Introduction

THE use of wireless communication systems has grownexplosively in recent years. According to the Cellular

Telephone Industry Association (CTIA), there were approx-imately 233 million subscriptions for wireless service in theUnited States in 2006; by the end of 2011 this number had

Manuscript received January 13, 2012; revised July 13, 2012; acceptedJanuary 11 2013. Date of publication March 7, 2013; date of current versionFebruary 5, 2014. This work was supported in part by ONR under ContractN00014-10-0852.

R. Rahdar is with Bell Helicopter, Fort Worth, TX 75275 USA (e-mail:[email protected].).

J. T. Stracener and E. V. Olinick are with the Department of EngineeringManagement, Information, and Systems, Bobby B. Lyle School of Engi-neering, Southern Methodist University, Dallas, TX 75275 USA (e-mail:[email protected]; [email protected]).

Color versions of one or more of the figures in this paper are availableonline at http://ieeexplore.ieee.org.

Digital Object Identifier 10.1109/JSYST.2013.2244799

grown to over 331 million [1]. Due to the fact that many Amer-icans have multiple subscriptions, this is a wireless penetrationof over 104% of the potential market [2]. In addition, CTIAreports that the percentage of wireless-only households in theU.S. has tripled from 10% in 2006 to over 30% in 2011, whilethe number of 911 calls per day made from wireles/cellularphones (mobile stations) has increased from 260 000 to over400 000 in the same period [1]. Locating emergency callersin wireless communication systems—mobile station locationestimation—has emerged as an essential public safety issue.Motivated by Federal Communications Commission (FCC)requirements, methodologies for improving the accuracy ofmobile station location estimation have become an importantresearch area over the past few years.

A Public Safety Answering Point (PSAP), or 911 Center,is a call center responsible for answering emergency calls anddispatching appropriate services, such as police, fire fighters,and ambulances. In a wireline network with E911 (E911)service, automated number identification information givesthe PSAP call back capability in case the emergency callis disconnected. E911 also enables the PSAP to identify anemergency call’s originating address through the use of anautomated location identification database.

In wireless communication systems, however, the mobilestation (MS) has no fixed static address because it can be atany geographical location (e.g., at the owner’s home, on theroad, out of city or state, or even out of the country). The 911call from a mobile station may not be routed to the nearest911 center, and the dispatcher may not receive the callbackphone number or the location of the caller. This can lead toa disaster if the caller does not know their location or cannotcommunicate their location because they are unable to speak.The delivery of wireless location data that allows the receivingPSAP to promptly and effectively dispatch the appropriateemergency services to the correct location is essential towireless 911 services.

When a mobile station initiates a 911 call in a wirelessnetwork, the closest cell tower (base station) picks up thesignal. The base station (BS) transmits the caller’s voice signal,phone number, and the tower’s identification code to a mobileswitching center. The mobile switching center then forwardsthis information to the appropriate PSAP, which subsequentlyprocesses location information to dispatch local responders tolocate and assist the caller. A typical flow of information in awireless 911 call is shown in Fig. 1. Although it is possibleto identify the base station closest to where a wireless call is

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RAHDAR et al.: SYSTEMS ENGINEERING APPROACH TO IMPROVING THE ACCURACY OF MOBILE STATION LOCATION ESTIMATION 15

Fig. 1. Wireless 911: flow of information.

initiated, it is not yet possible to identify the exact location ofa mobile station making an emergency call.

In 1996, the FCC adopted regulations for wireless callsto 911 to ensure compatibility with E911 emergency calling;these wireless E911 regulations require all wireless serviceproviders to report accurate mobile station location informa-tion to the E911 operator at the PSAP [3]. At the time,the FCC called for a phased implementation of the wirelessE911 regulations. In Phase 0, wireless service providers wererequired to transmit any 911 call received by their network toa PSAP regardless of whether or not the caller subscribed totheir service [4]. In Phase I, the service providers were obligedto provide PSAPs with the mobile phone callback numberand the location of the cell tower (BS) that received the call.Knowing the location of the BS that received the 911 call gaveemergency responders a rough estimate of the location of theMS; in Phase II, however, service providers were required torelay longitude and latitude of the MS to the PSAPs with thefollowing accuracy and reliability:

1) for network-based solutions: 100 m for 67% of calls,300 m for 95% of calls;

2) for handset-based solutions: 50 m for 67% of calls, 150m for 95% of calls.

Phase I was implemented by the end of 1998, and theregulations allowed service providers a five-year time windowfor implementing Phase II [3]. As noted in [5], however,“providing the [required] E911 service in a manner that iseconomically feasible for the carriers has proven to be quite achallenge;” Phase II has not been fully implemented and theFCC has fined several national service providers for failingto meet their requirements [5]. In September 2007, the FCCadopted a report and order to clarify Phase II location accuracyrequirements. The order required carriers to meet interim andannual benchmarks over the next five years and achieve fullcompliance with the E911 regulations by September 11, 2012[6].

In a 2010 report, the FCC noted that as many as 40% ofemergency calls made from wireless devices fail to provide ac-curate mobile station location estimation [7]. Present wirelesssystems are still unable to provide PSAPs with mobile station

location estimates that meet the FCC requirements. Thereare numerous national stories, sometimes ending tragically,highlighting the inability of wireless E911 to locate people.Pinpointing the location of mobile stations presents someunique challenges due to the hostile effects of the wirelessenvironment such as noise, electromagnetic interference, mul-tipath, non-line-of-sight (NLOS) propagation, shadow fading,and Doppler shifts. In most situations the MS is not in directpath line-of-sight (LOS) with the BS. With no LOS path,the transmitted signal can only reach the receiver throughreflection, diffraction, or scattering. In this case, the signaltakes a longer time to reach the BS than it would with a LOSpath. This delay is added to the distance measurement as anadditional error that is called NLOS error. This additional errormay be large and thus may cause the mobile station locationestimate to be far from the true location. The field trialsperformed by Woo et al. [8] showed that the location distanceerror due to NLOS paths can be more than 500 m. Obstaclesthat commonly cause NLOS errors include buildings, trees,hills, and mountains. Extensive studies have been carried outto mitigate NLOS effects but none adequately achieved theaccuracy required by the FCC, and our survey of the literatureindicates that improvement is needed.

This paper presents a methodology to improve the accuracyof network-based mobile station location estimation in aNLOS environment. The methodology consists of two stages.In the first stage, a series of time of arrival (TOA) rangemeasurements are made from each BS to the MS. Binaryhypothesis testing on the standard deviation of the rangemeasurements at a given BS is used to determine if themeasures are taken under NLOS conditions. Then, if possible,any BS deemed to be NLOS is eliminated from the estimationin the second stage, in which the selected time measurementsof several BSs are combined through least squares to estimatethe location of the mobile station.

The remainder of this paper is organized as follows. SectionII is an overview of the Vee model of the systems engineeringprocess used to develop the methodology described above.The application of the Vee model to improving mobile stationlocation estimation is demonstrated in Sections III through VI.The requirements for the methodology are defined in SectionIII. Section IV includes a short discussion of techniquesfor mobile station location estimation and a brief surveyof the NLOS error mitigation literature. Our mobile stationlocation estimation methodology is developed in Section V,and Section VI summarizes the results of a simulation studyused to test its performance. Conclusions from the study aregiven in Section VII.

II. Systems Engineering Process

In this paper, the systems engineering process is used todevelop a methodology for improving the accuracy of network-based mobile station location estimation. While there are manydefinitions, systems engineering as applied here is an approachand process for developing the preferred solution to a set ofrequirements. This process usually consists of the followingseven tasks: 1) state the problem; 2) investigate alternatives;


Fig. 2. Systems engineering process.

Fig. 3. SE Vee model.

3) model the system; 4) integrate; 5) launch the system;6) assess performance; and 7) re-evaluate (SIMILAR). Thissystems engineering process is shown in Fig. 2, which isadapted from [9].

The systems engineering Vee model was selected to providethe framework for development of an improved methodology.The objective was to ensure capture of requirements, evaluatethe different methods in the literature, to develop the bestsolution (methodology) to meet the established requirementsand verify and validate it. The Vee model was developed byKevin Forsberg and Harold Mooz at the Center for SystemsManagement [10]. Since then, it has been refined and appliedin many different industries. The Vee model is a systemdevelopment model designed to simplify the understanding ofthe complexity associated with developing systems [11]. TheVee shape is derived by the concept of an evolving engineeringprocess, moving from left to right with time where the left sideof the Vee depicts the decomposition and definition of thesystem requirements and specifications at the beginning of thesystem’s life cycle. After the system or product is developed,responsibility passes back to the right side of the Vee forintegration and verification. Ultimately, the completed systemis validated to measure how well it meets the user’s needs.The adapted Vee model shown in Fig. 3 captures the processof developing a methodology for locating a mobile station,then verifying and validating it to satisfy the requirements.

In the following sections, the general principles of theVee model are used in developing the new methodology forimproved mobile station location estimation. Our applicationof the Vee model for the E911 application is described morethoroughly in [12]. The process begins with the customerneeds and requirements on the upper left side of the Veewith decomposition and definition activities as described inSection III. The next step on the Vee (Section IV) summarizesthe literature survey and trade studies used to establish the

best technique and down select to the best alternative. Thisis followed by the methodology development described inSection V. The right side of the Vee for this application(verification and validation of the methodology developed inSection V) is described in Section VI.

III. Needs and Requirements

Emergency 911 service is a vital part of our nation’semergency response and disaster preparedness system. Findingthe location of mobile stations has emerged as an essentialpublic safety feature of cellular systems. To comply withFCC regulations, wireless carriers will have to ensure E911coverage for 95% of their subscriber base at each PSAP [3],[6]. The accuracy of different mobile station location estima-tion techniques has been studied, but their accuracy is ofteninadequate and unreliable for many location based services.Although the complete removal of the NLOS impact may beimpractical, different techniques can be used to mitigate itsadverse effect and thereby improve accuracy of mobile stationlocation estimation.

Based on the FCC mandate and the wireless technologyperformance, the following requirements were derived witheach one being measurable and verifiable:

1) the methodology shall address the greatest impairmentto the mobile station location estimation;

2) the methodology shall identify and mitigate the NLOSeffects;

3) the methodology shall be comparable with the bestalternatives;

4) the methodology shall meet the FCC mandates.

IV. Alternatives

Rahdar [12] gives a detailed discussion of the investiga-tion and selection of alternatives for mobile station locationestimation. The investigation has two main parts: selectinga technology for estimating the mobile station location, andthen improving the implementation of that technology with amethod for mitigating NLOS errors.

A. Mobile Station Location Estimation

There are a number of technological alternatives for locatingthe mobile station. The location technologies are typicallygrouped into two main categories: handset-based and network-based. In handset-based systems, the MS determines its lo-cation from signals received from nearby BSs or from theglobal positioning system (GPS). In network-based methods,


the network infrastructure is used to identify the location ofthe mobile station.

Two arguments in favor of handset-based systems are thatcommercial/civilian-grade GPS can be extremely accurate un-der optimal conditions—hence the more stringent FCC accu-racy requirements—and that cell phones with GPS capabilityare becoming increasingly prevalent as evidenced by Apple’sreport that it sold over 37 million GPS-enabled iPhones in thefinal quarter of 2011 [14]. However, there are still a significantnumber of cell phones in use that do not support GPS, and evenwhen the vast majority of wireless users have GPS-enabledphones there will still be a need for network-based solutionsas the accuracy of handset-based technology such as GPS canbe reduced by atmospheric conditions, terrain types, and inurban/indoor settings [15], [16].

The advantage of network-based methods is that they canbe implemented non intrusively without affecting the mobilehandsets. The accuracy of network-based methods varies,with cell identification as the least accurate and triangula-tion/trilateralization as the most accurate. The accuracy ofnetwork-based methods is closely dependent on the concentra-tion of base station cells, with urban environments achievingthe highest possible accuracy [17]. After surveying a varietyof network-based methods, such as TOA (see Section V-A),time difference of arrival [18], cell identification [19], receivedsignal strength indicator [20], angle of arrival [21], and hybridmethods (e.g., [22], [23]), Rahdar [12] selects TOA as thebasic technology for mobile station location estimation.

B. NLOS Mitigation

Several approaches to identify and mitigate NLOS errors inmobile station location estimation have been studied in recentyears. Wylie and Holtzman [24] showed that it is possible todistinguish LOS from NLOS measurements at each BS byusing the time history of the range measurements in a hypoth-esis testing method. Likewise, Borras et al. [25] formulatethe NLOS identification problem as a binary hypothesis testwhere the range measurements are modeled as being corruptedby additive noise with various probability distributions. Theysolve the binary hypothesis test under several assumptions andpropose decision criteria for determining if a BS is LOS orNLOS. Chen [26] developed a residual-based algorithm tomitigate the NLOS errors in mobile station location estimation.This method was also used in [27]–[29]. The residual-basedmethod relies on a large number of measurements that aregrouped into subsets. Intermediate location estimates are pro-duced from each subset of the measurements and are evaluatedby their residuals [26], [29]–[31]. The final location estimateis obtained by weighting the different intermediate results.The method is effective when only a few measurements arecorrupted by NLOS effects. Studies such as [24], [25], [28],[31]–[34] apply statistical parameter estimation of the NLOSerror to solve the mobile station location estimation problem.These methods depend largely on the accuracy of the NLOSerror model, and satisfactory location accuracy is expected ifthe model and distribution parameters can be well tuned on site[35]. Methods exploiting mathematical optimization models,often with geometrical constraints, have been proposed in

Fig. 4. TOA location estimation using three LOS BSs.

[35]–[42]. A variety of filtering-related methods have beenproposed (e.g., [43]–[45]) to reduce the NLOS effect and totrack moving targets by using motion dynamics.

V. Methodology Development

Our mobile station location estimation methodology buildsupon several concepts from the literature. In Section V-A, wedescribe the TOA measurement method for calculating thedistance (range) between the MS and a BS, and determiningthe location of the MS. In Sections V-B and V-C, we describemethods proposed in the literature for using the TOA mea-surement method in the presence of measurement error and asimple hypothesis testing method for deciding if a BS is LOSor NLOS, respectively. We then describe our new methodologyin subsection V-D. Throughout this paper we assume that thereare N BSs, whose known 2-D locations are denoted by (xi, yi),i = 1, 2, . . . , N, within range to receive a 911 signal from astationary MS whose location is to be determined and whoseunknown coordinates are denoted by (x, y).

A. TOA Measurement Method

The TOA measurement method is used to estimate thedistance (range) between the MS and a BS. Since the wirelesssignal travels at the speed of light (c = 3 × 108m/s), theestimated distance between the MS and BSi is

ri = c(ti − t0) (1)

where t0 is the time instant at which the MS initiates the calland ti is the time of arrival of the signal at BSi. Using theestimated distance from the MS to three BSs, the location ofthe MS is then determined using trilateralization as illustratedin Fig. 4.

B. Mobile Station Location Estimation in the Presence ofMeasurement Error

The true distance between the MS and BSi is given by

di = ‖((x, y) − (xi, yi))‖ =√

(x − xi)2 + (y − yi)2. (2)


Under ideal circumstances (2) holds and ri = di. In practice,however, there is some measurement error even when a BShas a line of sight with the mobile station. Thus, ri is typicallymodeled as an unbiased Gaussian estimate of the true distance

ri = di + ni =√

(x − xi)2 + (y − yi)2 + ni (3)

where ni is the measurement noise and is a zero-mean Gaus-sian random variable with a standard deviation of σ in therange of 60 m to 150 m [24]. Note that in this paper, we modelmeasurement noise with a variety of probability distributions.

In the case of NLOS, the measurement noise and a NLOSerror both exist and the distance estimates ri are known to bepositively biased estimates of the true distance [26] given by

ri =√

(x − xi)2 + (y − yi)2 + ni + εi (4)

where εi is the NLOS error.The standard deviation of a series of M TOA distance

measurements from the MS to BSi is denoted by si andcalculated as

si =

√√√√ 1

M − 1

M∑j=1

(rij − ri)2 (5)

where rij is the jth measurement in the series and ri is themean of the M measurements that is calculated as

ri =1

M

M∑j=1

rij. (6)

To describe the least squares (LS) algorithm proposed byCheung et al. [46] for mobile station location estimation inthe presence of measurement error, let R =

√x2 + y2 and � =[

x y R2]T

. � can be estimated using LS

� = argmin�(A� − b)T (A� − b) = (AT A)−1AT b (7)

where

A =

⎡⎢⎢⎢⎣

x1 y1 −0.5x2 y2 −0.5...

......

xN yN −0.5

⎤⎥⎥⎥⎦ (8)

� =

⎡⎣ x

y

R2

⎤⎦ (9)

b =1

2

⎡⎢⎢⎢⎣

x1 + y1 − r21

x2 + y2 − r2...

xN + yN − r2N

⎤⎥⎥⎥⎦ . (10)

Cheung et al. [46] also describe a constrained weighted leastsquares (CWLS) algorithm in which a weighting matrix W isadded to (7) to improve performance

� = argminθ(A� − b)T W(A� − b) (11)

TABLE I

Type I and Type II Errors

H0 is true H0 is falseAccept H0 Correct decision Type II errorReject H0 Type I error Correct decision

subject to

qT � + �T P� = 0 (12)

where

P =

⎡⎣1 0 0

0 1 00 0 0

⎤⎦ (13)

q =

⎡⎣ 0

0−1

⎤⎦ . (14)

The weighting matrix for (11) is W = (BQB)−1 where B =diag (2r1, 2r2, . . . , 2rN ) and Q = diag (s2

1, s22, . . . , s2

N ).

C. LOS/NLOS Identification

NLOS errors can severely degrade mobile station locationestimation accuracy. Therefore, if possible, they should be re-moved from any mobile station location estimation procedure.If three of the N BSs can be identified as LOS, the MSlocation can be determined using TOA range estimates andthe LS algorithm described above without the need to mitigatethe NLOS error. In this section we describe a methodologyproposed by Wylie and Holtzman [24] to discriminate betweenLOS versus NLOS measurement.

The LOS/NLOS identification problem can be treated as abinary hypothesis testing problem exploiting the fact that thestandard deviation of NLOS errors is greater than that of theLOS errors [24]. That is, if BSi is NLOS, then it is likely ina sufficiently large series of TOA measurements that si willbe larger than σ; where σ is the standard deviation of theLOS errors. This hypothesis testing problem can be stated asfollows. The null hypothesis, denoted by H0, is that the BS isLOS, and the alternative hypothesis, denoted by H1, is that itis NLOS. Given a set of M TOA measurements at BSi, thehypothesis test deems the BS to be LOS if si ≤ σ. Otherwise,if si is above the threshold value σ, the hypothesis test deemsthe BS to be NLOS. In this test the null hypothesis, H0, willbe rejected in favor of H1 for relatively large values of si. Atype I error is committed when H0 is rejected when, in fact,it is true. A type II error occurs when H0 is wrongly acceptedwhen it is false. There errors are summarized in Table I.

D. New Mobile Station Location Estimation Methodology

Our new mobile station location estimation (MSLE)Methodology may be described as the following two-stageprocedure.

Stage 1: Take a series of M TOA distance measurementsfrom the MS to BSi, apply the hypothesis test described aboveand designate BSi as LOS or NLOS accordingly. Repeat this


process at each of the other BSs until one of two stoppingcriteria are met: 1) three BSs have been designated as LOS(i.e., as soon as trilateralization can be performed with a highdegree of confidence), and 2) distance measurements havebeen taken, and hypothesis tests have been performed, for allN BSs.

Stage 2: If Stage 1 ends due to criterion 1, then applyLS to the distance measurement averages from the threeBSs designated as LOS to estimate the location of the MS.Otherwise, apply LS to the distance measurement averagesfrom the three BSs whose M distance measurements in Stage 1had the smallest standard deviations to estimate the locationof the MS.

Intuitively, the methodology can be described as estimatingthe MS location with measurements taken from the first threeBSs that appear (based on the hypothesis test) to have aLOS with the MS or, if there are fewer than three such BSs,measurements from any BSs that appear to have a LOS withthe MS and the best NLOS BSs.

VI. Verification and Validation

A. Simulation Environment

Monte Carlo simulations using MATLAB were used to eval-uate the performance of the MSLE methodology. Following afrequently cited example from the literature, [47], a 5-cell 2-Dcellular system was used. The base stations are located at thefollowing points in the plane: BS1 = (4

√3, 12), BS2 = (4

√3,

20), BS3 = (8√

3, 16), BS4 = (8√

3, 8), BS5 = (5√

3, 4). TheMS was located at (6

√3, 8). Note that x–y coordinates are

given in kilometers.For these simulations, the measurement noise ni was mod-

eled using three different types of probability distributions,namely, the uniform, normal, and triangular. The uniform andnormal probability distributions are frequently used in themobile station location estimation literature. The triangulardistribution is defined by three parameters, [min, mode, max],where min, mode, and max are the smallest, most frequent,and largest values, respectively. It is often used in cases wheredata is limited, or difficult and/or expensive to collect [48].

Each simulation experiment consisted of 1000 independentruns. In simulations using the uniform distribution, the mea-surement noise ni was selected to be over the range fromzero to 200 m for all five base stations. Thus, the LOS/NLOSthreshold for the hypothesis test was about σ = 60 mwhich is approximately the standard deviation of the uniformdistribution on [0, 200]. When using the normal distribution,the measurement noise ni was set to have a mean of 100mand standard deviation of 50m for all base stations. Thus, theLOS/NLOS threshold for the hypothesis test was σ = 50 m.For the triangular distribution ni was set to be over the rangefrom zero to 200 m for all base stations with a mode of 100m.The triangular distribution [0, 100, 200] has a mean of 100 andstandard deviation of approximately 41, and so the LOS/NLOSthreshold for the hypothesis test in these simulations was aboutσ = 41 m. In all simulations, the NLOS error εi for any NLOSBS was modeled using the uniform distribution on the rangefrom zero to 1300 m.

TABLE II

Simulated Hypothesis Test Results with 2 NLOS BS

# of ErrorsBSi LOS/NLOS Mean si Type I Type II

1 LOS 60.59 371 —2 NLOS 294.97 — 03 LOS 60.59 385 —4 NLOS 294.78 — 05 LOS 60.65 386 —

TABLE III

Simulated Hypothesis Test Results with 5 NLOS BS

BS (i) LOS/NLOS Mean si # of Type II Errors1 NLOS 294.90 02 NLOS 294.91 03 NLOS 294.78 04 NLOS 295.08 05 NLOS 295.22 0

B. Simulation Results

To evaluate the potential for the hypothesis test to correctlymake LOS/NLOS determinations in the simulation environ-ment described above we made 1,000 simulation runs in whichBSs 1, 3, and 5 were LOS with respect to the MS andBSs 2 and 4 were NLOS. In each run, M = 500 distancemeasurements were simulated at each BS. For each BS, TableII shows the average value of si (in meters) and the numbertimes the hypothesis test correctly designated the BS as LOSor NLOS over the 1000 runs. Observe that in this experimentthe hypothesis test made the correct LOS/NLOS designationover 60% of the time for BSs with LOS and 100% of the timefor BSs with NLOS. Table III shows results from a similarexperiment in which all five BSs were NLOS. Based on theresults in Tables II and III, we conclude that it is possible todistinguish between LOS and NLOS measurements using thehypothesis test in the simulation environment described above.

1) Mobile Station Location Estimation Accuracy: TablesIV–VI summarize the results of our simulation runs. For theseruns we considered seven different cases. In cases 1, 2, and3, a single simulation run consisted of randomly selecting asubset of four out of the five BSs, randomly selecting a subsetof those four BSs to be NLOS, simulating M = 500 distancemeasurements at each of the four BSs, and then applying threemobile station location estimation algorithms: LS with all fourBSs, CWLS with all four BSs, and our MSLE methodology.In cases 4, 5, 6, and 7, a single simulation run consisted ofrandomly selecting a subset of the five BSs to be NLOS,simulating M = 500 distance measurements at each of thefive BSs, and then applying the three mobile station locationestimation algorithms mentioned above. For a given locationestimate, we used the root mean square error (RMSE) as themeasure of goodness. In Tables IV–VI, we list the percentageof RMSEs that were within the allowable FCC limits.

As demonstrated in Tables IV–VI, the MSLE methodologyoutperformed the two other algorithms in all but three cases:case 1 (4 BS/0 NLOS), case 4 (5 BS/0 NLOS) and case 7 (5BS/3 NLOS). Table VII summarizes the MSLE methodology’s


TABLE IV

Performance Comparison of Algorithms With Uniform

Distribution for LOS errors

RMSELS CWLS MSLE

#of %in %in %in %in %in % inBS/NLOS 100 m 300 m 100 m 300 m 100 m 300 m

4/0 100 100 100 100 76 1004/1 0 56 9 37 72 994/2 12 25 11 12 71 995/0 100 100 100 100 90 915/1 0 60 0 40 87 915/2 12 22 0 10 86 895/3 0 18 0 9 0 16

TABLE V

Performance Comparison of Algorithms With Normal

Distribution for LOS Errors

RMSELS CWLS MSLE

#of %in %in %in %in %in %inBS/NLOS 100 m 300 m 100 m 300 m 100 m 300 m

4/0 100 100 100 100 75 1004/1 0 60 7 39 71 1004/2 10 24 4 10 70 1005/0 100 100 100 100 90 935/1 0 60 0 41 90 915/2 10 22 0 11 91 925/3 0 22 2 9 0 3

TABLE VI

Performance Comparison of Algorithms in Five-Cell

Simulations With Triangular Distribution for LOS Errors

RMSELS CWLS MSLE

#of %in %in %in %in %in % inBS/NLOS 100 m 300 m 100 m 300 m 100 m 300 m

4/0 100 100 100 100 100 1004/1 0 62 2 40 100 1004/2 10 28 0 10 71 1005/0 100 100 100 100 100 1005/1 0 62 0 42 100 1005/2 10 20 0 10 89 905/3 0 19 0 15 0 3

performance with the three different distributions for the mea-surement noise. For the uniform probability distribution, thecalculated RMSEs are within 100 m and 300 m more than 71%of time; exceeding 67% as required by FCC. For the normalprobability distribution, the calculated RMSEs are within 100m and 300 m over 69% of time and above 67% as requiredby FCC. Also, for the triangular probability distribution, thecalculated RMSEs are within 100 m and 300 m over 74% ofthe time, which is also above 67% as required by FCC.

In cases where all base stations had a LOS path with theMS (case 1 and case 4), the RMSEs of the location estimatesfrom the LS and CWLS procedures were always within 100m, whereas those from the MSLE methodology were within100 m 76% of the time in case 1 and 90% in case 4 when

TABLE VII

MSLE Performance Comparison With Three Distributions

RMSEUniform Normal Triangular

#of %in %in %in %in %in % inBS/NLOS 100m 300m 100m 300m 100m 300m

4/0 76 100 75 100 100 1004/1 72 99 71 100 100 1004/2 71 99 70 100 71 1005/0 90 91 90 93 100 1005/1 87 91 90 91 100 1005/2 86 89 91 92 89 905/3 0 16 0 3 0 3

the measurement errors were generated from the uniformdistribution, and within 100 m 75% of the time in case 1 and90% of the time in case 4 when the errors were generated fromthe normal distribution. These results suggest a refinement tothe MSLE methodology that might yield improved results incases where all BSs have an LOS path with the MS.

1) Ignore the first stopping criterion in Stage 1 and insteadtake TOA measurements from all N BSs.

2) Stage 2:a) Let N ′ be the number of BSs deemed by the

hypothesis test to be LOS.b) If N ′ ≥ 3, then apply LS using all N ′ LOS BSs.c) If N ′ < 3, then apply LS using all N ′ LOS

BSs and the 3 − N ′ NLOS BSs with the smalleststandard deviations in their TOA measurements.

Note, however, that one of the appealing features of the MSLEmethodology, aside from improved accuracy, is that it can savevaluable time by stopping TOA measurements as soon as threeBSs are deemed to have LOS with the MS. When N ′ is largerthan 3, the methodology described above requires extra time totake the range measurements at the additional N ′−3 BSs; eachadditional LOS BS used in the estimation adds an equationto the LS problem (7), which means it could take longer toperform the calculations to estimate the location of the MS.Although the wireless E911 regulations do not have specifictime limits for the mobile station location estimation process,it is clearly important that the PSAP receive the most accurateestimate possible in as short a time as possible. Thus, a trade-off between processing time and accuracy must be made whendeciding which version of the MSLE methodology to use.

VII. Conclusion

This paper presented a methodology to improve the ac-curacy of mobile station location estimation in an NLOSenvironment. The methodology built on methods previouslypresented in the literature, involving hypothesis testing todetermine which BSs were LOS, and which were NLOS andthe use of least squares to estimate MS location. A uniquefeature of this methodology development, compared to otherapproaches in the literature, was the application of the systemsengineering process to provide a framework for evaluatingpreviously proposed methods and to guide development ofan improved methodology to meet established requirements.


Based on a simulation study, the methodology appears tohave potential for significantly improving the LS locationestimate in certain situations. A large-scale simulation studyto characterize these situations is the subject of an on-goinginvestigation.

It was important to note that our methodology was designedfor network-based solutions. It seemed likely that some timewithin in the next decade the FCC will require all wirelessservice providers to meet the more stringent requirements thatare presently mandated only for handset-based systems [15][49]. Thus, we anticipated a need to develop mobile stationlocation estimation methodologies for hybrid systems of GPS-based and network-based technologies in the near future.

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Reza Rahdar (M’01) received the B.S. degree inelectrical engineering from Concordia University,Montreal, QC, Canada, in 1988, and the M.S. de-grees in operations research in 2003 and in sys-tems engineering in 2006 from Southern MethodistUniversity (SMU), Dallas, TX, USA, and the Ph.D.degree with a major in applied science, concentrationin systems engineering from SMU in 2010.

He is currently a Senior Engineering Specialist(Systems Engineering) with Bell Helicopter, FortWorth, TX, USA, and an Adjunct Professor of

systems engineering with Embry-Riddle Aeronautical University, DaytonaBeach, FL, USA.

Jerrell T. Stracener received the B.S. degree fromthe Arlington State College, in 1965, and the M.S.and Ph.D. degrees from Southern Methodist Univer-sity, Dallas, TX, USA, in 1969 and 1973, respec-tively.

He is the Founding Director of the SouthernMethodist University (SMU) Systems EngineeringProgram and also teaches graduate-level coursesin systems analysis methods and applications, anddirects and conducts systems engineering research.He is the SMU Lead Senior Researcher with the

Systems Engineering Research Center, the first University Affiliated ResearchCenter funded by the Department of Defense (DOD) to focus on challengingsystems engineering issues facing the DOD and related defense industries. Hewas the Co-Founder and Leader of the SAE Reliability, Maintainability, andSupportability Division (G-11).

Eli V. Olinick received the B.S. degree in appliedmathematics from Brown University, Providence, RI,USA, and the M.S. and Ph.D. degrees in industrialengineering and operations research from the Uni-versity of California, Berkeley, CA, USA, in 1994and 1999, respectively.

He is currently an Associate Professor with theDepartment of Engineering Management, Informa-tion, and Systems, Bobby B. Lyle School of Engi-neering, Southern Methodist University, Dallas, TX,USA. His current research interests include applied

optimization, especially network design problems.Dr. Olinick is the Past Chair of the INFORMS Technical Section on

Telecommunications.

a systems engineering approach to improving the accuracy of mobile station location estimation

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