560 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL…bbcr.uwaterloo.ca/~wzhuang/papers/17_Li_TWC2.pdf · 560 ieee transactions on wireless communications, vol. 4, ... (nlos) propagation

560 IEEE TRANSACTIONS ON WIRELESS COMMUNICATIONS, VOL. 4, NO. 2, MARCH 2005

Nonline-of-Sight Error Mitigation in Mobile LocationLi Cong, Student Member, IEEE and Weihua Zhuang, Senior Member, IEEE

Abstract—The location of mobile terminals has received consid-erable attention in the recent years. The performance of mobile lo-cation systems is limited by errors primarily caused by nonline-of-sight (NLOS) propagation conditions. We investigate the NLOSerror identification and correction techniques for mobile user loca-tion in wireless cellular systems. Based on how much a priori knowl-edge of the NLOS error is available, two NLOS mitigation algo-rithms are proposed. Simulation results demonstrate that with theprior information database, the location estimate can be obtainedwith good accuracy even in severe NLOS propagation conditions.

Index Terms—Angle of arrival (AOA), mobile location, non-line-of-sight (NLOS) propagation, time difference of arrival(TDOA), wideband code-division multiple-access (CDMA) cel-lular systems.

I. INTRODUCTION

MOBILE location has received considerable attentionin the recent years. Generally, two different location

schemes have been extensively investigated [1]–[3]: one is atime-based scheme, to measure the time of arrival (TOA) ortime difference of arrival (TDOA) of incoming signals; theother is to measure the angle of arrival (AOA), which involvesthe use of an antenna array. Because TOA/TDOA and AOAapproaches have their own advantages and limitations, a hybridTDOA/AOA mobile location scheme is proposed in [4] and [5]for the future wideband code-division multiple access (CDMA)cellular systems. To achieve high location accuracy and mini-mize the increased cost on mobile station (MS) receivers, thelocation scheme combines the TDOA measurements from theforward link pilot signals with the AOA measurement at thehome base station (BS) from the reverse link pilot signal.

The major error sources in the mobile location includeGaussian measurement noise and nonline-of-sight (NLOS)propagation error, the latter being the dominant factor [2]. Afield test shows that the average NLOS range error can be aslarge as 0.589 km in an IS-95 CDMA system [6], which ismuch greater than the average Gaussian measurement noise. Toprotect location estimates from NLOS error corruption, NLOSerror mitigation techniques have been investigated extensivelyin the literature [6]–[15]. Most of these techniques assume that

Manuscript received February 21, 2003; revised August 4, 2003 and De-cember 21, 2003; accepted February 23, 2004. The editor coordinating the re-view of this paper and approving it for publication is H. Boelcskei. This workwas supported in part by the Canadian Institute for Telecommunications Re-search (CITR) and by the National Science and Engineering Research Council(NSERC) of Canada.

L. Cong is with Research and Development, SE/NIT, UTStarcom, Hangzhou310053, China (e-mail: [email protected]).

W. Zhuang is with the Centre for Wireless Communications (CWC),Department of Electrical and Computer Engineering, University of Waterloo,Waterloo, Ontario N2L 3G1, Canada (e-mail: [email protected];[email protected]).

Digital Object Identifier 10.1109/TWC.2004.843040

NLOS corrupted measurements only consist of a small portionof the total measurements. Since NLOS corrupted measure-ments are inconsistent with line-of-sight (LOS) expectations,they can be treated as outliers. Similar to the global positioningsystem (GPS) failure detection algorithm in [16], measurementerrors are first assumed to be Gaussian noise only, then the leastsquare residuals are examined to determine if NLOS errors arepresent [8], [9], [12]. Unfortunately, this approach fails to workwhen multiple NLOS BSs are present, as the outliers tend tobias the final estimate precision to reduce the residuals. Thisbehavior motivates the use of deletion diagnostics in whichthe effects of eliminating various BSs from the total set arecomputed and ranked, as in [9] and [12]. Other approachesinclude using the well-established robust estimation theory,such as the Huber Window [17], to form an estimator which isinsensitive to small numbers of outliers.

All the above-mentioned algorithms in the literature only workwell with a large size of samples and a small number of outliers.However, in apractical cellular system, two problems arise: 1) thenumber of available BSs is always limited and 2) multiple NLOSBSs are likely to occur. It has been shown that even by increasingthe correlation time or enforcing an idle period to reduce interfer-ence, typically only 3–6 BSs can be heard by the MS at any time[18]. Among those BSs, one cannot assume that the majority areLOSBSs. This isbecause in macrocells, the propagation betweenan MS and its home BS is usually modeled as NLOS when the MSisfarawayfromtheBS.HomeBScanonlybeviewedasLOSifwefocus our attention on large NLOS bias and neglect small NLOSerrors caused by local scatterers around the MS. All other neigh-boringBSscanbeNLOSsince theyare fartherawayfromtheMS.Inmicrocells, although theMSis typically modeledasbeingLOSwith its home BS, one cannot expect the MS to be LOS with othersurrounding BSs. Thus, we can only reasonably assume that thehome BS is LOS BS and that all other BSs can be NLOS BS inthe worst case. Several approaches are proposed in [2], [13], and[14] toreduceestimationerrorsforTOAwhenthemajorityofBSsare NLOS. Based on the fact that NLOS error always appears as apositive bias in TOA measurements, a constrained optimizationis used to reduce the NLOS bias [2], [14].

Generally, the distributions of NLOS errors are locationdependent. When the MS is stationary or slowly moving,the NLOS error can be assumed to be static. That gives riseto nonparametric approaches based on empirical data fromvarious locations. For example, pattern recognition algorithms[19]–[21] have been proposed to improve the handoff perfor-mance. Based on the statistical pattern of the received signalstrength, the system can determine if a user has arrived at ornear a certain location and if a handoff is necessary. Due to thesignal strength attenuation caused by multipath effect and shad-owing, this can only be used for rough estimation of the MS

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CONG AND ZHUANG: NONLINE-OF-SIGHT ERROR MITIGATION IN MOBILE LOCATION 561

location. To obtain a more accurate location estimate and to en-sure one-to-one correspondence of the pattern and the location,other characteristics of the signal have to be exploited. In [22],a database of delay measurements at fixed locations is used. Itrequires survey samples of field measurements taken at knownlocations to generate approximate conditional density functionsof user location given a delay measurement. A mapping methodutilizing location database and a ray launch simulation toolis proposed in [11] to improve GPS positioning accuracy forthe NLOS situation. These approaches give significantly betterlocation accuracy at the cost of setting up and maintaining anempirical database. The data can come from field measure-ments conducted during the cellular system planning and/orcomputer-aided prediction based on digital terrain and landcover information [23], [24]. A field trial conducted in NewYork City [25] suggests that it takes 500 human hours of workto build up an accurate mapping database covering 50 kmof metropolitan area, and the estimated cost is $1000 per cell(of radius 1 km). Therefore, it is not impractical to set up theempirical database which includes the NLOS information at allpossible MS locations.

In this paper, we continue to investigate the NLOS error miti-gation problem in TDOA and TDOA/AOA location schemes.Our results can be extended to a TOA scheme as well. De-pending on how much a priori information is available, two ap-proaches are proposed: an NLOS state estimation (NSE) algo-rithm can be used if some prior information on NLOS errors isavailable from the empirical database; in the case where we donot have any knowledge about NLOS, an improved residual al-gorithm can be applied to detect a small number of NLOS BSs.Simulation results demonstrate that location accuracy improve-ment is possible even in severe NLOS propagation conditions.

The paper is organized as follows. The system model is givenin Section II. Section III describes the proposed NLOS mitiga-tion algorithms. The performance of the proposed NLOS miti-gation techniques is studied via simulation and presented in Sec-tion IV. Final conclusions are drawn in Section V.

II. SYSTEM MODEL

The system model under consideration is a wideband CDMAcellular system. We focus on the case of macrocells and two-di-mensional (2-D) mobile location. The BS serving the target MS(to be located), denoted by , is called the home BS for theMS. All neighboring BSs can get involved in an MS locationprocess, provided the signal-to-interference-plus-noise ratio(SINR) of the signal from each BS is above a certain thresholdat the MS. At all times, the MS keeps monitoring the forwardpilot channel signal levels received from the neighboring BSsand reports to the network those that cross a given set ofthresholds. The cross correlators at the MS receiver are capableof measuring the TDOA between the signal from the home BSand that from any other BS.

Adaptive antenna arrays have been proposed for radio trans-mission in third-generation cellular communication systems tofacilitate the initial acquisition, time tracking, Rake-receiver co-herent reference recovery, and power-control measurements for

the MS. If an adaptive antenna array is available at the BS site,the home BS can dedicate a spot beam to a single MS underits jurisdiction by dynamically changing the direction of the an-tenna pattern as the MS moves to provide the arriving azimuthangle of the signal from the MS. This AOA measurement can beused together with TDOA measurements for improved locationaccuracy.

It is assumed that at any time the MS to be located can receiveforward-link pilot signals from its home BS and at least oneneighboring BS. Upon receiving the location service request,two types of measurements are carried out for location purposes[4], [5].

1) TDOA measurements at the MS receiver:The MS receiver can measure the time arrival differ-ence between the pilot signals of a nonhome BS and thehome BS by a pseudo-random (PN) code tracking loopwhich cross correlates the pilot signal from the non-home BS with the pilot signal from the home BS. Thepilot signal from each of the neighboring BSs can beused in the MS location, provided that the SINR of thereceived signal at the MS is above a certain threshold.The TDOA measurements can be obtained with an ac-curacy better than a half-chip duration if wireless prop-agation channel impairments are not severe [26]. How-ever, for nonhome BSs, fading, and delay spread dueto multipath propagation can introduce large errors toTDOA measurements.

2) AOA measurements at the home BS:With an adaptive antenna array, the home BS steers itsantenna spot beam to track the dedicated reverse-linkpilot signal from the MS for improved reception. Thisprovides the arriving azimuth angle (with respect toa specified reference direction) of the signal from theMS. In a macrocell environment, the AOA measure-ments can be obtained with an accuracy of a few de-grees [3].

The forward-link TDOA measurements are forwarded to thehome BS via the wireless channel, where both the forward-linkTDOA and reverse-link AOA measurements are combined to-gether. Based on the NLOS situation, some measurements willbe chosen to give a location estimate of the MS.

A BS is said to be LOS BS if there exists a direct path from theBS to the MS. Since we are mainly interested in NLOS errorsthat cause a large deviation to the MS location estimate, it is rea-sonable to neglect NLOS errors resulting from local scatterersnear the MS, as those errors are relatively small. Therefore, inthe rest of this paper, an NLOS BS means that there does notexist a direct path from that particular BS to the MS, and thesignal has to travel an extra distance of several hundred metersto reach the MS via reflection.

It is possible that the home BS does not have LOS propaga-tion with the MS, therefore adding bias to all the TDOA mea-surements and to the AOA measurement. In Section III-C, wepresent a residual algorithm which can detect the NLOS homeBS situation. The NLOS bias can then be reduced by referencingthe TDOA with an LOS nonhome BS and discarding the homeBS’s AOA measurement.


Fig. 1. Hybrid TDOA/AOA location.

The generalized location estimation problem in matrix formis given by

(1)

where denotes the measurement ma-trix, is the number of equations, is the true location of theMS, is a function of and is usually nonlinear, is the zeromean Gaussian noise vector, and is the NLOS error vector.Let denote the minimum number of BSs needed for locationestimation. We have for TDOA location andfor hybrid TDOA/AOA location. When there are BSsavailable for location, the redundant BSs will provide andegree of freedom in determining the NLOS BSs. As illustratedin Fig. 1, the hybrid TDOA/AOA location equations [5] that in-corporate the measurement noise and NLOS error are given by

(2)

where is the speed of light, is the measured TDOA betweenthe th BS and is the distance from the MS to the thBS, is the distance between the MS and , and arethe TDOA measurement noise and NLOS error, respectively,

is the AOA measurement noise, and are thecoordinates of the MS and home BS, respectively. We assumethat and are independent Gaussian random variables withzero mean and variances and , respectively. If has anLOS path to the MS, then ; otherwise, is a positiverandom variable with mean and variance . We fur-ther assume that , which is consistent with field testresults [6]. Note that the number of BSs is in TDOA locationand in TDOA/AOA location.

III. NLOS ERROR MITIGATION ALGORITHMS

Depending on how much a priori information we have aboutNLOS error prior probabilities and distributions, three cases canbe distinguished.

1) The exact distribution of the random NLOS error foreach BS at the MS location is known. This is an easybut unrealistic case. We use this, however, as a startingpoint for the design of NLOS error mitigation algo-rithm, which is then extended to more realistic situa-tions, for example, by replacing unknown NLOS errorsby estimated values or values measured a priori.

2) Limited prior information of the NLOS errors is avail-able. For example, at the MS location the probability ofeachBSbeingNLOSandthemeanoftheNLOSerrorareknown for theMS location. This type of information cancome from a database of field measurements or a com-putersimulationutilizingraytracingtechniquesanddig-ital terrain plus land cover information.

3) No information of the NLOS error is available. Thissituation is obviously the most interesting case from apractical point of view, but also the most difficult onein the design of NLOS error mitigation algorithms.

A. Ideal Case: With Known NLOS Statistics

Let denote the prior probability of being LOSat the MS location, and . The locationequation for becomes

(3)

(4)

As mentioned earlier, usually the measurement noise andare modeled as zero-mean Gaussian random variables with

variance and , respectively. Theoretically, if we know theexact distribution of NLOS errors , we can have the optimummaximum likelihood (ML) detection of the NLOS BSs. The MLestimator aims at maximizing the joint conditional probabilitydensity function (pdf) of the measurement matrix

(5)

where is the joint pdf of measurement errors .Under the assumption that NLOS errors and Gaussian measure-ment noise are independent random variables, we have

(6)

where is the pdf of the Gaussian measurementnoise, and is the pdf of the NLOS error plus noiseand is usually unknown. Numerical methods can be used to findthe location which maximizes the conditional pdf given in (6).This ML estimator actually combines the NLOS BS identifica-tion and NLOS error correction into one single step and is ableto achieve the optimum result when the empirical NLOS errordistributions are accurate.

Given a set of TDOA measurements, a three–dimensional(3-D) plot of the conditional pdf in (6) over the home BScoverage area usually reveals multiple peaks (local maxima), asshown in Fig. 2, each corresponding to a possible NLOS/LOSBS scenario, and the magnitude of the peak corresponding to


Fig. 2. Joint conditional pdf of the TDOA estimator (four BSs).

Fig. 3. Joint conditional pdf of the TDOA/AOA estimator (four BSs).

the relative likelihood of such scenario. The location corre-sponding to the highest peak (global maxima) is the output ofthe location estimator. Fig. 3 shows the same conditional pdf

for TDOA/AOA location. The additional AOA informationhelps to suppress some peaks so there is less ambiguity as towhere the true MS location is.


Because making a wrong NLOS/LOS BS scenario decisioncan introduce a significant root mean square (rms) location error(as large as several hundred meters), we propose a soft-decisionlocation estimator to further reduce the location error. Insteadof giving a hard location estimate, the soft-decision robust esti-mator outputs several possible MS location estimates and theirrelative likelihoods. As the MS continues to carry out new mea-surements, the time history data will help to reduce the ambi-guity of the MS location, since the movement of the MS in ashort period of time is limited to a small region.

To make a soft decision, we need to separate the NLOS BS(s)identification and correction into two steps. For each , ahypothesis test can be employed to determine its NLOS status.First, consider a simple case where only one NLOS BS is present.We use the maximum a posteriori probability (MAP) criterionto make a decision based on the actual measurement in orderto minimize the average false NLOS identification rate. Theposterior probability is given by

The decision rule is then

(7)

Therefore, making a decision about requires the knowledgeof prior probability of and the conditional probability

, which in turn requires the knowledgeof the true MS location. The intermediate MS location estimateusing all BSs except can be used to approximate the trueMS location.

Now let us consider the case of multiple NLOS BSs in TDOAand TDOA/AOA location. In the worst case, all of these BSsare NLOS BSs. Let denote the systemstate, where if is NLOS, and zero otherwise. Thereare altogether possible states and the task of NLOS BS de-tection is to correctly determine the right system state. Letdenote the special state that all BSs are LOS. To optimally de-termine the NLOS state, we propose the following NLOS stateestimation (NSE) algorithm.

1) For each of the possible states , obtain a locationestimate using the known NLOS information.

2) Using to approximate the true MS location and cal-culate the weighted a posteriori probability for eachpossible state

(8)

where is a weight assigned to state, and .

3) Calculate the ratio for each of theNLOS states.

4) For a hard decision, the state which has the largest ratiois selected, and the corresponding ML estimate is theoutput location. For a soft decision, those states whoseratio is above a certain threshold are selected, and

the magnitude of the ratio corresponds to the relativelikelihood of that NLOS state.

If the prior probabilities are un-known, the weight in (8) can be used to control the falsealarm rate and detection probability. For example, a heavierweight for LOS state provides a cushion for false alarm,but also reduces the NLOS detection probability. The optimalvalues of the weights depend on the desired detection proba-bility and false alarm rate, and of course how severe the NLOSsituation is. Since minimum rms location error is the final goal,a cost/reward function can be formulated which includes thepenalty of a false alarm and the reward of a correct detection interms of rms errors. The optimal values of the weights are thevalues that minimize the cost function.

In summary, if we have an empirical database available fromfield measurements which provides the information ofand the stochastic model of , we can deriveand then apply the NSE algorithm. The algorithm can work forboth TDOA and TDOA/AOA location systems, under the as-sumptions that the NLOS errors, the TDOA, and AOA measure-ment errors are all independent.

B. With Limited a Priori Information

In reality, modeling the NLOS error is a difficult task, as theNLOS error is location dependent, influenced mainly by terrainsand buildings. A much more realistic assumption is that for eachBS we know (the mean of the NLOS error) and(the prior probability that is an NLOS BS) for differentlocations.

To approximate , we treat the NLOSerror as a constant bias superimposed on the zeromean Gaussian noise . Then

(9)

The NSE algorithm can then be used again to provide a hard orsoft decision. One difference is that in Step 1) before we makean estimate for each state, NLOS errors are compensated bysubtracting the NLOS bias from the measurements of if

.An even more interesting case is that we know nothing about

the NLOS error except its bound of magnitude. For example, theNLOS error for , if present, is greater than 300 m. To obtaina suboptimal solution in this case, algorithms designed under thegeneralized likelihood ratio (GLR) [27] can be used. For eachstate, the ML estimator estimates not only the MS location , butalso the values of NLOS errors . Then,can be approximated by using to replace in (9). How-ever, that imposes a limit on the total number of NLOS BSs, asthe equations will be underdetermined when more thanNLOS BSs are present. For example, in TDOA location, fouravailable BSs can only determine one NLOS BS when we applythe NLOS identification algorithm. With the additional AOA in-formation, two NLOS BSs can be identified.

In the case when the empirical value of is not avail-able, a blind estimator can be used which arbitrarily sets the


value of . When , this blind ML estimatorbecomes the conventional LOS ML estimator. cor-responds to a very aggressive estimator which treats every BSas NLOS BS. The value of can be selected based on theSINR and/or desired robustness to the NLOS error.

C. Worst Case: No Knowledge of the NLOS Error

In the worst case, we do not have any knowledge about theNLOS error. If a limited number of BSs is available, and themajority are NLOS, little can be done to reduce NLOS errors.Therefore, to derive NLOS mitigation algorithms in the worstcase, we have to assume that only a small subset of the totalavailable BSs are NLOS BSs. It is worth mentioning that moreNLOS BSs does not necessarily mean a larger bias in the finalMS location estimate. NLOS BSs tend to bias the final estimatein such a way that the estimated location moves away from thoseBSs, so more NLOS BSs increase the chance of those NLOSerrors cancelling each other. Taking the case of for ex-ample, a large estimation error usually happens when one or twoNLOS BSs are present.

We further assume that the home BS is LOS BS. Later, wewill discuss the case of the home BS being NLOS. Based onthe assumptions, we can make use of analytical redundancy re-lationships for NLOS error mitigation. The first step is to iden-tify NLOS BSs among all the available BSs. Since nothing isknown about NLOS errors, we have to treat NLOS corruptedmeasurements as outliers and rely solely on our knowledge ofGaussian measurement noise to detect NLOS BSs. Let de-note the number of NLOS BSs. Once the value of is known,two scenarios can follow: 1) if there are sufficient BSs (i.e.,

) to make a location estimate after the NLOSBSs being identified and removed, we can obtain an improvedMS location estimate using only the LOS BSs and 2)otherwise, we can only issue a warning that the output MS loca-tion estimate is not reliable due to NLOS errors or resort to somerobust estimators (if they exist) that are insensitive to NLOS er-rors.

Two popular approaches are used in the outlier detectiontheory: one is to use the residual ranking and the other is basedon the “ edit rule.” The latter is based on the fact that forthe Gaussian noise, the probability of observing a measure-ment further than three standard deviations from the mean isapproximately 0.3%. The approach requires the knowledge ofthe Gaussian measurement noise variance, which is usuallysatisfied in practice.

Residual ranking can work very well when we have a largenumber of BSs and one of them is NLOS BS. A residualweighting algorithm was first proposed in [9] for the TOAlocation scheme. It divides all available BSs into subsets andweights the location estimate from each subset according totheir residuals to obtain the final estimate. Similar approachesfor AOA and TDOA have been proposed in [8] and [12], re-spectively. For a given measurementand a reference location , the residual in [8], [9], and [12]can be generalized as . If , the residualreflects the magnitude of the NLOS error, since . Bytrying different combinations of candidate BSs and ranking

the residuals, the NLOS BSs can be identified with a certainprobability.

The residual algorithms have several limitations. First, it doesnot make use of the variance of Gaussian noise . Signals fromdifferent BSs usually have different SINRs, thus different noisevariance . The residual should be weighted according toso that the BS with a larger noise component will have less con-tribution in the overall residual. Second, the NLOS error isalways positive. If for , it is less likelythat is NLOS BS, as compared with where

. However, the square operation in the residual re-moves the sign of . Finally, as the residual is in a sum-mation form, it can only indicate how likely a group ofcandidate BSs contains NLOS BSs, but not which one(s). Wehave to rely on the residual ranking of all possible combinationsto determine the NLOS BSs. Therefore, the previously proposedresidual algorithms do not perform well when the number ofcandidate BSs is small.

In the following, we propose a new residual algorithm, whichcombines the two approaches in the outlier detection. Since wehave no knowledge of the NLOS error, we have to rely on theconditional probability

(10)

For a measured value and a reference location , the corre-sponding conditional cumulative density function (cdf) providesa measure of how likely the random Gaussian noise will makethe TDOA measurement smaller than and is given by

(11)

We define the new residual to be this cdf. Hence, the higherthe new residual, the more likely the BS is biased by NLOSerror(s). This new residual is asymmetric, giving more weighton the positive (i.e., ) side; it also takes theGaussian noise variance into account. Therefore, by directlyranking the residuals for each candidate BS, or comparing themwith a given threshold, we can overcome the limitations of theprevious residual algorithms.

On the contrary, a very small residual of indicates a highprobability of being LOS BS, provided that the referencelocation is close to the true value. This can be used in the specialcase when the home BS (i.e., ) is NLOS BS. We can then use

as the new home BS, making all the TDOA measurementsusing as the reference BS instead. In this way, the NLOSerrors remain positive in TDOA.

The new residual algorithm works for both TDOA andTDOA/AOA in the same manner. Similar to every residualalgorithm, the approximation of the true MS location, , playsan important role. Ideally, we should use the true location ofthe MS, but it is not achievable and can only be used as aperformance benchmark. We can use measurement data fromall the BSs to determine an overall location estimate and useit as the approximated MS location. Under the assumption thatthe AOA measurement at the home BS is independent of TDOA


Fig. 4. Asymmetric pdf for robust estimation.

measurements [12], the AOA measurement can help to improvethe accuracy of the reference location and therefore improvethe performance of the proposed identification algorithm. InSection IV, we shall see that the additional AOA measurementin the hybrid TDOA/AOA location helps to obtain a moreaccurate MS location approximation and thus better NLOSidentification accuracy.

The newly proposed algorithm of identifying NLOS BSsusing TDOA or TDOA/AOA measurements has the followingsteps.

1) Use the TDOA measurements from all the non-home BSs and, if the hybrid scheme, the AOA fromthe home BS as well, to obtain an initial MS locationestimate .

2) Calculate the new residual in (11) for each of thenonhome BS.

3) If any of the residuals is above a threshold , issuea warning that NLOS BSs are present and rank the

residuals. If we know the number of NLOSBSs, , pick up the BSs with the largest residuals;otherwise, compare the residual with the threshold ,and those BSs with residuals larger than the thresholdwill be deemed as NLOS BSs.

When we have a fairly large number of BSs (for example,), a deletion diagnostics scheme can be used to improve

the accuracy of . For each subset of the BSs (size 3 and up), cal-culate the reference location using measurements from all BSsin the subset and obtain the residual for each BS in the subset.Find the largest subset which satisfies the threshold for each of

the residuals. If that subset can be found, use that subset’s outputas a reference location and calculate the residuals; ifthat subset does not exist, the location estimate using all mea-surements will be used to calculate the residual, as described inStep 1).

The choice of the threshold affects both the detection prob-ability and false alarm probability. Both probabilities decreasewhen increases. For a given false alarm probabilityshould be a function of .

After successfully identifying the NLOS BSs, the next step isto remove the location bias caused by the NLOS errors. Withoutany knowledge of the NLOS errors, ideally we should removethose NLOS BSs from the set and use only LOS BSs for the lo-cation estimate. However, if the number of remaining LOS BSsis not enough for location estimation, we will have to use mea-surements from NLOS BSs as well. A simple approach can beused: use an asymmetric pdf to model the effect of NLOSand noise, as shown in Fig. 4, to make the estimator less sensitiveto the positive NLOS errors. The variance increase at the rightside (i.e., ) is called a tuning constant; larger values of itproduce more resistance to the NLOS errors, but at the expenseof lower efficiency when NLOS errors are not present. There-fore, the tuning constant should be chosen to give a reasonablyhigh efficiency in the LOS case and still offer protection againstNLOS errors.

The residual approach works well when we have a largenumber of available BSs, among which only a small number ofBSs are NLOS BSs. When multiple NLOS BSs are present, atleast some knowledge of NLOS statistics will be required forNLOS error mitigation.


Fig. 5. Seven-cell system layout.

IV. SIMULATION RESULTS

This section presents simulation results to demonstrate theperformance of the proposed residual algorithm and the NSEalgorithm. We assume that the standard deviation of the TDOAmeasurement noises km and the mean NLOS bias

km for , typical values confirmedby field tests [6]. For the 2-D array BS layout, we consider acenter hexagonal cell (where the home BS resides) with six ad-jacent hexagonal cells of the same size, as shown in Fig. 5. Thecell radius is 5 km and the MS location is uniformly distributedin the center cell. Each simulation is performed by 5000 inde-pendent runs.

For macrocells, there are usually multiple NLOS BSs. In theworst case, the majority or all of the BSs are NLOS. Our simu-lation results show that five or six out of seven BSs being NLOSis usually not as devastating as when three or four out of sevenBSs are NLOS. The reason is that more NLOS BSs increasesthe chance of NLOS bias cancelling each other. As a result, wepresent the simulation results mainly for a medium size of theNLOS BS set.

A. NLOS BS Identification Using Residual

To study the performance of the proposed residual algorithm,we randomly select a certain number of BSs as NLOS BSs andintroduce a positive bias to their measurements. Assuming noknowledge of the NLOS errors, the newly proposed residual iscalculated for each nonhome BS using a reference MS locationand then compared to the threshold . If the largest residual isfound to be above the threshold, a warning is issued indicatingthat NLOS BSs are present. We can further rank the residualsto identify those NLOS BSs. A false alarm occurs when thewarning is issued but no NLOS BS is present. A miss detectionoccurs when the algorithm fails to issue the warning in the caseof an NLOS situation. The rates of successfully identifying allor part of the NLOS BSs are also obtained via simulation.

We first consider the case of TDOA-only location. It is clearthat using the true location as the reference location consis-tently achieves the best performance, regardless of the MS/BSsgeometric layout. In a practical situation, we can use all theavailable TDOA measurements from all the BSs to obtain anapproximation of the true MS location. Table I compares the

TABLE INLOS BS IDENTIFICATION RATE FOR TDOA ONLY LOCATION USING

ESTIMATED MS LOCATION

TABLE IINLOS BS IDENTIFICATION RATE FOR TDOA/AOA LOCATION USING

ESTIMATED MS LOCATION

NLOS BS’s identification rates in different scenarios, using theapproximated location and the proposed residual ranking algo-rithm with the number of NLOS BSs being known. It is observedthat the proposed algorithm works well when we have a largenumber of BSs and only a small portion of these BSs are NLOS.For example, in the case of seven BSs and one NLOS BS, thealgorithm can successfully identify the NLOS BS with a proba-bility of 0.813. When the number of NLOS BSs increases, how-ever, the probability of detecting all of them decreases. It is alsoclear that when the number of total available BSs is small, thedetection rate suffers. In the case of two NLOS BSs out of fourBSs, the algorithm can only identify those two BSs with a prob-ability of 0.346.

By using the additional AOA information, we can furtherimprove the NLOS BS identification performance. This isachieved by using the AOA information together with theTDOA measurements to get an improved true MS locationapproximation. When the AOA measurement is accurate, theimproved reference location improves the detection rates sig-nificantly. In Table II, the detection rates for different numbersof BSs and NLOS BSs are compared, with degree.Taking the case of three NLOS BSs, for example, it is clear thatthe additional AOA information greatly improves the detectionaccuracy. With the AOA measurement, the algorithm alsoperforms more consistently when the total number of BSs issmall and depends less on the MS/BSs geometric layout. Thesame case of four BSs and two NLOS BSs in Table II yields acorrect detection rate of 0.601.

If the number of NLOS BSs is unknown, we should use thethreshold for the residual values to determine NLOS BSs.There is a tradeoff between the missed detection rate and thefalse alarm rate when choosing the value of , as shown inFigs. 6 and 7. A smaller reduces the missed detection ratebut increases the false alarm rate at the same time. The value of


Fig. 6. Comparison of false alarm rates.

Fig. 7. Comparison of missed detection rates.

can be chosen according to the desired false alarm and detec-tion probabilities as well as the total number of BSs. It is alsoobserved that for a certain , the additional AOA measurementslightly increases the false alarm rate but reduces the missed de-tection rate significantly, especially for a small number of BSs.

B. NSE Algorithm Performance

We now study the TDOA location accuracy using empiricaldata of the NLOS error prior probability and mean value. A total

of four BSs ( , and ) are included and the meanNLOSerror kmforall theNLOSBSs.Thestandarddeviation of the TDOA measurement is 0.07 km. We compare thehard-decision rms location errors in three scenarios: 1) using theNLOS mean and prior probability to correct the NLOS error; 2)using only the NLOS error mean to correct the NLOS error; and3) using TDOA measurements from all available BSs with noNLOS correction. Note that in the second scenario, the weightassigned to the state of all BSs being LOS can be used to controlthe false alarm rate. We let for all other system state .Assigning a larger weight of will reduce the false alarm rate,


Fig. 8. Comparison of location accuracy for different NLOS situations. (a) One NLOS BS (BS ) with probability 0.5. (b) Maximum of three NLOS BSs(BS ;BS , and BS ), each with probability 0.5.

at the cost of an increased miss detection rate. On the other hand,a smaller weight of will improve the location accuracy in thecase of a heavy NLOS situation.

Let us first consider a light NLOS situation. Among the fourBSs, is the only BS which can be NLOS with probability0.5. The NSE algorithm performance is shown in Fig. 8(a),where the -axis coordinate represents the probability of the rmslocation error smaller than the -axis coordinate. It is observedthat applying the NLOS correction with prior probability infor-mation gives the best performance. However, the NLOS correc-

tion algorithm using only the NLOS error mean performs worsethan no NLOS correction at all, due to a large number of falsealarms in this light NLOS propagation environment. A largereduces the location error significantly.

When the NLOS situation gets worse, for example, multipleNLOS BSs are present, the NLOS correction scheme usingNLOS error means and prior probabilities still gives the bestperformance; however, the performance gain over no NLOScorrection becomes smaller, as shown in Fig. 8(b), where threeof the four BSs are NLOS with probability 0.5. In this situation,


Fig. 9. Comparison of location accuracy for different NLOS situations. (a) Maximum of three NLOS BSs (BS ;BS , and BS ), each with probability 0.1. (b)Maximum of three NLOS BSs (BS ;BS , and BS ), each with probability 0.9.

even without NLOS prior probabilities information, NLOScorrection using mean only starts to outperform the no NLOScorrection case.

The NLOS error prior probability plays an important rolein the NLOS mitigation. In Fig. 9(a), three of the four BSsare NLOS with probability 0.1. Since the prior probability issmall, the NLOS correction using mean values actually per-forms worse than that using all measurements without NLOScorrection. That is because the NLOS correction based on themean NLOS error without the prior probability tends to assume

that NLOS and LOS situations happen equally likely. We canassign a proper value to the weight to alleviate this problem.Fig. 9(b) illustrates the opposite situation, when three of the fourBSs are NLOS with probability 0.9. In this case, the NLOS cor-rection without the prior probability gives much better locationestimate as compared with the no NLOS correction scheme. Inall cases, NLOS correction using the mean and the prior proba-bility information always performs the best.

Fig. 10 shows the decrease of rms location error as the numberof BSs increases. It can be observed that as the number of avail-


Fig. 10. Comparison of location accuracy, where each BS (except home BS) is NLOS with probability 0.5.

Fig. 11. Location accuracy using four BSs (BS ;BS ;BS , and BS ), each nonhome BS being NLOS with probability 0.9.

able BSs increases, the performance gain of the proposed NLOSmitigation scheme increases significantly.

It is also observed during the simulation that if the prior in-formation about the NLOS errors is not accurate (for example,the known NLOS mean deviates from the true value slightly),the NLOS mitigation algorithm can still provide performanceimprovement. We consider a four-BS case and deliberately addGaussian noise to the NLOS prior probability and NLOS mean.The standard deviation of the noise on the NLOS mean is 0.1km, and standard deviation of the noise on the NLOS prior prob-ability is 0.1. Fig. 11 shows the impact of using inaccurate prior

information on the location accuracy for the case of four BSswith a maximum of three NLOS BSs ( , and ), eachwith probability 0.9 (the NLOS prior probability is denoted byvector [0, 0.9, 0.9, 0.9]). Table III summaries the NSE algo-rithm performance when NLOS prior information is not accu-rate. From the results we can see that even using inaccurate priorprobability and/or inaccurate mean, the NSE algorithm still pro-vides better accuracy as compared to the case of no NLOS cor-rection at all. The only exception is when all three neighboringBSs are NLOS with probability 0.5 and inaccurate NLOS priorprobabilities are used.


TABLE IIIRMS LOCATION ERROR IN km USING INACCURATE PRIOR INFORMATION, FOUR BSS

Fig. 12. Comparison of the performances of different NLOS mitigation algorithms for a five-BS case. (a) Maximum of four NLOS BSs (BS ;BS ;BS , andBS ), each with probability 0.5. (b) Maximum of four NLOS BSs (BS ;BS ;BS , and BS ), each with probability 0.9.

Fig. 12 compares the performance of the proposed NSE algo-rithm with the residual weighting scheme in [9]. When appliedto TDOA and TDOA/AOA location, the residual weighting al-

gorithm requires at least five BSs. That is because the algorithmdivides all available BSs into subsets and weights the locationestimate from each subset according to their residuals. By the


definition of the residual in [9], a subset of size 4 and up is re-quired. So in Fig. 12(a), we consider the case of andwe assume that four of the nonhome BSs can be NLOS withprobability 0.5. It is observed that both the NSE algorithm andthe residual weighting algorithm can mitigate the NLOS error,and the NSE algorithm outperforms the residual weighting algo-rithm. Fig. 12(b) corresponds to a severe NLOS situation wherethe four nonhome BSs can be NLOS with probability 0.9. Inthis case, the residual weighting algorithm does not providemuch performance gain. The NSE algorithm, on the other hand,greatly improves location accuracy, even when imperfect priorinformation is in use.

V. CONCLUSION

This paper studies the NLOS error mitigation techniques fortime-based location systems. Based on the knowledge of NLOSerror statistics, two different NLOS mitigation algorithms areproposed. A new residual algorithm is used for NLOS BS identi-fication. The algorithm requires only the knowledge of Gaussiannoise statistics. It can effectively identify a small number ofNLOS BSs. Utilizing an accurate empirical database, the pro-posed ML location estimator can achieve the best location ac-curacy, even in the case where most BSs are NLOS BSs. Sim-ulation results demonstrate that an accurate location estimate ispossible even in severe NLOS conditions.

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Li Cong (S’93) received the B.Eng. and M.Eng.degrees from Southeast University, China, and theM.Eng. from Nanyang Technological University,Singapore, all in electrical engineering. He receivedthe Ph.D. degree in electrical and computer engi-neering from the University of Waterloo, Waterloo,Ontario, Canada.

He is currently working as a Senior system En-gineer at UTStarcom. His research interests includeOFDM-based mobile broadband wireless systemsand location/navigation technology.

Weihua Zhuang (M’93–SM’01) received the B.Sc.and M.Sc. degrees from Dalian Maritime University,Liaoning, China, and the Ph.D. degree from the Uni-versity of New Brunswick, Fredericton, NB, Canada,all in electrical engineering.

Since October 1993, she has been with the De-partment of Electrical and Computer Engineering,University of Waterloo, ON, Canada, where she is aProfessor. She is a coauthor of the textbook WirelessCommunications and Networking (EnglewoodCliffs, NJ: Prentice Hall, 2003). Her current research

interests include multimedia wireless communications, wireless networks, andradio positioning.

Dr. Zhuang is a licensed professional engineer in the Province of Ontario,Canada. She received the Premier’s Research Excellence Award (PREA) in2001 from the Ontario Government for demonstrated excellence of scientificand academic contributions. She is an Editor of the IEEE TRANSACTIONS

ON WIRELESS COMMUNICATIONS and an Associate Editor of the IEEETRANSACTIONS ON VEHICULAR TECHNOLOGY.

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