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Investigation on a NLOS Error Mitigation Algorithm for TDOA Mobile Location Li Hemin, Deng Zhongliang , Yu Yanpei State Key Laboratory of Information Photonics and Optical Communications Beijing University of Posts and Telecommunications, Beijing lihemin@bupt.edu.cn, dengzhl@bupt.edu.cn, yyp@bupt.edu.cn TDOA data based on T1P1 channel model, to Abstract： eliminate the impact of NLOS error. The positioning precision of this method depends on the In typical Urban environment ， non-Line-Sight （ approximation degree between the channel model and NLOS） propagation between the base station (BS) the actual environment. And the complex and and mobile station (MS) became the main factor of changeable channel environment limits its the positioning error. As a result, the study on the application. Some other technology reduces the mitigation of its negative influence becomes a focus. influence of NLOS error by indirect method, which Base on Chan algorithm, this paper presents a TDOA uses the geometry relationship to reduce the NLOS mobile location algorithm, which can improve the error [3][4][5]. This algorithm improve the positioning accuracy effectively. The positioning positioning accuracy effectively in multiple base process includes NLOS error identification and its stations, but the actual environment , the mobile mitigation. First, the Wylie algorithm is used to station is difficult to receive a more stations signal identify the existence of NLOS. And then, the time of and limits its precision with a further rise. arrival (TOA) is update based on the difference of TOA and the distance between BS and MS. This 2. TDOA Measurement Model coordinate of the MS is estimated by using Chan algorithm in the process of this distance calculating. Assuming M base stations participate in positioning Simulation results show that this algorithm can process, they are BS1，BS2，„„,BSm . Among mitigate the NLOS error and improve the location them, BS1 is service station of the mobile stations. accuracy in different environment effectually. τi is TOA measured value from MS to BSi, τi,1 represents TDOA measured value from MS to BSi Keywords: NLOS error; Chan algorithm; mobile and BS1. Therefore formula (1) can been get location; location estimate n nlos i， 1 0 i， 1 i i (1) 1. Introduction where i， 0 1 denotes the difference of the Since the Federal Communication Committee (FCC) light-of-sight (LOS) distance from MS to BSi and declared the requirement of E-911 which ask for the accuracy of mobile location to be up to 100m under BS1. ni denotes the Gauss noise which is always 67% probability in 1996, researcher take more and existence in system measurement. nlos i is NLOS more attention on location technology in cellular network. Location Based Service (LBS) also will be error, and it is independent with ni . necessary for the cellular network, especially the 3G network. Now. Wireless locating method is mainly In different channel environment, the additional delay based on time of arrival(TOA)、time difference of because of NLOS can be evaluated based on the arrival（TDOA） and angle of arrival（AOA）. But COST259 model, which generally be considered to TOA and TDOA location technology are easily be a typical channel model in assessing location changed by NLOS 、 multipath and other factors. technology based on time. The probability density is AOA positioning technology needs special much as bellow； array antenna. So NLOS error mitigation algorithm in 1 positioning became the focus in location technology exp( ) 0 researcher. f ( ) rms rms 0 0 （2） In NLOS error mitigation technology can be divided into direct method and indirect method. In the direct method, NLOS error is mitigation by data processing Where rms is Root-Mean-Square delay spread technology [1][2]. Reference [1] ,[2] reconstruct determined by channel environment. In MS positioning process, NLOS average excess delay N 1 nlos i can be approximately considered as equal. ri,1(t j ) ai,1 (n)t n j n0 Base on Greenstein model rms is shown as: (6) Where ri,1(t j ) is the TDOA of BS i and BS 1 . rms T1d y {a i,1(n)} n 0 (3) N 1 Where T1 is the median of delay spread 1km away The unknown coefficients can been from BS. d is the distance between MS and BS. The obtained by Least-square technology. And after numeric area of is from 0.5 to 1. y denotes smoothing, the measured data is shown as: random variable subject to lognormal distribution N 1 with 0 mean and 4~6 dB standard deviation. rms s i ,1 (t j ) ai,1 (n)t n ˆ j n0 (7) is a random variable, and the mean and standard deviation ofτi,1 can be formulated as below:[6][7] The standard deviation of TDOA in NLOS environment is as below: 2 K 1 E（ i ,1） [exp （ mi） - exp( m1 )] exp( ) 1 2 （4 i,1 ˆ K (si,1 (t j ) ri,1 (t j )) 2 j 0 ） (8) where K is the number of measuring samples. And 2 [exp 2m i） exp( 2m1 )] （ the standard deviation in LOS environment is shown （5） as: [( 2 exp( 2 ) exp( )] 2 2 i21 E{ni2,1 (t )} , Where mi ， 2 is the mean and variance of (9) Where ni,1 (t ) is the measuring noise. ln rms . Secondly, judge weather NLOS error exists: 3. NLOS Error Mitigation Algorithm H 0： i,1 i,1 ˆ In this paper, a modified algorithm based on the Chan algorithm is proposed, Chan algorithm is a kind of H 1： i,1 i,1 ˆ (10) not recursively hyperbolic equations solution with In H1, NLOS error exists in the measured data. analytical expression solution. The algorithm has the small amount of calculation and higher precision in B, Improvement Based on Chan Algorithm Gaussian distribution noise environment. But in non line-of-sight environment, positioning accuracy of Based on Chan algorithm presented in reference [9], Chan algorithm dropped significantly. we propose an improved method. Let Ri ,1 , Li ,1 be the TDOA data in LOS environment and in NLOS To alleviate the NLOS error, three steps of the modified algorithm are introduced in the following environment. So we get Ri,1 i Li,1 , text. In step A, we introduce the identify method of NLOS error. And step B discusses the improvement 0 i 1 . The TDOA hyperbolic equation is as method based on Chan algorithm. Finally, the section follows: technology of weight μis presented in step C. i L2,1 2i Li ,1L1 K i 2 X i ,1 x 2Yi ,1 y K1 i A NLOS Error Identify (11) By least-square technology, the error vector of the Based on reference [8], this paper presents a method, equations is shown as: which uses measurement noise standard deviation acquired from the historical measurements of TDOA, h Ga za 0 (12) to judge whether NLOS error exists. The method Where bases on the fact that the standard deviation of measurements samples in NLOS environment is larger than it in LOS environment. The judgment method can been summarized as follows: Firstly, we process the measured data of TDOA by smoothing filter using N order polynomial technology. The N order polynomial of TDOA measured data is shown as: To be convenient for explanation, assume BS 1 , X Y2,1 2 L2,1 BS 2 , BS 3 , BS 4 to be 4 BSs that participate in 2,1 Ga X 3,1 Y3,1 3 L3,1 position. In step A, we have obtained which TDOA value exist NLOS error.. And we presume L2,1 and L3,1 exist NLOS error. L4,1 is measured in LOS X M ,1 YM ,1 m LM ,1 environment. 2 L2,1 X 2 Y2 X 12 Y12 2 2 2 2 Firstly, in order to get the value of weight i , we 1 3 L3,1 X 3 Y3 X 1 Y1 2 2 2 2 h assume primarily that L3,1 is measured in LOS 2 2 environment. That is to be 3 =1. In step B, we m LM ,1 X M YM X 1 Y1 2 2 2 2 have the conclusion that m i n , where m=0, Firstly, we assume that x, y, L1 are independence. n=1. So we set gradient g (n m) 10 So we can get: between m=0 and n=1, and get 1 T za Ga 1Ga Ga 1h T 2 m g, m 2g, , n . i in step B is (13) Where E T c 2 BQB ， replace by 2 (q ), q 1,2,10 every . one And of ten these estimated B diag 0 2 L2， , 1 0 3 L3， ,, 1 0 m Lm ,1 ， Q position can been obtained from formula (16). Using these coordinate of the estimated points, residuals of denotes covariance matrix of TDOA. each points can be calculated by the formula as below: Because x, y, L1 are dependence. We use fx(q) i (q) Li,1 least-square technology again. And za is get : ( ( BS i (1) z p (1)) 2 ( BS i (2) z p (2)) 2 （16 1 z a GaT 1Ga GaT 1h (14) ( BS 1 (1) z p (1)) 2 ( BS 1 (2) z p (2)) 2 ) 0 Where B diag x X 1， y Y1 , L1 0 0 ） 1 0 ( za ,1 x1 ) 2 Ga 0 1 h ( za , 2 x2 ) 2 Secondly, we can select the least value from these （ q） residual fx, and the corresponding 2 is what 1 1 2 za ,3 we select. Then m, n and the gradient g are updated by the follow formulas: The last estimated position is shown as follow: m （ q） g , n （ q） g , 2 2 X1 z p za g g / 10 (17) Y1 OR Formulas (11) 、(13) 、(14)、(15) 、(16) 、(17) is X1 calculated circularly until the gradient z p za g 0.004 . In other word, we need calculate three Y1 (15) times circularly. Eliminate the fuzzy solution by using priori information. Thirdly, we assume that L2,1 is measured in LOS In this step, how to select the value of weight μ environment, and that is to say 2 1 . So we can becomes a key problem. So we will put forward the get the value of 3 (q) using the same method method of the selection of μ in the next step. with the process of counting （ q） . 2 C, Selection of Weight μ Finally, （ q） 2 and 3 (q) we get in the 350 above steps is put in the equation (12). Formulas (14) 300 、(15) and (16) are used again to figure out the position estimation result. This Algorithm 250 Chan Algorithm 4. Simulation RMSE(n)/m 200 To test the performance of the algorithm proposed in this paper, we can take the typical seven stations cell 150 model as the simulation model for location in cellular network. And the NLOS error is simulated based on 100 X: 30 Y: 67.68 the COST259 model introduced in the Part Ⅱ. We suppose the channel type as urban. So the parameter 50 in (4) are set with the type value as T1 0.4， 0 0.5 . And the standard deviation of y is 4 dB. 0 5 10 15 20 25 30 Noise(n)/m So the NLOS error of certain position between BS Figure 1 Compare the mean square error performance and MS is changeable, and subject to the typical with Chan algorithm index distribution, induced in PartⅡ. 1 We use the approach this paper proposed to do the CDF（ Cumulative Distribution Function） simulation. The simulated results are shown in Figure X: 125.2 1、Figure 2、Figure 3、Figure 4、and Figure 5. Y: 0.96 0.8 This Algorithm From the figures, we can find that the algorithm this paper present have a good performance for the Chan Algorithm mobile location in the NLOS environment. Figure 1 0.6 show that the mean square error performance has improvement markedly compared with Chan algorithm. In Figure 2、Figure3 and Figure 4, we set 0.4 the standard deviation of random noise as 30m ,in the other word 100ns. The comparison of location error Cumulative Distribution Function (CDF) is shown in 0.2 Figure 2. And the comparison of position estimation error is shown in Figure 3. The mean error have 0 reduce from 204.5 m to 59.4 m. Figure 4 show the 0 200 400 600 800 1000 location estimate results for fix point. Location Error/m Figure 2 CDF of Location error The comparison of the mean square error performance is shown in Figure 5, when the gradient 900 g=0.1, 0.02, 0.004, 0.0008, that is the times of This Algorithm 800 iteration is 1, 2, 3, 4. Theoretically, the more times of Chan Algorithm iteration, we can get the more precise location 700 estimation results. But the calculated quantity will significantly increase, with the increasing of times of 600 Location Error /m iteration. And Figure 5 also show the improvement of 500 the precision of location estimation will be limited, when g<0.02. So g=0.02 will be a good choice. 400 300 200 100 0 0 20 40 60 80 100 Location Times Figure 3 Location Error 350 study, we will develop the technology to improve the real position position estimation precision more accurately. positioning results 300 References 250 [1] P. Deng ,L. Liu，P. Z. Fan，An NLOS Error Y Coordinate/m Mitigation Method Based on TDOA Reconstruction for Cellular Location Services， 200 Journal of Radio Science，accepted，to appear ，2002 150 [2] Deng Ping ， Investigation on the Location Technology in Cellular Network. PHD Thesis of 100 Southwest Jiaotong University，2002.5 [3] S. Venkatesh and R. M. Buehrer ， “ NLOS 50 Mitigation Using Linear Programming in 200 250 300 350 400 Ultrawideband Location –Aware Networks，” X Coordinate /m IEEE Trans. Vehicular Technology, vol.56, no.5 Figure 4 Location estimate results for fix point pp.3182-3198, Sept.2007 [4] R. A. Al-Nimnim, A. H. Muqaibel，and M. A. 120 Landolsi，“Improved weighting algorithm for NLOS radiolocation,” Proceedings of the 2009 110 IEEE 9th Malaysia International Conference on g=0.1 Communications, Kuala Lumpur, Malaysia, pp. 100 g=0.02 730-735, Dec. 2009 90 g=0.004 [5] W. Ke and L. N. Wu ，“Constrained Least RMSE(n)/m g=0.0008 Squares Algorithm for TOA-Based Mobile 80 Location Under NLOS Environments ， ” Wireless Communications, Networking and 70 Mobile Computing WiCom’09. 5th International Conference，Beijing China, pp.1-4，Sept. 2009 60 [6] X. H. TIAN and G. S. LIAO, “An Effective 50 TOA-Based Location Method for Mitigation the Influence of the NLOS Propagation,” Acta 40 Electronic SINICA, vol.31, no.9, pp. 1429-1432, 0 5 10 15 20 25 30 Sept.2003. Noise(n)/m [7] H. Asplund et. al., A Channel Model for Figure 5 the mean square error performance in Positioning, COST 259 TD20, Bern, Switzerland, different gradient 1998. [8] M. P. Wyllie ， and J. Holtzman, The 5. Conclusion Non-Line-of-Sight Problems in Mobile Location Estimation，WINLAB TR-121, June 1996. In this paper, a modified NLOS error mitigation [9] Y. T. Chan and K. C. Ho, A Simple and Efficient algorithm based on Chan algorithm is proposed. The Estimator for Hyperbolic Location，IEEE Trans. simulation results in section Ⅳ show the algorithm On Signal Processing , Vol.42, No.8 1994，pp. have good performance in NLOS environment. And 1905-1915 it achieves highly positioning accuracy in typical urban environment. So it has the strong practicability for mobile location in cellular system. In the further