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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
                                                                                                n0
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
                                                                                         n0  (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  2i 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

				
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