The Virtual Antenna of Measurement Report Based
Method for Mobiles Location
Tao Fu, Benxiong Huang, Yijun Mo
E.I. Department of Huazhong University of Science & Technology, Wuhan 430074, China Abstract: Location base services (LBS) have been applied in many fields, and the researches of network based location methods are always on the least square methods, such as Taylor Series, Kalman filter, Chan algorithm, etc. Our practical measurement has proofed that utilization of
unmodified propagation models (Okumura-Hata) would cause significant errors. This paper deals with an escalating method to utilize more available information of measurement reports (MR) for accuracy enhancement. The nearby MRs are combined as a time series for Kalman filter, and received signal level of the virtual antenna is defined for more sensitive position weight. We also propose a step-by-step rotation algorithm to utilize the antenna azimuth for accessing the mobile station position. This approach turns out to be successful, achieving accuracies of the fingerprints in practical test runs. Further improvement is possible by recursively filtering original cells and substitution of Taylor Series.
Key words: location based service (LBS); virtual antenna; measurement report (MR); enhanced CI-RXLEV (CI-RXLEV-E) algorithm; position error size (PES).
In the field of cellular network optimization, there are always two kinds of data sources: drive test and operation & management center – radio (OMC-R) database. Drive test, including the call
quality test (CQT), could get details of the wireless signal and protocol procedures of the air interface. But the limitation is that the data collected by drive test only reflects the places passed by the test engineers. Most of the places, such as forests and indoors, couldn’t be measured due to
the land ownership and humanity of engineers. OMC-R database receives statistics of all equipment operations. The statistics are averages or sums of the operations during a time interval, such as an hour, and it couldn’t characterize the equipment status for any moment or places. So it’s
necessary to conceive a new kind of data sources for grasping particulars of the whole network. Based on the particulars, signal covers, frequency reuses, user capacities, and scrambles of the cells could be optimized more precisely.
Measurement report (MR) is a data segment of the cellular air interface generated by mobile station (MS). As in a GSM system, it’s forwarded from the serving cell to base station controller
(BSC), and includes the time stamp, received signal levels (RXLEVs) of at most 6 neighbor cells, RXLEV, timing advance (TA) and received signal quality (RXQUAL) of the serving cell , similar for UMTS , researchers considered to intercepted it through direct transport application part (DTAP) of the Abis interface for data sources of the network optimization -. The precondition of getting the signal cover and frequency conflicts of the cells is to locate where the MR is generated at. There have been many network based location methods suggested, such as
angle of arrival (AOA), time of arrival (TOA), time difference of arrival (TDOA), fingerprints, and their hybrid methods -. Significant attention has been drawn to the mitigation of the Nonline-of-sight (NLOS) effect in recent years. Kegen focuses on the identification of NLOS conditions by employing the statistical decision theory, and derives analytical expressions of the probability of detection (POD) and the probability of false alarm (PFA) for all the scenarios considered . Wann proposes a modified TOA estimation error test and a hybrid TOA/AOA estimation error test for identification of line of sight (LOS) base stations (BSs), and formulates hybrid TOA/AOA squares of normalized estimation errors via adopting the approximate maximum likelihood estimation . To locate the MS without requiring a priori information about the NLOS error, Chen presents utilizes two TOA circles and two AOA lines to find all the possible intersections . Tseng considers that network- and satellite-based systems both have their advantages and limitations under different environments, and proposes the hybrid location estimation schemes, which combine both the satellite-and the network-based signals . Xie suggests a grid-search based technique which is the combination of AOA, TOA and fingerprints . Though position accuracy could be enhanced through the hybrid methods, AOA, especially the direction of angle (DOA) estimated by beam forming of the smart antenna, is encountered the fiducial direction determination and complexity of the environment being much higher than the conceivability of simulation when practicing. Due to the structure of cellular access network and billions of existing users in China, TOA could be estimated by only one BS for the MS, and also the precision is limited.
MR based methods which utilize parameters extracted from MRs and the cell configuration database (CCD), such as the CI, CI-RXLEV, CI-TA, fingerprinting, etc. -, are a selective ways for MS positioning without modification of the existing access equipments and MSs. CCD includes the parameters of cells measured by engineers, such as the transmitting power, frequency, BS height, antenna azimuth, etc. In our previous work, it has been proved that position error of above methods except fingerprinting are always too large to network optimizations . Although fingerprinting methods achieve relatively high accuracy, construction of the database always requires great human resource and costly maintenance. So we investigate the parameters of MR based methods for further accuracy enhancement.
This paper is structured as follows. In Section 2, we introduce the previous work, including practical data collection, enhanced CI-RXLEV (CI-RXLEV-E) method and the maximal probability of position error (MPPE) criterion. In Section 3, a new method called virtual antenna which combines multiple MRs generated by the same UE in a short time interval and synthesizes signal attributes of the cells is proposed. Section 4 presents the performance of the virtual antenna method based on the field measurement. In Section 5, we give a conclusion and a discussion of our future work.
2 Previous Work
2.1 Field Measurement
In order to get practical MRs, we carried out a field measurement in Huangshi with the help of Huangshi Branch of China Mobile Communications Corporation (CMCC) on a sunny day. Huangshi is a middle scale city which has over 2.5 millions inhabitants. The urban area is 180
square kilometers, and most of the buildings are lower than 30 meters, shown in Figure 1. The cellular network is GSM, and power controls of all the cells were opened. The test tool is a drive test system, which includes an engineering phone Ericsson T61, a notebook PC DELL A840 installed with Window XP sp2 and test software TEMS v5.1.2 , and a GPS set BU 353 . The average horizontal accuracy of BU 353 is 10 meters and the average velocity accuracy is 0.1 meters/second.
Figure 1 Huangshi Terrain
To get data of different terrains, we put the drive test system in a car and drove every publicly accessible street in the metropolitan area. The phone was always held by us for simulating the practical users. Our measurement statuses included the static, pedestrian, and vehicle. Over 300 calls are started by us, and the duration of each call is at least 60 seconds. When coming back to the laboratory, we selected 100 MRs for each call and converted them into a SQL SERVER database which also stored the copy of CCD. Then the neighbor cells of MRs were matched to the cell configuration records by the same broadcast control channels (BCCHs) and base station identity codes (BSICs).
2.2 Enhanced CI-RXLEV Algorithm
Many MR based methods, such as CI, CI-AVG, CI-RXLEV, CI-TA, and Taylor series combined with propagation model, have been compared in our previous work. Unexpected, CI method proved to be the highest accurate. With analysis of the results, we found that some distances between the serving cell and neighbor cells were much longer than common propagation radius of the cells, and the position error size (PES) always grew up with the increase of the distances. We attributed the phenomenon to the manual errors of CCD and effects of complicated terrains, and then suggest a threshold of the distances to abandon information of the neighbor cells which were far from the serving cell for the methods . The threshold is described as
0,df！?SNrdsn？；Rd,，, (1) ;；?iSNRdf,?iSNrdsn？?
where (x, y) is the longitude and latitude of the cell whose identifier number is i. N is the number ii
of all cells contained in a MR, and the maximal value of N is 7. R is the RXLEV which relates to i
cell i. (x, y) is the MR position to be solved. d is the distance between the serving cell and SN
neighbor cell of a MR, and f is the empirical threshold. r-dsn
(2) is applied for CI-AVG, CI-RXLEV and Taylor series which all utilize neighbor cells’
RXLEVs, and the results shows that Taylor series is lower than CI-RXLEV due to the inaccuracy of Okumura-Hata. If f was endowed with 2400 meters, the average PES could be reduced from r-dsn
over 600 meters to about 330 meters by the Enhanced CI-RXLEV (CI-RXLEV-E) which was an approximation algorithm and could be described as
NN??；；xy))iiii，?ii，，11，?,,, (2) xy，;；NN，?；；))ii，?ii，，11??
2.3 PES Estimation of the CI-RXLEV-E
As the parameters of CI-RXLEV-E are only the cell positions, RXLEVs and number of the
cells, we also found some relationship between the parameters and PESs . The cell positions reflect propagation distances, and the distances are ranged from dozen meters to several kilometers. On another hand, the range of RXLEVs collected by our practical measurement is always from 30 to 63. As (2) expatiates, RXLEV denotes the position weight, and its fluctuation is much smaller than the propagation distance, and so long propagation distances would signify the big PES. The statistics of the distances, such as average and deviation, could be calculated for PES estimation. As the path loss relates to the distances, average and deviation of the RXLEVs are also selected for estimation. Also the covariance of the propagation distance and RXLEV could be described via the deviations. As received signal strength (RSS) is negatively corresponding to the propagation path, and the estimated position would be far from the practical one if the correlation is broken. So we proposed an expression to estimate the PES as
fffffsadsarsddsdr？？？？sN？scoreEdEDdDN，；；, (3) ;；;；;；;；
where score denotes the PES, E denotes the mathematical expectation, the index coefficients f, s-ad
f, f, f, and f are all empirical values to be fitted. The results of least square method s-ars-dds-drs-n
calculated in our previous work showed that if f, f, f, f, and f were endowed with 1, 1, s-ads-ars-dds-drs-n
1, 1, 1, and 1 respectively, the average difference between the scores and PESs would be about 190 meters.
3 The Virtual Antenna Method
3.1 Relative Definitions
Some related definitions are explained before explication of the virtual antenna method.
Definition 1: MRT. It’s the MR to be positioning.
Definition 2: MRC. It’s the MR generated with MRT during a short time interval.
Definition 3: GP. It’s the position of MRT recorded by GPS set. It could as the practical
Definition 4: EP. It’s the position of MRT estimated by any location method.
3.2 Notation of the Virtual Antenna
The notation of virtual antenna is based on some interesting facts during the analysis of measurement results. As the Position Accuracy couldn’t be improved satisfactorily by one kind of
available information, and unmodified propagation model for distance estimation is also
inaccurate, the purpose of enhancement is to utilize as more information as possible, and the procedure of enhancement is step-by-step. Before expatiation of the facts, the MRT is combined with MRCs for time series utilization, and then the cells of a time series could all be extracted and classified into three categories as the general number of cells administrated by a BS is three: the first category cell is the one which belongs to a BS, and there isn’t another cell belonging to the
BS; the second category cell is the one which belongs to a BS, and there is only another cell belonging to the BS; the third category cell is the one which belongs to a BS, and there are two other cells belonging to the BS.
We select 14000 MRs for statistics, and Figure 2 shows the relationship between the categories of the cells and the average distance from the cell to GP.
Figure 2 Relationship between the cell category and average distance from the cell to GP
It could be found that the distance decreases with the growth of category sequence. That means the deviation of antenna transmitting directing decimates the RSS, and the second and third category cells always signify the nearby MS. So the virtual antenna could be considered as the antenna of the BS, and RXLEV of it is defined as
；；，f, (4) )？vrCi，i1
where C denotes the category sequence number, i is the number of each cell which belongs to the same BS, ε is RLXEV of the virtual antenna. f is an empirical parameter which could enhance vr-C
the availability of position weight. It alternates with the category of the cells, and f could be r-1
normalized as 1.
To get more available information for accuracy enhancement, the azimuth of cell antenna is also studied. Though AOA estimated by the antenna array is adaptive, the number and strengths of received signals reflect the transmitting direction of cell antennas to a certain extent. Figure 3 shows the difference from antenna azimuth of the first category cell and the direction from GP to the BS.
Figure 3 Deviations distribution from the first category antenna azimuths to MS direction
It could be found that most of the differences are less than 40 degrees. Though the antenna azimuth of the second or third category cell of which RXLEV is the largest could also roughly indicate the direction from GP to the BS, the azimuths and RXLEVs of the other cells are available for direction accuracy enhancement. We propose the relationship between the direction and second category cell attributes as
??？ij,f(，？？, (6) ??；；;；;；(？ijrji2
where Ф is the direction estimated by cell attributes, and it could as the azimuth of the virtual antenna. Cell i and cell j belong to the second category and the same BS. θ and θ are the azimuths ij
of cell i and cell j. f is an empirical value which describes the correlation of path loss and Ф-r
transmitting direction. To be noticed, the average of θ and θ denotes the middle of the angle ij
clipped by θ and θ. If the absolute difference equates to 180 degrees, the cell antenna azimuth that ij
relates to the bigger RXLEV is regarded as the virtual antenna azimuth, and if the absolute difference is larger than 180 degrees, the middle line should be redefined as (360 + θ + θ) / 2, and ij
also the deflection affected by the difference of RXLEVs (ε and ε) should be reverse. ji
The relationship between the direction and third category cell is the double recycle of (5). Firstly, the cell whose RXLEV is the largest will be selected out, and another random cell is also selected. They are combined for a temporary virtual antenna azimuth calculated by (5). Then the temporary virtual antenna azimuth is combined with the remainder for the final virtual antenna azimuth. As the temporary virtual antenna reflects information quality of the two cells, the weights of azimuth and RXLEV should both be doubled.
2？??4tk, (6) f(，？？,??；；;；;；(？tkrkt33
where θ is azimuth of the temporary virtual antenna. Cell i, cell j and cell k belong to the thrid t
category and the same BS. ε is the temporary RXLEV, and it’s the average of ε and ε. Also if the tij
absolute difference between θ and θ is larger than 180 degrees, the first part (2θ + θ) / 3 of (6) tktk
should be redefined as (720 + 2θ + θ) / 3, and also the deflection affected by the difference of tk
RXLEVs (ε and ε) should be reverse. tk
As RSS, azimuth, and MR time series of the virtual antenna are defined, some utilization of the attributes is advanced for CP estimation.
3.3 Time Series of MRs
According to affects of the receiver noise, terrains, and user status, accurately locating MS with stochastic RXLEV is unnecessary. Time series of the MRs is a good way for enriching information. We utilize Kalman filter ,  to smooth the CP. The MR delivery period is 480 milliseconds, and the time delay of reconstructing a communication link is much longer than the period. So MRCs could be distinguished using the time stamp, and combined with MRT for time series.
Define a four-dimensional (4D) stochastic process
T：?, (7) Sxyvv，,,,xy??
where v and v are longitude and latitude direction components of the MS velocity. We assume xy
that S satisfies the discrete linear recursion
, (8) SkTSkGWk，？？？11;；;；;；
where k denotes the discrete time sequence. T is the one-step transition matrix, and G is the velocity noise driving matrix. They are defined as
100，t00：?：?，?，?010，t00，?，?, , (9) T，G，，?，?0010，t0，?，?00010，t????
where Δt is the period of MR delivery. W denotes the noise of status S, and W ； N(0, Q), where
Q could be described as
2：??000x，?2000?y，?, (10) Q，2，?000?vx，?2000，??vy??
2222where σ and σ are the estimated covariance of x and y coordinates, σ and σ are the xyvxvy
estimated component covariance of MS speed. If the user car running on a road, the x and y component noises of user positions are not the same due to the heading direction. Though  and
222 assumed that σ and σ both reflect the noise power of position status, we defined σ and xyx222σ, σ and σ respectively. yvxvy
The observation equation of the Kalman filter is
, (11) YkhSvk，？;；;；;；k
Twhere Y is the measurement vector, and could also be described as [x, y, v, v]. h is the xy
transmitting matrix, and could be described as I. v is the measurement noise, and v ； N(0, R).
As the x and y components of measurement noise are not the same, R is defined as
2：??000Rx，?2000?Ry，?, (12) Q，2，?000?Rvx，?2000，??Rvy??2222where σ and σ are the measurement covariance of x and y coordinates, σ and σ are the xyvxvy
measurement component covariance of the speed.
The corresponding algorithm is described as
？1. (13) KkPkkPkkRk，？？？/1/1：?;；;；;；;；??
With initial values S and P estimated by the first and second observation vectors, the 00
recursion could get more accurate CP by time series estimation.
3.4 Utilization of the Virtual Antenna Azimuth
RXLEV of the virtual antenna has been substituted for (1) to realizing more precise position weight. As the PES solved by time series isn’t satisfied, we also utilize the defined azimuth for
more available location information. Data fusion for combining 2 different kinds of information has been researched by  and . But the method couldn’t get significant improvement as the
results are estimated respectively using two kind of the information beforehand. So we describe the problem of virtual antenna azimuths utilization as below:
clip,?? (14) ;；~?ii
where (x’, y’) is the initial position estimated by Kalman filter. (x, y) is position of the virtual ii
antenna i. λ denotes the direction from MS to BS, and could be solved by i
：?. (15) ~，？？atnyyxx/;；;；iii??
As the virtual antenna azimuth doesn’t indicate λ precisely, α is cited for describing the clip i
angle between the azimuth and λ. i
The traditional solution of (14) is to get the intersection points of the virtual antenna scope lines. But it has some limitations. For example, Computations will be exponentially complicated by the growth of intersection points. Moreover, M may not be exist if the clip between any pair of
0virtual antenna azimuths is larger than 0. So we propose a step by step method to approach M, as
shown in Figure 4.
Figure 4 Rotation method utilizes the virtual antenna azimuths
Points A, B, C and D are the positions where virtual antennas are at. Half-lines a, b, c and d are the azimuths, and the segment lines made up by short line segments are the scope lines of azimuths defined by α. The intersection points constitute the polygon M, and the central point of M could be seemed as CP to be solved. Point E is the Initial CP calculated by the previous work, and could be seemed as a reference position. Our purpose is to move E to the central point of M. So we rotate E with center A and radius AF at a certain degree, and then E is moved to F. Then we rotate F with center B and radius BG at certain degrees, and F is moved to G. Then we rotate G with center C and radius CG at certain degrees, and G is moved to H. Then we rotate H with center D and radius DH at certain degrees, and H is moved to I. Then the point I could be rotated with center A and radius AI again. It could be found that if rotation degree is infinite small, with the increasing number of rotation times, CP will infinitely approximate to the center point of M.
The key point of the rotation is the algorithm of rotation degrees, including whether rotating CP and calculation terms of rotation degrees.
As the event clip(λ, θ) > α is probabilistic, an empirical value of α should be found out for ii
determining whether rotating CP.
'?RPTclip1,,~?？??;；;；;；iiNv? (16) PT，;；?'PTclip1,,？！?;；?~?;；iiNv?
where P(T) is the CP calculated by T times of rotations, and its initial value is the results estimated by Kalman filter. R is the rotation expression.
Some parameters are conceived to enhance the availability of rotation degree, such as the estimation score, propagation distance, and RXLEV of the cells. Estimation score proposed by the previous work indicate PES calculated by (13). If propagation loss is certain, RXLEV of the cells negatively relates to clip(λ, θ). The propagation distance negatively relates to RSS. So expression ii
of the rotation degree is defined as
fff；？；？dscore；？r；，(fdscoreclip；?,, (17) ;；；？？？？iNviciciNvi
where the center point of rotation circle is virtual antenna I, and г is the rotation degree. Ф is the
virtual antenna azimuth, and its subscript c denotes the category of virtual antenna. θ is the
direction from virtual antenna i to CP calculated by its forward rotation. f, f, f, and f г-Nvг-dг-rг-score
are all to be fitted.
We applied 14000 MRs for least square fitness. 100 MRs are selected from each call and the
parameters of CI-RXLEV-E combined with time series. PES Estimation and virtual antenna
method are fitted procedurally. The minimal duration of calls is always 20 seconds, and so the
number of MR time series is set as 40. Fitness ranges and step sizes of these parameters are also
shown as below:
Table 1 Empirical parameters of CI-RXLEV-E combined with time series Parameter Expression Range Minimal Step Size Fitness Value
f (3) [1500, 4000] (m) 5 (m) 2640 (m) dsn
ε (8) [2, 8] 0.05 4.75 2
ε (8) [3, 12] 0.05 9.45 3
Table 2 Empirical parameters of PES estimation
Parameter Expression Range Minimal Step Size Fitness Value
f (4) [-3, 3] 0.05 1.35 s-ad
f (4) [-3, 3] 0.05 1.2 s-ar
f (4) [-3, 3] 0.05 -0.2 s-dd
f (4) [-3, 3] 0.05 -1.8 s-dr
f (4) [-3, 3] 0.05 -1.05 s-N
Table 3 Empirical parameters of rotation degree Parameter Expression Range Minimal Step Size Fitness Value
f (10) [1, 6] 0.05 2.75 Ф-r
α (16) [0, 180] 5 145 1
α (16) [0, 180] 5 180 2
α (16) [0, 180] 5 80 3
f (18) [0.001, 0.2] 0.002 0.03 г-1
f (18) [0.001, 0.2] 0.002 0.026 г-2
f (18) [0.001, 0.2] 0.002 0.038 г-3
f (18) [-3, 3] 0.05 -2.1 г-d
f (18) [-3, 3] 0.05 0.75 г-r
f (18) [-3, 3] 0.05 1.85 г-score
4.2 Accuracies Comparison
We select 10000 MRs that haven’t been fitted for location methods comparison, 100 MRs are selected from each call, and PESs of several methods are shown in Figure 5.
Figure 5 Position accuracies of the location methods
Table 4 PES statistics of the location methods
PES (meters) Location method 50% 90%
CI 347 940
CI-RXLEV-E 215 767
Virtual Antenna 177 380
Fingerprints (Down town) 94 291
Fingerprints (Residential) 277 984
Table 4 also shows the PES statistics. The data of fingerprints is cited from . It could be found that the virtual antenna method performs much better than CI and CI-RXLEV-E, and it’s
close to fingerprints. The average PES calculated by virtual antenna method is 196.09 meters.
In this paper, a notation of virtual antenna is suggested to locating and tracing the mobiles in a cellular network. The previous has proofed that direct utilization of propagation models (Okumura-Hata) would cause significant errors, and the Position Accuracy enhancement should be an escalating procedure. In order to enrich the available information, the time series of MRs is combined by Kalman filter for smoothing positions calculated by CI-RXLEV-E, and also the position weight of this algorithm is enhanced by the definition of virtual antenna RXLEV. As the virtual antenna azimuth is defined and indicates the direction from MS to BS more precisely, a step-by-step rotation algorithm is proposed for utilize the static information of cell antenna azimuth. The field measurement results show that the virtual antenna method is capable of achieving similar performance as the fingerprints method with greatly reduced manpower and material cost. Future work will be devoted to recursively filtering original cells with the accurate results calculated by the virtual antenna method, also Taylor Series location will be tried for virtual antenna azimuth.
This work was supported by a grant from Important National Natural Science & Technology Specific Projects (No. 2009ZX03004-004-04).
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