Mobile Location Tracking in DS CDMA Networks Using Forward Link Time Difference of Arrival and Its Application to Zone-Based Billing M. Oguz Sunay and Ibrahim Tekin Bell Labs, Lucent Technologies 67 Whippany Road Whippany, NJ 07981
[email protected],
[email protected] Abstract - Due to the FCC requirement that operators of mobile communications networks be able to accurately locate mobile callers requesting emergency assistance via 911 by the year 2001, there has been substantial research and development activities dedicated to examining cellular positioning options. Fueled by this new requirement, the network operators are also considering other, profitable services that make use of the mobile location. With codedivision multiple access (CDMA) being deployed by a variety of cellular and PCS providers in the form of the IS-95 standard, developing an approach for location in CDMA networks is imperative. This paper is concerned with developing a solution that does not require any changes to the existing cellular standard nor any changes to the mobile station architecture. Results of field trials conducted in boroughs of New York City will be introduced to show the accuracy and shortcomings of the technique. Application of this technique to provide a zone-based billing service is also introduced in this paper.
I. Introduction The United States Federal Communications Commission (FCC) has required that, by 2001, operators of mobile communications networks be able to accurately locate mobile callers requesting emergency assistance via 911. The FCC report and order required a phased implementation of progressively increasing emergency services functionality in wireless 911 systems. Initially, it is required that all wireless carriers implement basic 911 service by October 1997. This basic service includes the capability to process emergency calls without user validation, including handsets without Mobile Identification Numbers if requested by the Public Safety Answering Point (PSAP), and to process calls accommodating speech or hearing disabilities. The FCC mandates that by March 1998, wireless carriers implement Phase I Enhanced 911 (E-911) service. Phase I E-911 service includes the capability to transmit the originating number of an emergency call as well as the location of the cell site (and corresponding sector, if it exists) receiving the call to the PSAP. In the final phase of E-911 implementation, to be completed by October 1, 2001, the wireless operator must provide latitude and longitude estimates of the caller's position within an accuracy that is dependent on the technology it uses. If the Location Determination Technology (LDT) is mobile handset based and requires new, modified or upgraded handsets, then an accuracy of 50m for 67% of the calls and 150m for 95% of the calls is required. Similarly, LDTs that are network based are required to provide an accuracy of 100m for 67% of the calls and 300m for 95% of the calls [1]. Today, the primary motivation for implementing position location is conformance with FCC regulations.
However, there are also other position location applications that are of interest to service providers. These applications provide carriers the opportunity to differentiate themselves from competitors through better emergency services and additional services such as mobile yellow pages, equipment tracking, location specific advertising, navigation assistance, network optimization and zone-based billing [2]. A variety of basic technologies are available for accurate position location. These technologies may be loosely grouped into handset-based technologies such as the ones utilizing the Global Positioning System (GPS) and network-based technologies that exploit the cellular infrastructure to obtain geolocation information. Each of these groups may be further divided into two. First, the MS uses signals transmitted by the BSs to calculate its own position and second, the BSs measure the signals transmitted by the MS and relay them to a central site for processing [3]. Theoretically, the position of a receiver can be estimated from the measurements of the arrival times, directions of arrival, or Doppler shifts of electromagnetic waves sent by various transmitters whose exact locations are known [4]. Forward link hyperbolic location systems, often called forward link time difference of arrival (TDOA) systems, locate a mobile by processing signal arrival-time measurements from three or more base stations. The arrival time measurements from two base stations are combined to produce a relative arrival time that, in the absence of noise and interference, restricts the possible mobile location to a hyperboloid with the two stations as foci. Mobile location is estimated from the intersection of two or more hyperboloids determined from at least three base stations. In the current IS-95 based CDMA networks, all base stations continually transmit pilot signals which amount to approximately 20% of the total transmitted power. Therefore, forward link time difference of arrival algorithms are readily applicable to IS-95 systems, where the relative arrival times of three or more pilot signals emanating from different base stations are used for the location estimation. II. Forward Link Time Difference of Arrival (TDOA) Method The requirement for the forward link TDOA to work is for the mobile to detect at least three pilots in a tightly synchronized network. The relative arrival times of the signals from the visible base stations are then used to form hyperboloids, the intersection of which gives us the location estimates. If there is information from more than base stations, it is possible to form more than two hyperboloids and find the intersection of all of the hyperboloids.
As in Figure 1, assume that the coordinates of the three base stations are known. Without any loss of generality, one can form local coordinates where BS1 is centered at the origin and BS2 is somewhere along the local y-axis. The local coordinates of the BS3 and MS can then easily be calculated relative to those of BS1 and BS2. In other words, assume that the coordinates of the three base stations are as follows: BS1: (0,0) BS2: (0,y2) BS3: (x3,y3)
coordinates and t2-t1 as well as t3-t1 is measured and thus c1 and c2 are known as well. The two equations in (3) can be solved in many different ways. They can be solved iteratively using the Steepest Descent Method, or visually by plotting the hyperboloids, using Taylor series expansion etc. It is also possible to solve the set of equations analytically (for a twodimensional solution) since it is possible to reduce the problem to the solution of a quadratic equation [5]. For a three-dimensional solution, the problem becomes a quartic equation whose analytical solution, though algebraically more complicated, is still available. Taking the squares of both sides of the equalities in (3) yields,
MS (x , y )
2c1 x 2 + y 2 = y 22 − c12 − (2 y 2 ) y
d3 d2
d1
2
2 3
2 3
2 2
Provided that x2+y2 is not equal to zero, (4) can be re-written as,
BTS (x 3 , y 3 ) BTS (x 1 , y 1 )
(4)
2c 2 x + y = x + y − c − ( 2 x3 ) x − ( 2 y 3 ) y 2
BTS (x 2 , y 2 )
x = βy + α Figure 1: Base Stations and Mobile Configuration
where
Furthermore, assume that the mobile station is located at, MS: (x0,y0) The distance between the mobile station and each of the base stations is calculated using, d 1 = c ⋅ t1 d 2 = c ⋅ t2
β=
2 y 2 c2 − 2 y3 c1 2 x3 c1
α=
x c + y c − y c −c c +c c 2 x3 c1 2 3 1
2 3 1
(6) 2 2 2
2 c1 ( β
2
+ 1) y 2 + ( 2 βα ) y + α
2
=
(7)
y − c − (2 y 2 ) y
where t1,t2 and t3 are the time it takes for the pilots to travel from BS1, BS2 and BS3 to the MS, respectively and c is the speed of light. Now, for the 1.25 MHz IS-95-B system, the arrival times can be described in terms of chip offsets using the following ratio, (2)
where PN_OFFi is the offset between the actual PN chip of the i'th base station (which is the base station identification) and its measured counterpart. The TDOA algorithm draws two hyperboloids using, c1 = d 2 − d1 = c ⋅ (t2 − t1 ) = x 2 + ( y − y2 ) 2 − x 2 + y 2
2 1 2
Now, substituting (5) into (4) results in
2 2
PN _ OFFi sec 1.2288 ⋅ 106
2 1 2
(1)
d 3 = c ⋅ t3
ti =
(5)
(3)
c2 = d3 − d1 = c ⋅ (t3 − t1 ) =
( x − x3 )2 + ( y − y3 )2 − x 2 + y 2
The above two equations have two unknowns, x and y. y2,x3 and y3 are known from the base station GPS
2 1
which results in
[4c [4α
]
[
]
( β 2 + 1) − 4 y 22 y 2 + 8 βα c 12 + 4 ( y 22 − c 12 ) y 2 y + (8) 2 2 c 1 − ( c 22 − c 12 ) 2 = 0 .
2 1
]
(8) is a quadratic equation whose roots give the two y coordinates of the intersection points of the hyperboloids. The corresponding x coordinates may be found using (5). In an ideal world, where there are no detection errors, no non-line-of-sight multipath and perfect synchronization amongst the base stations, the TDOA algorithm will always converge to the true mobile position. However, in the wireless channel, none of these conditions hold. Especially, in urban areas, there is a very high probability that most of the received multipaths will be non-line-of-sight. Synchronization errors and detection errors (measurement errors) are also present. All such impairments cause errors in the location estimation algorithm [6]. If the pilots follow a direct line of path as illustrated in Figure 1, and if the arrival times of the pilots can be detected exactly, the TDOA approach always gives the true mobile
location. This ideal case is illustrated for a specific example in Figure 2. Here, true line of sight time of signal arrivals, t1,t2,t3 are calculated for three base stations and a mobile station using (1). These values are then inputted into the set of equations given in the previous section to come up with the intersection points of the two hyperboloids. As predicted, the true mobile location lies on one of the intersection points. Figure 3, on the other hand, represents a situation where all possible impairments are present. In both figures the 'x' represents the base stations and the 'o' represents the mobile station. In Figure 3, the solid curves are the hyperboloids drawn using a single point in the set of actual measured data and the dotted curves are the hyperboloids if there were no impairments, i.e., if a genie were to tell us the true distances between the mobile and all three base stations. The 'o' represents the estimated mobile location whereas the 'o' represents the true mobile location. It is possible to improve the accuracy of the TDOA algorithm estimates using two different averaging schemes provided that measurement fixes are utilized: 1. Averaging the measured PN offsets from the visible base station 2. 2-D Averaging of the estimated location coordinates Of the two schemes, the first one is usually not possible due to the fact that the visible pilots observed by the mobile frequently change making the available sample pool too small to achieve a sensible average. On the other hand, averaging the location estimates can be performed even if the estimates are calculated using different sets of base stations. The averaging of the coordinates could be performed using a sliding window of size k where increasing the size increases the average accuracy of location estimates of stationary or low speed mobiles but at expense of an increased start-up time for the algorithm to start producing estimates. One should note that a large k would naturally decrease the accuracy of location estimates of high speed mobiles. III. Application of Forward Link TDOA to IS-95 As stated in the previous section, the forward link TDOA algorithm requires the knowledge of the coordinates of the base stations as well as the arrival times of the pilots they transmit at the mobile station. Such information from at least three base stations is necessary. These values are readily available in the IS-95 system and no standard changes are necessary to implement the algorithm [7]. In the current system, at a given time, the mobile station knows only the coordinates of the active base station(s) and therefore does not have sufficient information to perform the calculation. This is because the three base stations used for location estimation need not be all active base stations. In fact, this would severly limit the applicability of the algorithm as a well designed cellular system would try to minimize the number of active base stations, limiting soft handoffs to situations only when it is beneficial to the network and/or user. For this reason, the mobile location estimation needs to be performed at the
network end. The network has information on the coordinates of all of the base stations. Furthermore, the mobile station regularly informs the network about the PN offsets for all visible base stations in the form of a 'Pilot Strength Measurement Message' which is sent on the Access Channel when the mobile is idle and on the Reverse Traffic Channel when the mobile is in traffic. This message is sent whenever the received power level of one of the pilots from the Active, Candidate or Neighbor Set base stations crosses one of the thresholds, T_ADD or T_DROP. The base station may also order the mobile to send this message. The experiments held at Bronx, NY and Whippany, NJ show that the frequency of this message may be as fast as multiple messages per one second or as slow as one message per 2 seconds depending on a variety of external factors. Actual Mobile Location obtained from GPS 5000 4000 3000 2000 1000 0 -1000 -2000 -3000 -4000 -5000 -5000 -4000
-3000 -2000 -1000
0
1000
2000
3000
4000
5000
Figure 2: Calculation of the Mobile Location using TDOA – The ideal case IV. Experimental Results for Forward Link TDOA Experiments were conducted in Bronx, NY on 12/12/1997 and mobile Pilot Strength Measurement Messages (PSMMs) were recorded using Qualcomm's Mobile-DM over the course of approximately 8 minutes. The mobile was moving at a constant speed of 30 mph during the data collection. In 8 minutes, 100 PSMMs that provided measurements for at least 3 sufficiently strong pilots were transmitted by the mobile (There were other PSMMs as well, but they had less than three pilot reportings). Using these measurements along with the base station latitude and longitude information, TDOA algorithm was invoked, both as a memoryless system and with memory in the form of a sliding window of size k. Solutions to the intersections of the two hyperboloids were found both analytically and iteratively. The observed error in estimating the mobile location using the memoryless TDOA algorithm is shown in Figure 4 as a function of the contents of the consecutive PSMMs . The mean of the estimation error was found as 289 meters. Figures 5 and 6 show the estimation error versus PSMM number when TDOA with memory is invoked using sliding window sizes of 10 and 20, respectively. It is seen from the figures that adding memory to the TDOA algorithm lowers the observed estimation error considerably and helps track a low speed moving mobile. The actual mobile movement over the course of the experiment versus the
estimated mobile locations using the memoryless TDOA and TDOA with a memory window size of 20 is shown in Figure 7.
which the TDOA based zone-billing service may on occasion work inaccurately. The size of this gray area depends on the accuracy of the TDOA algorithm. Error in Mobile Location Estimation 300
Actual Mobile Location obtained from PN Offsets 5000
250
4000 3000
200
Error in meters
2000 1000 0 -1000
150
100
-2000 -3000
50
-4000 -5000 -5000 -4000
0 -3000 -2000
-1000
0
1000
2000
3000
4000
0
5000
Figure 3: Calculation of the Mobile Location using TDOA – Effects of impairments
10
20 30 40 50 60 70 Pilot Strength Measurement Message No
80
90
Figure 5: Error in Location Estimation for TDOA with Memory (Window Size = 10) Error in Mobile Location Estimation 180
Error in Mobile Location Estimation 1400
160 1200
140 120
1000
Error in meters
100 800
80 600
60 40
400
20 200
0 0 0 0
10
20
30
40
50
60
70
80
90
100
10
20 30 40 50 60 Pilot Strength Measurement Message No
70
80
Pilot Strength Measurement Message No
Figure 4: Error in Location Estimation for Memoryless TDOA
Figure 6: Error in Location Estimation for TDOA with Memory (Window Size = 20)
V. Forward Link TDOA to Enable Zone-Billing
To illustrate, consider Figure 8. If the mobile user is in the center of its home-zone (i.e., at home), the TDOA algorithm may estimate its location to be anywhere within the small circle centered around the mobile's true location (Note that, in reality, the two dimensional error distribution of the TDOA algorithm is not circular but rather an arbitrary geometric form dependent on the surrounding environment and the coordinates of the base stations involved in the location estimation.). If the radius of this circle is smaller than r, then one can safely state that the TDOA algorithm will provide the correct information for billing purposes 100% of the time whenever the mobile is at the home zone origin. As the mobile moves away from the center of the home-zone, as shown in Figure 8, the uncertainty area around it moves with it also. Clearly, the TDOA will start giving non-zero error probabilities for billing if the uncertainty area passes beyond the home-zone threshold. For example, for exact mobile locations of A and B, the billing error will be zero, but for
Consider a system in which subscriber specific homezones are defined. The aim is to provide two different types of billing strategies to subscribers: one for the times the mobile is in its home-zone and another when it is outside as shown in Figure 8. If the Forward link TDOA were to be used to realize this scenario, then the definition of each subscriber's home zone should consist of a zone origin whose coordinates are known (shown as A in Figure 8) and a radius r which defines the size of the zone. If the distance between the estimated mobile location and the home-zone origin is greater than the specified radius, the mobile is considered to be outside the home-zone and should be billed accordingly. If, on the other hand, this distance is smaller than the radius, the mobile is assumed to be inside its home-zone. However, the TDOA algorithm provides the location estimates with non-zero error, which in return, approximately corresponds to a gray area in
locations C and D, there will be non-zero probabilities of making billing errors. Now, assume that the home-zone of a given user is circular and has a radius of r=1 km. The data collected in Bronx which was discussed in the previous section can be used to generate probability distributions for the errors in location estimation. Using these, one can calculate the probability of error in making billing errors when the mobile is located at different locations inside and outside its home-zone. The probability of making billing errors increases as one moves towards the boundary of the homezone and is symmetric around this boundary. Therefore, statistically, the non-zero errors in billing close to the boundary would cause no profit loss to the cellular operator, as there would be equal number of outside home zone users mistaken as home zone users as home zone users mistaken as outside home zone users. It might, however, generate some unhappy customers as well as some happy ones. The memoryless TDOA algorithm and the TDOA algorithms with memory window sizes of 10 and 20 have been tested against the 1 km home-zone and probability of making false billing decisions were calculated for different mobile locations. The results are tabulated in Table 1. From the table, it is clear that the TDOA algorithm with memory provides better results. Mobile Movement 3000 BS1 BS2 BS3 Memoryless TDOA TDOA with Memory Actual Location
2000
1000
0
-1000 Y Coordinates in meters
VI. Conclusions Provided that one can guarantee at least three pilots would be visible to every subscriber with sufficient strength, TDOA algorithm may be implemented to provide input to the zonebilling service. The use of TDOA, as well as any other geolocation algorithm, for this purpose, would create a gray zone around the boundaries of the home-zones in which nonzero billing errors would be possible. As one moves closer to the boundary of its home zone, the error of making an error will increase. The more accurate the geolocation algorithm is, the smaller the gray zone will be. Therefore, averaging over multiple measurements will help reduce the error probability.
Distance from Home-Zone Center 0m 100 m 200 m 300 m 400 m 500 m 600 m 700 m 800 m 900 m 1 km 1.1 km 1.2 km 1.3 km 1.4 km 1.5 km 1.6 km 1.7 km 1.8 km 1.9 km 2 km 2.1 km 2.2 km
Probability of Error in Billing Decision No Window size Window windowing = 10 size = 20 3% 4% 4% 5% 7% 10% 15% 22% 39% 75% 100% 75% 39% 22% 15% 10% 7% 5% 4% 4% 3% 1% 0%
0% 0% 0% 0% 0% 0% 0% 0% 16% 48% 100% 48% 16% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%
0% 0% 0% 0% 0% 0% 0% 0% 0% 39% 100% 39% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0% 0%
-2000
-3000 -3500 -3000
-2500 -2000 -1500 -1000 -500 X Coordinates in meters
0
500
1000
1500
Figure 7: Mobile Tracking Using TDOA
Table 1: Probability of Billing Errors for a Home-Zone of Radius 1 km References [1] [2]
Home Zone Billing Type I
Outside Home Billing Type II
[3]
[4]
.A
.B
.C
.D
[5]
r [6]
Figure 8: Use of the Location Estimation Algorithm for Zone-Billing
[7]
CTIA Targeted Information, "FCC Adopts New Rules for Wireless E911 Phase II Requirements," Septermber 15, 1999. T.S. Rappaport, J.H. Reed and B.D. Woerner, "Position Location Using Wireless Communications on Highways of the Future," IEEE Communications Magazine, vol. 34, no. 10, pp. 33-41, October 1996. J.J. Caffery, Jr. and G.L. Stuber, "Overview of Radiolocation CDMA Cellular Systems," IEEE Communications Magazine, vol. 36, no. 4, pp. 38-45, April 1998. D.J. Torrieri, "Statistical Theory of Passive Location Systems," IEEE Transactions on Aerospace and Electronic Systems, vol. AES-20, no. 2, pp. 183-198, March 1984. B.T. Fang, "Simple Solutions for Hyperbolic and Related Position Fixes," IEEE Transactions on Aerospace and Electronic Systems, vol. AES-26, no. 5, pp. 748-753, September 1990. K.C. Ho and Y.T. Chan, "Solution and Performance Analysis of Geolocation by TDOA," IEEE Transactions on Aerospace and Electronic Systems, vol. AES-29, no. 4, pp. 1311-1322, October 1993. TIA/EIA IS-95-A, "Mobile Station-Base Station Compatibility Standard for Dual-Mode Wideband Spread Spectrum Digital Cellular System," 1994.
