INTRODUCTION OVERVIEW OF WLS/GPS MINIMUM-VARIANCE HYBRID ALGORITHM

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1 Design and Performance of a Minimum- Variance Hybrid Location Algorithm Utilizing and Cellular Received Signal Strength for Positioning in Dense Urban Environments David S. De Lorenzo, Stanford University Sherman C. Lo, Stanford University Per K. Enge, Stanford University Marty Feuerstein, Polaris Wireless Tarun K. Bhattacharya, Polaris Wireless Steve Spain, Polaris Wireless Zhengjiu Kang, Polaris Wireless BIOGRAPHY Dr. David De Lorenzo received the Ph.D. degree in Aeronautics and Astronautics from Stanford University, here he orks as a researcher in the Laboratory. His current research is in GNSS softare receivers, adaptive beamsteering antenna arrays, indoor and urban reception of radio signals, and navigation system security and integrity. Dr. Sherman Lo is a research associate at the Stanford University Laboratory, here he is the Associate Investigator for Stanford University efforts on the technical evaluation of Loran. Dr. Per Enge is a Professor of Aeronautics and Astronautics at Stanford University, here he is the Kleiner-Perkins, Mayfield, Sequoia Capital Professor in the School of Engineering. He directs the Stanford University Research Laboratory. Dr. Marty Feuerstein has more than years experience in research, development, and deployment of ireless products, including ork at Northern Telecom, AirTouch, Lucent Technologies, Bell Laboratories, and Metaave Communications. Dr. Feuerstein earned the Ph.D. degree in Electrical Engineering from Virginia Tech. Dr. Tarun K. Bhattacharya has over 5 years experience in the design and development of advanced signal processing systems for commercial and military applications. Dr. Bhattacharya s areas of expertise include spatio-temporal filtering, neural netorks, pattern recognition, time-frequency distributions, geolocation, and multi-target tracking ith data fusion. Dr. Steve Spain serves as Chief Technology Architect of Polaris Wireless. Dr. Spain has more than 5 years of experience in the development of estimation, control, and signal processing applications for defense and commercial customers, including ork at Tera Research, Integrated Systems, Inc., Advanced Decision Systems, ESL Inc., and Systems Control Inc. Dr. Spain earned the Ph.D. degree in Electrical Engineering from Stanford University. Dr. Zhengjiu Kang has been a principal algorithm engineer at Polaris Wireless since 5, here his major responsibility has been focusing on Location Based Services (LBS) algorithm and system R&D. Before he joined Polaris Wireless, he orked at UtopiaCompression Corp. as a senior R&D scientist. Dr. Kang received his Ph.D. degree in Electrical Engineering from the University of California at Los Angeles in 4. ABSTRACT This paper shos ho the complementary advantages of and cellular received signal strength (RSS) positioning methods improves location estimation performance in dense urban environments. In general, techniques ork best in rural or suburban environments here there is only moderate building or

2 landscape clutter to interrupt sky visibility or to introduce multipath errors from reflected satellite signals. In contrast, cellular techniques ork best in urban environments here the density and geometry of cell toers is favorable. Test results sho that cellular-rss effectively can be used to eliminate outliers (location errors > km, such as those associated ith cell-id fallback mode), hile can improve the accuracy of the combined solution. Based on field trial data, the accuracy of the Minimum-Variance Hybrid Algorithm (in dense urban environments) is approximately 45m for 67% of E9 calls and m for 95% of E9 calls. INTRODUCTION Ubiquitous positioning locating a user or a device anyhere and at any time is the ultimate goal for navigation engineers. This effort is driven not only by consumer acceptance and market uptake of Location Based Services (LBS), but also by government directives such as the FCC s E9 mandate. The FCC ireless Enhanced 9 standard requires cellular netork carriers to estimate the location of a mobile handset making a 9 emergency call, and to provide this information to the dispatcher in a timely manner []. Phase II of the standard specifies accuracy targets generally to ithin 5 to 3 meters over a selected geographic region. The Global Positioning System () is the preferred solution for lo-cost commercial positioning, as seen in personal navigation devices and mobile handsets. Hoever, the performance of in mobile handsets is problematic in meeting the guidelines of the E9 standard for several reasons. First, mobile handset operation during 9 emergency calls frequently occurs in urban, dense urban, or indoor environments []. Second, as navigation is not the primary purpose of a mobile handset, the design and placement of the L-band antenna is non-ideal leading to further performance degradation [3, 4]. Many technologies have been developed to meet the challenges of urban navigation, particularly as applied to E9 mobile handset location. Assisted- (A-) increases acquisition sensitivity and decreases time-tofirst-fix (TTFF) [5]. Other techniques leverage information measured by the handset and reported to the netork during the course of active and/or standby modes of operation. These techniques include estimating the location of the handset based on the coordinates of the serving cell toer [6], using timing information to trilaterate handset location [7], and pattern-matching to the received signal strength (RSS) measurements of the serving cell toer and of neighbor cell toers [8, 9]. This paper shos ho the complementary advantages of -based and cellular-rss-based positioning methods improves location estimation performance in dense urban environments. In general, techniques ork best in rural or suburban environments here there is only moderate building or landscape clutter to interrupt sky visibility or to introduce multipath errors from reflected satellite signals. In contrast, cellular techniques ork best in urban environments here the density and geometry of cell toers is favorable. First, this paper derives a method of combining and cellular-rss location estimates. This method utilizes quality-of-fix attributes reported by the and RSSbased algorithms to minimize the error variance of the location estimate, and incorporates cross-checking beteen and cellular-rss estimates for outlier exclusion to avoid contaminating the position solution. The algorithm operates in the position domain, simplifying vendor- and hardare-specific implementation issues. This minimum-variance combiner represents an optimal use of the and cellular-rss location and uncertainty estimates to calculate handset location. Second, this location technique is verified ith field trial data from several dense urban markets in the U.S., Canada, and Japan. This field trial data allos demonstration of the procedures for determining algorithm parameters, and enables performance comparison beteen, cellular-rss, and /RSS methods. The implementation procedure involves multiple steps to align various information inputs, to detect and to filter outliers, and to develop the optimal solution. One major step is to develop correspondence beteen the uncertainty values output by the and by the cellular-rss positioning engines; for example, as different chipset vendors have different means and metrics to report uncertainties, the algorithm accounts for these differences and aligns them ith those reported by the cellular-rss location engine. Test results sho that cellular-rss effectively can be used to eliminate outliers (location errors > km), hile can improve the accuracy of the combined solution. Based on field trial data, the accuracy of the Minimum- Variance Hybrid Algorithm (in dense urban outdoor environments) is approximately 45m for 67% of E9 calls and m for 95% of E9 calls. OVERVIEW OF / MINIMUM-VARIANCE HYBRID ALGORITHM Wireless Location Signatures () uses received signal strength and netork timing measurements from the serving cell toer and from neighboring cell toers to estimate handset location. processing uses pseudorange measurements to several satellites to

3 9 8 7 CDF of / A- Field Test Data - Market # CDF of / A- Field Test Data - Market # Percentage Dense urban donton >5 indoor/outdoor calls Percentage Dense urban donton > indoor/outdoor calls Estimate A- Esimate Error (m) Estimate A- Esimate Error (m) Estimation Errors Market # Market # 67% 95% 67% 95% Estimate 6 m 94 m 65 m 79 m A- Estimate 77 m m 65 m 9 m Figure. & location estimation accuracy. estimate handset location. In cases here time-tofix exceeds the limits established for the E9 call flo, a fallback position estimate derived from the location of the serving cell toer (and antenna sector) is presented instead (fallback to cell-id positioning mode may or may not be reported back through the netork). Figure shos and location estimation accuracy from field trials of simulated E9 calls in to dense urban test markets. Note particularly that - accuracy in these field trials is roughly comparable beteen and, but also that the error distributions have long tails (especially for test market #) hich is associated ith severe urban multipath and cell-id fallback inaccuracy. The Minimum-Variance Hybrid Algorithm represents an optimal use of and location and uncertainty estimates to calculate handset location. Namely, if it ere knon a priori hich estimate ere better ( or ), then more eight could be applied to that estimate in the final positioning report. Furthermore, if there ere a method to detect outliers, those estimates hich are likely to deviate significantly from the core of the error distributions, then the contribution from those estimates also could be excluded from the final positioning report. Specifically, a minimum-variance estimator seeks an optimal method for combining estimates, in this case estimates taken from to error populations associated ith and ith, and then combining those estimates in a ratio determined from their respective population variances. In other ords, e seek an estimator hich utilizes data from more than one source and combines that data using eighting coefficients hich minimize the error variance of the final result (see Appendix A for a derivation). For and location estimates p r and p r, of knon or estimated error variance and, the location estimate r p p r is calculated as follos: r r + p p () To minimize location error variance under the constraint that +, the eighting coefficients are calculated as follos (see Appendix A): + To summarize, the minimum-variance algorithm blends and estimates to improve accuracy, by ()

4 Engine A- Engine Estimate (lat/lon & uncertainty) Estimate (lat/lon & uncertainty) Minimum-variance / A- Hybrid Figure. Minimum-variance / algorithm. leveraging complementary features of and and by seeking to eliminate large errors and outliers. The eighting coefficients in the algorithm depend on and estimation uncertainties although, as ill be discussed belo, uncertainty reporting can be problematic as it not standardized by chipset vendor or handset implementation. Finally, this is a positiondomain algorithm, meaning that it does not need to access (nor can it modify) the intermediate location processing steps in other ords, it consider and to be location black boxes (see Figure ). When the minimum-variance estimator is applied for the purpose of combining and location estimates, then there are several factors of hich to be aare.. The estimation of -D location on the surface of the Earth often can be decomposed into independent and orthogonal estimates of North/South location (latitude) and East/West location (longitude) this de-coupling characteristic applies (on average) to location estimates from and from. This means that the location estimation problem can be broken don into separate problems of determining latitude and longitude using and estimates. It follos from this that the total positioning error of the minimum-variance estimate can be calculated from the square root of the sum of the squares of the North/South error and of the East/West error.. The and location estimates are mutually independent (the error variances may or may not be mutually independent, but the minimum-variance algorithm does not require variance independence, so this distinction ill not be further discussed). This means that the error magnitude for one of the estimates does not correlate ith the error magnitude of the other estimate. 3. When expressed in units of meters, the latitude and longitude estimation errors for either method ( or ) have equal variance. (This may not be true either for or for. Currently the Polaris Location Engine reports only one value of uncertainty. Some applications report elliptical error estimates, but to date these neither have proven ell-matched to the field trial data nor have been useful in characterizing the estimation errors. If this circumstance no longer holds for nely tested markets, either for or for, then this assertion can be re-visited.) This means that each calculation of location ill rely on one measure of estimation variance for and one measure of estimation variance for ; each of these variances ill apply both to the North/South estimate as ell as to the East/West estimate for their respective positioning methods. 4. The and location estimates are zeromean (unbiased) and approximately normally distributed (Gaussian). (The normality requirement is eak, due to the Central Limit Theorem.) This means that the minimum-variance estimator derived in Appendix A applies to the problem of combining and location estimates, assuming some mechanism exists to

5 9 8 7 CDF of / A- Field Test Data - Market # CDF of / A- Field Test Data - Market # Percentage Dense urban donton >5 indoor/outdoor calls Percentage Dense urban donton > indoor/outdoor calls 3 3 Estimate A- Esimate / A- Minimum Variance Hybrid Min. Variance / Best-fit Tuning Parameters Error (m) Estimate A- Esimate / A- Minimum Variance Hybrid Min. Variance / Best-fit Tuning Parameters Error (m) Estimation Errors Market # Market # 67% 95% 67% 95% Estimate 6 m 94 m 65 m 79 m A- Estimate 77 m m 65 m 9 m Min. Variance Hybrid 44 m m 48 m 33 m Min. Variance Hybrid / Compromise 55 m 37 m 56 m 44 m Figure 3. Minimum-variance / location estimation accuracy. estimate the and location error variances. 5. In cases here either -based or -based estimation suffers a gross failure, then there should be a mechanism for detecting and then excluding these outliers. The heuristic tools to detect and to exclude outliers, as is to be expected, are market dependent and ill be discussed further belo. 6. There is a relationship beteen the uncertainty reported by the and positioning applications and the error variance of the North/South and East/West estimates. (It is not clear that this must or even should be the case in theory ithout delving into the core of the and/or applications; it only is necessary to sho that this is the case in practice.) This means that there ill be functions to map uncertainty (hoever it is derived and in hatever units it is reported) to error variance (in meters-squared) both for and for. This final requirement is the most stringent to consider in developing the Minimum-Variance Hybrid Estimator, as it is likely that the relationship beteen reported uncertainty and error variance ill be handset dependent certainly so for as the calculation of uncertainty depends on the implementation of the chipset vendor, and possibly so for if there are dependencies on antenna gain pattern, analog hardare design, signal poer estimation algorithms, etc. The possible requirement to develop a handset-specific Minimum-Variance Hybrid Algorithm is beyond the scope of this note, and is not discussed further here. APPLYING THE / MINIMUM-VARIANCE HYBRID ALGORITHM The folloing is an overvie of the steps involved in executing the / Minimum-Variance Hybrid Algorithm (accuracy results summarized in Figure 3). The first steps check the validity of the assertions required to combine the and the location estimates in a minimum-variance fashion. The next steps are designed to fix the algorithm parameters (i.e., determine the functions that map uncertainty to error variance and develop the and outlier exclusion criteria). The final steps invoke the algorithm on and location estimates these final steps are those that ould

6 X & Y Errors vs. Reported Uncertainty Test Handset # 3 X & Y Errors vs. Reported Uncertainty Test Handset # X & Y Standard Deviation y.558*x.53*x y.558*x y.8*x X & Y Standard Deviation 5 5 y.8*x data linear Reported Uncertainty A- X & Y Errors vs. Reported Uncertainty A- Test Handset # Uncertainty Uncertainty 5 5 A- X & Y Errors vs. Reported Uncertainty A- Test Handset # A X & Y Error Standard Deviations (m) Reported Uncertainty ReportedUncertainty 5 3x A Reported Uncertainty Uncertainty Uncertainty 3 Figure 4. Plotting and uncertainty vs. standard deviation. be deployed in an operational minimum-variance system. The first steps evaluate error characteristics: independence of latitude vs. longitude, independence of vs., normality of and.. Plot latitude vs. longitude errors for and for ; plot vs. latitude errors; plot vs. longitude errors; calculate R value (also called coefficient of determination ) beteen errors (but only for total errors less than some threshold, e.g., 5m); verify that R value is suitably lo (i.e., <<.5).. Plot histograms of latitude and longitude errors for and for ; confirm zero-mean and nominally Gaussian in appearance (may have long tails due to outliers); calculate standard deviations of and latitude and longitude errors. The next steps fix the algorithm parameters mapping uncertainty to standard deviation and determine outlier exclusion criteria.. Plot reported uncertainty vs. error standard deviation by binning data in suitable ranges (see Figure 4). Note that the proprietary Location Engine enables consistent uncertainty reporting across several markets, hile the uncertainty reporting is not standardized across different handsets.

7 Test Handset # Test Handset #.53 UC W UC W UC W UC W A- 5 3 UC G 5 UC G 3 5 UC G 5 Figure 5. Mapping and uncertainty to standard deviation.. Determine mapping functions beteen uncertainty and latitude and longitude standard deviation (see Figure 5). Lat Lon + + Lat Lon Lat Lon (4) 3. Establish outlier exclusion criteria, e.g.: a. scatter plot and error magnitudes vs. reported uncertainty to estimate reported uncertainty threshold above hich and estimates may be considered outliers b. plot and errors vs. -to- separation to identify separation threshold above hich estimates may be considered outliers For the field trial data analyzed to date, if the -to- position estimates ere separated by more than 5m, then positioning errors ere reduced by defaulting to the position estimate (i.e., considering the estimate to be an outlier): To execute the minimum-variance algorithm on and positioning estimates { Lat, } and { Lon Lat, Lon } ith estimated variances and, calculate the estimate { Lat, } : Lon (3) and the standard deviation in latitude/longitude as: (5) + Based on the field trial data summarized in Figure, minimum-variance / positioning accuracies improve by ~3-4% for the - value (see Figure 3 and the 3 rd ro of results shon in the table contained therein). Furthermore, the 95% accuracy improves dramatically, removing the long tails of the error distributions arising predominantly from outliers and cell-id fallback mode position estimates. These results are based on market- and handset-specific calibration of the mapping functions beteen reported uncertainty and latitude and longitude standard deviation. A practical implementation considers a compromise that avoids this labor-intensive step. Parameter sensitivity studies determined that a reasonable compromise set the mapping functions to be: ˆ ˆ. + 3 m m UC (6)

8 With these compromise modeling parameters applied to the field trial data from markets # and #, the - accuracy improvement still exceeds ~%, and the outlier exclusion benefits to the 95% positioning accuracy continue to persist. / Minimum-Variance Hybrid Algorithm represents near-optimal use of and location and uncertainty estimates. ACKNOWLEDGMENTS The authors gratefully acknoledge the support of the Stanford University Center for Position, Navigation, and Time. REFERENCES. Federal Communication Commission, 999, Enhanced 9 Wireless Services, F. van Diggelen and C. Abraham,, Indoor Technology, CTIA Wireless. 3. M. Phocas, J. Bickerstaff, and T. Haddrell, 4, Jamming the Enemy Inside!, Proc. ION GNSS 4, pgs T. Haddrell, M. Phocas, and N. Ricquier, 8, A Ne Approach to Cellphone Antennas, Proc. ION GNSS 8, pgs G.M. Djuknic and R.E. Richton,, Geolocation and Assisted, Computer, vol. 34, no., pgs Y. Zhao,, Standardization of Mobile Phone Positioning for 3G Systems, IEEE Communications Magazine, vol. 4, no. 7, pgs S. Wang, J. Min, B.K. Yi, 8, Location Based Services for Mobiles Technologies and Standards, IEEE ICC Beijing A.J. Weiss, 3, On the Accuracy of a Cellular Location System Based on RSS Measurements, IEEE Trans. Vehicular Technology, vol. 5, no. 6, pgs J. Zhu, S. Spain, T. Bhattacharya, and G.D. Durgin, 6, Performance of an Indoor/Outdoor RSS Signature Cellular Handset Location Method in Manhattan, Proc. Antennas and Propagation Soc. Intl. Symposium, pgs APPENDIX: MINIMUM-VARIANCE ESTIMATION Given: Find:. p and p are independent and unbiased estimates of an unknon quantity p. the error in estimate p is Gaussian ith standard deviation 3. the error in estimate p is Gaussian ith standard deviation. the minimum-variance estimate for p called p. the standard deviation of the error in this estimate Method: The eighted sum of to estimates and p : p p + p p (A.) The constraint that the sum of the eights equals unity: and + (A.) The variance of the eighted sum of independent, zero-mean, normally distributed variables hose variances are and : ( ) ( ) + (A.3) Substitute for : Expand: ( ) (( ) ) + (A.4) + + (A.5)

9 Differentiate ith respect to, noting that d and d d : d i + + d d (A.6) Minimize by setting d and divide through by : d, + (A.7) Solve for : + (A.8) Substitution likeise can sho that: (A.9) +