The median value τm of the NOLS error is set to be 0.3 in this thesis. The parameter me is the distance from the latest estimated MS’s position to the last one. The VBS algorithm terminates if the value of me is smaller than the given threshold. The threshold is set to be 0.1 meters in the thesis. The proposed VBS algorithm including both the VBS-CG and the VBS-MG schemes is compared with the two-step LS method, the TSE algorithm, and the LLOP approach via simulations. The performance evaluation of each case is obtained after executing 100 times. The layout of each case is also presented with the information of the iteratively-estimated MS’s position and the added virtual base stations.
In Case(1), a regular triangle layout with the MS locates at the center of the gravity is considered. As shown in Fig. 4.1, the proposed VBS algorithm is compared to other existing methods. Since the GDOP effect in the regular triangle is the slightest at the center of gravity where the MS lies, the improvements obtained from the VBS algorithm is small. In Fig. 4.2,
0 100 200 300 400 500 600 700 800 0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Average Position Error <= Abscissa
RMS Error (m)
Two−Step LS The CG−based VBS The MG−based VBS TSE
LLOP
Figure 4.1: Performance Comparison between the Location Estimation Schemes under NLOS Environments in Case(1) (with Median Value of the NLOS Noises: τm=0.3 µs)
the location estimates of the MS’s position and the added virtual base stations of the CG and the MG methods in the VBS algorithm are presented. Obviously, the location estimates of the two methods both approach to the MS’s position till the iterations converge.
In Case(2), the MS’s position is located closer to a base station. As shown from Fig. 3.2 to 3.5, the GDOP effect is a concave function and will become worse around any of the base stations. The performance of the proposed VBS algorithm is better than the other methods as presented in Fig. 4.3. Compared with the two-step LS method, the accuracy improvement of the proposed VBS algorithm at the 60% average error is about 80 meters. The result implies that the proposed VBS algorithm still can perform well while the MS is in a poor geometric environment. It is noted that the performance of the CG-based and the MG-based selection methods seem to be the same duo to the regular triangle layout. The MS location estimates of the these two method in Case(2) are shown in Fig. 4.4.
The performance comparison is also held in a non-regular triangle layout. The MS is located at the center of the gravity of the non-regular triangle layout as given in Case(3). The comparison of performance is shown in Fig. 4.5 and the location estimates of the CG and
−1000 −800 −600 −400 −200 0 200 400 600 800 1000
The estimated MS of the CG−based VBS The estimated MS of the MG−based VBS True MS
The VBs of the CG−based VBS The VBs of the MG−mode VBS
Figure 4.2: The Positioning Processes of the VBS Schemes under NLOS Environments in Case(1) (with Median Value of the NLOS Noises: τm =0.3 µs)
0 100 200 300 400 500 600 700
Average Position Error <= Abscissa
RMS Error (m)
Figure 4.3: Performance Comparison between the Location Estimation Schemes under NLOS Environments in Case(2) (with Median Value of the NLOS Noises: τm=0.3 µs)
−30000 −2000 −1000 0 1000 2000 3000 4000 500
1000 1500 2000 2500 3000
x−axis
y−axis
# of the VBSs of the CG−based and the MG−based VBS are: 5 and 4
BSs
The estimated MS of the CG−based VBS The estimated MS of the MG−based VBS True MS
The VBs of the CG−based VBS The VBs of the MG−mode VBS
Figure 4.4: The Positioning Processes of the VBS Schemes under NLOS Environments in Case(2) (with Median Value of the NLOS Noises: τm =0.3 µs)
the MG method are illustrated in Fig. 4.6. Since the layout is no more a regular triangle, the performance of the proposed VBS algorithm is better than that of other methods by 20 meters even if the MS is located at the center of the gravity.
The layout in Case(4) is designed as a non-regular triangle and the MS’s is lied closer to a base station. The performance comparison in Case(4) is shown in Fig. 4.7. The performance of the VBS algorithm is superior to other methods. Although the poor layout and MS’s position is presented, the proposed VBS algorithm promotes an improvement at the 60%
average error by 50 meters while comparing with the two-step LS method. One thing to be mentioned is that the minimum GDOP value in a non-regular triangle layout may occur at a point around the center of gravity rather than indeed at the center of gravity. Hence, the performance of the selection method based on the minimum GDOP is better than that of the CG-based method. In Fig. 4.8, both the CG and the MG based VBS algorithm can direct the estimated MS’s position approaching to the true position evidently.
The relationship of the NLOS error and the Root-Mean-Squared Error (RMSE) is dis-cussed, too. The 60% average position error is chosen as a criterion while comparing the
0 100 200 300 400 500 600 700 800 900 1000
Average Position Error <= Abscissa
RMS Error (m)
Figure 4.5: Performance Comparison between the Location Estimation Schemes under NLOS Environments in Case(3) (with Median Value of the NLOS Noises: τm=0.3 µs)
−600 −400 −200 0 200 400 600 800 1000
The estimated MS of the CG−based VBS The estimated MS of the MG−based VBS True MS
The VBs of the CG−based VBS The VBs of the MG−mode VBS
Figure 4.6: The Positioning Processes of the VBS Schemes under NLOS Environments in Case(3) (with Median Value of the NLOS Noises: τm =0.3 µs)
0 100 200 300 400 500 600 700 800
Average Position Error <= Abscissa
RMS Error (m)
Figure 4.7: Performance Comparison between the Location Estimation Schemes under NLOS Environments in Case(4) (with Median Value of the NLOS Noises: τm=0.3 µs)
−2500 −2000 −1500 −1000 −500 0 500 1000 1500 2000
−1000
The estimated MS of the CG−based VBS The estimated MS of the MG−based VBS True MS
The VBs of the CG−based VBS The VBs of the MG−mode VBS
Figure 4.8: The Positioning Processes of the VBS Schemes under NLOS Environments in Case(4) (with Median Value of the NLOS Noises: τm =0.3 µs)
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0
50 100 150 200 250 300 350 400
RMS Error (m)
Mean Value of the NLOS Error Two−Step LS
The CG−based VBS The MG−based VBS TSE
LLOP
Figure 4.9: The Comparison of the 60% Average Position Errors of the Location Estimation Methods under Different NLOS Errors
performance of the TSE algorithm, the two-step LS method, the LLOP approach and the proposed VBS algorithm under various NLOS environments. The median value τm=0.3 is selected to properly fulfill the NLOS error in the suburban areas. As shown in Fig. 4.9, the performance of the proposed VBS algorithm is apparently better than that of other methods, especially when the value of τm raises.
Chapter 5
Conclusion
The NOLS errors will cause large positive biases while measuring the time information data. The inaccuracies of the range measurements consequentially make the conventional location algorithms, like the two-step LS method [23], fail to estimate the MS’s position. The GLE algorithm [34] skillfully joins the geometric constraints into the two-step LS method to improve the location estimation under the NLOS-corrupted environments. Additionally, the GDOP effect in a communication layout is considered as well. The lower the GDOP value is, the slighter the effect of geometry can affect the positioning processes. The assisted virtual base stations can be added to reduce the GDOP values inside the layout. The proposed CG-based and the MG-based methods which intend to make the MS be at the location where the GDOP value is minimum can be utilized to select the virtual base stations. The proposed VBS algorithm not only imposes the geometric constraints but also iteratively adds the virtual base stations into the conventional two-step LS method. Different layouts and MS’s positions are examined to verify the improvement of the proposed VBS algorithm in the location estimation. The performance shows that the proposed VBS algorithm can perform better than other methods, especially the environments with poor geometric layout and large NLOS errors.
Bibliography
[1] SnapTrack, ”Location Technologles for GSM, GPRS, and UMTS
Network,” a QUALCOMM Company white paper, Jan. 2003 See
http://www.cdmatech.com/resources/pdf/location tech wp 1-03.pdf.
[2] D. Porcino, ”Performance of a OTDOA-IPDL Positioning Receiver for 3GPP-FDD Mode,”
IEE 3G Mobile Communication Technologies, pp. 221-225, Mar. 2001.
[3] Y. T. Chan, C. H. Yau, and P. C. Yau, ”Linear and Approximate Maximum Likelihood Localization from TOA Measurements,” IEEE Signal Processing and Its Applications, Vol.
2, pp. 295-298, Jul. 2003.
[4] R. O. Schmidt, ”Multiple emitter location and signal parameter estimation,” IEEE Trans.
Antennas and Propagation, Vol. 34, Issue 3, pp. 276-280, Mar. 1986.
[5] E. G. Strom, S. Parkvall, S. L. Miller,and B. E. Ottersten, ”Propagation delay estimation of DS-CDMA signals in a fading environment,”IEEE GLOBECOM., pp. 85-89, Nov. 1994.
[6] B. M. Radich and K. M. Buckley, ”The Effect of Source Number Underestimation on MUSIC Location Estimates,” IEEE Trans. on Signal Processing, Vol. 42, pp. 233-236, Jan. 1994.
[7] P. Luukkanen and J. Joutsensalo, ”Comparison of MUSIC and matched filter delay esti-mators in DS-CDMA,”IEEE Personal, Indoor and Mobile Radio Communications, Vol. 3, pp. 830-834, Sep. 1997.
[8] E. G. Strom, S. Parkvall, S. L. Miller, and B.E. Ottersten, ”Propagation delay estima-tion in asynchronous direct-sequence code-division multiple access systems,”IEEE Trans.
Communications, Vol. 44, Issue 1, pp. 84-93, Jan. 1996.
[9] S.Gazor, S. Affes and Y. Grenier, ”Robust Adaptive Beamforming via Target Tracking,”
IEEE Trans. on Signal Processing, Vol. 44, Issue 6, pp. 1589 - 1593, Jun. 1996.
[10] S. Affes, S. Gazor, and Y. Grenier, ”An Algorithm for Multisource Beamforming and Multitarget Tracking,” IEEE Trans. Signal Processing, Vol. 44, Issue 6, pp. 1512-1522, Jun. 1996.
[11] K. Harmanci, J. Tabrikian, and J. L. Krolik, ”Relationships Between Adaptive Minimum Variance Beamforming and Optimal Source Localization,” IEEE Trans. Signal Processing, Vol. 48, Issue 1, pp. 1-12, Jan. 2000.
[12] K. Kaemarungsi and P. Krishnamurthy, ”Properties of Indoor Received Signal Strength for WLAN Location Fingerprinting”,IEEE Mobile and Ubiquitous Systems, pp. 14-23, Aug. 2004.
[13] J. Kwon, B. Dundar, and P. Varaiya, ”Hybrid Algorithm for Indoor Positioning Using Wireless LAN”,IEEE Vehicular Technology Conference, Vol. 7, pp.4625-4629, Sep. 2004.
[14] K. Kaemarungsi and P. Krishnamurthy, ”Modeling of Indoor Positioning Systems Based on Location Fingerprinting,”IEEE INFOCOM, Vol. 2, pp. 1012-1022, Mar. 2004.
[15] M. Hata, ”Empirical Formula for Propagation Loss in Land Mobile Radio Services,”
IEEE Trans. Vehicular Tech., Vol. 29, Issue 3, pp. 317-325, Aug. 1980.
[16] S. Y. Seidal and T. S. Rappaport, ”Site Specific Propagation Prediction for Wireless In-Building Personal Communication System Design,” IEEE Trans. Vehicular Yechnology, Vol. 43, Issue 4, pp. 879-891, Nov. 1994.
[17] T. Imai and T. Fujii, ”Indoor Micro Cell Area Prediction System using Ray-tracing for Mobile Communication Systems”IEEE Personal, Indoor and Mobile Radio Communica-tions, Vol. 1, pp. 24-28, Oct. 1996.
[18] K. R. Chang and H. T. Kim: ”Improvement of the computation efficiency for a ray-launching model”IEEE Antennas and Propagation, Vol. 145, Issue 4, pp. 303-308, Aug.
1998.
[19] S. T. Tan and H. S. Tan, ”Improved Three-Dimensional Ray Tracing Technique for Microcellular Propagation Models ” IEEE Electronics Letters, Vol. 31, Issue 17, pp.1503-1505, Aug. 1995.
[20] Z. Sandor, L. Nagy, Z. Szabo, and T. Csaba, ”3D Ray Launch and Moment Method for indoor radio propagation purposes,”IEEE Personal, Indoor and Mobile Radio Propagation, Vol. 1, Sept. 1997, pp.130-134.
[21] W. H. Foy, ”Position-Location Solutions by Taylor-Series Estimation,” IEEE Trans.
Aerosp. Electron. Syst., Vol. 12, pp. 187-194, Mar. 1976.
[22] X. Wang, Z. Wang, and B. O’Dea, ”A TOA-Based Location Algorithm Reducing the Errors due to Non-Line-of-Sight (NLOS) Propagation,”IEEE Trans., Vol. 52, Jan. 2003.
[23] Y. T. Chen, and K. C. Ho, ”A Simple and Efficient Estimator for Hyperbolic Location,”
IEEE Trans. Signal Processing, Vol. 42, pp. 1905-1915 , 1994.
[24] L. Cong, and W. Zhuang, ”Hybrid TDOA/AOA Mobile User Location for Wideband CDMA Cellular Systems,” IEEE Trans. Wireless Communications, Vol. 1, pp. 439-437, Jul. 2002.
[25] Jr. J. Caffery, ”A New Approach to The Geometry of TOA Location,” IEEE Vehicular Technology Conference, Vol. 4, pp.1943 - 1949, Sep. 2000.
[26] S. Venkatraman, Jr. J. Caffery, ”Hybrid TOA/AOA techniques for mobile location in non-line-of-sight environments,”IEEE Wireless Communications and Networking Conference, Vol. 1, pp. 274-278, Mar. 2004.
[27] J. Caffery Jr. and G. L. Stuber, ”Subscriber location in CDMA cellularnetworks,” IEEE Trans. Veh. Technol., vol.47, pp.406-416, May 1998.
[28] M. I. Silventoinen, T. Rantalainen, ”Mobile Station Emergency locating in GSM,” IEEE International Conference on Personal Wireless Communications, India, Feb. 1996.
[29] P. C. Chen, ”A Non-Line-of-Sight Error Mitigation Algorithm in Location Estimation,”
Proc, IEEE Wireless Communication and Networking Conf., pp. 316-320, Sep. 1999.
[30] M. P. Wylie and J. Holtzman, ”The Non-Line of Sight Problem in Mobile Location Estimation,” Proc. IEEE Int. Conf. Universal Personal Communications, Vol.2, pp.827-831, Sep. 1996.
[31] J. Borras, P. Hatrack and N. B. Mandayam, ”Decision Theoretic Framework for NLOS Identification,” VETEC, Vol. 2, pp.1583 - 1587, May 1998.
[32] B. L. Le, K. Ahmed, and H. Tsuji, ”Mobile Location Estimation with NLOS Mitigation Using Kalman Flitering,”WCNC, Vol 3, pp.1969-1973, Mar. 2003.
[33] S. Venkatraman, J. Caffery, Jr., and H.-R. You, ”A Novel ToA Location Algorithm using LoS Range Estimation for NLoS Environments,” IEEE Trans. on Vehicular Technology, Vol. 53, Issue 5, pp. 1515-1524, Sep. 2004.
[34] C. L. Chen and K. T. Feng, ”An efficient geometry-constrained location estimation al-gorithm for NLOS environments,” Wireless Networks, Communications and Mobile Com-puting, 2005 International Conference, vol.1, pp.244-249, Jun. 2005.
[35] J. Chaffee and J. Abel, ”GDOP and the Cramer-Rao Bound,” PLANS, pp. 663-668, Apr.
1994.
[36] N. Leavnon, ”Lowest GDOP in 2D Scenarios,IEE Proc.-Radar, Sonar Navig., Vol. 147, No. 3, pp.149-155, Jun. 2000.
[37] L. J. Greenstein, V. Erceg, Y. S. Yeh, and M. V. Clark, ”A New Path-Gain/ Delay-Spread Propagation Model for Digital Cellular Channels,” IEEE Trans. on Vehicular Technology, Vol. 46, pp. 477-485, May 1997.