Abstract: Determining the position of an emitter on Earth by using a satellite cluster has many important applications, such as in navigation, surveillance, and remote sensing. However, in realistic situations, a number of factors, such as errors in the measurement of signal parameters, uncertainties regarding the position of satellites, and errors in the location of calibration sources, are known to degrade the accuracy of target localization in satellite geolocation systems. We systematically analyze the performance of multi-satellite joint geolocation based on time difference of arrival (TDOA) measurements. The theoretical analysis starts with Cramér–Rao bound (CRB) derivations for four localization scenarios under an altitude constraint and Gaussian noise assumption. In scenario 1, only the TDOA measurement errors of the emitting source are considered and the satellite positions are assumed to be perfectly estimated. In scenario 2, both the TDOA measurement errors and satellite position uncertainties are taken into account. Scenario 3 assumes that some calibration sources with accurate position information are used to mitigate the influence of satellite position perturbations. In scenario 4, several calibration sources at inaccurate locations are used to alleviate satellite position errors in target localization. Through comparing the CRBs of the four localization scenarios, some valuable’s insights are gained into the effects of various error sources on the estimation performance. Two kinds of location mean-square errors (MSE) expressions under the altitude constraint are derived through first-order perturbation analysis and the Lagrange method. The first location MSE provides the theoretical prediction when an estimator assumes that the satellite locations are accurate but in fact have errors. The second location MSE provides the localization accuracy if an estimator assumes that the known calibration source locations are precise while in fact erroneous. Simulation results are included to verify the theoretical analysis.

多星联合定位理论性能分析

[1]Bardelli, R., Haworth, D., Smith, N., 1995. Interference localization for the EUTELSAT satellite system. Proc. IEEE Int. Conf. on Globecom, p.1641-1651.

[2]Cheung, K.W., So, H.C., Ma, W.K., et al., 2006. A constrained least squares approach to mobile positioning: algorithms and optimality. EURASIP J. Appl. Signal Process., 2006: 1-23.

[3]Ding, W., 2014. The geolocation performance analysis for the constrained Taylor-series iteration in the presence of saellite orbit perturbations. Sci. China Inform. Sci., 44(2):231-253.

[4]Ha, T.T., Robertson, R.C., 1987. Geostationary satellite navigation systems. IEEE Trans. Aerosp. Electron. Syst., 23(2):247-254.

[5]Haworth, D.P., Smith, N.G., Bardelli, R., et al., 1997. Interference localization for EUTELSAT satellites—the first European transmitter location system. Int. J. Satell. Commun., 15(4):155-183.

[6]Ho, K.C., Xu, W.W., 2004. An accurate algebraic solution for moving source location using TDOA and FDOA measurements. IEEE Trans. Signal Process., 52(9):2453-2463.

[7]Ho, K.C., Yang, L., 2008. On the use of a calibration emitter for source localization in the presence of sensor position uncertainty. IEEE Trans. Signal Process., 56(12):5758- 5772.

[8]Ho, K.C., Lu, X.N., Kovavisaruch, L., 2007. Source localization using TDOA and FDOA measurements in the presence of receiver location errors: analysis and solution. IEEE Trans. Signal Process., 55(2):684-696.

[9]Ho, K.C., Chan, Y.T., 1993. Solution and performance analysis of geolocation by TDOA. IEEE Trans. Aerosp. Electron. Syst., 29(4):1311-1322.

[10]Ho, K.C., Chan, Y.T., 1997. Geolocation of a known altitude object from TDOA and FDOA measurements. IEEE Trans. Aerosp. Electron. Syst., 33(3):770-783.

[11]Huang, Y., Benesty, J., Elko, G.W., et al., 2001. Real-time passive source localization: a practical linear-correction least-squares approach. IEEE Trans. Speech Audio Process., 9(8):943-956.

[12]Kovavisaruch, L., Ho, K.C., 2005. Modified Taylor-series method for source and receiver localization using TDOA measurements with erroneous receiver positions. Proc. IEEE Int. Symp. on Circuits and Systems, p.2295-2298.

[13]Lee, K.E., Ahn, D.M., Lee, Y.J., et al., 2000. A total squares algorithm for the source location estimation using GEO satellites. Proc. 21st Century Military Communications Conf., p.271-275.

[14]Lu, X.N., Ho, K.C., 2006a. Taylor-series technique for source localization using AOAs in the presence of sensor location errors. Proc. 4th IEEE Workshop on Sensor Array and Multichannel Processing, p.190-194.

[15]Lu, X.N., Ho, K.C., 2006b. Analysis of the degradation in source location accuracy in the presence of sensor location error. Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, p.925-928.

[16]Marzetta, T.L., 1993. A simple derivation of the constrained multiple parameter Cramer-Rao bound. IEEE Trans. Acoust. Speech Signal Process., 41(6):2247-2249.

[17]Mason, J., 2004. Algebraic two-satellite TOA/FOA position solution on an ellipsoidal Earth. IEEE Trans. Aerosp. Electron. Syst., 40(3):1087-1092.

[18]Mušicki, D., Koch, W., 2008. Geolocation using TDOA and FDOA measurements. Proc. 11th IEEE Int. Conf. on Information Fusion, p.1-8.

[19]Mušicki, D., Kaune, R., Koch, W., 2010. Mobile emitter geolocation and tracking using TDOA and FDOA measurements. IEEE Trans. Signal Process., 58(3):1863-1874.

[20]Niezgoda, G.H., Ho, K.C., 1994. Geolocalization by combined range difference and range rate difference measurements. Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, p.357-360.

[21]Pattison, T., Chou, S.I., 2000. Sensitivity analysis of dual- satellite geolocation. IEEE Trans. Aerosp. Electron. Syst., 36(1):56-71.

[22]Witzgall, H., 2014. Ground vehicle Doppler geolocation. Proc. IEEE Int. Conf. on Aerospace, p.1-8.

[23]Wu, S.L., Luo, J.Q., 2009. Influence of position error on TDOA and FDOA measuring of dual-satellite passive location system. Proc. 3rd IEEE Int. Symp. on Microwave, Antenna, Propagation and EMC Technologies for Wireless Communications, p.293-296.

[24]Yang, K., An, J.P., Bu, X.Y., et al., 2010. Constrained total least-squares location algorithm using time-difference- of-arrival measurements. IEEE Trans. Veh. Technol., 59(3):1558-1562.

[25]Yang, K.H., Jiang, L.Z., Luo, Z.Q., 2011. Efficient semidefinite relaxation for robust geolocation of unknown emitter by a satellite cluster using TDOA and FDOA measurements. Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, p.2584-2587.

[26]Yang, L., Ho, K.C., 2010a. On using multiple calibration emitters and their geometric effects for removing sensor position errors in TDOA localization. Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing, p.14-19.

[27]Yang, L., Ho, K.C., 2010b. Alleviating sensor position error in source localization using calibration emitters at inaccurate locations. IEEE Trans. Signal Process., 58(1):67-83.

[28]Yu, H., Huang, G., Gao, J., 2012. Constrained total least-squares localization algorithm using time difference of arrival and frequency difference of arrival measurements with sensor location uncertainties. IET Radar Sonar Navig., 6(9):891-899.