×

Direct position determination of multiple noncircular sources with a moving array. (English) Zbl 1371.94604

Summary: Compared with conventional two-step localization methods, direct position determination (DPD) is a promising technique that offers superior performance under low signal-to-noise ratio conditions. However, existing DPD methods mainly focus on complex circular sources without considering noncircular signals, which can be exploited to enhance the localization accuracy. This study proposes an improved subspace data fusion (SDF)-based DPD algorithm for multiple noncircular sources with a moving array. By constructing and decomposing the extended covariance matrices, extended noise subspaces are obtained for all positions of the moving array. The source positions are then directly estimated by fusing the extended noise subspaces without computing the intermediate parameters, thereby avoiding the data association problem inherent in two-step methods. Our proposed DPD algorithm combines the low complexity of SDF with the high robustness to noise and sensor errors that comes from exploiting signal noncircularity. Specifically, a closed-form expression for the localization mean square error (MSE) of the algorithm and the stochastic Cramér-Rao bound for strict-sense noncircular signals are derived. Simulation results validate our theoretical prediction for MSE and also demonstrate that the proposed algorithm outperforms other localization methods in terms of accuracy and capacity to resolve noncircular sources.

MSC:

94A29 Source coding
94A12 Signal theory (characterization, reconstruction, filtering, etc.)
Full Text: DOI

References:

[1] H. Abeida, J.-P. Delmas, MUSIC-like estimation of direction of arrival for noncircular sources. IEEE Trans. Signal Process. 54(7), 2678-2690 (2006) · Zbl 1373.94527 · doi:10.1109/TSP.2006.873505
[2] H. Abeida, J.-P. Delmas, Statistical performance of MUSIC-Like algorithms in resolving noncircular sources. IEEE Trans. Signal Process. 56(9), 4317-4329 (2008) · Zbl 1390.94063 · doi:10.1109/TSP.2008.924143
[3] A. Amar, A.J. Weiss, Direct position determination of multiple radio signals. IEEE Int. Conf. Acoust. Speech Signal Process. 2, ii-81-4 (2004) · Zbl 1107.94378
[4] A. Amar, A.J. Weiss, A decoupled algorithm for geolocation of multiple emitters. Sig. Process. 87(10), 2348-2359 (2007) · Zbl 1186.94039 · doi:10.1016/j.sigpro.2007.03.008
[5] D. Bruno, M. Oispuu, E. Ruthotto, Localization of multiple sources with a moving array using subspace data fusion, in Information Fusion, 2008 11th International Conference on. IEEE (2008), pp.1-7
[6] P. Chargé, Y. Wang, J. Saillard, A non-circular sources direction finding method using polynomial rooting. Sig. Process. 81(8), 1765-1770 (2001) · Zbl 1076.94510 · doi:10.1016/S0165-1684(01)00071-8
[7] J.-P. Delmas, H. Abeida, Stochastic Cramér-Rao bound for noncircular signals with application to DOA estimation. IEEE Trans. Signal Process. 52(11), 3192-3199 (2004) · Zbl 1370.94102 · doi:10.1109/TSP.2004.836462
[8] Z.J. Fu, K. Ren, J.G. Shu, X.M. Sun, F.X. Huang, Enabling personalized search over encrypted outsourced data with efficiency improvement. IEEE Trans. Parallel Distrib. Syst. 27(9), 2546-2559 (2016)
[9] J. Li, L. Yang, F. Guo, Coherent summation of multiple short-time signals for direct positioning of a wideband source based on delay and Doppler. Digit. Signal Proc. 48(C), 58-70 (2016) · doi:10.1016/j.dsp.2015.09.008
[10] S.C. Nardone, M.L. Graham, A closed-form solution to bearings-only target motion analysis. IEEE J. Ocean. Eng. 22(1), 168-178 (1997) · doi:10.1109/48.557551
[11] M. Oispuu, U. Nickel, Direct detection and position determination of multiple sources with intermittent emission. Sig. Process. 90(12), 3056-3064 (2010) · Zbl 1197.94101 · doi:10.1016/j.sigpro.2010.05.010
[12] I. P. Pokrajac, D. Vučić, One-step signal selective direct positioning algorithm of cyclostationary signals, in 2010 5th European Conference on Circuits and Systems for Communications (ECCSC) (2010), pp. 298-301 · Zbl 1390.94063
[13] A.M. Reuven, A.J. Weiss, Direct position determination of cyclostationary signals. Sig. Process. 89(12), 2448-2464 (2009) · Zbl 1197.94114 · doi:10.1016/j.sigpro.2009.04.009
[14] J.Y. Shen, A.F. Molisch, J. Salmi, Accurate passive location estimation using TOA measurements. IEEE Trans. Wireless Commun. 11(6), 253-257 (2011)
[15] P. Stoica, A. Nehorai, T. Söderström, Decentralized array processing using the MODE algorithm. Circuits Syst. Signal Process. 14(1), 17-38 (1995) · Zbl 0815.93078 · doi:10.1007/BF01183746
[16] T. Tirer, A.J. Weiss, High resolution direct position determination of radio frequency sources. IEEE Signal Process. Lett. 23(2), 192-196 (2016) · doi:10.1109/LSP.2015.2503921
[17] L. Tzafri, A.J. Weiss, High-resolution direct position determination using MVDR. IEEE Trans. Wireless Commun. 15(9), 6449-6461 (2016) · doi:10.1109/TWC.2016.2585116
[18] D. Wang, Y. Wu, Statistical performance analysis of direct position determination method based on Doppler shifts in presence of model errors. Multidimens. Syst. Signal Process. 1-34 (2015)
[19] D. Wang, G. Zhang, C.Y. Shen, J. Zhang, Direct position determination algorithm for constant modulus signals with single moving observer. Acta Aeronaut. Astronaut. Sin. 37(5), 1622-1633 (2016)
[20] M. Wax, T. Kailath, Optimum localization of multiple sources by passive arrays. IEEE Trans. Acoust. Speech Signal Process. 31(5), 1210-1217 (1983) · doi:10.1109/TASSP.1983.1164183
[21] A.J. Weiss, Direct position determination of narrowband radio frequency transmitters. IEEE Signal Process. Lett. 11(5), 513-516 (2004) · doi:10.1109/LSP.2004.826501
[22] A.J. Weiss, A. Amar, Direct position determination of multiple radio signals. EURASIP J. Appl. Signal Process. 1, 37-49 (2005) · Zbl 1107.94378 · doi:10.1155/ASP.2005.37
[23] F. Wen, Q. Wan, L.Y. Luo, Time-difference-of-arrival estimation for noncircular signals using information theory. AEU Int. J. Electron. Commun. 67(67), 242-245 (2013) · doi:10.1016/j.aeue.2012.08.006
[24] Y. Xia, C.C. Took, D.P. Mandic, An augmented affine projection algorithm for the filtering of noncircular complex signals. Sig. Process. 90(6), 1788-1799 (2010) · Zbl 1197.94145 · doi:10.1016/j.sigpro.2009.11.026
[25] J.X. Yin, Y. Wu, D. Wang, An auto-calibration method for spatially and temporally correlated noncircular sources in unknown noise fields. Multidimens. Syst. Signal Process. 27(2), 511-539 (2016) · Zbl 1380.94063 · doi:10.1007/s11045-015-0316-9
[26] H. Zhang, L. Li, W. Li, Independent vector analysis for convolutive blind noncircular source separation, in IEEE 2010 International Symposium on Intelligent Signal Processing and Communication Systems (ISPACS) (2010), pp. 1-4
[27] X.D. Zhang, Matrix Analysis and Application (Tsinghua University Press, Beijing, 2004)
[28] Y.H. Zhang, X.M. Sun, B.W. Wang, Efficient algorithm for K-barrier coverage based on integer linear programming. China Commun. 13(7), 16-23 (2016) · doi:10.1109/CC.2016.7559071
[29] J.F. Zhang, T.S. Qiu, A novel covariance based noncircular sources direction finding method under impulsive noise environment. Sig. Process. 98(8), 252-262 (2014) · doi:10.1016/j.sigpro.2013.11.006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.