Abstract
Single-station passive localization technology avoids the complex time synchronization and information exchange between multiple observatories, and is increasingly important in electronic warfare. Based on a single moving station localization system, a new method with high localization precision and numerical stability is proposed when the measurements from multiple disjoint sources are subject to the same station position and velocity displacement. According to the available measurements including the angle-of-arrival (AOA), time-of-arrival (TOA), and frequency-of-arrival (FOA), the corresponding pseudo linear equations are deduced. Based on this, a structural total least squares (STLS) optimization model is developed and the inverse iteration algorithm is used to obtain the stationary target location. The localization performance of the STLS localization algorithm is derived, and it is strictly proved that the theoretical performance of the STLS method is consistent with that of the constrained total least squares method under first-order error analysis, both of which can achieve the Cramér-Rao lower bound accuracy. Simulation results show the validity of the theoretical derivation and superiority of the new algorithm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abatzoglou TJ, Mendel JM, Harada GA, 1991. The constrained total least squares technique and its applications to harmonic superresolution. IEEE Trans Signal Process, 39(5):1070–1087. https://doi.org/10.1109/78.80955
Antreich F, Nossek JA, Seco–Granados G, et al., 2011. The extended invariance principle for signal parameter estimation in an unknown spatial field. IEEE Trans Signal Process, 59(7):3213–3225. https://doi.org/10.1109/TSP.2011.2140107
Bamler R, 1991. Doppler frequency estimation and the Cramer–Rao bound. IEEE Trans Geosci Remote Sens, 29(3):385–390. https://doi.org/10.1109/36.79429
Bar–Shalom O, Weiss AJ, 2014. Emitter geolocation using single moving receiver. Signal Process, 105:70–83. https://doi.org/10.1016/j.sigpro.2014.05.006
Belouchrani A, Aouada S, 2003. Maximum likelihood joint angle and delay estimation in unknown noise fields. IEEE Int Conf on Acoustics, Speech, and Signal Processing, p.V–265. https://doi.org/10.1109/ICASSP.2003.1199919
Carevic D, 2007. Automatic estimation of multiple target positions and velocities using passive TDOA measurements of transients. IEEE Trans Signal Process, 55(2): 424–436. https://doi.org/10.1109/TSP.2006.885745
Chalise BK, Zhang YD, Amin MG, et al., 2014. Target localization in a multi–static passive radar system through convex optimization. Signal Process, 102:207–215. https://doi.org/10.1016/j.sigpro.2014.02.023
de Moor B, 1994. Total least squares for affinely structured matrices and the noisy realization problem. IEEE Trans Signal Process, 42(11):3104–3113. https://doi.org/10.1109/78.330370
Doğançay K, 2005. Bearings–only target localization using total least squares. Signal Process, 85(9):1695–1710. https://doi.org/10.1016/j.sigpro.2005.03.007
Eldar YC, 2006. Uniformly improving the CramÉr–Rao bound and maximum–likelihood estimation. IEEE Trans Signal Process, 54(8):2943–2956. https://doi.org/10.1109/TSP.2006.877648
Foy WH, 1976. Position–location solutions by Taylor–series estimation. IEEE Trans Aerosp Electron Syst, AES–12(2): 187–194. https://doi.org/10.1109/TAES.1976.308294
Giacometti R, Baussard A, Cornu C, et al., 2016. Accuracy studies for TDOA–AOA localization of emitters with a single sensor. IEEE Radar Conf, p.1–4. https://doi.org/10.1109/RADAR.2016.7485185
Golub GH, van Loan CF, 2012. Matrix Computations (4th Ed.). The Johns Hopkins University Press, Baltimore, USA.
Griffin A, Alexandridis A, Pavlidi D, et al., 2015. Localizing multiple audio sources in a wireless acoustic sensor network. Signal Process, 107:54–67. https://doi.org/10.1016/j.sigpro.2014.08.013
Hao BJ, Li Z, Si JB, et al., 2012. Passive multiple disjoint sources localization using TDOAs and GROAs in the presence of sensor location uncertainties. IEEE Int Conf on Communications, p.47–52. https://doi.org/10.1109/ICC.2012.6364164
Ho KC, Lu XN, 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. https://doi.org/10.1109/TSP.2006.885744
Jia TY, Wang HY, Shen XH, et al., 2017. Bearing–only multiple sources localization and the spatial spectrum. OCEANS, p.1–5. https://doi.org/10.1109/OCEANSE.2017.8084819
Kay SM, 1993. Fundamentals of Statistical Signal Processing, Volume I: Estimation Theory. Prentice Hall, Englewood Cliffs, New Jersey, USA, p.465–466.
Knapp C, Carter G, 1976. The generalized correlation method for estimation of time delay. IEEE Trans Acoust Speech Signal Process, 24(4):320–327. https://doi.org/10.1109/TASSP.1976.1162830
Lemma AN, van der Veen AJ, Deprettere EF, 2003. Analysis of joint angle–frequency estimation using ESPRIT. IEEE Trans Signal Process, 51(5):1264–1283. https://doi.org/10.1109/TSP.2003.810306
Lemmerling P, de Moor B, van Huffel S, 1996. On the equivalence of constrained total least squares and structured total least squares. IEEE Trans Signal Process, 44(11): 2908–2911. https://doi.org/10.1109/78.542454
Li J, Zhao YJ, Li DH, 2014. Accurate single–observer passive coherent location estimation based on TDOA and DOA. Chin J Aeronaut, 27(4):913–923. https://doi.org/10.1016/j.cja.2014.06.004
Li JZ, Pang HW, Guo FC, et al., 2015. Localization of multiple disjoint sources with prior knowledge on source locations in the presence of sensor location errors. Dig Signal Process, 40:181–197. https://doi.org/10.1016/j.dsp.2015.02.003
Li MH, Lu YL, 2008. Angle–of–arrival estimation for localization and communication in wireless networks. 16th European Signal Processing Conf, p.1–5.
Liu FL, Wang JK, Du RY, 2010. Unitary–JAFE algorithm for joint angle–frequency estimation based on Frame–Newton method. Signal Process, 90(3):809–820. https://doi.org/10.1016/j.sigpro.2009.08.013
Liu RR, Wang YL, Yin JX, et al., 2017. Passive source localization using importance sampling based on TOA and FOA measurements. Front Inform Technol Electron Eng, 18(8):1167–1179. https://doi.org/10.1631/FITEE.1601657
Luise M, Reggiannini R, 1995. Carrier frequency recovery in all–digital modems for burst–mode transmissions. IEEE Trans Commun, 43(2–4):1169–1178. https://doi.org/10.1109/26.380149
Markovsky I, van Huffel S, 2007. Overview of total leastsquares methods. Signal Process, 87(10):2283–2302. https://doi.org/10.1016/j.sigpro.2007.04.004
Mir HS, Sahr JD, Hatke GF, et al., 2007. Passive source localization using an airborne sensor array in the presence of manifold perturbations. IEEE Trans Signal Process, 55(6):2486–2496. https://doi.org/10.1109/TSP.2007.893936
Raykar VC, Kozintsev IV, Lienhart R, 2005. Position calibration of microphones and loudspeakers in distributed computing platforms. IEEE Trans Speech Audio Process, 13(1):70–83. https://doi.org/10.1109/TSA.2004.838540
Rockah Y, Schultheiss PM, 1987a. Array shape calibration using sources in unknown location—Part I: far–field sources. IEEE Trans Acoust Speech Signal Process, 35(3): 286–299. https://doi.org/10.1109/TASSP.1987.1165144
Rockah Y, Schultheiss PM, 1987b. Array shape calibration using sources in unknown locations—Part II: near–field sources and estimator implementation. IEEE Trans Acoust Speech Signal Process, 35(6):724–735. https://doi.org/10.1109/TASSP.1987.1165222
Shen H, Ding Z, Dasgupta S, et al., 2014. Multiple source localization in wireless sensor networks based on time of arrival measurement. IEEE Trans Signal Process, 62(8): 1938–1949. https://doi.org/10.1109/TSP.2014.2304433
So HC, Lin LX, 2011. Linear least squares approach for accurate received signal strength based source localization. IEEE Trans Signal Process, 59(8):4035–4040. https://doi.org/10.1109/TSP.2011.2152400
Sun M, Ho KC, 2011. An asymptotically efficient estimator for TDOA and FDOA positioning of multiple disjoint sources in the presence of sensor location uncertainties. IEEE Trans Signal Process, 59(7):3434–3440. https://doi.org/10.1109/TSP.2011.2131135
Sun XY, Li JD, Huang PY, et al., 2008. Total least–squares solution of active target localization using TDOA and FDOA measurements in WSN. 22nd Int Conf on Advanced Information Networking and Applications, p.995–999. https://doi.org/10.1109/WAINA.2008.150
Torrieri DJ, 1984. Statistical theory of passive location systems. IEEE Trans Aerosp Electron Syst, AES–20(2): 183–198. https://doi.org/10.1109/TAES.1984.310439
Wang D, Zhang L, Wu Y, 2007. Constrained total least squares algorithm for passive location based on bearing–only measurements. Sci China Ser F Inform Sci, 50(4): 576–586. https://doi.org/10.1007/s11432-007-0023-8
Wang D, Zhang L, Wu Y, 2009. The structured total least squares algorithm research for passive location based on angle information. Sci China Ser F Inform Sci, 52(6): 1043–1054. https://doi.org/10.1007/s11432-009-0114-9
Wang L, Hu AQ, Bai GW, et al., 2011. Enhanced constrained total least squares estimator in TDOA localization for WSNs. Int Conf on Computer Science and Service System, p.389–392. https://doi.org/10.1109/CSSS.2011.5974564
Wang YY, Chen JT, Fang WH, 2001. TST–MUSIC for joint DOA–delay estimation. IEEE Trans Signal Process, 49(4):721–729. https://doi.org/10.1109/78.912916
Weiss AJ, Friedlander B, 1989. Array shape calibration using sources in unknown locations—a maximum likelihood approach. IEEE Trans Acoust Speech Signal Process, 37(12):1958–1966. https://doi.org/10.1109/29.45542
Wu H, Chen SX, Zhang YH, et al., 2015. Robust structured total least squares algorithm for passive location. J Syst Eng Electron, 26(5):946–953. https://doi.org/10.1109/JSEE.2015.00103
Yang K, An JP, Bu XY, et al., 2010. Constrained total least–squares location algorithm using time–difference–ofarrival measurements. IEEE Trans Veh Technol, 59(3): 1558–1562. https://doi.org/10.1109/TVT.2009.2037509
Yang L, Ho KC, 2009. An approximately efficient TDOA localization algorithm in closed–form for locating multiple disjoint sources with erroneous sensor positions. IEEE Trans Signal Process, 57(12):4598–4615. https://doi.org/10.1109/TSP.2009.2027765
Yin JX, Wu Y, Wang D, 2014. On 2–D direction–of–arrival estimation performance for rank reduction estimator in presence of unexpected modeling errors. Circ Syst Signal Process, 33(2):515–547. https://doi.org/10.1007/s00034-013-9654-8
Yu H, Huang G, Gao J, 2012. Constrained total least–squares localisation algorithm using time difference of arrival and frequency difference of arrival measurements with sensor location uncertainties. IET Radar Sonar Navig, 6(9): 891–899. https://doi.org/10.1049/iet-rsn.2011.0205
Author information
Authors and Affiliations
Corresponding author
Additional information
Project supported by the National Natural Science Foundation of China (Nos. 61201381, 61401513, and 61772548), the China Postdoctoral Science Foundation (No. 2016M592989), the Self-Topic Foundation of Information Engineering University, China (No. 2016600701), and the Outstanding Youth Foundation of Information Engineering University, China (No. 2016603201)
Rights and permissions
About this article
Cite this article
Chen, X., Wang, D., Liu, Rr. et al. Structural total least squares algorithm for locating multiple disjoint sources based on AOA/TOA/FOA in the presence of system error. Frontiers Inf Technol Electronic Eng 19, 917–936 (2018). https://doi.org/10.1631/FITEE.1700735
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1631/FITEE.1700735
Key words
- Single-station
- Structural total least squares
- Inverse iteration
- Angle-of-arrival (AOA)
- Time-of-arrival (TOA)
- Frequency-of-arrival (FOA)
- Disjoint sources