Abstract
In this work, we consider the joint estimation of time delay, Doppler velocity and Doppler rate of unknown wideband signals, in the sense that the time delay migration over time and Doppler shift migration over signal frequency are non-ignorable. By partitioning the received signals into short-time segments, a novel wideband signal model is presented and the maximum likelihood (ML) estimator is derived. With better compensation of parameter migrations, higher estimation accuracy might be achieved through the derived ML estimator. The signal-specific Cramer–Rao lower bound analysis for the wideband cases is also presented. To avoid the multidimensional search of the ML estimator, a fast estimation algorithm based on the time-reverse transform and the second-order Keystone transform is proposed. In this fast estimation algorithm, these parameters could be estimated through successive one-dimensional searches. Simulation results show that the fast estimation algorithm could achieve comparable performance with the ML estimator with a much lower computational complexity.
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References
K. Borowiec, M. Malanowski, Accelerating rocket detection using passive bistatic radar, in 17th International Radar International, (2016), pp. 1–5. https://doi.org/10.1109/IRS.2016.7497376
Y.T. Chan, K.C. Ho, Joint time-scale and TDOA estimation: analysis and fast approximation. IEEE Trans. Signal Process. 53(8), 2625–2634 (2005)
X. Chen, J. Guan, N. Liu, Y. He, Maneuvering target detection via Radon-fractional fourier transform-based long-time coherent integration. IEEE Trans. Signal Process. 62(4), 939–953 (2014)
Z. Deng, M. Fu, X. Wu, Y. Zhang, Doppler rate estimation on coherent sinusoidal pulse train and its Cramer–Rao lower bound. Signal Process. 101, 229–241 (2014)
I. Djurovic, M. Simeunovic, P. Wang, Cubic phase function: a simple solution to polynomial phase signal analysis. Signal Process. 135, 48–66 (2017)
M.L. Fowler, X. Hu, Signal models for TDOA/FDOA estimation. IEEE Trans. Aerosp. Electron. Syst. 44(4), 1543–1550 (2008)
H. Hmam, Optimal sensor velocity configuration for TDOA–FDOA geolocation. IEEE Trans. Signal Process. 65(3), 628–637 (2017)
K.C. Ho, L. Xiaoning, L. Kovavisaruch, 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 (2007)
R. Horn, Maxtrix Analysis (Cambridge University Press, Cambridge, 1985)
D. Hu, Z. Huang, X. Chen, J. Lu, A moving source localization method using TDOA, FDOA and Doppler rate measurements. IEICE Trans. Commun. 99(3), 758–766 (2016)
P. Huang, G. Liao, Z. Yang, X.G. Xia, J. Ma, X. Zhang, An approach for refocusing of ground moving target without target motion parameter estimation. IEEE Trans. Geosci. Remote Sens. 55(1), 336–350 (2017)
P. Huang, G. Liao, Z. Yang, X.G. Xia, J. Ma, J. Zheng, Ground maneuvering target imaging and high-order motion parameter estimation based on second-order keystone and generalized hough-haf transform. IEEE Trans. Geosci. Remote Sens. 55(1), 320–335 (2017)
P. Huang, G. Liao, Z. Yang, X.G. Xia, J.T. Ma, J. Ma, Long-time coherent integration for weak maneuvering target detection and high-order motion parameter estimation based on keystone transform. IEEE Trans. Signal Process. 64(15), 4013–4026 (2016)
S. Kay, Fundamentals of Statistical Signal Processing-Estimation Theory (Prentice-Hall, Englewood Cliffs, 1993)
Y.H. Kim, D.G. Kim, J.W. Han, K.H. Song, H.N. Kim, Analysis of sensor-emitter geometry for emitter localisation using TDOA and FDOA measurements. IET Radar Sonar Navig. 11(2), 341–349 (2017)
H. Li, D. Ma, R. Wu, A low complexity algorithm for across range unit effect correction of the moving target via range frequency polynomial-phase transform. Digit. Signal Process. 62(Supplement C), 176–186 (2017)
X. Li, G. Cui, W. Yi, L. Kong, Coherent integration for maneuvering target detection based on Radon-Lv’s distribution. IEEE Signal Process Lett. 22(9), 1467–1471 (2015)
X. Li, G. Cui, W. Yi, L. Kong, Fast coherent integration for maneuvering target with high-order range migration via TRT-SKT-LVD. IEEE Trans. Aerosp. Electron. Syst. 52(6), 2803–2814 (2016)
X. Li, G. Cui, W. Yi, L. Kong, Manoeuvring target detection based on keystone transform and Lv’s distribution. IET Radar Sonar Navig. 10(7), 1234–1242 (2016)
X. Li, G. Cui, W. Yi, L. Kong, Sequence-reversing transform-based coherent integration for high-speed target detection. IEEE Trans. Aerosp. Electron. Syst. 53(3), 1573–1580 (2017)
X. Li, L. Kong, G. Cui, W. Yi, A low complexity coherent integration method for maneuvering target detection. Digit. Signal Process. 49, 137–147 (2016)
X. Li, L. Kong, G. Cui, W. Yi, Detection and RM correction approach for manoeuvring target with complex motions. IET Signal Process. 11(4), 378–386 (2017)
X. Li, L. Kong, G. Cui, W. Yi, Y. Yang, ISAR imaging of maneuvering target with complex motions based on ACCF–LVD. Digit. Signal Process. 46(Supplement C), 191–200 (2015)
X. Lv, G. Bi, C. Wan, M. Xing, Lv’s distribution: principle, implementation, properties, and performance. IEEE Trans. Signal Process. 59(8), 3576–3591 (2011)
M. Malanowski, K. Kulpa, J. Misiurewicz, Acceleration estimation for passive coherent location radar, in IEEE Radar Conference, (2008), pp. 1–5. https://doi.org/10.1109/RADAR.2008.4721010
M. Malanowski, K. Kulpa, K.E. Olsen, Extending the integration time in dvb-t-based passive radar, in 2011 European Radar Conference, (2011), pp. 190–193
D.J. Nelson, D.C. Smith, Scale cross-ambiguity and target resolution. Digit. Signal Process. 19(2), 194–200 (2009)
X. Rao, H. Tao, J. Su, X. Jian, Z. Xiangyang, Detection of constant radial acceleration weak target via IAR-FRFT. IEEE Trans. Aerosp. Electron. Syst. 51(4), 3242–3253 (2015)
G.S. Song, T.N.T. Goodman, F. Shang, Joint estimation of time delay and doppler shift for band-limited signals. IEEE Trans. Signal Process. 58(9), 4583–4594 (2010)
S. Stein, Algorithms for ambiguity function processing. IEEE Trans. Acoust. Speech Signal Process. 29(3), 588–599 (1981)
J. Su, H. Tao, J. Xie, X. Rao, X. Guo, Imaging and doppler parameter estimation for maneuvering target using axis mapping based coherently integrated cubic phase function. Digit. Signal Process. 62, 112–124 (2017)
G. Sun, M. Xing, X.G. Xia, Y. Wu, Z. Bao, Robust ground moving-target imaging using deramp-keystone processing. IEEE Trans. Geosci. Remote Sens. 51(2), 966–982 (2013)
Z. Sun, X. Li, W. Yi, G. Cui, L. Kong, Detection of weak maneuvering target based on keystone transform and matched filtering process. Signal Process. 140(Supplement C), 127–138 (2017)
K. Tan, W. Li, Imaging and parameter estimating for fast moving targets in airborne SAR. IEEE Trans. Comput. Imaging 3(1), 126–140 (2017)
S. Tao, T. Ran, S.R. Rong, A fast method for time delay, doppler shift and doppler rate estimation, in International Conference Radar, (2006), pp. 1–4. https://doi.org/10.1109/ICR.2006.343509
H.L.V. Trees, Detection, Estimation, and Modulation Theory, Pert III: Radar-Sonar Signal Processing and Gaussian Signals in Noise (Wiley, Hoboken, 2001)
Y. Wang, K.C. Ho, Tdoa positioning irrespective of source range. IEEE Trans. Signal Process. 65(6), 1447–1460 (2017)
Y. Wang, Y. Wu, An efficient semidefinite relaxation algorithm for moving source localization using TDOA and FDOA measurements. IEEE Commun. Lett. 21(1), 80–83 (2017)
A.J. Weiss, Direct geolocation of wideband emitters based on delay and Doppler. IEEE Trans. Signal Process. 59(6), 2513–2521 (2011)
L.G. Weiss, Wavelets and wideband correlation processing. IEEE Signal Process. Mag. 11(1), 13–32 (1994). https://doi.org/10.1109/79.252866
Y. Wu, G. Sun, X.G. Xia, M. Xing, Z. Bao, An improved SAC algorithm based on the range-keystone transform for Doppler rate estimation. IEEE Geosci. Remote Sens. Lett. 10(4), 741–745 (2013)
Z. Xin, G. Liao, Z. Yang, P. Huang, J. Ma, A fast ground moving target focusing method based on first-order discrete polynomial-phase transform. Digit. Signal Process. 60(Supplement C), 287–295 (2017)
J. Xu, X.G. Xia, S.B. Peng, J. Yu, Y.N. Peng, L.C. Qian, Radar maneuvering target motion estimation based on generalized Radon-Fourier transform. IEEE Trans. Signal Process. 60(12), 6190–6201 (2012)
A. Yeredor, E. Angel, Joint TDOA and FDOA estimation: a conditional bound and its use for optimally weighted localization. IEEE Trans. Signal Process. 59(4), 1612–1623 (2011)
W. Yu, W. Su, H. Gu, Ground moving target motion parameter estimation using Radon modified Lv’s distribution. Digit. Signal Process. 69(Supplement C), 212–223 (2017)
J. Zhang, T. Su, J. Zheng, X. He, Novel fast coherent detection algorithm for radar maneuvering target with jerk motion. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 10(5), 1792–1803 (2017)
L. Zhang, B. Yang, M. Luo, Joint delay and Doppler shift estimation for multiple targets using exponential ambiguity function. IEEE Trans. Signal Process. 65(8), 2151–2163 (2017)
W.Q. Zhang, Fast Doppler rate estimation based on fourth-order moment spectrum. Electron. Lett. 51(23), 1926–1928 (2015)
X. Zhang, H. Li, J. Liu, B. Himed, Joint delay and Doppler estimation for passive sensing with direct-path interference. IEEE Trans. Signal Process. 64(3), 630–640 (2016)
J. Zheng, T. Su, H. Liu, G. Liao, Z. Liu, Q.H. Liu, Radar high-speed target detection based on the frequency-domain deramp-keystone transform. IEEE J. Sel. Top. Appl. Earth Obs. Remote Sens. 9(1), 285–294 (2016)
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Xiao, X., Guo, F. Joint Estimation of Time Delay, Doppler Velocity and Doppler Rate of Unknown Wideband Signals. Circuits Syst Signal Process 38, 85–104 (2019). https://doi.org/10.1007/s00034-018-0816-6
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DOI: https://doi.org/10.1007/s00034-018-0816-6