Range, radial velocity, and acceleration MLE using frequency modulation coded LFM pulse train

Linearly frequency modulation (LFM) pulse train and linearly stepped frequency (LSF) pulse train are mostly used in radar systems. However, the estimation performance of target motion parameters may be affected by the high recurrent lobe levels and the rangeDoppler coupling phenomenon appearing in ambiguity function (AF). In multi-target scenarios, the estimation performance becomes even worse. The Costas frequency-modulation coded (CFMC) LFM pulse train has an ideal thumbtack-shaped AF, thus it can provide motion parameter estimation with high precision. However, the estimation of target motion parameter for the coherent CFMC LFM pulse train has not been investigated in depth. In this paper, we first analyze the properties of the AF of the CFMC LFM pulse train. Based on its convexity and narrow mainlobe width, a fast method to implement the maximum likelihood estimator (MLE) is proposed to estimate the motion parameters. To reduce the computation complexity, the Chirp-Z Transform (CZT) is introduced. Then, the CramerRao lower bounds (CRLBs) on range, velocity and acceleration for frequency-modulation coded (FMC) pulse train are derived. It is shown that the CRLBs are relevant to the frequency coding patterns. Finally, Monte Carlo simulations are performed to verify the performance of the MLE. The results show that the performance of our proposed method can achieve the CRLBs when the signal-noise ratio (SNR) is higher than the threshold SNR.

[1]  S. Golomb,et al.  Constructions and properties of Costas arrays , 1984, Proceedings of the IEEE.

[2]  P. Grant,et al.  A study of auto- and cross-ambiguity surface performance for discretely coded waveforms , 1990 .

[3]  Panayiotis Frangos,et al.  Two-dimensional ISAR model and image reconstruction with stepped frequency-modulated signal , 2008 .

[4]  Charles V. Jakowatz,et al.  Phase gradient autofocus-a robust tool for high resolution SAR phase correction , 1994 .

[5]  S. R. Rogers,et al.  On analytical evaluation of glint error reduction for frequency-hopping radars , 1991 .

[6]  Sailes K. Sengijpta.  Fundamentals of Statistical Signal Processing: Estimation Theory , 1995 .

[7]  Yingning Peng,et al.  Radon-Fourier Transform for Radar Target Detection (II): Blind Speed Sidelobe Suppression , 2011, IEEE Transactions on Aerospace and Electronic Systems.

[8]  Yichuan Yang,et al.  ISAR imaging of maneuvering target with complex motions based on ACCF-LVD , 2015, Digit. Signal Process..

[9]  J. R. Bellegarda,et al.  The hit array: an analysis formalism for multiple access frequency hop coding , 1991 .

[10]  Gang Li,et al.  Velocity Estimation and Range Shift Compensation for High Range Resolution Profiling in Stepped-Frequency Radar , 2010, IEEE Geoscience and Remote Sensing Letters.

[11]  T. Sauer,et al.  Robust range alignment algorithm via Hough transform in an ISAR imaging system , 1995 .

[12]  Qing Huo Liu,et al.  Radar High-Speed Target Detection Based on the Scaled Inverse Fourier Transform , 2015, IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing.

[13]  Zishu He,et al.  Comments on "Discrete Frequency-Coding Waveform Design for Netted Radar Systems" , 2008, IEEE Signal Process. Lett..

[14]  S.A.S. Werness,et al.  Moving target imaging algorithm for SAR data , 1990 .

[15]  Liu Jing,et al.  Motion compensation based on entropy-like function optimization for MMW Costas frequency hopped radar , 2004, Proceedings 7th International Conference on Signal Processing, 2004. Proceedings. ICSP '04. 2004..

[16]  Tianyao Huang,et al.  Fundamental Limits of HRR Profiling and Velocity Compensation for Stepped-Frequency Waveforms , 2014, IEEE Transactions on Signal Processing.

[17]  Huadong Meng,et al.  Suppressing autocorrelation sidelobes of LFM pulse trains with genetic algorithm , 2008 .

[18]  K. Erickson,et al.  Combinatoric collaboration on Costas arrays and radar applications , 2004, Proceedings of the 2004 IEEE Radar Conference (IEEE Cat. No.04CH37509).

[19]  Scott T. Rickard,et al.  Costas Arrays, Number of Hops, and Time-Bandwidth Product , 2013, IEEE Transactions on Aerospace and Electronic Systems.

[20]  S. R. Rogers.  Tracking accuracies of frequency-hopping radars , 1990, IEEE Conference on Aerospace and Electronics.

[21]  Yingning Peng,et al.  Radon-Fourier Transform for Radar Target Detection, I: Generalized Doppler Filter Bank , 2011, IEEE Transactions on Aerospace and Electronic Systems.

[22]  Sandeep Gogineni,et al.  Frequency-Hopping Code Design for MIMO Radar Estimation Using Sparse Modeling , 2012, IEEE Transactions on Signal Processing.

[23]  Wei Yi,et al.  A low complexity coherent integration method for maneuvering target detection , 2016, Digit. Signal Process..

[24]  Richard P. Bocker,et al.  ISAR motion compensation using the burst derivative measure as a focal quality indicator , 1992, Int. J. Imaging Syst. Technol..

[25]  T. Abatzoglou,et al.  Range, radial velocity, and acceleration MLE using radar LFM pulse train , 1998 .

[26]  Alberto Moreira,et al.  An Autofocus Approach for Residual Motion Errors With Application to Airborne Repeat-Pass SAR Interferometry , 2008, IEEE Transactions on Geoscience and Remote Sensing.

[27]  V. Umapathi Reddy,et al.  Low-Complexity Design of Frequency-Hopping Codes for MIMO Radar for Arbitrary Doppler , 2010, EURASIP J. Adv. Signal Process..

[28]  J.P. Costas,et al.  A study of a class of detection waveforms having nearly ideal range—Doppler ambiguity properties , 1983, Proceedings of the IEEE.

[29]  Zhang Xin,et al.  Evaluation of Welch-Costas Frequency Hopping Pattern for OFDM Cellular System , 2007, 2007 IEEE 18th International Symposium on Personal, Indoor and Mobile Radio Communications.

[30]  D. Wehner.  High Resolution Radar , 1987 .

[31]  E. J. Kelly,et al.  The Radar Measurement of Range, Velocity and Acceleration , 1961, IRE Transactions on Military Electronics.

[32]  Ivan Seskar,et al.  On cross-ambiguity properties of Welch-Costas arrays when applied in SS/FH multiuser radar and sonar systems , 1994, Proceedings of IEEE 3rd International Symposium on Spread Spectrum Techniques and Applications (ISSSTA'94).

[33]  A. Lazarov,et al.  Correlation-spectral 2-D ISAR image reconstruction from linear frequency modulation signals , 2001, 2001 Microwave Electronics: Measurement, Identification, Applications. Conference Proceedings. MEMIA'2001 (Cat. No.01EX474).

[34]  Karthikeyan Umapathy,et al.  Audio Signal Processing Using Time-Frequency Approaches: Coding, Classification, Fingerprinting, and Watermarking , 2010, EURASIP J. Adv. Signal Process..

[35]  Phillip A. Bello,et al.  Joint estimation of delay, Doppler, and Doppler rate , 1960, IRE Trans. Inf. Theory.

[36]  Xiang Li,et al.  A FrFT Based Algorithm for Doppler Frequency Rate Estimation from LFM Coherent Pulse Train: A FrFT Based Algorithm for Doppler Frequency Rate Estimation from LFM Coherent Pulse Train , 2010 .

[37]  Fu Qiang,et al.  Simultaneously Velocity Measuring and HRR Profiling with a Novel CSF Sequence , 2006, 2006 CIE International Conference on Radar.

[38]  Edward L. Titlebaum,et al.  Multiuser sonar properties for Costas array frequency hop coded signals , 1990, International Conference on Acoustics, Speech, and Signal Processing.

[39]  Yingning Peng,et al.  Radar Maneuvering Target Motion Estimation Based on Generalized Radon-Fourier Transform , 2012, IEEE Transactions on Signal Processing.

[40]  Yahong Rosa Zheng,et al.  A comparative study of compressed sensing approaches for 3-D synthetic aperture radar image reconstruction , 2014, Digit. Signal Process..

[41]  Zhiling Wang,et al.  Joint estimation of motion parameters using Newton's method , 2015, IEEE Transactions on Aerospace and Electronic Systems.

[42]  P. P. Vaidyanathan,et al.  MIMO Radar Ambiguity Properties and Optimization Using Frequency-Hopping Waveforms , 2008, IEEE Transactions on Signal Processing.

[43]  Yingning Peng,et al.  Radon-Fourier Transform for Radar Target Detection (III): Optimality and Fast Implementations , 2012, IEEE Transactions on Aerospace and Electronic Systems.

[44]  Xiang-Gen Xia,et al.  Fast implementation of generalised Radon-Fourier transform for manoeuvring radar target detection , 2012 .

[45]  Zishu He,et al.  Orthogonal Discrete Frequency-Coding Waveform design for MIMO radar , 2008 .

[46]  H. A. Said,et al.  Design and realization of an efficient VLIC architecture for a linear frequency modulation (LFM) pulse compression in pulsed radars using FPGA , 2013, 2013 Africon.