A Novel Doppler Rate Estimator Based on Fractional Fourier Transform for High-Dynamic GNSS Signal

When the fractional Fourier transform (FRFT) is introduced into the weak and high-dynamic global navigation satellite system (GNSS) signal acquisition, the 2-D search cell will be transferred to a 3-D one with respect to the code chip, the Doppler shift, and the Doppler rate. The proper determinations of the code bin and Doppler shift bin in the acquisition process have already been covered in the previous researches. The aim of this paper is to provide an exhaustive analysis of the approach to specify an optimal FRFT order bin, in terms of the Doppler shift rate. The lower and upper bound of FRFT order ranges is determined by the incoming signal dynamics. Then, we propose a precise model to yield an optimal FRFT order bin. Besides, a novel and fast Doppler estimator based on the non-linear least square (NLS) method is presented to improve the performance of the digital FRFT implementation. Finally, an alternate search procedure is proposed to reduce the singular estimations of the NLS method. The simulating examples demonstrate the performance of the proposed algorithms. It has been verified that the computation efficiency and the estimation accuracy have been significantly improved by proposed techniques.

[1]  Mahmoud H. Annaby,et al.  Difference operators and generalized discrete fractional transforms in signal and image processing , 2018, Signal Process..

[2]  Hua Yu,et al.  Parameter Estimation of Wideband Underwater Acoustic Multipath Channels based on Fractional Fourier Transform , 2016, IEEE Transactions on Signal Processing.

[3]  Tomaso Erseghe,et al.  Unified fractional Fourier transform and sampling theorem , 1999, IEEE Trans. Signal Process..

[4]  Haldun M. Özaktas,et al.  The fractional fourier transform , 2001, 2001 European Control Conference (ECC).

[5]  Teng Long,et al.  Adaptive Correlation Space Adjusted Open-Loop Tracking Approach for Vehicle Positioning with Global Navigation Satellite System in Urban Areas , 2015, Sensors.

[6]  Luís B. Almeida,et al.  The fractional Fourier transform and time-frequency representations , 1994, IEEE Trans. Signal Process..

[7]  Lei Zhang,et al.  An Acquisition Algorithm Based on FRFT for Weak GNSS Signals in A Dynamic Environment , 2018, IEEE Communications Letters.

[8]  Frank van Diggelen,et al.  A-GPS: Assisted GPS, GNSS, and SBAS , 2009 .

[9]  Hamid Aghvami,et al.  Direct sequence spread spectrum matched filter acquisition in frequency-selective Rayleigh fading channels , 1994, IEEE J. Sel. Areas Commun..

[10]  Fabio Dovis,et al.  A test-bed implementation of an acquisition system for indoor positioning , 2010 .

[11]  Rodney A. Walker,et al.  GPS Fault Detection with IMU and Aircraft Dynamics , 2011, IEEE Transactions on Aerospace and Electronic Systems.

[12]  Gozde Bozdagi Akar,et al.  Digital computation of the fractional Fourier transform , 1996, IEEE Trans. Signal Process..

[13]  M. Petovello,et al.  A Stand-Alone Approach for High-Sensitivity GNSS Receivers in Signal-Challenged Environment , 2017, IEEE Transactions on Aerospace and Electronic Systems.

[14]  Cyril Botteron,et al.  Feasibility study of GNSS as navigation system to reach the Moon , 2015 .

[15]  Carmine Clemente,et al.  Waveform design for communicating radar systems using Fractional Fourier Transform , 2018, Digit. Signal Process..

[16]  Naser El-Sheimy,et al.  An improved DE-KFL for BOC signal tracking assisted by FRFT in a highly dynamic environment , 2018, 2018 IEEE/ION Position, Location and Navigation Symposium (PLANS).

[17]  Andrew G. Dempster,et al.  Dichotomous search of coarse time error in collective detection for GPS signal acquisition , 2014, GPS Solutions.

[18]  Luis J. Morales-Mendoza,et al.  Exploring the Cross-Correlation as a Means for Detecting Digital Watermarks and Its Reformulation Into the Fractional Calculus Framework , 2018, IEEE Access.

[19]  Majeed M. Hayat,et al.  Clutter Suppression via Hankel Rank Reduction for DFrFT-Based Vibrometry Applied to SAR , 2017, IEEE Geoscience and Remote Sensing Letters.

[20]  Robert Grover Brown,et al.  Introduction to random signals and applied Kalman filtering : with MATLAB exercises and solutions , 1996 .

[21]  You He,et al.  Space-Range-Doppler Focus-Based Low-observable Moving Target Detection Using Frequency Diverse Array MIMO Radar , 2018, IEEE Access.

[22]  Daming Shi,et al.  Maximum Amplitude Method for Estimating Compact Fractional Fourier Domain , 2010, IEEE Signal Processing Letters.

[23]  G.J.R. Povey,et al.  A fast acquisition technique for a direct sequence spread spectrum signal in the presence of a large Doppler shift , 1996, Proceedings of ISSSTA'95 International Symposium on Spread Spectrum Techniques and Applications.

[24]  Peter Teunissen,et al.  Nonlinear least squares , 1990 .

[25]  Lin Yang,et al.  Blind third-order dispersion estimation based on fractional Fourier transformation for coherent optical communication , 2018 .

[26]  Yuan Liang,et al.  Embedding WFRFT Signals Into TDCS for Secure Communications , 2018, IEEE Access.

[27]  Yang Gao,et al.  Improvement of carrier phase tracking in high dynamics conditions using an adaptive joint vector tracking architecture , 2018, GPS Solutions.

[28]  S. Hinedi,et al.  High-dynamic GPS tracking , 1988 .

[29]  Xiang Feng,et al.  Cognitive Tracking Waveform Design Based on Multiple Model Interaction and Measurement Information Fusion , 2018, IEEE Access.

[30]  J. Chen,et al.  Detecting the spatial chirp signals by fractional Fourier lens with transformation materials , 2018 .

[31]  Yunfei Liu,et al.  Iterative Interpolation for Parameter Estimation of LFM Signal Based on Fractional Fourier Transform , 2013, Circuits Syst. Signal Process..

[32]  Zhen Liu,et al.  Fast FRFT-Based Algorithm for 3-D LFM Source Localization With Uniform Circular Array , 2018, IEEE Access.

[33]  Jose A. Lopez-Salcedo,et al.  Use of weak GNSS signals in a mission to the moon , 2014, 2014 7th ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing (NAVITEC).

[34]  Nan Gao,et al.  An integrated land vehicle navigation system based on context awareness , 2015, GPS Solutions.

[35]  N. El-Sheimy,et al.  Wavelet de-noising for IMU alignment , 2004, IEEE Aerospace and Electronic Systems Magazine.

[36]  Yang Gao,et al.  Effect and mitigation of oscillator vibration-induced phase noise on carrier phase tracking , 2017, GPS Solutions.

[37]  Seung-Hyun Kong,et al.  A-GNSS Sensitivity for Parallel Acquisition in Asynchronous Cellular Networks , 2010, IEEE Transactions on Wireless Communications.

[38]  Peter S. Maybeck,et al.  Stochastic Models, Estimation And Control , 2012 .

[39]  Na Liu,et al.  Signal reconstruction from recurrent samples in fractional Fourier domain and its application in multichannel SAR , 2017, Signal Process..

[40]  You He,et al.  Maneuvering Target Detection via Radon-Fractional Fourier Transform-Based Long-Time Coherent Integration , 2014, IEEE Transactions on Signal Processing.

[41]  S. Fujioka,et al.  Nonlinear Filtering Methods for the INS/GPS In-Motion Alignment and Navigation , 2006 .

[42]  Andreas Polydoros,et al.  A Unified Approach to Serial Search Spread-Spectrum Code Acquisition - Part I: General Theory , 1984, IEEE Transactions on Communications.

[43]  Ahmet Serbes,et al.  Compact Fractional Fourier Domains , 2017, IEEE Signal Processing Letters.

[44]  Cyril Botteron,et al.  GNSS/INS/Star Tracker Integrated Navigation System for Earth-Moon Transfer Orbit , 2014 .

[45]  Xuan Xia,et al.  Fractional Fourier transform-based unassisted tracking method for Global Navigation Satellite System signal carrier with high dynamics , 2016 .

[46]  Gérard Lachapelle,et al.  Performance analysis of a stand-alone high-sensitivity receiver , 2002 .

[47]  Elliott D. Kaplan.  Understanding GPS : principles and applications , 1996 .