A fine acquisition algorithm based on fast three-time FRFT for dynamic and weak GNSS signals

doi:10.23919/JSEE.2023.000017

Journal of Systems Engineering and Electronics ›› 2023, Vol. 34 ›› Issue (2): 259-269.doi: 10.23919/JSEE.2023.000017

• ELECTRONICS TECHNOLOGY •

A fine acquisition algorithm based on fast three-time FRFT for dynamic and weak GNSS signals

YI PAN¹^,*(), Sheng ZHANG¹(), Xiao WANG¹(), Manhao LIU¹(), Yiran LUO²()

¹ Key Laboratory of Advanced Sensor and Integrated System, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
² Department of Aeronautical and Aviation Engineering, Hong Kong Polytechnic University, Hong Kong 999077, China

Received:2021-08-31 Online:2023-04-18 Published:2023-04-18
Contact: YI PAN E-mail:willboc@126.com;tenetwang@yeah.net;liumh19@mails.tsinghua.edu.cn;yiran.gnss@gmail.com
About author:
PAN Yi was born in 1988. He received his Ph.D. degree in signal and information processing from Chongqing University of Posts and Telecommunications in 2019. He is currently a postdoctoral in electronic science and technology from Tsinghua University Shenzhen International Graduate School. His research interests include spread spectrum signal detection and processing, image and motion sensor information processing, and communication oriented Internet of Things operating system. E-mail: willboc@126.com

ZHANG Sheng was born in 1975. He received his Ph.D. degree in electronic engineering from Tsinghua University in 2004. He is currently an associate professor in microelectronics from Tsinghua University Shenzhen International Graduate School. His research interests include intelligent sensor information processing algorithm and application specific integrated circuit design, intelligent Internet of Things, aeronautical communication, wireless communication, and chip design. E-mail: zhangsh@sz.tsinghua.edu.cn

WANG Xiao was born in 1996. He received his B.S. degree in electronic engineering from Tsinghua University, Beijing, China, in 2019, where he is currently pursuing his M.S. degree with the Department of Electronic Engineering, Tsinghua University. His research interests include context representation, machine learning, context awareness computing, croudsourcing and croudsensing, edge computing, and novel schemes in Internet of Things and smart environment. E-mail: tenetwang@yeah.net

LIU Manhao was born in 1996. He received his B.S. degree in communication engineering from Beijing University of Posts and Telecommunications, Beijing, China, in 2019. He is currently working towards his M.E. degree with the Department of Electronic Engineering, Tsinghua University, Beijing, China. His current research interests include indoor localization network and indoor navigation. E-mail: liumh19@mails.tsinghua.edu.cn

LUO Yiran was born in 1991. She received her B.S. degree in electronic information science and technology from Sichuan University, China, in 2014, and joint Ph.D. degree in geomatics engineering from University of Calgary, Canada, and in information and communication engineering from Beijing Institute of Technology, China, in 2020. She is currently a postdoctoral researcher with the Department of Aeronautical and Aviation Engineering, Hong Kong Polytechnic University. Her research interests include Global Navigation Satellite System (GNSS) signal processing, GNSS software-defined radio design, and navigation and localization in harsh environments E-mail: yiran.gnss@gmail.com
Supported by:
This work was supported by Shenzhen Science and Technology Program (JCYJ20180508152046428).

Abstract

Abstract:

As high-dynamics and weak-signal are of two primary concerns of navigation using Global Navigation Satellite System (GNSS) signals, an acquisition algorithm based on three-time fractional Fourier transform (FRFT) is presented to simplify the calculation effectively. Firstly, the correlation results similar to linear frequency modulated (LFM) signals are derived on the basis of the high dynamic GNSS signal model. Then, the principle of obtaining the optimum rotation angle is analyzed, which is measured by FRFT projection lengths with two selected rotation angles. Finally, Doppler shift, Doppler rate, and code phase are accurately estimated in a real-time and low signal to noise ratio (SNR) wireless communication system. The theoretical analysis and simulation results show that the fast FRFT algorithm can accurately estimate the high dynamic parameters by converting the traditional two-dimensional search process to only three times FRFT. While the acquisition performance is basically the same, the computational complexity and running time are greatly reduced, which is more conductive to practical application.

Key words: Global Navigation Satellite System (GNSS) signal, fractional Fourier transform (FRFT), acquisition, high-dynamics, weak-signal

YI PAN, Sheng ZHANG, Xiao WANG, Manhao LIU, Yiran LUO. A fine acquisition algorithm based on fast three-time FRFT for dynamic and weak GNSS signals[J]. Journal of Systems Engineering and Electronics, 2023, 34(2): 259-269.

Figures/Tables 15

Fig 1

Fig 2

Fig 3

Fig 4

Fig 5

Fig 6

Fig 7

Fig 8

Fig 9

Fig 10

Fig 11

Table 1

Fig 12

Fig 13

Table 2

References 30

1	VEETTIL S V, AQUINO M Statistical models to provide meaningful information to GNSS users in the presence of ionospheric scintillation. GPS Solutions, 2021, 25 (2): 54- 66. doi: 10.1007/s10291-020-01083-x
2	ISSA H, STIENNE G, REBOUL S, et al A probabilistic model for on-line estimation of the GNSS carrier-to-noise ratio. Signal Processing, 2021, 183 (4): 107992.
3	LI Y, ZOU X H, LIU P Y, et al Four-element array for GNSS attitude determination using IRLS: an improved rounding of long-short baseline approach. IEEE Trans. on Vehicular Technology, 2020, 69 (5): 4920- 4934. doi: 10.1109/TVT.2020.2978862
4	SUN Y Optimal parameter design of continuous phase modulation for future GNSS signals. IEEE Access, 2021, 99, 58487- 58502.
5	WANG C H, CUI X W, ZHU Y H, et al Thermal noise performance analysis for dual binary phase-shift keying tracking of standard BOC signals. IET Radar, Sonar & Navigation, 2020, 14, 1019- 1028.
6	AIKAWA Y Integrated optical digital-to-analogue converter for a 2-bit BPSK-modulated signal based on a silicon photonics waveguide. Electronics Letters, 2020, 56 (16): 830- 832. doi: 10.1049/el.2020.0950
7	ZHAO H W, ZHANG Z C, LUO X Z, et al Quality monitoring and biases estimation of BOC navigation signals. Journal of Systems Engineering and Electronics, 2019, 30 (3): 474- 484. doi: 10.21629/JSEE.2019.03.05
8	YOON S, CHAE K, SUN Y K A new approach to local signal design for enhanced TMBOC signal tracking. Journal of Electrical Engineering and Technology, 2020, 15 (4): 1837- 1845. doi: 10.1007/s42835-020-00451-4
9	JULIEN O, MACABIAU C, CANNON E, et al ASPeCT: unambiguous sine-BOC(n, n) acquisition/tracking technique for navigation applications. IEEE Trans. on Aerospace and Electronic Systems, 2007, 43 (1): 150- 162. doi: 10.1109/TAES.2007.357123
10	LOHAN E S Statistical analysis of BPSK-like techniques for the acquisition of Galileo signals. Journal of Aerospace Computing, Information, and Communication, 2006, 3 (5): 234- 243. doi: 10.2514/1.17441
11	YAO Z, CUI X W, LU M Q, et al Pseudo- correlation-function-based unambiguous tracking technique for sine-BOC signals. IEEE Trans. on Aerospace and Electronic Systems, 2010, 46 (4): 1782- 1796. doi: 10.1109/TAES.2010.5595594
12	SPANGENBERG S M, SCOTT I, MCLAUGHLIN S, et al An FFT-based approach for fast acquisition in spread spectrum communication systems. Wireless Personal Communications, 2000, 13 (1/2): 27- 55.
13	PAN Y, ZHANG T Q, ZHANG G, et al A novel acquisition algorithm based on PMF-apFFT for BOC modulated signals. IEEE Access, 2019, 7, 46686- 46694. doi: 10.1109/ACCESS.2019.2909787
14	YAN K, ZIEDAN N I, ZHANG H, et al Weak GPS signal tracking using FFT discriminator in open loop receiver. GPS Solution, 2016, 20 (2): 225- 237. doi: 10.1007/s10291-014-0431-3
15	FAN B, ZHANG K, QIN Y L, et al Discrete chirp-Fourier transform-based acquisition algorithm for weak global positioning system l5 signals in high dynamic environments. IET Radar, Sonar and Navigation, 2013, 7 (7): 736- 746. doi: 10.1049/iet-rsn.2012.0249
16	WON J H, PANY T, EISSFELLER B Iterative maximum likelihood estimators for high-dynamic GNSS signal tracking. IEEE Trans. on Aerospace and Electronic Systems, 2012, 48 (4): 2875- 2893. doi: 10.1109/TAES.2012.6324667
17	XIA X, ZHAO J K, LONG H H, et al Fractional Fourier transform-based unassisted tracking method for global navigation satellite system signal carrier with high dynamics. IET Radar, Sonar and Navigation, 2016, 10 (3): 506- 515. doi: 10.1049/iet-rsn.2015.0219
18	LUO Y R, ZHANG L, SHEIMY N An improved DE-KFL for BOC signal tracking assisted by FRFT in a highly dynamic environment. Proc. of the IEEE Position, Location and Navigation Symposium, 2018, 1525- 1534.
19	OZAKTAS H M, ARIKAN O, KUTAY M A, et al Digital computation of the fractional fourier transform. IEEE Trans. on Signal Processing, 1996, 44 (9): 2141- 2150. doi: 10.1109/78.536672
20	WEI D Y, ZHANG Y J Fractional Stockwell transform: theory and applications. Digital Signal Processing, 2021, 115, 103090. doi: 10.1016/j.dsp.2021.103090
21	CHEN Y L, GUO L H, GONG Z X The concise fractional Fourier transform and its application in detection and parameter estimation of the linear frequency-modulated signal. Acta Acustica, 2015, 40 (6): 761- 771.
22	ZHANG X P, LIAO G S, ZHU S Q, et al Efficient compressed sensing method for moving targets imaging by exploiting the geometry information of the defocused results. IEEE Geoscience and Remote Sensing Letters, 2015, 12 (3): 517- 521. doi: 10.1109/LGRS.2014.2349035
23	ZHANG K, ZHAO S H, LIN T, et al Frequency- multiplying dual-chirp microwave waveform generation based on a dual-drive DP-MZM. Space Electronic Technology, 2020, 4, 109- 116.
24	HAO G C, GUO J, BAI Y X, et al Novel method for non-stationary signals via high-concentration time-frequency analysis using SSTFrFT. Circuits Systems and Signal Processing, 2020, 39, 5710- 5728.
25	GAO L, QI L, GUAN L The property of frequency shift in 2D-FRFT domain with application to image encryption. IEEE Signal Processing Letters, 2021, (28): 185- 189.
26	GUO Z, LU M F, WU J M, et al Fast FRFT-based method for estimating physical parameters from Newton ’s rings. Applied Optics, 2019, 58 (14): 3926- 3931. doi: 10.1364/AO.58.003926
27	PEI S C, DING J J Relations between Gabor transforms and fractional fourier transforms and their applications for signal processing. IEEE Trans. on Signal Processing, 2007, 55 (10): 4839- 4850. doi: 10.1109/TSP.2007.896271
28	LUO Y R, ZHANG L, RUAN H An acquisition algorithm based on FRFT for weak GNSS signals in a dynamic environment. IEEE Communication Letters, 2018, 22 (6): 1212- 1215. doi: 10.1109/LCOMM.2018.2828834
29	VANNEE D J R, COENEN A New fast GPS code-acquisition technique using FFT. Electronics Letters, 1991, 27 (2): 158- 160. doi: 10.1049/el:19910102
30	KONG S H A deterministic compressed GNSS acquisition technique. IEEE Trans. on Vehicular Technology, 2013, 62 (2): 511- 521. doi: 10.1109/TVT.2012.2220989

Algorithm	Δp	$ {\hat k_{\rm{d}}} $ /Hz	$ {\hat f_{\rm{d}}} $ /Hz	k_error/%	f_error/%
Traditional FRFT	0.01	2909.2	2058.1	6.08	0.89
	0.001	3118.3	2035.7	0.92	0.21
	0.0001	3116.4	2035.7	0.85	0.21
Fast FRFT without LI	−	3126.9	2035.5	1.19	0.22
Fast FRFT with LI	−	3118.4	2035.6	0.92	0.22

Parameter	Traditional FRFT			Fast FRFT
Parameter	$\Delta P=0.01$	$\Delta P=0.001 $	$\Delta P=0.000\;1$	Fast FRFT
Cost time	1.54	15.92	155.56	0.28

[1]	Shuang CONG, Xiang ZHANG, Shiqi DUAN. Design and simulation of the ATP system considering the advanced targeting angle in quantum positioning system [J]. Journal of Systems Engineering and Electronics, 2022, 33(5): 1227-1236.
[2]	Peng SHANG, Xue WANG, Decai ZOU, Ziyue CHU, Yao GUO. Acquisition performance of B1I abounding with 5G signals [J]. Journal of Systems Engineering and Electronics, 2022, 33(3): 563-574.
[3]	Cunxiang XIE, Limin ZHANG, Zhaogen ZHONG. Quasi-LFM radar waveform recognition based on fractional Fourier transform and time-frequency analysis [J]. Journal of Systems Engineering and Electronics, 2021, 32(5): 1130-1142.
[4]	Chao WU, Erxiao LIU, Zhihua JIAN. Two-step compressed acquisition method for Doppler frequency and Doppler rate estimation in high-dynamic and weak signal environments [J]. Journal of Systems Engineering and Electronics, 2021, 32(4): 831-840.
[5]	Meiyan PAN, Jun SUN, Yuhao YANG, Dasheng LI, Sudao XIE, Shengli WANG, Jianjun CHEN. Improved TQWT for marine moving target detection [J]. Journal of Systems Engineering and Electronics, 2020, 31(3): 470-481.
[6]	Wenqi QIU, Qingxi ZENG, Chang GAO, Chade LYU. Fine Doppler shift acquisition algorithm for BeiDou software receiver by a look-up table [J]. Journal of Systems Engineering and Electronics, 2020, 31(3): 612-625.
[7]	Yuanfa JI, Xiaoqian CHEN, Qiang FU, Xiyan SUN, Weimin ZHEN. Reconstruction of sub cross-correlation cancellation technique for unambiguous acquisition of BOC(kn, n) signals [J]. Journal of Systems Engineering and Electronics, 2019, 30(5): 852-860.
[8]	Mussa Ally DIDA, Hao HUAN, Ran TAO, Teng WANG, Didar URYNBASSAROVA. Constant envelope FrFT OFDM: spectral and energy efficiency analysis [J]. Journal of Systems Engineering and Electronics, 2019, 30(3): 467-473.
[9]	Yi Pan, Tianqi Zhang, Gang Zhang, and Zhongtao Luo. Analysis of an improved acquisition method for high-dynamic BOC signal [J]. Journal of Systems Engineering and Electronics, 2016, 27(6): 1158-1167.
[10]	Rongling Lang, Xinyue Li, Fei Gao, and Liang Yang. Re-scaling and adaptive stochastic resonance as a tool for weak GNSS signal acquisition [J]. Journal of Systems Engineering and Electronics, 2016, 27(2): 290-296.
[11]	Qingxi Zeng, Linlin Tang, Pengna Zhang, and Ling Pei. Fast acquisition of L2C CL codes based on combination of hyper codes and averaging correlation [J]. Journal of Systems Engineering and Electronics, 2016, 27(2): 308-318.
[12]	Chao Wu, Luping Xu, Hua Zhang, and Wenbo Zhao. Code acquisition method based on wavelet transform filtering [J]. Systems Engineering and Electronics, 2015, 26(6): 1169-1176.
[13]	Ying Ma, Xiangyuan Bu, Hangcheng Han, and Qiaoxian Gong. Combined algorithm of acquisition and anti-jamming based on SFT [J]. Systems Engineering and Electronics, 2015, 26(3): 431-440.
[14]	Ying Xu, Lijuan Xu, Hong Yuan, and Ruidan Luo. Direct P-code acquisition algorithm based on bidirectional overlap technique [J]. Journal of Systems Engineering and Electronics, 2014, 25(4): 538-.
[15]	Shuyi Jia, Guohong Wang, and Shuncheng Tan. Radial acceleration estimation of multiple high maneuvering targets [J]. Journal of Systems Engineering and Electronics, 2014, 25(2): 183-193.

A fine acquisition algorithm based on fast three-time FRFT for dynamic and weak GNSS signals

RichHTML

PDF (PC)

Knowledge

Abstract

Cite this article

Share this article

Figures/Tables 15

References 30

Related Articles 15

Recommended Articles

Metrics

Comments