A tracking algorithm based on adaptive Kalman filter with carrier-to-noise ratio estimation under solar radio bursts interference

doi:10.23919/JSEE.2025.000061

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (4): 880-891.doi: 10.23919/JSEE.2025.000061

• • 上一篇

收稿日期:2023-09-18 接受日期:2024-07-30 出版日期:2025-08-18 发布日期:2025-09-04

A tracking algorithm based on adaptive Kalman filter with carrier-to-noise ratio estimation under solar radio bursts interference

Xuefen ZHU¹^,*(), Ang LI¹(), Yimei LUO¹(), Mengying LIN¹(), Gangyi TU²()

¹ School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China
² School of Electronics and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received:2023-09-18 Accepted:2024-07-30 Online:2025-08-18 Published:2025-09-04
Contact: Xuefen ZHU E-mail:zhuxuefen@seu.edu.cn;angli@seu.edu.cn;luoyimei19970316@163.com;linmengying@seu.edu.cn;tugangyi@nuist.enu.cn
About author:
ZHU Xuefen was born in 1983. She received her B.S. degree in instrument science and optoelectronic engineering from Hefei University of Technology, Hefei, China, in 2004, and Ph.D. degree in navigation, guidance and control engineering from Southeast University, Nanjing, China, in 2010, respectively. She was a visiting Ph.D. student at the Navigation Signal Analysis and Simulation (NAVSAS) Group, Istituto Superiore Mario Boella (ISMB), Turin, Italy, from September 2007 to May 2009. She was a visiting scholar in the Department of Aerospace Engineering Science, University of Colorado, Boulder in the United States from October 2015 to October 2016. She is a professor in the School of Instrument Science and Engineering, Southeast University, China. Her research interests include global navigation satellite system (GNSS) signal processing and GNSS/inertial navigation system (INS) integration technologies. E-mail: zhuxuefen@seu.edu.cn

LI Ang was born in 1999. He received his B.S. degree in instrument science and optoelectronic engineering from Hefei University of Technology, Hefei, China, in 2022. He is currently working toward his Eng.D. degree in electronic and information engineering from Southeast University, Nanjing, China. His research focuses on global navigation satellite system (GNSS) receivers and prediction of total electron concentration in the ionosphere. E-mail: angli@seu.edu.cn

LUO Yimei was born in 1997. She received her B.S. degree in technique and instrumentation of measurements from China University of Mining and Technology, Beijing, China, in 2019, and M.S. degree in measurement technology and instrument from Southeast University, Nanjing, China, in 2021. Her research focuses on solar radio bursts detection. E-mail: luoyimei19970316@163.com

LIN Mengying was born in 1994. She received her B.S. degree in electrical engineering and automation from Wuhan Institute of Technology, Wuhan, China, in 2017, and Ph.D. degree in measurement technology and instrument from Southeast University, Nanjing, China, in 2023. Her research focuses on ionospheric modeling and predicting. E-mail: linmengying@seu.edu.cn

TU Gangyi was born in 1981. He received his B.S. degree in instrument science and optoelectronic engineering from Hefei University of Technology, Hefei, China, in 2004, and Ph.D. degree in measurement technology and instrument from Southeast University, Nanjing, China, in 2010. He was an associate director of the Institute of China Shipbuilding Industry Corporation from 2016 to 2020. He has been a professor in the School of Electronic and Information Engineering, Nanjing University of Information Science and Technology, since 2021. His researches focus on external emitter radar system, electronic warfare system simulation, intelligent collaborative detection, software radio, and embedded system design. E-mail: tugangyi@nuist.enu.cn
Supported by:
This work was supported by the Foundation of Key Laboratory of Micro-inertial Instrument and Advanced Navigation Technology, Ministry of Education, China and the National Natural Science Foundation of China (61873064).

摘要/Abstract

Abstract:

Solar radio burst (SRB) is one of the main natural interference sources of Global Positioning System (GPS) signals and can reduce the signal-to-noise ratio (SNR), directly affecting the tracking performance of GPS receivers. In this paper, a tracking algorithm based on the adaptive Kalman filter (AKF) with carrier-to-noise ratio estimation is proposed and compared with the conventional second-order phase-locked loop tracking algorithms and the improved Sage-Husa adaptive Kalman filter (SHAKF) algorithm. It is discovered that when the SRBs occur, the improved SHAKF and the AKF with carrier-to-noise ratio estimation enable stable tracking to loop signals. The conventional second-order phase-locked loop tracking algorithms fail to track the receiver signal. The standard deviation of the carrier phase error of the AKF with carrier-to-noise ratio estimation outperforms 50.51% of the improved SHAKF algorithm, showing less fluctuation and better stability. The proposed algorithm is proven to show more excellent adaptability in the severe environment caused by the SRB occurrence and has better tracking performance.

Key words: solar radio burst (SRB), global positioning system (GPS), adaptive Kalman filter (AKF), tracking algorithm

. [J]. Journal of Systems Engineering and Electronics, 2025, 36(4): 880-891.

Xuefen ZHU, Ang LI, Yimei LUO, Mengying LIN, Gangyi TU. A tracking algorithm based on adaptive Kalman filter with carrier-to-noise ratio estimation under solar radio bursts interference[J]. Journal of Systems Engineering and Electronics, 2025, 36(4): 880-891.

图/表 16

参考文献 31

1	ZENG H C, DENG J D, WANG P W A spawning particle filter for defocused moving target detection in GNSS-based passive radar. Journal of Systems Engineering and Electronics, 2023, 34 (5): 1085- 1100. doi: 10.23919/JSEE.2023.000033
2	NG Y, GAO G X GNSS multireceiver vector tracking. IEEE Trans. on Aerospace and Electronic Systems, 2017, 53 (5): 2583- 2593. doi: 10.1109/TAES.2017.2705338
3	BILGEN B, INAL C. An open-source software for geodetic deformation analysis in GNSS networks. Earth Science Informatics, 2022, 15(3): 2051−2062.
4	TRANQUILLA J Digital baseband processor for the GPS receiver modeling and simulations. IEEE Trans. on Aerospace and Electronic Systems, 1993, 29 (4): 1343- 1349. doi: 10.1109/7.259538
5	JIN L, LV P, CUI X W, et al. Adaptive Kalman tracking algorithm for new generation GNSS signals. Journal of Tsinghua University (Science and Technology), 2012, 52(9): 1249−1254, 1259. (in Chinese)
6	DE PAULA E R, MARTINON A R F, CARRANO C, et al. Solar flare and radio burst effects on GNSS signals and the ionosphere during September 2017. Radio Science, 2022, 57(10): 1−15.
7	MCKEE S R, CILLIERS P J, LOTZ S, et al The effects of solar radio bursts on frequency bands utilised by the aviation industry in sub-Saharan Africa. Journal of Space Weather and Space Climate, 2023, 13 (1): 1- 11.
8	KLOBUCHAR J A, KUNCHES J M, VANDIERENDONCK A J Eye on the ionosphere: potential solar radio burst effects on GPS signal to noise. GPS Solutions, 1999, 3 (2): 69- 71. doi: 10.1007/PL00012794
9	SATO H, JAKOWSKI N, BERDERMANN J, et al Solar radio burst events on 6 September 2017 and its impact on GNSS signal frequencies. Space Weather, 2019, 17 (6): 816- 826. doi: 10.1029/2019SW002198
10	BISWAS T, PAUL A Effects of the relative dynamics of ionospheric irregularities and GPS satellites on receiver tracking loop performance. Radio Science, 2023, 58 (10): 1- 16.
11	JING S, ZHAN X X, LIU B Y, et al. Weak and dynamic GNSS signal tracking strategies for flight missions in the space service volume. Sensors , 2016, 16(9): 1412.
12	SKONE S, LACHAPELLE G, YAO D, et al. Investigating the impact of ionospheric scintillation using a GPS software receiver. Proc. of the 18th International Technical Meeting of the Satellite Division of the Institute of Navigation, 2005: 1126−1137.
13	LEE J, MORTON Y T J, LEE J, et al Monitoring and mitigation of ionospheric anomalies for GNSS-Based safety critical systems: a review of up-to-date signal processing techniques. IEEE Signal Processing Magazine, 2017, 34 (5): 96- 110. doi: 10.1109/MSP.2017.2716406
14	WARD P W. Performance comparisons between FLL, PLL and a novel FLL-assisted-PLL carrier tracking loop under RF interference conditions. Proc. of the 11th International Technical Meeting of the Satellite Division of the Institute of Navigation, 1998: 783−795.
15	CURRAN J T, LACHAPELLE G, MURPHY C C Improving the design of frequency lock loops for GNSS receivers. IEEE Trans. on Aerospace and Electronic Systems, 2012, 48 (1): 850- 868. doi: 10.1109/TAES.2012.6129674
16	ZHANG H Y, XU L P, JIAN Y, et al A 2-step GPS carrier tracking loop for urban vehicle applications. Journal of Systems Engineering and Electronics, 2017, 28 (5): 817- 826. doi: 10.21629/JSEE.2017.05.01
17	VILA-VALLS J, CLOSAS P, NAVARRO M, et al Are PLLs dead? A tutorial on Kalman filter-based techniques for digital carrier synchronization. IEEE Aerospace and Electronic Systems Magazine, 2017, 32 (7): 28- 45. doi: 10.1109/MAES.2017.150260
18	ZHANG Q L, XU W Q, ZHANG W W, et al Multi-hypothesis square-root cubature Kalman particle filter for speaker tracking in noisy and reverberant environments. IEEE/ACM Trans. on Audio Speech and Language Processing, 2020, 28, 1183- 1197.
19	SAGE A P, HUSA G W. Adaptive filtering with unknown prior statistics. Proc. of the Joint Automatic Control Conference, 1969: 760−769.
20	ZHENG Z, LIU S R, ZHANG B T. An improved Sage-Husa adaptive filtering algorithm. Proc. of the 31st Chinese Control Conference, 2012: 5113–5117.
21	ZHAI H Q, WANG L H. A SINS/CNS/GPS online calibration method based on improved Sage-Husa adaptive filtering algorithm. Proc. of the 8th International Conference on Automation, Robotics and Applications, 2022: 159–164.
22	HUANG W G, ERCHA A, SHEN H, et al Impact of intense L-band solar radio burst on GNSS performance and positioning accuracy. Chinese Journal of Radio Science, 2018, 33 (1): 1- 7.
23	KINTNER P M, O’HANLON B, GARY D E, et al Global positioning system and solar radio burst forensics. Radio Science, 2009, 44 (1): 1- 6.
24	CHAURASIYA S K, PATEL K, SINGH A K. Total electron content forecasting with neural networks during intense geomagnetic storms of the solar maximum and moderate years of solar cycle 24 in the low latitude Indian region. Astrophysics and Space Science, 2018, 368(9): 79.
25	DING X Y, WANG Q Design of carrier tracking loop based on adaptive strong tracking Sage-Husa Kalman filter. Electronics Optics & Control, 2019, 26 (10): 12- 16.
26	BALA B, LANZEROTTI L J, GARY D E, et al Noise in wireless systems produced by solar radio bursts. Radio Science, 2002, 37 (2): 1- 7.
27	JIANG C, WANG S L, WU B, et al A state-of-charge estimation method of the power lithium-ion battery in complex conditions based on adaptive square root extended Kalman filter. Energy, 2021, 219, 119603. doi: 10.1016/j.energy.2020.119603
28	QIAO S H, FAN Y S, WANG G F, et al. Radar target tracking for unmanned surface vehicle based on square root Sage-Husa adaptive robust Kalman filter. Sensors, 2022, 22(8): 2924.
29	HUANG H Q, WU H, ZHANG S, et al An improved Sage-Husa adaptive Kalman filtering applied to cooperative navigation of autonomous underwater vehicles. Proc. of the IEEE International Symposium on Industrial Electronics, 2022, 570- 575.
30	GUO Y J, YANG D Q, CHEN Z Z Object tracking on satellite videos: a correlation filter-based tracking method with trajectory correction by Kalman filter. IEEE Journal of Selected Topics in Applied Earth Observations and Remote Sensing, 2019, 12 (9): 3538- 3551. doi: 10.1109/JSTARS.2019.2933488
31	WANG Q, SHANG F, DU L M, et al Influence of B1 code correlation loop for vector tracking structures under complicated environment. Journal of Systems Engineering and Electronics, 2019, 30 (6): 1053- 1063. doi: 10.21629/JSEE.2019.06.01

Station	Longitude/°E	Latitude/°N	Elevation/m
M0SE	12.49	41.89	120.6
POTS	13.07	52.38	144.4
ZIMM	7.47	46.87	956.4
SAN VITO	17.83	40.63	−

Scene number	Scene feature	SNR/dB
Scene number	Scene feature	The first stage (0−30 s)	The second stage (31−60 s)
1	Low SNR	−22	−22
2	Extreme low SNR	−36	−36
3	Abrupt decrease in SNR	−15	−38

Error type	Statistics	First stage of the third scene	Second stage of the third scene
Residual mean	Second-order PLL	$ 6.26 \times {10^{ - 3}} $	$ 8.17 \times {10^{ - 2}} $
	5 ms coherent integration second-order PLL	$ 2.32 \times {10^{ - 3}} $	$ 4.30 \times {10^{ - 2}} $
	KF	$ 3.52 \times {10^{ - 3}} $	$ 8.99 \times {10^{ - 3}} $
	Improved SHAKF	$ 3.70 \times {10^{ - 3}} $	$ 3.45 \times {10^{ - 3}} $
	AKF with $ C/N_0 $ estimation	$ 3.46 \times {10^{ - 3}} $	$ 3.32 \times {10^{ - 3}} $
Standard deviation	Second-order PLL	$ 7.81 \times {10^{ - 3}} $	$ 1.03 \times {10^{ - 1}} $
	5 ms coherent integration second-order PLL	$ 2.95 \times {10^{ - 3}} $	$ 5.53 \times {10^{ - 2}} $
	KF	$ 3.12 \times {10^{ - 3}} $	$ 1.13 \times {10^{ - 2}} $
	Improved SHAKF	$ 2.92 \times {10^{ - 3}} $	$ 1.18 \times {10^{ - 3}} $
	AKF with $ C/N_0 $ estimation	$ 2.91 \times {10^{ - 3}} $	$ 5.96 \times {10^{ - 4}} $

A tracking algorithm based on adaptive Kalman filter with carrier-to-noise ratio estimation under solar radio bursts interference

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