基于Savitzky-Golay滤波和互模糊函数的时频差参数估计算法

doi:10.12305/j.issn.1001-506X.2025.05.02

Abstract

Abstract:

Aiming to address the issue of low accuracy in parameter estimates in low signal-to-noise ratio scenarios of time difference and frequency difference of small satellites in low orbit with small antenna size and small gain, and the correlation between noise affects the accuracy of parameter estimation, a joint estimation algorithm based on a combination of Savitzky-Golay (S-G) smoothing filtering and cross-ambiguity function (CAF) is proposed. Firstly, the signal is smoothed using S-G filtering to reduce noise. Then, combined with the sliding window segment processing, the high-order cumulant is used to eliminate the influence of noise caused by correlation. Finally, the time difference and frequency difference estimates are obtained by searching for the peak value of the CAF. Simulation results show that the proposed algorithm can enhance the precision of time difference estimation by 3.3% and frequency difference estimation by 1.5% compared with the second-order CAF algorithm under the condition of -5 dB signal-to-noise ratio. Therefore, the proposed algorithm can effectually enhance the precision of the estimation of parameters in non-ideal signal environments, such as low signal-to-noise ratio.

Key words: parameter estimation, Savitzky-Golay (S-G) filtering, cross-ambiguity function (CAF), higher order cumulant, sliding window

CLC Number:

TN971

You ZHANG, Yonghui HUANG, Zhihao LI, Tianshu CUI, Zhugang WANG. Parameter estimation algorithm for time-frequency difference using Savitzky-Golay filtering and cross-ambiguity function[J]. Systems Engineering and Electronics, 2025, 47(5): 1395-1403.

Figures/Tables 11

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References 31

1	郭福成, 李金洲, 张敏. 无源定位原理与方法[M]. 北京: 国防工业出版社, 2021.
	GUO F C , LI J Z , ZHANG M . Passive location theories and methods[M]. Beijing: National Defense Industry Press, 2021.
2	OLSEN K E , ASEN W . Bridging the gap between civilian and military passive radar[J]. IEEE Aerospace and Electronic Systems Magazine, 2017, 32 (2): 4- 12. doi: 10.1109/MAES.2017.160030
3	田中成, 刘聪锋. 无源定位技术[M]. 北京: 国防工业出版社, 2015.
	TIAN Z C , LIU C F . Passive locating technology[M]. Beijing: National Defense Industry Press, 2015.
4	欧阳鑫信, 姚山峰, 杨宇翔, 等. 跳频信号的相参与非相参积累时频差估计方法[J]. 系统工程与电子技术, 2021, 43 (5): 1184- 1190. doi: 10.12305/j.issn.1001-506X.2021.05.04
	OUYANG X X , YAO S F , YANG Y X , et al. Coherent and non-coherent integration TDOA/FDOA estimation method of frequency-hopping signals[J]. Systems Engineering and Electronics, 2021, 43 (5): 1184- 1190. doi: 10.12305/j.issn.1001-506X.2021.05.04
5	FOWLER M L , HU X . Signal models for TDOA/FDOA estimation[J]. IEEE Trans.on Aerospace and Electronic Systems, 2008, 44 (4): 1543- 1550. doi: 10.1109/TAES.2008.4667729
6	GUO F Y , ZHANG Z J , YANG L S . TDOA/FDOA estimation method based on dechirp[J]. IET Signal Processing, 2016, 10 (5): 486- 492. doi: 10.1049/iet-spr.2015.0460
7	WANG Y Q , SUN G C , WANG Y , et al. A multi-pulse cross ambiguity function for the wideband TDOA and FDOA to locate an emitter passively[J]. Remote Sensing, 2022, 14 (15): 3545. doi: 10.3390/rs14153545
8	CLEMENTS Z, HUMPHREYS T E, ELLIS P. Dual-satellite geolocation of terrestrial GNSS jammers from low earth orbit[C]// Proc. of the IEEE/ION Position, Location and Navigation Symposium, 2023: 458-469.
9	WU R S , ZHANG Y X , HUANG Y N , et al. A novel long-time accumulation method for double-satellite TDOA/FDOA interfe-rence localization[J]. Radio Science, 2018, 53 (1): 129- 142. doi: 10.1002/2017RS006389
10	HU D X , HUANG Z , ZHANG S Y , et al. Joint TDOA, FDOA and differential Doppler rate estimation: method and its performance analysis[J]. Chinese Journal of Aeronautics, 2018, 31 (1): 137- 147. doi: 10.1016/j.cja.2017.11.005
11	KIM D G , PARK G H , KIM H N , et al. Computationally efficient TDOA/FDOA estimation for unknown communication signals in electronic warfare systems[J]. IEEE Trans.on Aerospace and Electronic Systems, 2017, 54 (1): 77- 89.
12	OUYANG X X , YAO S F , WAN Q . Multiple signal TDOA/FDOA joint estimation with coherent integration[J]. Electronics, 2023, 12 (9): 2151. doi: 10.3390/electronics12092151
13	周力存. 面向双星干扰源定位的时频参数估计方法研究[D]. 西安: 西安电子科技大学, 2017.
	ZHOU L C. The research on TDOA/FDOA estimation for double-satellites interference source location[D]. Xi'an: Xidian University, 2017.
14	LIU G H, REN J J. Improved generalized cross correlation communication radiation source time difference estimation method[C]//Proc. of the IEEE 6th International Conference on Electronics and Communication Engineering, 2023: 11-15.
15	唐娟, 行鸿彦. 基于二次相关的时延估计方法[J]. 计算机工程, 2007, 33 (21): 265- 267. doi: 10.3969/j.issn.1000-3428.2007.21.094
	TANG J , XING H Y . Time delay estimation based on second correlation[J]. Computer Engineering, 2007, 33 (21): 265- 267. doi: 10.3969/j.issn.1000-3428.2007.21.094
16	SRIVASTAVA M , ANDERSON C L , FREED J H . A new wavelet denoising method for selecting decomposition levels and noise thresholds[J]. IEEE Access, 2016, 4, 3862- 3877. doi: 10.1109/ACCESS.2016.2587581
17	KUANG W C , YANG P , LAI Y X , et al. Joint empirical mode decomposition and optimal frequency band estimation for adaptive low-frequency noise suppression[J]. Circuits, Systems, and Signal Processing, 2023, 42 (7): 4170- 4196. doi: 10.1007/s00034-023-02309-2
18	王璟, 张立芳, 杨巨生, 等. 基于小波和经验模态分解的波长调制信号降噪研究[J]. 激光与光电子学进展, 2022, 59 (18): 481- 487.
	WANG J , ZHANG L F , YANG J S , et al. Noise reduction of wavelength-modulated signal based on wavelet and empirical mode decomposition[J]. Laser & Optoelectronics Progress, 2022, 59 (18): 481- 487.
19	YAO Z J , LIU X J , YANG W J , et al. A coarse-to-fine denoising method for dynamic calibration signals of pressure sensor based on adaptive mode decompositions[J]. Measurement, 2020, 163, 107935- 107946. doi: 10.1016/j.measurement.2020.107935
20	鲁一冰, 刘文清, 张玉钧, 等. 一种自适应层进式Savitzky-Golay光谱滤波算法及其应用[J]. 光谱学与光谱分析, 2019, 39 (9): 2657- 2663.
	LU Y B , LIU W Q , ZHANG Y J , et al. An adaptive hierarchical Savitzky-Golay spectral filtering algorithm and its application[J]. Spectroscopy and Spectral Analysis, 2019, 39 (9): 2657- 2663.
21	位秀雷, 刘树勇. 多级奇异值分解和SG的通信雷达信号降噪方法[J]. 武汉理工大学学报(交通科学与工程版), 2020, 44 (4): 658- 662. doi: 10.3963/j.issn.2095-3844.2020.04.014
	WEI X L , LIU S Y . Noise reduction method of communication radar signal based on multilevel singular value decomposition and Savitzky-Golay[J]. Journal of Wuhan University of Technology (Transportation Science & Engineering), 2020, 44 (4): 658- 662. doi: 10.3963/j.issn.2095-3844.2020.04.014
22	CHETOUI M , AOUN M , MALTI R . Continuous-time MISO fractional system identification using higher-order-statistics[J]. Fractional Calculus and Applied Analysis, 2024, 27 (4): 1611- 1638. doi: 10.1007/s13540-024-00297-x
23	DANDAWATE A V , GIANNAKIS G B . Differential delay-Doppler estimation using second and higher-order ambiguity functions[J]. IEE Proceedings F, Radar and Signal Processing, 1993, 140 (6): 410- 418. doi: 10.1049/ip-f-2.1993.0060
24	SCHMID M , RATH D , DIEBOLD U . Correction to "Why and how Savitzky-Golay filters should be replaced"[J]. ACS Mea-surement Science Au, 2023, 3 (3): 236. doi: 10.1021/acsmeasuresciau.3c00017
25	DOMBI J , DINEVA A . Adaptive Savitzky-Golay filtering and its applications[J]. International Journal of Advanced Intelligence Paradigms, 2020, 16 (2): 145- 156. doi: 10.1504/IJAIP.2020.107011
26	SMITH W W , STEFFES P G . Time delay techniques for satellite interference location system[J]. IEEE Trans.on Aerospace and Electronic Systems, 1989, 25 (2): 224- 231. doi: 10.1109/7.18683
27	SHIN D C, NIKIAS C L. Complex ambiguity function based on fourth-order statistics for joint estimation of frequency-delay and time-delay of arrival[C]//Proc. of the 27th Asilomar Conference on Signals, Systems and Computers, 1993: 461-465.
28	BUDROWEIT J . RF systems on chip and mixed-signal front-end devices: game-changing RF technologies for space applications[J]. IEEE Microwave Magazine, 2023, 24 (2): 49- 56. doi: 10.1109/MMM.2022.3217988
29	SARDA K, CAJACOB D, ORR N, et al. Making the invisible visible: precision RF-emitter geolocation from space by the hawkeye 360 pathfinder mission[C]//Proc. of the AIAA/USU Conference on Small Satellites, 2018.
30	WONG S, KASHYAP N, JASSEMI-ZARGANI R, et al. Analysis of a space-based passive radiofrequency (RF) sensing system for geolocating targets on the Earth's surface[R]. Ottawa: Defence Research and Development Canada, 2021.
31	宋小勇, 毛悦, 宗文鹏, 等. 三星编队TDOA定位精度分析[J]. 测绘学报, 2023, 52 (10): 1631- 1639. doi: 10.11947/j.AGCS.2023.20220269
	SONG X Y , MAO Y , ZONG W P , et al. Analyzing the geolocation precision of TDOA using formation-flying cluster of three microsatellites[J]. Acta Geodaetica et Cartographica Sinica, 2023, 52 (10): 1631- 1639. doi: 10.11947/j.AGCS.2023.20220269

轨道根数	主星	辅星1	辅星2
轨道长轴/m	6 953 137.0	6 953 137.0	6 953 137.0
轨道偏心率	0.000 1	0.000 1	0.000 1
轨道倾角/(°)	97.3	97.3	97.3
轨道升交点经度/(°)	120.0	119.993 6	119.987 4
近点角距/(°)	0.0	0.0	0.0
平近点角/(°)	0.00	1.039 68	2.071 8

SNR/dB	二阶CAF/ms	本文算法/ms	提升精度/%
0	0.009 1	0.009 5	4.395 6
-5	0.009 0	0.009 3	3.333 3
-10	0.008 8	0.009 0	2.272 7

SNR/dB	二阶CAF/Hz	本文算法/Hz	提升精度/%
0	1 052.6	1 025.4	2.584 1
-5	1 090.2	1 074.2	1.467 6
-10	1 112.4	1 098.6	1.240 6

组别	无滤波	中值滤波	S-G滤波	二阶累积量	四阶累积量	TDOA/ms	FDOA/Hz
1	√	-	-	√	-	0.009 11	1 052.6
2	-	√	-	√	-	0.009 17	1 048.5
3	-	-	√	√	-	0.009 32	1 032.4
4	√	-	-	-	√	0.009 23	1 040.8
5	-	√	-	-	√	0.009 28	1 038.9
6	-	-	√	-	√	0.009 53	1 025.4

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Parameter estimation algorithm for time-frequency difference using Savitzky-Golay filtering and cross-ambiguity function

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