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

系统工程与电子技术 ›› 2025, Vol. 47 ›› Issue (5): 1395-1403.doi: 10.12305/j.issn.1001-506X.2025.05.02

• 电子技术 • 上一篇

基于Savitzky-Golay滤波和互模糊函数的时频差参数估计算法

张游¹^,², 黄永辉¹, 李志豪¹^,³, 崔天舒⁴, 王竹刚¹^,*

1. 中国科学院国家空间科学中心复杂航天系统电子信息技术重点实验室, 北京 100190
2. 中国科学院大学电子电气与通信工程学院, 北京 100049
3. 中国科学院大学计算机科学与技术学院, 北京 100049
4. 中国航天科技创新研究院, 北京 100088

收稿日期:2024-04-23 出版日期:2025-06-11 发布日期:2025-06-18
通讯作者: 王竹刚
作者简介:张游 (2000—), 女, 硕士研究生, 主要研究方向为无源定位、参数估计
黄永辉 (1974—), 男, 研究员, 博士, 主要研究方向为航天器测控通信、智能电磁信号处理、空间数据系统标准化
李志豪 (1998—), 男, 博士研究生, 主要研究方向为无源定位、信号处理
崔天舒 (1986—), 男, 高级工程师, 博士, 主要研究方向为射频机器学习
王竹刚 (1974—), 男, 正高级工程师, 博士, 主要研究方向为卫星测控通信

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

You ZHANG¹^,², Yonghui HUANG¹, Zhihao LI¹^,³, Tianshu CUI⁴, Zhugang WANG¹^,*

1. Key Laboratory of Electronics and Information Technology for Complex Space Systems, National Space Science Center, Chinese Academy of Sciences, Beijing 100190, China
2. School of Electronic, Electrical and Communication Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
3. School of Computer Science and Technology, University of Chinese Academy of Sciences, Beijing 100049, China
4. China Academy of Aerospace Science and Technology Innovation, Beijing 100088, China

Received:2024-04-23 Online:2025-06-11 Published:2025-06-18
Contact: Zhugang WANG

摘要/Abstract

摘要：

针对低轨小卫星天线尺寸小, 增益小, 在低信噪比下时频差参数估计值精度不高, 以及噪声之间的相关性影响参数估计准确度的问题, 提出一种基于S-G(Savitzky-Golay)平滑滤波和互模糊函数的联合估计算法。首先, 对信号进行S-G平滑滤波以削弱噪声。然后, 在结合滑窗分段处理的同时, 利用高阶累积量消除相关性噪声带来的影响。最后, 搜索互模糊函数峰值得到时频差估计值。仿真结果表明, 在-5 dB信噪比条件下, 相较于二阶互模糊函数算法, 该算法能够使时差估计精度提高3.3%, 频差估计精度提高1.5%。因此, 在较低信噪比等非理想信号环境下, 该算法能够有效提升参数估计精度。

关键词: 参数估计, Savitzky-Golay滤波, 互模糊函数, 高阶累积量, 滑窗

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

中图分类号:

TN971

张游, 黄永辉, 李志豪, 崔天舒, 王竹刚. 基于Savitzky-Golay滤波和互模糊函数的时频差参数估计算法[J]. 系统工程与电子技术, 2025, 47(5): 1395-1403.

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.

图/表 11

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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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基于Savitzky-Golay滤波和互模糊函数的时频差参数估计算法

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

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