基于正负频率频谱叠加的实时高精度频率估计算法

doi:10.12305/j.issn.1001-506X.2026.09.01

系统工程与电子技术 ›› 2026, Vol. 48 ›› Issue (9): 2889-2897.doi: 10.12305/j.issn.1001-506X.2026.09.01

• 电子技术 •

基于正负频率频谱叠加的实时高精度频率估计算法

杨诗雯¹(), 陈颍滨²(), 吴仕皇¹(), 谢晓爵¹(), 张贻雄¹(), 罗跃东²()

1. 厦门大学电子科学与技术学院，福建厦门 361102
2. 西安卫星测控中心，陕西西安 710000

收稿日期:2025-10-21 修回日期:2025-11-20 接受日期:2025-12-03 出版日期:2026-04-24 发布日期:2026-04-24
通讯作者: 张贻雄 E-mail:yangshiwen@stu.xmu.edu.cn;17319229225@163.com;wushihuang@stu.xmu.edu.cn;xjxie@stu.xmu.edu.cn;zyx@xmu.edu.cn;luoyuedong_2000@163.com
作者简介:杨诗雯（2002—），女，硕士研究生，主要研究方向为激光雷达信号处理、频率估计
陈颍滨（1987—），男，工程师，硕士，主要研究方向为雷达信号处理、卫星测控
吴仕皇（2002—），男，硕士研究生，主要研究方向为调频连续波激光雷达
谢晓爵（2002—），男，博士研究生，主要研究方向为毫米波雷达、激光雷达数据处理
罗跃东（1981—），男，高级工程师，博士，主要研究方向为航天测控、信号与信息处理
基金资助:
科技部重点研发计划（2022YFB3902400）；国家自然科学基金（ 62471414）；雄安新区科技创新专项（2022XAGG0181）资助课题

Real-time and high-precision frequency estimation algorithm based on positive and negative frequency spectrum superposition

Shiwen Yang¹(), Yingbin Chen²(), Shihuang Wu¹(), Xiaojue Xie¹(), Yixiong Zhang¹(), Yuedong Luo²()

1. School of Electronic Science and Engineering，Xiamen University，Xiamen 361102，China
2. Xi’an Satellite Control Center，Xi’an 710000，China

Received:2025-10-21 Revised:2025-11-20 Accepted:2025-12-03 Online:2026-04-24 Published:2026-04-24
Contact: Yixiong Zhang E-mail:yangshiwen@stu.xmu.edu.cn;17319229225@163.com;wushihuang@stu.xmu.edu.cn;xjxie@stu.xmu.edu.cn;zyx@xmu.edu.cn;luoyuedong_2000@163.com

摘要/Abstract

摘要：

针对传统频率估计算法中无迭代算法估计精度低、易受噪声干扰，而有迭代算法计算复杂度高、实时性差的问题，提出一种实时高精度的频率估计算法。首先建立实正弦信号模型，利用信号正负频率的频谱叠加消除由负频率频谱泄露引起的误差，得到初步频率估计值；接着引入离散时间傅里叶变换进行一次频移处理增强算法的抗噪声性能，同时提高估计精度。仿真结果表明，所提算法相对现有高精度频率估计算法能够在计算复杂度减小17.4%，运算时间缩短33.4%的基础上获得接近克拉美罗下界的估计性能，具有较好的工程应用前景。

关键词: 频率估计, 离散傅里叶变换, 离散时间傅里叶变换, 克拉美罗下界

Abstract:

To address the issues of traditional low estimation accuracy algorithms, where non-iterative algorithms suffer from low estimation accuracy and high susceptibility to noise interference, while iterative algorithms are plagued by high computational complexity and poor real-time performance, a real-time and high-precision frequency estimation algorithm is proposed. Firstly, a real sine signal model is established to eliminate errors caused by negative frequency spectrum leakage by superimposing the positive and negative frequency spectra of the signal, and obtain preliminary frequency estimates. Then, a discrete-time Fourier transform is introduced for frequency shift processing to enhance the anti noise performance of the algorithm and improve the estimation accuracy. Simulation results demonstrate that compared with existing high-precision frequency estimation algorithms, the proposed algorithm can achieve estimation performance close to the Cramér-Rao lower bound（CRLB） while reducing computational complexity by 17.4% and shortening operation time by 33.4%, thus possessing promising prospects for engineering applications.

Key words: frequency estimation, discrete Fourier transform (DFT), discrete-time Fourier transform (DTFT), Cramér-Rao lower bound (CRLB)

中图分类号:

TN 911.72

杨诗雯, 陈颍滨, 吴仕皇, 谢晓爵, 张贻雄, 罗跃东. 基于正负频率频谱叠加的实时高精度频率估计算法[J]. 系统工程与电子技术, 2026, 48(9): 2889-2897.

Shiwen Yang, Yingbin Chen, Shihuang Wu, Xiaojue Xie, Yixiong Zhang, Yuedong Luo. Real-time and high-precision frequency estimation algorithm based on positive and negative frequency spectrum superposition[J]. Systems Engineering and Electronics, 2026, 48(9): 2889-2897.

图/表 11

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参考文献 31

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算法	SNR
算法	0	5	10	15
所提算法	−47.65	−50.17	−52.58	−54.92
JT算法	−47.65	−50.17	−52.58	−54.92
AM算法	−47.64	−50.16	−52.58	−54.92
HAQSE算法	−47.67	−50.17	−52.56	−54.85
Z-Rife算法	−46.77	−49.25	−51.63	−53.94
Candan算法	−45.88	−48.41	−50.88	−53.40
CRLB	−49.25	−51.75	−54.25	−56.75

算法	复数乘	复数加	时间/s
所提算法	$(N/2) \cdot {\log _2}\;N + 2N + 3$	$N \cdot {\log _2}\;N + 2N - 2$	0.07 14
JT算法	$(N/2) \cdot {\log _2}\;N + 4N$	$N \cdot {\log _2}\;N + 4N - 4$	0.10 81
AM算法	$(N/2) \cdot {\log _2}\;N + 4N$	$N \cdot {\log _2}\;N + 4N - 4$	0.10 78
HAQSE算法	$(N/2) \cdot {\log _2}\;N + 4N$	$N \cdot {\log _2}\;N + 4N - 4$	0.10 93
Z-Rife算法	$(N/2) \cdot {\log _2}\;N$+2	$N \cdot {\log _2}\;N$+4	0.02 03
Candan算法	$(N/2) \cdot {\log _2}\;N$+5	$N \cdot {\log _2}\;N$+3	0.02 19

算法	平均RMSE/m
所提算法	0.1024
JT算法	0.1229
AM算法	0.1893
HAQSE算法	0.1893
Z-Rife算法	0.1142
Candan算法	0.1057

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基于正负频率频谱叠加的实时高精度频率估计算法

Real-time and high-precision frequency estimation algorithm based on positive and negative frequency spectrum superposition

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