基于Z变换和改进FRI的LFM信号参数估计方法研究

doi:10.12305/j.issn.1001-506X.2024.07.07

摘要/Abstract

摘要：

为了完成线性调频(linear frequency modulation, LFM)信号的稀疏采样，并利用稀疏数据对原始信号参数进行估计，本文提出了一种基于Z变换和改进有限新息率(finite rate of innovation, FRI)的LFM信号参数估计方法。以Z变换理论为基础，设计了一种数学模型，一旦信号能够表达成该数学模型的结构形式，就能通过Z变换和零化滤波器的方法估计信号参数。然后，利用了自相关延迟的FRI结构对LFM信号采样，该结构不仅完成了LFM信号的稀疏采样，而且稀疏采样结果能够与数学模型结构相符。在理论上通过数学论证的方式证明了所提方法能够用于获取LFM信号参数信息，并通过仿真和实测数据验证了所提方法的有效性，理论和实验结果表明该方法只需要4个采样点就能实现对LFM信号的参数估计，并且实验中的参数估计误差均在3%以内，极大的提高有限新息率采样的参数估计效率。

关键词: 线性调频信号, 有限新息率, 零化滤波器, Z变换, 参数估计

Abstract:

In order to complete the sparse sampling of linear frequency modulation (LFM) signals and use the sparse data to estimate the original signal parameters, we have learned the parameter estimation methods of finite rate of innovation (FRI) sampling and annihilating filter, on this basis, we propose a parameter estimation method based on mathematical model combined with Z-transform. Once the signal expression form is consistent with the structure of the mathematical model, the signal parameters can be estimated by the proposed method. Therefore, we used an autocorrelation delay structure to process the LFM signal, and the output results can be consistent with the mathematical model. It is demonstrated that the proposed method for estimating the parameters of LFM signals is theoretically feasible. The effectiveness of the proposed method is verified by simulation and measured data. The theoretical and experimental results show that the method can realize the parameter estimation of LFM signal only with 4 sampling points, and the parameter estimation error in the experiment is within 3%, which greatly improves the parameter estimation efficiency of FRI sampling.

Key words: linear frequency modulation (LFM) signal, finite rate of innovation (FRI), annihilating filter, Z-transform, parameter estimation

中图分类号:

TN91
TN92

孟硕, 孟晨, 王成. 基于Z变换和改进FRI的LFM信号参数估计方法研究[J]. 系统工程与电子技术, 2024, 46(7): 2228-2236.

Shuo MENG, Chen MENG, Cheng WANG. Research on LFM signal parameter estimation method based on Z-transform and improved FRI[J]. Systems Engineering and Electronics, 2024, 46(7): 2228-2236.

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a_n	$\tilde{a}_n$	u_n	$\tilde{u}_n$
2	1.999	1	1.000
3	3.002	2	1.999
4	3.994	3	3.000
5	5.011	4	3.999
6	5.988	5	5.000
7	7.007	6	5.999
8	7.998	7	7.000

方法	通道数量	采样频率/MHz	采样点数	重构RMSE	时间/s
RD	1	50	500	0.045	38.7
MWC	10	20	2 000	0.019	102.3
FRI	1	0.4	4	0.023	10.2

方法	通道数量	采样频率/MHz	采样点数	重构RMSE	时间/s
RD	1	50	1 021	0.065	52.7
MWC	10	20	8 041	0.027	167.9
FRI	1	0.196	4	0.031	13.3

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