基于插值修正的I-Rife频率估计算法

doi:10.19678/j.issn.1000-3428.0069553

摘要/Abstract

摘要：

频率估计是信号处理中的关键技术。当信号频率接近快速傅里叶变换(FFT)的离散频点时, I-Rife算法的频率估计误差较大。针对该问题, 提出基于插值修正的I-Rife频率估计算法。首先, 利用I-Rife算法插值的2条谱线判断频率修正方向, 在该修正方向上进行单点插值, 并将I-Rife算法中最大谱线和次大谱线之间的区域划分为3个小区域。然后, 通过比较该单点插值和I-Rife算法中2条谱线的幅值判断信号频率位于哪个小区域, 并计算更精确的频移因子。最后, 利用Rife算法计算出修正后的频率估计值。通过理论分析可知, 所提算法使信号频率始终接近相邻离散频点的中心区域, 克服了现有I-Rife算法当信号频率接近离散频点时估计误差大的问题, 从而提高了频率估计精度。仿真结果表明, 所提算法在低信噪比(SNR)并且信号频率接近离散频点时的频率估计精度高于I-Rife算法, 且误差更接近克拉美罗下界(CRLB)。而且, 所提算法比现有算法具有更好的稳定性。

关键词: Rife算法, I-Rife算法, 频率估计, 插值修正, 克拉美罗下界

Abstract:

Frequency estimation is a crucial signal-processing technology. The I-Rife algorithm exhibits large frequency estimation errors when the signal frequency is close to the frequency samples of the Fast Fourier Transform (FFT). To address this, an I-Rife frequency estimation algorithm based on interpolation modification is proposed. First, two frequency samples interpolated by I-Rife are utilized to determine the direction of frequency correction. A single-point frequency sample is interpolated in this direction, and the region between the maximum and second maximum frequency samples in the I-Rife algorithm is divided into three smaller regions. Subsequently, by comparing the magnitudes of the interpolated frequency sample and the two frequency samples in the I-Rife algorithm, a smaller region where the signal frequency is located is determined and a more accurate frequency-shifting factor is calculated. Finally, the Rife algorithm is used to obtain the corrected frequency estimation value. Theoretical analysis indicates that the proposed algorithm maintains the signal frequency close to the central region of two neighboring discrete frequency samples and thus effectively overcomes the issue of large estimation errors in the I-Rife algorithm when the signal frequency is close to the frequency samples. Simulation results show that the proposed algorithm achieves a higher frequency estimation accuracy than the I-Rife algorithm when the Signal-to-Noise Ratio (SNR) is low and the signal frequency is close to the frequency samples. Additionally, compared to that of the existing algorithms, its estimation error is closer to the Cramér-Rao Lower Bound (CRLB). Moreover, the proposed algorithm has better stability than existing algorithms.

Key words: Rife algorithm, I-Rife algorithm, frequency estimation, interpolation correction, Cramér-Rao Lower Bound (CRLB)

闻丹, 易辉跃, 张武雄, 许晖. 基于插值修正的I-Rife频率估计算法[J]. 计算机工程, 2025, 51(12): 161-170.

WEN Dan, YI Huiyue, ZHANG Wuxiong, XU Hui. I-Rife Frequency Estimation Algorithm Based on Interpolation Modification[J]. Computer Engineering, 2025, 51(12): 161-170.

https://www.ecice06.com/CN/Y2025/V51/I12/161

图/表 18

图1 SNR为-8 dB时FFT算法、Rife算法、I-Rife算法在不同频率下频率估计的RMSE

Fig.1 RMSE values of frequency estimation of FFT algorithm, Rife algorithm and I-Rife algorithm versus various frequency when SNR is -8 dB

图2 SNR为-8 dB时I-Rife算法频率估计的RMSE值随频偏的变化关系

Fig.2 RMSE values of frequency estimates of the I-Rife algorithm for different frequency biases when SNR is -8 dB

图3 SNR为-8 dB时各算法频率估计的MAE值

Fig.3 MAE values of frequency estimation of various algorithms when SNR is -8 dB

图4 SNR为8 dB时各算法频率估计的MAE值

Fig.4 MAE values for frequency estimation of various algorithms when SNR is 8 dB

图5 SNR为-8 dB时各算法频率估计的RMSE值

Fig.5 RMSE values for frequency estimation of various algorithms when SNR is -8 dB

图6 SNR为8 dB时各算法频率估计的RMSE值

Fig.6 RMSE values for frequency estimation of various algorithms when SNR is 8 dB

图7 不同SNR下信号频率为f₀时各算法频率估计的MAE值

Fig.7 MAE of frequency estimation of various algorithms versus SNR when the signal frequency is f₀

图8 不同SNR下信号频率为f₀时各算法频率估计的RMSE值

Fig.8 RMSE of frequency estimation of various algorithms versus SNR when the signal frequency is f₀

图9 不同SNR下信号频率为f₀+0.001Δ_f时各算法频率估计的MAE值

Fig.9 MAE of frequency estimation of various algorithms versus SNR when the signal frequency is f₀+0.001Δ_f

图10 不同SNR下信号频率为f₀+0.001Δ_f

Fig.10 RMSE of frequency estimation of various algorithms versus SNR when the signal frequency is f₀+0.001Δ_f

图11 不同SNR下信号频率为f₀+0.15Δ_f时各算法频率估计的MAE值

Fig.11 MAE of frequency estimation of various algorithms versus SNR when the signal frequency is f₀+0.15Δ_f

图12 不同SNR下信号频率为f₀+0.15Δ_f时各算法频率估计的RMSE值

Fig.12 RMSE frequency estimation of various algorithms versus SNR when the signal frequency is f₀+0.15Δ_f

图13 FMCW雷达测试平台

Fig.13 FMCW radar test platform

图14 各算法频率估计的误差

Fig.14 Errors of frequency estimation for various algorithms

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