## 2 Related Works
However, they did not derive selection criteria for the frequency division factor that affected the fitting outcome. The above algorithms all improved the frequency estimation accuracy to varying degrees. However, in terms of algorithm complexity, there was much less computation of the Rife algorithm than other algorithms, and it was easy to implement. Unfortunately, the Rife algorithm had specific requirements for the frequency range. Therefore, many researchers have improved and optimized the Rife algorithm. To further improve the ability of the Rife algorithm to solve spectral leakage, [PERSON] et al. [22] introduced the Hanning self-convolution window and proposed an enhanced Rife algorithm. They divided the proposed algorithm into two parts. In the first part, a Hanning window was added to the signal to reduce the picket fence effect. In the second part, the position of the quantized frequency point was determined. They selected the Rife algorithm to estimate the frequency directly when it was located in the central area of the maximum and sub-maximum spectral lines. On the contrary, the frequency shift Rife algorithm was used to shift the signal to the center area, and then frequency estimation was performed. They reduced the effects of spectral leakage but did not improve the signal's immunity to interference. The frequency interpolation method based on DFT was easily affected by noise, which led to an increase in error. [PERSON] et al. [23] analyzed this problem and proposed a high precision frequency estimation method based on third-order frequency deviation. They divided the frequency estimation into three stages. The Rife algorithm was used to roughly estimate the frequency and calculate the frequency deviation in the first stage. In the second stage, they judged whether the frequency deviation was within the optimal estimation range of the Rife algorithm and transferred the coarse estimated frequency deviation to the effective estimation range of the Rife algorithm. In the third stage, the frequency-shifted signal was re-interpolated and estimated. They improved the frequency estimation accuracy under a low SNR. Nonetheless, there was a lack of optimization of the algorithm performance within the optimal interval. [PERSON] et al. [24] used the three spectral lines adjacent to the maximum spectral line to estimate the frequency directly. They were inspired by the Quinn and Rife methods and proposed a novel combined Quinn-Rife estimator (CQRE). They combined the decision condition of the Quinn algorithm and the frequency deviation factor of the Rife algorithm and made a double judgment on the frequency deviation factor of the CQRE algorithm. In addition, they exploited the relationship between spectrum and phase to improve the stability of the CQRE algorithm. However, since both the Quinn and Rife algorithms had the same shortcomings, the improvement effect of the estimation accuracy was limited when the estimated frequency was closed to the quantization frequency point. Many frequency estimation algorithms increased computational complexity while improving performance. To balance the complexity and performance of signal frequency estimation, [PERSON] et al. [25] proposed an automatic segmentation-improved Quinn-Rife algorithm (ASIQ-Rife). They divided the quantized frequency points into three segments and judged them separately. If \(0\leq\delta\leq 0.15\), the improved Quinn algorithm was used for frequency estimation. If \(0.3\leq\delta\leq 0.5\), the frequency estimation method was the same as the Rife algorithm. If \(0.15<\delta<0.3\), the improved Quinn algorithm was used to determine the interpolation direction, and the Rife algorithm was used to calculate the frequency deviation. They adaptively selected the optimal estimation method in different frequency ranges, which improved the algorithm's stability. However, they did not consider the complexity of the algorithm. Whether the frequency estimation performance of the Rife algorithm was stable depended on the judgment of the interpolation direction.