## 2 Related Works  
The frequency measurement algorithms with a high accuracy can be categorized as autocorrelation-function-based time-domain frequency estimation algorithms and Fourier-transform-based frequency-domain estimation algorithms. Basic time-domain frequency estimation algorithms mainly include the Fitz algorithm [9] and the Kay algorithm [10] and their improved algorithms for the signal-to-noise ratio threshold and constraint parameters. These methods estimate the frequency value from the phase relationship. Frequency-domain frequency estimation algorithms primarily rely on spectral peaks for signal frequency estimation. Examples include the Rife algorithm and the Quinn algorithm [11], as well as improved algorithms designed to address errors that arise when estimated frequency values are close to quantized frequency points. Time-domain estimation algorithms have higher requirements on the signal, such as the signal length and signal-to-noise ratio threshold. In contrast, frequency estimation algorithms are more universally applicable [12]. In response to the fence effect and spectral leakage effects caused by the Fourier transform, [PERSON] et al. [13] proposed a fast and accurate frequency estimation method for monotone signals based on DFT interpolation. Firstly, the frequency deviation direction was accurately identified by the three-sample DFT phase difference, and then a new unbiased estimator was developed for an arbitrary number of samples, which solved the problems of the accuracy of the existing methods in noisy conditions and the bias in a small number of samples. However, the method was still limited by the signal-to-noise ratio threshold in finding the peak DFT in the initial coarse estimation. [PERSON] et al. [14] proposed the HAQSE algorithm, which employed a hybrid approach combining the half-shift and Q-shift DFT interpolation methods. The first iteration of the algorithm was modified using an unbiased A&M interpolator and then refined using the QSE algorithm to obtain the final frequency estimate. The algorithm required only two iterations, which reduced the computational cost, but the algorithm limited the computational length of the signal and performs poorly above a certain threshold. Among frequency estimation algorithms, the Rife algorithm, which relied on the ratio of spectral amplitude values, was widely utilized in signal processing due to its relatively low computational complexity and minimal requirements for signal length. However, misjudging the direction of the second-largest spectral value leads to substantial estimation errors when the signal-to-noise ratio is relatively low. Additionally, while the Rife algorithm provided a high accuracy when the estimated frequency was near the center of the quantization frequency, its performance deteriorated significantly and errors increased when the estimated frequency was close to the quantization frequency. In order to improve the accuracy of frequency interpolation algorithms in the frequency domain, [PERSON] et al. [15] proposed a non-iterative accurate frequency estimator using two DFT spectral lines. The method calculated the Fourier coefficients on the two spectral lines located midway between the two spectral lines adjacent to the maximum value and used the properties of sine function fitting to compute the amplitude ratios of the two intermediate spectral lines to the maximum spectral line, in order to estimate the position of the actual maximum magnitude Fourier coefficient. The complexity of the proposed method was lower than that of traditional methods. However, the method could only achieve CRLB performance under high signal-to-noise ratio conditions, and the estimation bias was larger when the frequency was close to the band edges. The primary sine frequency estimation method was only suitable for signals with zero padding, resulting in a decrease in frequency estimation performance. [PERSON] et al. [16] proposed a novel method for the frequency estimation of non-stationary discrete-time sinusoidal signals.