## 2 Related Works  
Frequency estimation of wireless sensor signals can be divided into non-distributed and distributed methods. For the distributed method, the distribution of the estimated values of each sensor is used to obtain the final frequency. [PERSON] et al. [16] proposed a frequency estimation method based on the minimum mean square error and P-value distribution. They defined appropriate cost functions and employed a distributed method to estimate signal frequency in wireless sensors. Although they improved the accuracy of sensor frequency estimation, unfortunately, they did not consider the strong noise environment and frequency estimation timeliness. The non-distributed method for a single sensor is mainly based on signal processing for estimation, so the anti-noise performance is better than distributed. It can meet the needs for real-time monitoring of the IoT. The non-distributed frequency estimation algorithms are classified into time domain estimation and frequency domain estimation. In the former, the autocorrelation function is used to estimate the frequency. [PERSON] et al. [17] used the autocorrelation ratio of the adjacent two sets of functions to correct the frequency estimation bias, which improved the estimation accuracy and frequency range. In the latter, the peak location of the FFT spectrum is used to estimate signal frequency. Compared with the latter, the former is more sensitive to the noise environment, and the range of frequency estimation was relatively limited. It is due to phase wrapping produced by the autocorrelation calculation. Therefore, we will improve the frequency estimation performance of wireless sensors in the frequency domain to avoid phase wrapping effects. The existing frequency estimation algorithms did not consider negative frequency components, which led to a lower bound on the estimation error. [PERSON] et al. [18] proposed an accurate frequency estimation algorithm for real sinusoidal signals to solve this problem and further improve the estimation accuracy. They proposed three new interpolators. These three new interpolators consist of two initial interpolators and a fine interpolator. The former was used to estimate the frequency roughly, and the latter was used to correct the estimation error. Their proposed algorithm removed the lower bound of the frequency estimation error and improved its accuracy. However, they did not optimize the estimation accuracy at a low signal-to-noise ratio (SNR). [PERSON] et al. [19] proposed a fast and efficient iterative discrete Fourier transform (DFT) interpolation algorithm called the q-shift estimation (QSE) algorithm. The proposed algorithm used the ratio of the two spectra in the vicinity of the DFT peak to compensate the signal for energy and performed multiple iterations of frequency shift. The results showed that as the number of iterations increases, the variance of frequency estimation gradually approaches the Cramer-Rao lower bound (CRLB), and the estimation accuracy was better than that of the Aboutanios and Mulgrew (A&M) algorithm. Because multiple iterative operations increased the algorithm's computational complexity, they further optimized and proposed a hybrid half-shift and q-shift estimation (HAQSE) algorithm [20]. They combined the QSE and A&M algorithms to control the number of iterative operations within two, thus reducing the algorithm's complexity. However, the estimation performance of the algorithm degraded when the signal was longer. [PERSON] et al. [21] proposed a frequency estimation algorithm based on the maximization three-point periodogram (T-PP). They used the Canda algorithm to obtain the deviation of the frequency initially and arbitrarily selected a frequency division factor within \(0\sim 1/N\). The position near the quantized frequency point was divided into three parts by the frequency division factor, and the corresponding frequencies were calculated, respectively. They obtained the final frequency by fitting the three frequency values.