Extended Noise Resistant Correlation Method for Period Estimation of Pseudoperiodic Signals

Improving the Accuracy of Estimates of the Pulse Sequence Period Using the Methodology of Complete Sufficient Statistics

“…Thus, the estimate of the pulse repetition period (27) is presented in the form (16). According to the uniqueness theorem for the effective estimate, the only effective estimate of the pulse repetition period is:…”

“…A closed-form maximum likelihood amplitude estimator is obtained in [15]. The extended noise-resistant correlation method to identify the period of pseudoperiodic signals is derived in [16]. Attempts are being made to use Fourier and wavelet transformation with windows of various kinds to increase the localization of signal energy [17], [18] or multithreshold circuits [19], [20] are used, which give a gain in the accuracy of the estimate in particular cases, however, in general, they carry the risk of estimation circuit work going from stable and equilibrium state.…”

A Scalable Gaussian Process for Large-Scale Periodic Data

“…Periodic data, such as speech signals (Nielsen et al, 2017), electrocardiogram (ECG) signals (Chandola and Vatsavai, 2011), and vibration signals (Fan et al, 2018), are commonly encountered in scientific research and industrial applications. Such signals are often analyzed via linear models, e.g., the maximum likelihood pitch estimation (MLPE) method (Wise et al, 1976) and the noise resistant correlation (NRC) method (Li et al, 2021), or nonlinear models, e.g., the nonlinear least square (NLS) method (Quinn and Thomson, 1991;Nielsen et al, 2017). These methods can provide desirable estimations and predictions in many applications, but they become less accurate when handling signals with a low signal-to-noise ratio (SNR) and may require very long signals to suppress the masking effect of strong background noises (Fan et al, 2018;Li et al, 2021).…”

“…Such signals are often analyzed via linear models, e.g., the maximum likelihood pitch estimation (MLPE) method (Wise et al, 1976) and the noise resistant correlation (NRC) method (Li et al, 2021), or nonlinear models, e.g., the nonlinear least square (NLS) method (Quinn and Thomson, 1991;Nielsen et al, 2017). These methods can provide desirable estimations and predictions in many applications, but they become less accurate when handling signals with a low signal-to-noise ratio (SNR) and may require very long signals to suppress the masking effect of strong background noises (Fan et al, 2018;Li et al, 2021). A key reason is that they do not appropriately model the circulant within-period correlation of periodic data, i.e., the autocorrelation between any two points in one period.…”

Improving the accuracy of estimates of the pulse sequence period using the methodology of complete sufficient statistics

“…A closed-form maximum likelihood amplitude estimator is obtained in 19 . The extended noise-resistant correlation method to identify the period of pseudo-periodic signals is derived in 20 . Attempts are being made to use Fourier and wavelet transformation with windows of various kinds to increase the localization of signal energy 21 , 22 or multi-threshold circuits 23 , 24 are used, which give a gain in the accuracy of the estimate in particular cases.…”