Estimators and Performance Bounds for Short Periodic Pulses

TL;DR

This paper develops new estimators and bounds for short periodic pulse signals, showing they outperform traditional multiharmonic models at low SNR in industrial applications.

Contribution

It introduces models for short periodic pulses with known and unknown shapes, deriving estimators and bounds that improve frequency estimation accuracy.

Findings

Proposed estimators outperform multiharmonic maximum likelihood estimators at low SNR.

Derived Fisher information matrices and Cramér-Rao bounds for the new models.

Numerical results confirm improved performance in noisy conditions.

Abstract

In many industrial applications, signals with short periodic pulses, caused by repeated steps in the manufacturing process, are present, and their fundamental frequency or period may be of interest. Fundamental frequency estimation is in many cases performed by describing the periodic signal as a multiharmonic signal and employing the corresponding maximum likelihood estimator. However, since signals with short periodic pulses contain a large number of noise-only samples, the multiharmonic signal model is not optimal to describe them. In this work, two models of short periodic pulses with known and unknown pulse shape are considered. For both models, the corresponding maximum likelihood estimators, Fisher information matrices, and approximate Cram\'er-Rao lower bounds are presented. Numerical results demonstrate that the proposed estimators outperform the maximum likelihood estimator based on the multiharmonic signal model for low signal-to-noise ratios.