Robust Algorithms for Pitch Detection and Parameter Estimation

Abstract

In a lot of applications signals recorded via a measurement system are analyzed to deeply understand the underlying process and infer unknown parameters. Often, the recorded signal is periodic, and the period is the parameter of major interest. Two typical examples are condition monitoring for non-destructive testing and electrocardiogram signal processing for diagnosis of heart diseases. In all real-world applications, random noise is prevalent and unavoidable. The strength of the noise depends on the measurement system itself and on the environment. Especially in heavy industry applications, e.g., environmental influences cause large outlying events of high strength. If neglected, these outlier can have a massive impact on standard estimation procedures like the principle of least squares. In this thesis we consider a typical periodic signal together with measurement noise and with outliers as it might occur in heavy industry applications. The goal of this thesis is to estimate the period of such signals. Three approaches will be discussed, namely maximum likelihood estimation, the approximate Bayesian computation approach and last but not least a cross-correlation approach. For maximum likelihood estimation, in principle no prior knowledge of the signals shape necessary for processing. However it will be shown that it is highly beneficial to take prior knowledge regarding the signals shape into account. This leads to a major improvement with respect to the robustness against outliers. Prior knowledge of the signals shape turns out to be highly beneficial for the approximate Bayesian computation and the cross-correlation approach, too. We will also discuss two preprocessing techniques that remove the outliers before the actual estimator is applied. This enables a computationally efficient application of known standard estimators in the presence of outliers. To examine the effect of the preprocessing techniques and to finally compare all estimation techniques the results with and without preprocessing are compared for every estimation approach for different example scenarios.submitted by Lukas SchiefermüllerUniversität Linz, Masterarbeit, 2020(VLID)504116