Parametric Estimation of Harmonically Related Sinusoids

Abstract

Mud-pulse telemetry is a method used for measurement-while-drilling (MWD)in the oil industry. The telemetry signals are corrupted by spurious mud pump noise consisting of a large number of harmonically related sinusoids. In order to denoise the signal, the noise parameters have to be tracked accurately in real time. There are well established parametric estimation techniques for determining various parameters of independent sinusoids. The iterative methods based on the linear prediction properties of the sinusoids provide a computationally e±cient way of solving the non linear optimization problem presented by these methods. However, owing to the large number of these sinusoids, incorporating the harmonic relationship in the problem becomes important.

This thesis is aimed at solving the problem of estimating parameters of harmonically related sinusoids. We examine the efficacy of IQML algorithm in estimating the parameters of the telemetry signal for varying SNRs and data lengths. The IQML algorithm proves quite robust and successfully tracks both stationary and slowly varying frequency signals. Later, we propose an algorithm for fundamental frequency estimation which relies on the initial harmonic frequency estimate. The results of tests performed on synthetic data that imitates real field data are presented. The analysis of the simulation results shows that the proposed method manages to remove noise causing sinusoids in the telemetry signal to a great extent. The low computational complexity of the algorithm also makes for an easy implementation on field where computational power is limited.