Parameter Estimation of Noise Corrupted Sinusoids

TL;DR

This paper explores various signal processing techniques like FIR filtering, FFT, autocorrelation, and nonlinear least squares to improve parameter estimation of noisy sinusoids, especially for low-frequency harmonic motion.

Contribution

It introduces alternative methods for estimating frequency and phase, and derives an autocorrelation function specific to harmonic motion.

Findings

FIR filtering and FFT enhance parameter estimation accuracy.

Autocorrelation functions can be tailored for harmonic motion.

Alternative estimation methods improve robustness against noise.

Abstract

Existing algorithms for fitting the parameters of a sinusoid to noisy discrete time observations are not always successful due to initial value sensitivity and other issues. This paper demonstrates the techniques of FIR filtering, Fast Fourier Transform, circular autocorreltion, and nonlinear least squares minimization as useful in the parameter estimation of amplitude, frequency and phase exemplified for a low-frequency time-delayed sinusoid describing simple harmonic motion. Alternative means are described for estimating frequency and phase angle. An autocorrelation function for harmonic motion is also derived.