Accurate and computationally efficient sinusoidal parameter estimation and tracking algorithm development

Abstract

Sinusoidal parameter estimation in additive white noise has been an important problem in signal processing and still now it is an active research area because of its wide variety of applications in multiple disciplines such as sonar, radar, digital communications and biomedical engineering. Among the sinusoidal parameters, frequency estimation is the crucial step, because it is a nonlinear function in the received data sequence. After determining frequencies, the remaining parameters can then be estimated straightforwardly. The purpose of this research is to develop accurate and computationally efficient estimators for sinusoidal parameters, namely, amplitudes, frequencies, phases, offsets and/or damping factors. In the first part of this thesis, the problem of sinusoidal parameter estimation in a stationary environment is addressed where the sinusoidal parameters are deterministic constants. Based on linear prediction (LP) property of sinusoidal signals and weighted least squares (WLS), frequency estimation algorithms for different signal models have been proposed. First, the damped sinusoidal model is considered, and accurate and computationally efficient estimators for single real tone are devised. Extension to multiple sinusoids is also investigated. It is noteworthy that many traditional approaches are not applicable for damped sinusoids because the extra parameters of damping factors need to determine and the corresponding correlation matrix cannot be utilized easily. Second, real and complex sinusoidal signals with constant offsets are investigated. Based on the techniques of LP and WLS again, an accurate frequency estimation approach for these signal models has been developed. Finally, a special signal model derived from the lossy wave equation is examined, and a simple and optimal algorithm for its parameter estimation is proposed. It is shown that the developed estimators can attain the corresponding Cramer-Rao lower bounds (CRLBs) for sufficiently large data lengths and/or the signal-to-noise ratio (SNR). Computer simulations are provided to confirm the effectiveness of the proposed algorithms. In the second part of this thesis, the problem of simultaneous estimation of sinusoidal parameters in a nonstationary environment is addressed, where the parameters vary with time. A recursive Gauss-Newton (RGN) algorithm is developed for adaptive tracking of a real single sinusoid in additive white noise. For estimation of multiple parameters which vary with different rates, the RGN methodology with multiple forgetting factors (MFF) is proposed to provide a flexible way of keeping track of the parameters appropriately. The developed RGN algorithm is then simplified for computational complexity reduction. The performance of the proposed algorithm is compared with the corresponding CRLB and their true values when the sinusoidal parameters are kept constant. Apart from the algorithm development, the variances of the parameter estimates have been derived and verified by computer simulations.

Date of Award	16 Feb 2009
Original language	English
Awarding Institution	City University of Hong Kong
Supervisor	Hing Cheung SO (Supervisor)