Applications of the Total Least Squares technique to frequency estimation.

Abstract

Estimating the frequencies of signals in a noisy environment has numerous applications in digital signal processing. In December 1980, Golub and Van Loan proposed a spectral estimator called the Total Least Squares (TLS) technique which is a refinement of the Least Squares (LS) technique. In this thesis, we first describe the origin of the TLS technique and its applications to frequency estimation. Furthermore, we present a numerical implementation for resolving two damped / undamped closely-spaced sinusoidal signals in white noise. Next, we introduce TLS extensions such as the Constrained Total Least Squares (CTLS) technique and the Linear Constraint Total Least Squares (LCTLS) technique. The CTLS addresses the case where the noise components are related and the LCTLS addresses the case where one desires to resolve between two narrowband signals close in frequency, one of which is known. Finally, we present a numerical implementation of the Recursive Total Least Squares (RTLS) technique and apply it to the case of a signal with a fixed frequency together with a signal with a time-varying frequency.