THE CONSTRAINED TOTAL LEAST-SQUARES TECHNIQUE AND ITS APPLICATIONS TO HARMONIC SUPERRESOLUTION

The total least squares (TLS) technique is a generalized least squares method to solve an overdetermined set of equations whose coefficients are noisy. The constrained total least squares (CTLS) method is a natural extension of TLS to the case when the noise components of the coefficients are algebraically related. The CTLS technique is developed here and some of its applications to superresolution harmonic analysis are presented. The CTLS problem is reduced to an unconstrained minimization problem over a small set of variables. A perturbation analysis of the CTLS solution is derived, and from it the root mean-square error (RMSE) of the CTLS solution, which is valid for small noise levels, is obtained in closed form. The complex version of the Newton method is derived and is applied to determine the CTLS solution. We also show that the CTLS problem is equivalent to a constrained parameter maximum-likelihood problem. Finally, the CTLS technique is applied to estimate the frequencies of sinusoids in white noise and the angle of arrival of narrow-band wavefronts at a linear uniform array. In both cases, the RMSE of the CTLS solution is very close to the Cramer-Rao bound (CRB), up to a threshold signal-to-noise ratio (SNR), and CTLS shows superior or similar accuracy to other advanced techniques.