Estimating linear regression parameters in the presence of non-white Gaussian noise with unknown covariance parameters
Gene B. Goldstein · University of Southern California Digital Library · 2015
Abstract : A number of problems that arise in radar and sonar applications can be regarded as parameter estimation problems, in which the desired signal, f(t, alpha), is imbedded in non-white, Gaussian noise. It is desired to estimate the unknown, nonrandom parameter vector, alpha, from observations (continuous or sampled) of the received noisy signal over a finite time interval (0,T). Here f(t,alpha) is a known nonstochastic function, and we shall consider the case when f(t,alpha) is linear in alpha. In this case, alpha is referred to as a linear regression vector. We shall investigate the variance of the Least-Square (LS) estimator and of the so-called Generalized-Least-Squares (GLS) estimator for alpha. Both are unbiased estimators for alpha.