IMPROVED AND ROBUST ESTIMATION OF NONRANDOM WAVEFORMS
Abstract
The problem of estimating nonrandom signal parameters when some a priori information about these parameters is available and when the contaminating noise is not gaussian or is only known in an approximate manner is considered in this work. Utilization of a priori knowledge in the estimation procedures is discussed by describing two general concepts: the minimax method and the generalized Bayes approach. It is seen that for certain kinds of constraints the minimax method provides a solution relatively easy to obtain and one whose mean squared error is smaller than those obtained by more conventional procedures such as the maximum likelihood method. For other types of constraints the generalized Bayes approach utilizing noninformative priors allows incorporation of constraints into the solution of the problem. Often the noninformative priors are not valid probability distribution functions; however, an a posteriori distribution will exist and can, in some sense, be interpreted as an appropriate posteriori distribution. An application of these two methods is illustrated in the estimation of the visual evoked response of the brain to a light stimulus. For cases where the contaminating noise is not gaussian or is only partially specified it is known that optimum procedures, designed under the assumption of exact knowledge of the noise model, can give poor results if the actual model departs even slightly from the assumed one. The main concepts and definitions of robust estimation procedures designed to overcome this problem are then discussed. It is pointed out that asymptotic results are not necessarily good indicators of the performance of the various methods for the small sample size problem and that some procedures, although having desirable properties, may be too complicated to compute for certain applications. A robust algorithm that avoids some of the disadvantages of previously derived methods and is more suitable for certain signal processing applications is presented. When, in addition to the presence of heavy tailed noise, there is knowledge that the signal-to-noise ratio is low it is shown that nonlinear robust procedures can be designed that greatly reduce the mean squared error when compared to linear methods. Several applications of the methods discussed in this work are presented.
Degree
Ph.D.
Subject Area
Electrical engineering
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