Optimal signal processing under uncertainty

"The design of optimal operators takes different forms depending on the random process constituting the scientific model and the operator class of interest. In all cases, operator class and random process must be united in a criterion (cost function) that characterizes the operational objective and, relative to the cost function, an optimal operator found. A common difficulty is uncertainty in the parameters of the scientific model. Then, in addition to optimization relative to the original cost function, optimization must take into account uncertainty relative to an uncertainty class of random processes. If there is a prior distribution (or posterior distribution if data are employed) governing likelihood in the uncertainty class, then one can choose an operator minimizing the expected cost over the uncertainty class. A critical point is that the prior distribution is not on the parameters of the operator model, but on the uncertainty relative to the parameters of the scientific model. The basic principle embodied in the book is to express the optimal operator under the joint probability space formed from the joint internal and external uncertainty in the same form as the optimal operator for a known model by replacing the mathematical structures forming the standard optimal operator with corresponding structures, called effective characteristics, that incorporate model uncertainty. For instance, in Wiener filtering the power spectra might be uncertain and be replaced by effective power spectra in the representation of the Wiener filter"--