Parametric estimation

An important engineering concept is that of modeling signals and systems in a manner that enables their study, analysis, and control. We seek models that are relatively easy to compute or estimate, yet at the same time provide insight into the salient characteristics of the signals or systems under study. One way to control the complexity of such models is through the use of parametric models. These are models that explicitly depend on a fixed number of parameters. In this chapter, we explore parametric models for signals and systems with a focus on the estimation of these model parameters under a variety of scenarios. Under statistical and deterministic formulations, we begin with models that are linear in their parameters and study both the batch and recursive formulations of these problems. We next apply these methods to problems in spectrum estimation, prediction, and filtering. Nonlinear modeling, universal methods, and order estimation are advanced topics that are also considered.