Estimation of Discrete Parameters in Linear Systems

Sammanfattning: Linear models are the by far most commonly used approach for describing physical signals and systems. As a result, the theory of linear models is quite extensive in areas like control theory and signal processing. However, in many applications a linear model is adequate only if some information of discrete nature is available. This thesis addresses the problem of how to treat and estimate this discrete information. Several applications on the problem of estimating discrete parameters in linear systems from measurements of its output are covered in the literature. Typically, the problem is treated separately in each context without overlapping. Orre objective of the present work is to discuss this problem in a general framework, relating proposed methods at a higher leve! of abstraction for revealing the main ideas.Estimators for discrete parameters are quite complex to compute, due to the fact that essentially every possible value of the discrete parameter has to be examined separately. The key question in applications is to find feasible expressions for the estimators, either exact or approximate. Besides the general discussion of the problem, the thesis contains more detailed treatments of four applications: mode! structure selection, detection, segmentation and blind equalization. The main topics covered in the applications consider the computation of optimal estimates, analysis and practical recursive schemes. Several statistical optimality criteria are examined, and a number of efficient computation schemes are presented. In the analysis, questions such as detectability, identifiability and efficiency are addressed. It is also investigated how different prior assumptions infiuence the estimates, and how their effects can be reduced by giving as non-informative priors as possible. This leads to estimation algorithms which contain almost no design variables.