Optimal strategies and tradeoffs for joint detection and estimation.

Abstract

This thesis treats the problem of joint (simultaneous) detection and estimation which arises when estimation of signal parameters is desired but signal presence is uncertain. In general, a joint detection and estimation algorithm cannot simultaneously achieve optimal detection and optimal estimation performance. There is therefore a need to have a methodology for quantifying the performance tradeoffs between detection and estimation. This thesis provides such a methodology. We develop a theory for optimal simultaneous decisions for a finite set of intermediate and terminal decision states. This theory specifies simultaneous decision rules which minimize the worst case decision error probability under an inequality constraint on the probability of a false decision for one of the intermediate or terminal decision states. The theory also specifies achievable lower bounds on the worst case performance of identically constrained decision rules. These bounds can be used to assess the tradeoffs between optimally performing intermediate decisions and optimally performing terminal decisions. Since the analytical evaluation of these lower bounds may be intractable for large dimensional decision spaces, we also provide methods for deriving weaker but more tractable bounds based on the Fano inequality of information theory. We apply our theory to a multi-component signal in noise problem arising in spectrum estimation, multiple target tracking, and multiple access communication. We identify three decision problems: signal detection, signal power estimation (order selection), and signal component estimation (classification). We show that the optimum constrained classifier is equivalent to a maximum likelihood classifier with a built-in Akaike-type order selection penalty which is optimum in terms of minimizing the worst case probability of classification error. By implementing the optimum constrained decision rule for each one of the three decision problems, we evaluate the corresponding lower bound. Using these bounds we perform a numerical study of the tradeoffs between detection, order selection, and classification at high error levels.