THE THEORY OF SIGNAL DETECTABILITY: EXTENSION TO THE DOUBLE COMPOSITE HYPOTHESIS SITUATION.
Abstract
The theory of signal detectability is extended to situations in which each of the two possible hypotheses are composite. The specific problem considered is that of detecting signals mixed with noise for examples in which uncertainties exist in both the signal and noise processes. The uncertain process parameters are considered to be both time invariant and time varying during the detection interval. A general optimum processor for the doubly composite detection situation is developed. The sequential processing technique results in a receiver design which provides practical memory requirements for arbitrary observation interval lengths and also exhibits adaptive or learning characteristics. Applications of the general theory to both the time invariant and time varying cases are considered. In addition, the adaptive nature of the sequential receiver is demonstrated both analytically and by digital computer simulation. For the time varying situation, the general theory is applied to develop a sequential optimum receiver for the detection of a certain signal in noise with uncertain and time varying parameters. The sequential realization results in a receiver which utilizes a practical memory size and attempts to track the varying parameters of the noise. These general results are then applied to the problem of detecting a signal in noise of varying level. The performance for this latter case is evaluated in terms of ROC curves. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1968
- Accession Number
- AD0672920
Entities
People
- Ronald L. Spooner
Organizations
- University of Michigan