Partially Known Signals and Noise 1.2 2003/06/13 2003/09/15 13:43:55.697 GMT-5 Don Johnson dhj@rice.edu Don Johnson dhj@rice.edu Eileen Krause erkrause@rice.edu Kyle Clarkson kclarks@rice.edu Elizabeth Gregory lizzardg@rice.edu Kevin Duh kevinduh@rice.edu Mariyah Poonawala mariyah@rice.edu Matthew Jeanes mjeanes@rice.edu Jeffrey Silverman jsilv@rice.edu Rather than assuming that aspects of the signal, such as its amplitude are beyond any set of justifiable assumptions and are thus "unknown," we may have a situation where these signal aspects are "uncertain." For example, the amplitude may be known to be within ten percent of a nominal value. If the case, we would expect better performance characteristics from a detection strategy exploiting this partial knowledge from one that doesn't. To derive detectors that use partial information about signal and noise models, we apply the approach used in robust model evaluation: find the worst-case combination of signal and noise consistent with the partial information, then derive the detection strategy that best copes with it. We have seen that the optimal detection strategy is found from the likelihood ratio: no matter what the signal and noise model are, the likelihood ratio yields the best decision rule. When applied to additive Gaussian noise problems, the performance of the likelihood ratio test increases with the signal-to-noise ratio of the difference between the two hypothesized signals. Since we focus on deciding whether a particular signal is present or not, performance is determined by that signal's SNR and the worst-case situation occurs when this signal-to-noise ratio is smallest. The results from robust model evaluation taught us to design the detector to the worst-case situation, which in our case roughly means employing matched filters based on the worst-case signal. Employing this approach results in what are known as robust detectors.