A Monte-Carlo Method for Locally Optimal Quantized Merging of Correlated Detection Statistics

Abstract

In the detection of unknown deterministic signals in noise, consideration may be restricted to statistics that are sufficient for detection of certain classes of signals. Here, the case of correlated statistics that are assumed to have analytically intractable probability distributions is considered. A locally optimal quantized detector that merges the multivariate sufficient statistics is proposed. Quantization is required for implementation, which utilizes a Monte-Carlo evaluation of the levels minimizing the mean squared error for a specific partitioning of the range space of the sufficient statistics. Performance improvement over the individual statistics and a test using the maximum of the individual statistics is illustrated with an example.