Analytic example of a Schweppe likelihood-ratio detector

A low-dimensional test problem with a known solution is used to verify various computer implementations of F.C. Schweppe´s likelihood detector (1965). In this case a closed-form solution is provided for a Schweppe likelihood detector in terms of an intermediate Kalman filter, as utilized in its implementation, for detecting the presence of a two-state signal model in Gaussian white noise. The associated error probabilities are also evaluated following a procedure that utilizes optimized Chernoff-like bounds for a tight approximation. A methodology is demonstrated for appropriately setting the decision threshold for this example as a tradeoff against allowable observation time. By using this or similar examples, certain qualitative and quantitative aspects of the software implementation can be checked for conformance to anticipated behavior as an intermediate benchmark, prior to modular replacement of the various high-order matrices appropriate to the particular application