Detection and estimation of signals in noise when one or both are non-Gaussian

An examination is made of the basic principles and results of the theory of detection and estimation of signals in noise, which is not limited to the condition that the useful signal and noise be Gaussian and that the noise be additive. Formulas are obtained [(23) and (25)] for likelihood ratios which are useful in the Markovian as well as in the non-Markovian case. The results are specialized for the case of diffusion noise and fixed but unknown signal parameters, when it is possible to effectively utilize the theory of conditional Markov processes. Estimation by the quasi-linear theory is also discussed, the applicability of which is limited not by the Markovian condition, but by the condition of high a posteriori accuracy. In conclusion, a generalization is given of the theory for the case of adaptive detection and estimation, when the a priori information is replaced by learning. In this case, application of the theory of conditional Markov processes makes it possible to obtain, besides the previous equations of Gaussian approximation, similar equations for the unknown parameters.