Optimal, causal, simultaneous detection and estimation of random signal fields in a Gaussian noise field

Two methods are presented for simultaneously detecting a random signal field and estimating its Markovian parameters in the qq prurience of a white Gaussian noise field. The first method provides the Neyman-Pearson decision rule for determining the absence-or-presence of the signal and the maximum {em a posteriori} likelihood estimators of the parameters. The second provides the Bayes decision rule for the absence-or-presence of the signal and the minimum mean-square error estimators of the parameters. Both methods allow continual causal detection and estimation based on the continuous space-time data, and their detection and estimation statistics are given in terms of a single statistic, which is the solution of a certain stochastic integral equation. Furthermore, an approximate scheme is developed for recursively generating this statistic by using spatially and temporally sampled data.