On relations between detection and estimation of discrete time processes

It is shown that, for discrete-time processes, both the causal minimum variance estimate of an arbitrary random signal process corrupted by additive white Gaussian noise, and the associated error covariance matrix, may be obtained, by simple formulas, from the likelihood ratio which arises in the optimum detection of the same signal. As a consequence of this result, the optimum detector is amenable to a causal estimator-correlator type interpretation. An example is worked out to illustrate the relations obtained