A Note on Least-Squares Estimates from Likelihood Ratios

In another paper we have shown that the likelihood ratio for detecting the presence of a finite-variance signal in additive white Gaussian noise can be expressed in terms of the causal least-squares estimate of the signal. In this paper a converse relation is derived. Comparisons are made with some related but nontrivially different results in the discrete-time case that were recently discussed in this journal by Esposito.