On a class of nonlinear estimation problems

The \´noise-in-noise\´ problem is viewed as an estimation problem rather than a detection problem. Specifically, this is the problem of estimating the random scale parameter \´a\´ from observations , where . Here, and are Gaussian processes with known covariances. The optimal mean-square estimator is nonlinear, and the bulk of the paper is concerned with methods for determining it. In particular, a computer algorithm based on steepest descent, is developed. Also, the relationship to the detection problem, particularly the so-called singular cases, is examined.