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On a class of nonlinear estimation problems

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1 Author(s)

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 x(t) , where x(t) = aS(t) + N(t) mbox{0 \leq t \leq T \leq \infty } . Here, S(t) and N(t) 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.

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IEEE Transactions on Information Theory  (Volume:10 ,  Issue: 4 )