Optimal adaptive multidimensional-time signal energy estimation on the background noise

TL;DR

This paper develops an adaptive method for optimally estimating the energy of a multidimensional signal observed in noise, ensuring asymptotic optimality in the classical L(2) norm.

Contribution

It introduces a novel adaptive approach for energy estimation that is asymptotically optimal in the classical norm for signals observed in noisy environments.

Findings

The method achieves asymptotic optimality in energy estimation.

The approach is adaptive and applicable to multidimensional signals.

The technique is effective in the presence of background noise.

Abstract

We construct an adaptive asymptotically optimal in the classical norm of the space L(2,\Omega) of square integrable random variables the Energy estimation of a signal (function) observed in some points (plan of experiment) on the background noise.