Quasi-Optimal and Optimal Estimates of the Amplitude of the Unlocalized Signal

Abstract

This paper focuses on the synthesis and the analysis of the algorithms for estimating the amplitude of a free-form video pulse with the unknown moments of appearance and disappearance, since such algorithms are expected to provide overcoming the prior parametrical uncertainty. Hardware and/or software implementations as well as performance of quasi-likelihood, maximum likelihood, and quasi-optimal estimation algorithms are also tested. One of the objectives of this paper is to find the closed analytical expressions for the biases and the variances of the introduced estimates, their accuracy increasing with signal-to-noise ratio. In order to obtain the quasi-likelihood estimate of the amplitude, instead of the unknown moments of appearance and disappearance, their expected values are used. It allows designing a measurer that is simply implemented technically. However, in this case, the loss in accuracy of the resulting estimate still occurs due to the difference between the expected and the real time parameters of a pulse. In order to improve the accuracy of the estimate, the adaptive maximum likelihood algorithm can be applied though it is rather complex in terms of technical implementation. In this paper, the quasi-optimal amplitude estimation algorithm that helps to develop both effective and technically simpler implemented measurer is proposed. It is not optimal, but its characteristics coincide with the corresponding characteristics of the adaptive maximum likelihood estimate under the big signal-to-noise ratio, as confirmed by the results of statistical simulation. The influence of prior ignorance of the time parameters on the quality of the signal amplitude estimate is also determined.