Measurability conditions of the signal parameter for a given prior knowledge

Abstract

It is assumed that in the physical phenomenon under investigation a one-dimensional signal is chosen as a measurement subject and the estimation of the numerical value of a certain parameter of such a signal is the main goal of all undertaken activities. In the paper, the formal framework and also the methodology are presented by which all the available knowledge about the investigated signal may be taken into account. First, the signal is modeled as a point in the multidimensional number space. Next, the entire available signal knowledge is broken down into a set of individual information items and each of them is modeled as a specific constraint introduced into such signal space, which leads to a geometrical interpretation. Consequently, the measurement of any parameter of the signal may be considered as acquiring the additional information item and may be modeled consistently with other items of the prior knowledge. Then measurability conditions of an interesting signal parameter with an acceptable value of the final uncertainty, have been formulated in the form of the following demands: (1) precise enough definition of the estimated parameter, guaranteeing parameter repeatability for the available knowledge; (2) sufficient stationarity of the investigated signal; and (3) appropriate manner and accuracy of the signal investigation for the available knowledge. The last demand has been discussed in detail: appropriate notions are introduced, necessary for the description and analysis of the information gathering process and for the information usability evaluation. Finally, an example of the signal mean-square value uncertainty analysis was presented for four cases of progressive signal knowledge.