Measuring the Moment and the Magnitude of the Abrupt Change of the Gaussian Process Bandwidth

Abstract

The maximum likelihood algorithm is introduced for measuring the unknown moment of abrupt change and bandwidth jump of a fast-fluctuating Gaussian random process. This algorithm can be technically implemented much simpler than the ones obtained by means of common approaches. The technique for calculating the characteristics of the synthesized measurer is presented and the closed analytical expressions for the conditional biases and variances of the resulting estimates are found using the additive local Markov approximation of the decision statistics. By statistical simulation methods, it is confirmed that the presented measurer is operable, while the theoretical formulas describing its performance well approximate the corresponding experimental data in a wide range of the parameter values of the analyzed random process.

Detecting an Unknown Abrupt Change in the Band Center of the Fast-Fluctuating Gaussian Random Process

“…In Fig.2., by solid lines the theoretical dependences are presented of the false alarm probability α upon the threshold c calculated by the formulas (18), (20), (22) In Fig.3., by solid lines, the theoretical dependences are presented of the missing probability β upon the value of the parameter q (11) calculated by the formula (38). The threshold value c is calculated by means of (18), (20), (22) according to the Neumann-Pearson criterion for the chosen level of false alarm probability that is 6 10 − in this case. Curve .…”

“…The expression (6) . And it should be noted that the physically realizable filter corresponding to it can always be implemented with the required accuracy [7].…”

“…[1]- [5]. Often enough, the observed random process is the fast-fluctuating one and has the same intensity within the working frequency band [6]- [9]. As it is shown in [8], [9], the introduction of the conditions of the fast fluctuations and the uniform spectral density of the random process allows us to significantly simplify the structure of the synthesized processing algorithms, especially in the presence of the parametric a priori uncertainty.…”

Development of Key Indicators for Power Supply Companies

“…Despite the efforts being made to fight debtors, energy companies are unable to obtain the required gross revenues included in tariffs, which results in a shortage of investment funds. One of the possible methods for assessing the risks of non-payment can be the use of probabilistic methods and statistical tools, such as those described in (Maksim et al, 2017;Salnikova et al, 2017;Chernoyarov et al, 2019). As a result, non-payments for used energy resources lead to higher prices for responsible payers, what generally causes a slowdown in economic growth in all regions of Russian Federation.…”