Alexandra V. Salnikova

Detection and estimation of abrupt changes in Gaussian random processes with unknown parameters

In this study work we propose technically simple way of definition of the abrupt change in the power parameters of the band Gaussian processes, with the measurement of their values before and after the imbalance and in the conditions of parametric prior uncertainty. For this purpose, we found new approximations of solving statistics under various hypotheses, and performed their maximization in case of the unknown parameters, and also developed block diagrams of the corresponding detectors and measurers in the form of relatively simple single-channel devices. With help of the analytical (local Markov approximation) and statistical computer modeling methods, we established that offered detectors and measurers are efficient, and theoretical formulas for their characteristics well conform to the corresponding experimental data in a wide range of parameter values of the analyzed process.

The estimate of the dispersion of the fast-fluctuating stationary Gaussian random process

In this study a new technique is presented for obtaining the single-channel estimate of the dispersion of the fast-fluctuating Gaussian random process with a free-form spectral density. This technique is the generalization of the discriminator-based method for the estimation of the signal parameter. It is established that the introduced estimate is the asymptotically unbiased and effective one. The facilities for its both analogue and digital hardware implementations are demonstrated.

On probability of the Gaussian random processes crossing the barriers

General expressions for the distribution functions of the absolute maximum of differentiable and nondifferentiable non-stationary Gaussian process are presented. It is then established that in particular cases the suggested asymptotic approximations are able to describe the true distributions under a wide range of the random processes parameters values.

The Fast Ray Tracing in Calculating the Geometrical Optics Reflected Field

We consider the problem of the computer-aided construction of geometrical optics electromagnetic wave propagation paths (ray tracing). We indicate the disadvantages of widely applied Shooting and Bouncing Rays method. We also provide the examples of its software implementation. As opposed to the employed approaches, the method and the algorithm synthesized on its basis are introduced for the reflected ray tracing where the search process is implemented faster and there are no disadvantages inherent in their common counterparts.

The comparative analysis of estimates of the time discontinuous parameter of the random pulse synthesized using Bayesian and maximum likelihood approaches

The algorithms for optimal and quasi-optimal estimation of the arrival time of a Gaussian random pulse with a priori known and inaccurately known duration, which is observed against the background of white Gaussian noise, is synthesized. The comparative analysis of the Bayesian (quasi-Bayesian) and maximum likelihood (quasi-likelihood) measurers of the arrival time is performed. The results of the statistical computer simulation of estimation algorithms are presented.