Oleg V. Chernoyarov

On parameter estimation for cusp-type signals

We consider the problem of parameter estimation by continuous time observations of a deterministic signal in white Gaussian noise. It is supposed that the signal has a cusp-type singularity. The properties of the maximum-likelihood and Bayesian estimators are described in the asymptotics of small noise. Special attention is paid to the problem of parameter estimation in the situation of misspecification in regularity, i.e., when the statistician supposes that the observed signal has this singularity, but the real signal is smooth. The rate and the asymptotic distribution of the maximum-likelihood estimator in this situation are described.

Statistical analysis of fast fluctuating random signals with arbitrary-function envelope under breach of consistency of discontinuous information parameter estimate

We carried out the synthesis and analysis of quasi-likelihood detector and measurer of a highfrequency random pulse with arbitrary-function envelope, unknown appearance time and inaccurately known duration. We introduced the asymptotically exact method of theoretical calculation of detection and estimation characteristics including anomalous errors effect, if conditions of the decision statistics regularity and consistency of discontinuous parameter estimate are not fulfilled. It has allowed us to define the efficiency of presented receivers analytically. By methods of statistical computer modeling we corroborated the adequacy of the considered analytical approach of the statistical analysis of discontinuous random pulse signals, and also we established its applicability borders for considered tasks.

On misspecifications in regularity and properties of estimators

The problem of parameter estimation by the continuous time observations of a deterministic signal in white gaussian noise is considered. The asymptotic properties of the maximul likelihood estimator are described in the asymptotics of small noise (large siglal-to-noise ratio). We are interested by the situation when there is a misspecification in the regularity conditions. In particular it is supposed that the statistician uses a discontinuous (change-point type) model of signal, when the true signal is continuously differentiable function of the unknown parameter.

Estimation of the number of orthogonal signals with unknown parameters

Algorithms for estimation of the number of signals with unknown amplitudes and several non-energy parameters are synthesized on the basis of the modified maximum likelihood method. Asymptotic values of the probabilities of the error in estimation of the signal number are determined. The effect of a reduced volume of the a priori domain of possible values and the dimensionality of the vector of unknown non-energy parameters on the quality of operation of the algorithms for estimation of the number of signals is investigated.

Radio waves attenuation model for a ray approximation

We considered the modeling problem of radio wave propagation processes indoors. We generalized all physical phenomena influencing the result. We also suggested the model for the radio-wave attenuation calculation and studied a radiowave attenuation into lossy dielectric. As a result, we obtained the analytical expressions that makes it possible to calculate a radio wavefront (angle of refraction), in case of its passing from ideal to lossy dielectric and with the attenuation coefficient caused by absorption. Besides, we output the asymptotic formula for the definition of an angle of refraction and calculated the dependences of an angle of refraction and an attenuation coefficient on an angle of incidence for some building materials.

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.

Estimating the Instants of Appearance and Disappearance of an Optical Pulse with the Rectangular Intensity Profile of an Unknown Height

The quasi-likelihood, maximum-likelihood, and quasi-optimal algorithms for estimating the instants of appearance and disappearance of an optical pulse with the rectangular intensity profile of an unknown height are synthesized and analyzed. The losses in estimation accuracy due to the a priori unknown intensity of the optical pulse are found.

Simulation of Discrete Source of Relative Signal Time Delays Measurement Errors in Multiposition Passive TDOA System

We present the software realization of the discrete source of errors which can be applied while simulating the procedures for the signal detection and the determination of radio source coordinates in multiposition passive time difference of arrival systems. We introduce and validate the probabilistic models of errors occurring during signal time delays measurements performed by such systems.

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.