Home – Home – Jornals – Avtometriya 2003 number 1

Quaternion signals specifying a group point object located in a three-dimensional space are considered. A similarity measure of these signals is introduced in the form of their scalar product. A quaternion matched filter is synthesized. Using the minimum distance criterion, the problem of recognizing completely known signals, signals with an unknown initial quaternion and unknown rotation angle is solved.

Exact formulas for the characteristics of detecting an inhomogeneous image with unknown area are derived by the maximum likelihood method.

A nonparametric method for time-frequency localization of broadband signal energy is developed on the basis of optimization problem solution with the l2-norm as the objective function. The method is effective in significant a priori uncertainty conditions and improves the performance of classical spatial spectral analysis methods and high-resolution methods.

Within the approach of physical mesomechanics of materials, a new method is proposed for numerical evaluation of surface-degradation processes (due to plastic deformation, electromigration, fatigue failure, etc.). Numerical characteristics of wavelet spectra and their two-dimensional graphical representation can be used both to estimate the quality and improve optical images (at the stage of preprocessing) and to analyze changes that occur under external loads applied to examined materials (at the stage of image analysis (recognition)).

A method for random variable set analysis is proposed for problems of reconstruction of stochastic dependences and pattern recognition. It is based on estimating the distribution functions of elements of the sets and their transforming by means of nonparametric procedures. Asymptotic properties of the models are investigated. Obtained results are of actual significance in processing of large bodies of statistic data.

The problem of optimal measurement data processing with singular errors present in the measurements is solved on the basis of one-step and multistep least squares methods. The obtained solutions ensure decomposition of the problems considered since they do not assume the conventional state space extension. Efficiency of the approach developed is illustrated by an example.

A hybrid algorithm for estimating sea surface current vectors from sequential satellite images is developed based on both the contour method and the relaxation labeling approach. Results obtained by the relaxation-contour algorithm show its advantage over contour-only estimates of current vectors. Using synoptic technique, these estimates are compared with those obtained by a manual procedure and also with the data of acoustic Doppler current profiler (ADCP), and reveal good agreement.

Nonparametric estimators of the spectral density of a discrete-time stationary random process are considered. Refined recommendations concerning construction and calculation of the classical periodogram estimator are formulated. The possibility of using the proposed constructions as impulse response functions of discrete-time flat-top low-pass filters is shown.

An algorithm for discrete spectral signal analysis in the modified Sobolev space W¹₂ is designed. Identity of the concepts of signal spectra in the spaces W¹₂ and L₂ is proved. It is shown that the accuracy of representing a discrete signal spectrum in the space W¹₂ is higher than that in the space L₂ if the sampling rate is less than the Kotelnikov frequency.

The Kiefer-Wolfowitz procedure of searching for the continuous convex function extreme is found by solving the problem of stochastic optimal control with experiments under continuous measurements with additive errors. Analytical solution properties are determined.

Relationships between smoothing windows and wavelet transform basis are obtained. A modification of trend estimator with an additional addend compensating for the bias and minimizing the mean square error of the estimator is proposed. It is shown that the bias compensation is a wavelet transform of the process observed. An algorithm for trend estimator calculation is designed.

A mathematical approach to classification of chemical compounds by the degree of toxicity in acute experiments is considered. The approach is evaluated on a wealth of experimental data and scientifically substantiated intervals of chemical compounds danger classes are established.