An algorithm for estimating the energy of a radio pulse when measuring a superconducting system qubit–resonator consisting of a superconducting resonator and a coupled qubit is proposed. The algorithm is based on the use of complete sufficient statistics and does not require a priori information about the level of additive white Gaussian noise in the process, as well as about the amplitude, initial phase, and temporal position of the radio pulse. The estimates are effective and consistent. The efficiency of the algorithm is estimated by means of computer simulation.

Digital algorithms for checking the functionality and measuring critical current of SIS-type Josephson junctions are proposed, taking into account the features of measurements under conditions of fluctuation noise and suitable for implementation in an automatic mode. A piecewise line approximation of the voltage-current characteristic is used following the typical voltage-current characteristic. To obtain the essential statistical information about the random component of the measurement results, the excitation of the Josephson junction by a periodic testing sequence of triangular current pulses was used. For a workable Josephson junction, there is a voltage jump in the vicinity of the critical current for each rising slope of the exciting pulses. The statistics of the threshold crossings on each pulse rising slope of the test pulse sequence are used to estimate the critical current. An efficient estimate of the critical current was obtained by using the maximum likelihood method. The results of statistical modeling confirm the correctness of using this method in the study of superconducting structures. The use of statistical methods makes it possible to improve technical control during serial production of Josephson junctions and debug the appropriate manufacturing technology.

the Proposed statistical model of the measuring signals in the system temporary reflectometry on the basis of which with the help of complete sufficient statistics the estimates of the parameters of the reflected signal. The imitating modeling which has confirmed a solvency and effectiveness ratings. On the basis of the principle of unbiased the synthesis of the unbiased uniformly most powerful detection algorithm parameter change of the slope of the linearly varying signal. Simulation has shown the efficiency of the algorithm and the feasibility of its application for the detection of small changes in the parameters of the measuring signals and systems temporal reflectometry.

The method was supposed to obtain an effective estimation of spectral line location parameter within gamma quanta energetic spectrum. The method is based on numerical solving of an equations set obtained by the maximum likelihood method applied to sample data functional description. The numerical modeling was carried out to prove the efficiency of the method supposed. The invariance to the background radiation level was shown. This feature is provided by the background statistical nature taken into account in sample data functional description.

A new method has been proposed to improve the procedure of gamma spectra interpretation. The procedure of spectra decomposing by the orthonormal basis and the way to obtain single spectral peak contribution have been developed.

The proposed technique significantly simplifies interpretation of secondary gamma radiation energy spectra obtained when specimen are irradiated with gamma quanta. The procedure of representation of the spectrum in the orthonormal basis is developed as well as the method of extracting individual contributions of separate spectral lines.

An algorithm for detecting spectral peak absorption in the secondary radiation from an object containing nitrogen compounds is proposed. The algorithm is based on the statistical invariance principle and has the property of automatically adjusting to signal-noise parameters. The algorithm was tested by simulation modeling and was shown to be applicable to real secondary-radiation spectra. The algorithm and the associated experimental hardware make it possible to implement a fundamentally new method for the automatic detection of nitrogen-containing compounds.