Determining the Number of Sinusoids Measured with Errors

This paper describes how a priori information about the signal parameters can influence the accuracy of estimating the number of these signals. This study considers sinusoidal signals and it is supposed that the parameters (amplitudes, frequencies and phases) of the received signals are known up to a certain error. The error probability of the maximum likelihood estimation of the number of sinusoids is calculated under this condition

Simulation of the measurer of the time of appearance and the average power of the random pulse signal

The maximum likelihood measurer is considered of the time of appearance and the average power of the fast fluctuating Gaussian band pulse against Gaussian white noise. The possibilities of its practical implementation are demonstrated and its accuracy characteristics are determined. By statistical simulation methods, the experimental values of biases and variances of the resulting estimates are found. The error ranges of the theoretical formulas describing the measurer performance are established. There have been determined the conditions of high a posteriori accuracy for the measurer operation, that is, such signal-to-noise ratios above which the anomalous errors in estimating the pulse time parameter are practically non-existent

The statistical properties of the probabilistic distributions generated by gamma statistics

We show that hyperexponential and hyper-Erlan

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 maximum likelihood estimator are described in the asymptotic of small noise (large signal-to-noise ratio). We are interested in 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

A simple method for increasing the equal-amplitude non-uniform linear thinned array directivity

Calculating the distances between the elements of the non-uniform array is usually carried out through its parametric optimization using the computational algorithms. In this paper, a simplified method is introduced and tested for determining the distances between the neighboring elements of the equal-amplitude non-uniform linear array that provides a significant increase in the array directivity while preserving the array thinning. The developed method allows both choosing the element spacing on the non-uniform linear array aperture and ensuring an increase in the array directive gain without applying the computational algorithms

Detection and measurement of the fast-fluctuating Gaussian random process dispersion abrupt change

We introduce the technically simple approach to the determination of the abrupt change of the unknown dispersion of the high-frequency fast-fluctuating Gaussian random process against white noise with an unknown spectral density. For this purpose, we determine new approximations of the decision statistics for various hypotheses, we carry out their maximization on unknown parameters, and we develop the block diagrams for the corresponding detector and measurer in the form of the comparatively simple single-channel units. For the analytical analysis of the performance of the synthesized algorithms, the asymptotically exact expressions for their characteristics, specifically - type I and type II error probabilities (when an abrupt change point is detected) and conditional biases and variances of the estimates (when measuring the parameters of the analyzed random process), are obtained by means of local Markov approximation method. We also illustrate a new procedure for determining the distribution law and the central moments of the estimate of the discontinuous parameter (abrupt change point), with an allowance of anomalous effects. The experimental testing of the presented theoretical results is implemented by the methods of statistical computer simulation

The distribution of the absolute maximum of the discontinuous stationary random process with Raileigh and Gaussian components

The purpose of this research is to find the asymptotically exact expressions for the distribution function and for the probability that the absolute maximum of the sum of statistically independent homogeneous Gaussian and Rayleigh random processes with nondifferentiable covariance function will exceed the specified threshold. In this study, the applicability boundaries of the introduced theoretical formulas are also determined by means of statistical simulation. The recommendations are presented concerning the application of the obtained expressions depending on the observation interval length and the interrelation of Gaussian and Rayleigh components of the analyzed random process. © 2019, International Association of Engineers. All rights reserve

Estimation of the position and time of emission of a source

We consider the problem of the estimation of the position on the plane and of the moment of beginning of emission of a source by observations from K detectors on the plane. We propose the conditions of regularity and identifiability, which allow us to use two general theorems by Ibragimov and Khasminskii and to describe the asymptotic behavior of the maximum likelihood and Bayes estimators. Then we propose the construction of a linear estimator of unknown parameters and study its properties in slightly more general situation. Special attention is payed to condition of identifiability

Secrecy of communications in data transmission by impulses with unknown moments of appearance and disappearance

We carried out a comparative analysis of the algorithms for detecting a rectangular impulse against Gaussian white noise under either authorized or unauthorized access to the tr ansmitted data. We presupposed that for data transmission the binary communication system is used and that the useful information in the data is whether the signal is present or absent. The case is that unauthorized access by the outsider takes place in the situation when the signal parameters are completely or partially unknown. We then define the degree of the transmitted data secrecy by the secrecy ratio determining how highly the threshold signal-to-noise ratio increases when there is the unauthorized access instead of the authorized one