Application of conditional averaging to time delay estimation of random signals

Abstract

The article presents the possibilities of using the function of conditional average value of a delayed signal (CAV) and the function of conditional average value of a delayed signal absolute value (CAAV) to determine the time delay estimation (TDE) of random signals. For discrete CAV and CAAV estimators, the standard uncertainties of the estimation of function values at extreme points and the standard uncertainties of the TDE were given and compared with the corresponding uncertainties for the direct discrete cross-correlation function (CCF) estimator. It was found that the standard uncertainty of TDE for CAV is lower than for CCF independent of signal-to-noise ratio

Measuring the Moment and the Magnitude of the Abrupt Change of the Gaussian Process Bandwidth

“…In order to establish the borders of applicability for the found approximate formulas for the characteristics of the synthesized maximum likelihood estimation algorithm, we demonstrate the statistical computer simulation of the measurer (5)…”

“…Let us find the characteristics of the measurer (5). For this purpose, we move from MLEs m λ , m Ω (5) to normalized…”

“…The problem of the statistical analysis of the abrupt change (i.e., instantaneous jumping) of the parameter values of a random process at some moment in time is studied in a number of papers [1]- [5]. In certain publications, the statement of this problem is accompanied by the assumption that the observable data realization has a normal distribution.…”

“…In certain publications, the statement of this problem is accompanied by the assumption that the observable data realization has a normal distribution. As a rule, the additional restrictions are also imposed referring to the processed samples being uncorrelated (and therefore independent) [1], [2] or to the specified model classes of the information signal [2]- [5], etc.…”

Measurements of Dispersed Phase Velocity in Two-Phase Flows in Pipelines Using Gamma-Absorption Technique and Phase of the Cross-Spectral Density Function

“…The best known one is the classic method of cross-correlation [17,18]. The other methods include a correlation analysis with the Hilbert transform [19], Hilbert-Huang transform [20], the method of the phase of cross-spectral density [21], differential and combined methods [18,22,23], and the methods using the conditional averaging of the signals [24].…”