Correlation function estimation by a polarity method using stochastic reference signals

1968 ◽  
Vol 14 (6) ◽  
pp. 796-801 ◽  
Author(s):  
H. Berndt
Keyword(s):  
Correlation Function ◽  
Function Estimation ◽  
Reference Signals

Convergence of distributions of correlation function estimation functionals

1979 ◽  
Vol 18 (4) ◽  
pp. 474-480
Author(s):  
A. V. Ivanov ◽  
N. N. Leonenko
Keyword(s):  
Correlation Function ◽  
Function Estimation

scholarly journals On the Correlation Function of an Arbitrary Distributed Continuous Markov Process

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Correlation Function ◽  
Diffusion Coefficients ◽  
Function Estimation ◽  
Stationary Probability Distribution ◽  
Nonlinear Stochastic Differential Equations ◽  
Continuous Markov Process ◽  
Current Value ◽  
Non Gaussian ◽  
The Given ◽  
And Diffusion

Continuous Markov processes widely used as a tool for modeling random phenomena in numerous applications, can be defined as solutions of generally nonlinear stochastic differential equations (SDEs) with certain drift and diffusion coefficients which together governs the process’ probability density and correlation functions. Usually it is assumed that the diffusion coefficient does not depend on the process' current value. Sometimes, in particular for presentation of non- Gaussian real processes this assumption becomes undesirable, leads generally to complexity of the correlation function estimation. We consider its analysis for the process with arbitrary pair of the drift and diffusion coefficients providing the given stationary probability distribution of the considered process.

scholarly journals Statistical Characteristics of Signal Parameter Estimation by Normalized Correlation Function Maximization

2018 ◽  
pp. 15-22
Author(s):  
I. V. Gogolev ◽  
G. Yu. Yashin
Keyword(s):  
Correlation Function ◽  
Colored Noise ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Schwarz Inequality ◽  
Nuisance Parameters ◽  
Statistical Characteristics ◽  
Function Estimation ◽  
Signal Parameter ◽  
White And Colored Noise

In this paper differences between Fisher Information Matrix (FIM) and inverse covariation matrix of normalized correlation estimations for white and colored noise are investigated. It’s shown that implementation of normalized correlation function estimation leads to modification of maximum likelihood estimation FIM elements, so in case of arbitrary energy affected parameter vector, variance of estimation by normalized correlation function maximization is not equal to Cramer–Rao lower bound. Statistical characteristics of joint Doppler stretch and delay estimation by maximization of normalized correlation function for signal with nuisance parameters are derived in this paper. It’s shown that normalized correlator is equal to wideband ambiguity function, but this method of estimation follows from Cauchy–Schwarz inequality without using energy conservation assumptions. Besides, it is proved that estimation of Doppler stretch and delay by normalized correlation function or WBAF of signal with random initial phase and gain is asymptotically unbiased and effective.

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