Statistical estimation of the parameters of a moving source from array data
type: Item
instance of: scholarly article
title: Statistical estimation of the parameters of a moving source from array data
zbMATH Open document ID: 0604.62095
author: Shean-Tsong Chiu
published in: The Annals of Statistics
publication date: 1986-01-01T00:00:00Z
review text: For the model \(X_ 1(t)=S(t)+e_ 1(t)\); \(X_ 2(t)=S(a_ 0+b_ 0t)+e_ 2(t)\), with known 'shifted signal', given by \(S(a+bt)\), a,b parameters and e(t) noise, the problem is to estimate the variable time delay, i.e. (a,b). One determines \((\hat a,\hat b)\) which maximizes the criterion: \[ Q_ T(a,b)=\sum_{| s| <T/2}\psi (\omega_ s)\underline d^ T_{X_ 2}(\omega_ s)\underline d^ T_{X_ 1}(- \omega_ s/b)\exp (-i\lambda a) \] where \(\underline d^ T_ s(\omega)\) is the Fourier transform of the signal S(t) at frequency \(\omega\), \(\psi\) is a weighting (empirical) function, \(\omega_ s=2\pi s/T\), \(s=0,\pm 1,... \). Under regularity conditions, it is proved that the derived estimate is consistent and asymptotically normal. Estimates of the spectra are also obtained, and applications to seismology are discussed in detail.
Mathematics Subject Classification ID: 62M99
Mathematics Subject Classification ID: 62M15
Mathematics Subject Classification ID: 60G35
Mathematics Subject Classification ID: 86A15
Mathematics Subject Classification ID: 74L05
zbMATH DE Number: 3976161
zbMATH Keywords: linear time delay model
zbMATH Keywords: simulations
zbMATH Keywords: periodogram
zbMATH Keywords: spectrum
zbMATH Keywords: Gaussian process
zbMATH Keywords: estimation criterion
zbMATH Keywords: Doppler effect
zbMATH Keywords: consistency
zbMATH Keywords: shifted signal
zbMATH Keywords: Fourier transform
zbMATH Keywords: asymptotically normal
zbMATH Keywords: seismology
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176349938
OpenAlex ID: W2050266221
DOI: 10.1214/AOS/1176349938
description: scientific article; zbMATH DE number 3976161