Best integer equivariant estimation for elliptically contoured distributions

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Abstract

This contribution extends the theory of integer equivariant estimation (Teunissen in J Geodesy 77:402–410, 2003) by developing the principle of best integer equivariant (BIE) estimation for the class of elliptically contoured distributions. The presented theory provides new minimum mean squared error solutions to the problem of GNSS carrier-phase ambiguity resolution for a wide range of distributions. The associated BIE estimators are universally optimal in the sense that they have an accuracy which is never poorer than that of any integer estimator and any linear unbiased estimator. Next to the BIE estimator for the multivariate normal distribution, special attention is given to the BIE estimators for the contaminated normal and the multivariate t-distribution, both of which have heavier tails than the normal. Their computational formulae are presented and discussed in relation to that of the normal distribution.

Original languageEnglish
Article number82
Pages (from-to)1-10
Number of pages10
JournalJournal of Geodesy
Volume94
Issue number9
DOIs
Publication statusPublished - 2020

Keywords

  • Best integer equivariant (BIE)
  • Best linear unbiased estimation (BLUE)
  • Contaminated normal
  • Elliptically contoured distribution (ECD)
  • Global navigation satellite system (GNSS)
  • Integer equivariant (IE) estimation
  • LAMBDA method
  • Multivariate normal
  • Multivariate t-distribution

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