Best integer equivariant estimation for elliptically contoured distributions

Journal article (2020)

Authors

P.J.G. Teunissen University of Melbourne, Mathematical Geodesy and Positioning - CEG , Curtin University of Technology
Research Group
Mathematical Geodesy and Positioning (CEG) (TU Delft)
Copyright: © 2020 P.J.G. Teunissen
DOI: https://doi.org/10.1007/s00190-020-01407-2
Best linear unbiased estimation (BLUE) Global navigation satellite system (GNSS) Multivariate t-distribution Best integer equivariant (BIE) Contaminated normal Elliptically contoured distribution (ECD) Integer equivariant (IE) estimation LAMBDA method Multivariate normal
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Published Date

2020

Language

English

Faculty

Civil Engineering & Geosciences

Department

Geoscience and Remote Sensing

Research Group

Mathematical Geodesy and Positioning

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.