Best integer equivariant estimation for elliptically contoured distributions

Teunissen, P.J.G.

doi:10.1007/s00190-020-01407-2

Best integer equivariant estimation for elliptically contoured distributions

Title

Best integer equivariant estimation for elliptically contoured distributions

Author

Teunissen, P.J.G. (TU Delft Mathematical Geodesy and Positioning; Curtin University of Technology; University of Melbourne)

Date

2020

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.

Subject

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

To reference this document use:

http://resolver.tudelft.nl/uuid:c0799aa2-99fc-4340-8867-07b95f11386b

DOI

https://doi.org/10.1007/s00190-020-01407-2

ISSN

0949-7714

Source

Journal of Geodesy, 94 (9), 1-10

Part of collection

Institutional Repository