Projected BIE
a new unbiased minimum variance estimator for the mixed-integer GNSS model
Peter J.G. Teunissen (The Hong Kong Polytechnic University, TU Delft - Civil Engineering & Geosciences, Curtin University)
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Abstract
Mixed-integer (MI) estimation theory is fundamental to carrier-phase GNSS, where real-valued parameters are coupled with integer ambiguities. The class of integer-equivariant (IE) estimators is the largest class that properly respects this structure. Its unbiased minimum mean-squared-error member is the best integer equivariant (BIE) estimator, whose precision is never worse than that of the BLUE and whose performance is often close to that of integer least-squares. Its practical drawback, however, is the need to evaluate an infinite sum. We introduce the projected-BIE (PBIE) estimator, a new unbiased minimum-variance IE-estimator with a finite representation. It is obtained by restricting the admissible periodic corrections in the canonical IE-representation and solving the resulting optimization problem. PBIE is valid for general observation distributions, has an exactly computable variance matrix, and is obtained from normal equations. We further show that PBIE has a dual optimality property: it is both minimum-variance in its class and the closest estimator in that class to the BIE. For normally distributed data, PBIE simplifies considerably and can be computed efficiently from the BLUE of the integer ambiguities.
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