Integer aperture bootstrapping: a new GNSS ambiguity estimator with controllable fail-rate

Abstract

In this contribution, we introduce a new bootstrap-based method for Global Navigation Satellite System (GNSS) carrier-phase ambiguity resolution. Integer bootstrapping is known to be one of the simplest methods for integer ambiguity estimation with close-to-optimal performance. Its outcome is easy to compute due to the absence of an integer search, and its performance is close to optimal if the decorrelating Z-transformation of the LAMBDA method is used. Moreover, the bootstrapped estimator is presently the only integer estimator for which an exact and easy-to-compute expression of its fail-rate can be given. A possible disadvantage is, however, that the user has only a limited control over the fail-rate. Once the underlying mathematical model is given, the user has no freedom left in changing the value of the fail-rate. Here, we present an ambiguity estimator for which the user is given additional freedom. For this purpose, use is made of the class of integer aperture estimators as introduced in Teunissen (2003). This class is larger than the class of integer estimators. Integer aperture estimators are of a hybrid nature and can have integer outcomes as well as non-integer outcomes. The new estimator is referred to as integer aperture bootstrapping. This new estimator has all the advantages known from integer bootstrapping with the additional advantage that its fail-rate can be controlled by the user. This is made possible by giving the user the freedom over the aperture of the pull-in region. We also give an exact and easy-to-compute expression for its controllable fail-rate.