Performance comparison of the BIE estimator with the float and fixed GNSS ambiguity estimators

Abstract

The goal of ambiguity resolution is to make optimal use of the integerness of the ambiguities, and it is the key to high precision GNSS positioning and navigation. However, it should only be applied in case the probability of correct integer ambiguity resolution, i.e. the success rate, is very close to one. In that case, the probability that the fixed baseline will be closer to the true but unknown baseline is larger than that of the float baseline. Clearly, this condition will not be fulfilled for each measurement scenario, and this means that for low success rates a user will prefer the float solution. However, there exists a baseline estimator that will always be superior to its float and fixed counterparts, albeit that this superiority is measured using a weaker optimality condition. This baseline estimator is the Best Integer Equivariant (BIE) estimator, which is unbiased and of minimum variance within the class of integer equivariant estimators. In this contribution, the three different estimators are compared. For that purpose, we will focus on the geometry-free GNSS models, either single frequency or dual frequency. The performance of the estimators is compared based on their probability density functions, the variances of the different estimators, and the probabilities that the baseline estimators are within a certain convex region symmetric with respect to the true baseline. This will provide information on whether or not the BIE estimator could be useful in positioning applications.