Gps, Integers, Adjustment and Probability

In this contribution we give a brief review of the theory of integer estimation as it has been developed for use with the Global Positioning System (GPS). First we consider the GPS observation equations (GPS and Integers). These observation equations are not of the usual type, since some of the parameters are known to be integer. This implies that an extention of ’classical’ adjustment theory is needed. Such an extention is presented by showing ways of how to solve integer adjustment problems (Integers and Adjustment). Different integer estimators are given and a class of admissible integer estimators is defined. Next we consider some qualitative aspects of an integer adjustment (Adjustment and Probability). It is argued that the usual qualitative description by means of second moments or variance-covariance matrices is not sufficient. A direct probabilistic description is needed instead. Such a description is presented by means of the probability mass function of the integer ambiguities. For GPS ambiguity resolution, the probability of correct integer estimation is particularly of interest (Probability and GPS). It describes the ambiguity succes rate and shows whether or not the estimated ambiguities may be treated deterministically. Since different integer estimators have different success rates, one is particularly interested in the estimator which maximizes this success rate. The answer is given by the theorem provided.