An optimality property of the integer least-squares estimator

A probabilistic justification is given for using the integer least-squares (LS) estimator. The class of admissible integer estimators is introduced an d classical adjustment theory is extended by proving that the integer LS es timator is best in the sense of maximizing the probability of correct integ er estimation. For global positioning system ambiguity resolution, this imp lies that the success rate of any other integer estimator of the carrier ph ase ambiguities will be smaller than or at the most equal to the ambiguity success rate of the integer LS estimator. The success rates of any one of t hese estimators may therefore be used to provide lower bounds for the LS su ccess rate. This is particularly useful in case of the bootstrapped estimat or.