Bounding the integer bootstrapped GNSS baseline’s tail probability in the presence of stochastic uncertainty

Differential carrier phase applications that utilize cycle resolution need the probability density function of the baseline estimate to quantify its region of concentration. For the integer bootstrap estimator, the density function has an analytical definition that enables probability calculations given perfect statistical knowledge of measurement and process noise. This paper derives a method to upper bound the tail probability of the integer bootstrapped GNSS baseline when the measurement and process noise correlation functions are unknown, but can be upper and lower bounded. The tail probability is shown to be a non-convex function of a vector of conditional variances, whose feasible region is a convex polytope. We show how to solve the non-convex optimization problem globally by discretizing the polytope into small hyper-rectangular elements, and demonstrate the method for a static baseline estimation problem.