A novel Bayesian ambiguity resolution technique for GNSS high precision positioning

A novel technique based on the Bayesian philosophy for the joint estimation of real and integer parameters in a linear model of measurements is presented. This technique is applied to the GNSS carrier phase ambiguity resolution problem, that is key for high precision positioning applications. The integer parameters are assumed to take values on a finite set, and the real ones are considered as a realization of a Gaussian random vector. Then, the posterior distribution of these parameters is sequentially determined as new measurements are incorporated. The obtained distribution is a mixed one, with a Gaussian continuous part and a discrete part that accounts for the probability of each of the elements of the finite set. From this posterior distribution, estimators for the integer and real parameters are derived. A MAP (Maximum A Posteriori) estimator modified with the addition of a confidence threshold is used for the integer part and a MMSE (Minimum Mean Squared Error) is used for the real parameters. The good performance of the proposed technique is illustrated through simulations where different satellite visibility conditions are considered. In addition, successful experimental results of high precision baseline estimation are also presented.