A General Solution to the Rank Deficient Integer Least Squares and its Application to GNSS Positioning

The contribution will present a general solution for the estimation of rank deficient integer parameters. A procedure will be presented that allows the computation of integer estimable function for any integer rank deficient least squares problem. The procedure is then applied to GNSS estimation problems. In the framework of undifferenced and uncombined GNSS models, the specific solution to some rank deficient integer least squares model will be presented, namely: the choice of pivot ambiguities in a network of receivers, GLONASS positioning, codeless positioning in the presence of ionospheric delay, satellite specific pseudorange biases estimation in the presence of ionospheric delay. It will been shown how the developed theory generalize previous results and ad hoc solutions present in the literature. Numerical results from real GNSS data will be presented too.