A study on three commonly used GNSS integer estimators with probability of correct estimation

Integer ambiguity resolution plays a key role in applications related to GNSS precise positioning. This contribution focuses on three commonly used integer estimators (IEs), i.e., integer rounding (IR), integer bootstrapping (IB) and integer least-squares (ILS). Contributions are mainly of four aspects. First, the objective function of IR and IB is given, respectively. Second, an upper bound for ILS is proposed. Third, a sorting technique is introduced to tighten the upper bound of IR/ILS after decorrelation. Fourth, the success-rate approximation for IR and ILS with bounded error is developed, respectively. Finally, real-collected data in PPP validate the following arguments. (i) Applying sorting technique after decorrelation can improve the tightness of IR upper bound a lot, but can only slightly tighten the ILS upper bound. (ii) The proposed ILS upper bound is almost as the same tight as the one in PS-LAMBDA software, much tighter than other known upper bounds. Unlike the PS-LAMBDA upper bound, the proposed ILS upper bound has the advantage of time efficiency for real-time applications. (iii) The proposed approximations produce more accuracy approximated success-rate than the frequently-used ambiguity dilution of precision (ADOP) based approximation.