ABSTRACTThe key to high precision parameter estimation in global navigation satellite system (GNSS) applications is to properly deal with the integer valued carrier‐phase ambiguities. The class of integer estimators fixes all ambiguities to integer values. This can also decrease the precision of the estimates of the non‐ambiguity parameters, if the fixing is incorrect. The best integer‐equivariant (BIE) estimator is optimal in the sense of minimizing the mean‐squared error (MSE) of both the ambiguities and the real valued parameters, regardless of the precision of the float solution. However, the BIE estimator comprises a search in the integer space of ambiguities, whose complexity grows exponentially with the number of ambiguities. This search is not feasible for large‐scale network solutions. To overcome this problem, a sequential BIE (SBIE) algorithm is proposed, which shows close to optimal performance with only linearly increasing complexity. Numerical simulations are used to verify the performance of the SBIE algorithm. Copyright © 2014 Institute of Navigation.