Sequential Best Integer-Equivariant Estimation for GNSS

Abstract

The 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.