A global navigation system includes a first navigation receiver located in a rover and a second navigation receiver located in a base station. Single differences of measurements of satellite signals received at the two receivers are calculated and compared to single differences derived from an observation model. Anomalous measurements are detected and removed prior to performing computations for determining the output position of the rover and resolving integer ambiguities. Detection criteria are based on the residuals between the calculated and the derived single differences. For resolving integer ambiguities, computations based on Cholesky information Kalman filters and Householder transformations are advantageously applied. Changes in the state of the satellite constellation from one epoch to another are included in the computations.