The positioning receiver according to the invention comprises means for storing configuration information and information on its reception conditions, which is processed in order to calculate a current and/or predicted precision of the positioning calculation. Advantageously, at least some of this information is integrated into a variation model of a Kalman filter integrated into the receiver. The invention notably allows a more rapid convergence on a reference precision in a mono-frequency operating mode and transitions between a mono-frequency and bi-frequency mode to be smoothed. Advantageously, the precision information is delivered graphically or in numerical form to the user.