A satellite-based positioning receiver includes processing channels, each processing channel being associated with a respective satellite from among N satellites, and an extended Kalman filter for performing a vector tracking for the set of satellites using signals received from the satellites. The extended Kalman filter performs a resetting on the basis of the phase error and code error received directly from the phase and code discriminators, of each channel, and the receiver is configured for calculating the code-wise and carrier-wise control signals for the code phase and carrier phase numerically-controlled oscillators, on the basis of data provided by the extended Kalman filter, for each channel.