A GNSS navigation system and navigation method for determining user position, user velocity, and improved uncertainty metrics for position and velocity. A measurement engine in an applications processor of the system determines pseudorange and delta range values over each time period for each received satellite signal, and also determines measurement noise variances for both pseudorange and delta range for the individual signals. The satellite-specific pseudorange and delta range measurement variances are used to determine the position and velocity uncertainties by a position engine, either by way of a least-squares linearization or by way of an enhanced Kalman filter. The uncertainties may be communicated to the system user, or used in generating an integrated position and velocity result from both the GNSS navigation function and an inertial navigation system result.