An improved system and method is disclosed for dynamically estimating the output variances of carrier-smoothing filters used, for example, in GPS receivers. By accurately estimating the output variances of the carrier-smoothing filters as they transition from initialization to steady-state operation, it is possible to calculate any required protection levels without having to wait for the filters to fully stabilize. As one example, a system for estimating output variances of a carrier-smoothing filter for use in a satellite navigation system receiver is disclosed, which includes a plurality of smoothing filters associated with a navigation processing unit in a satellite navigation receiver. One or more processors associated with the navigation processing unit executes an algorithm for each smoothing filter, which provides a method for dynamically calculating an output variance for a respective smoothing filter as it transitions in response to new input variance values. The method also predicts the settling point of the output variance for that smoothing filter given a set of pseudorange and carrier-phase values to be applied. Therefore, using this novel output variance prediction method, precision navigation applications such as, for example, airborne GPS-based precision landing system applications can begin operations with suitable calculated protection level values without having to wait for the smoothing filters to stabilize. Thus, such precision landing systems are available for use as soon as the required protection level values are reached.