1. A method of integrity monitoring for errors in a navigation system, the method comprising: receiving, in an onboard satellite receiver, a plurality of satellite signals transmitted from a plurality of space-based satellites; obtaining inertial measurements from one or more onboard inertial sensors; sending the satellite signals and the inertial measurements to an onboard processor operatively connected to the satellite receiver and the inertial sensors, wherein the integrity monitoring is performed by the processor and comprises: determining a full position solution for the navigation system based on the satellite signals and the inertial measurements; determining one or more position sub-solutions for the navigation system based on the satellite signals and the inertial measurements; setting values for unmodeled pseudorange biases; computing a transformation matrix of the unmodeled pseudorange biases for the full solution and all sub-solutions using a Kalman filter; computing a bias effect of the unmodeled pseudorange biases on an error of a filtered state vector component for all sub-solutions; and adding the bias effect of the unmodeled pseudorange biases on the error of the filtered state vector component to computed protection levels for both vertical and horizontal dimensions.