A navigation system , comprising: one or more inertial sensors that generate inertial measurements; a receiver configured to receive a plurality of signals transmitted from a plurality of space-based satellites; and a processor operatively coupled to the receiver and the inertial sensors, the processor configured to perform a method of integrity monitoring implemented as part of an advanced receiver autonomous integrity monitoring algorithm, wherein the integrity monitoring performed by the processor comprises: determining a full position solution for the navigation system based on the plurality of signals; determining one or more position sub-solutions for the navigation system based on the plurality of signals; setting nominal and maximum values for unmo deled 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 . one or more inertial sensors that generate inertial measurements; a receiver configured to receive a plurality of signals transmitted from a plurality of space-based satellites; and a processor operatively coupled to the receiver and the inertial sensors, the processor configured to perform a method of integrity monitoring implemented as part of an advanced receiver autonomous integrity monitoring algorithm, wherein the integrity monitoring performed by the processor comprises: determining a full position solution for the navigation system based on the plurality of signals; determining one or more position sub-solutions for the navigation system based on the plurality of signals; setting nominal and maximum values for unmo deled 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 . determining a full position solution for the navigation system based on the plurality of signals; determining one or more position sub-solutions for the navigation system based on the plurality of signals; setting nominal and maximum values for unmo deled 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 . <EOS>