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.