A quasi tightly coupled (QTC) aided INS (AINS) process has an inertial navigator system with a loosely-coupled AINS Kalman filter that constructs INS-GNSS position measurements, a GNSS position engine that computes a position fix from observables and an externally provided a priori position and position VCV matrix. An INS position seeding process in which the externally provided a priori position to the GNSS position engine is an antenna position computed from the INS position and attitude solution. An observable subspace constraint (OSC) process computes an OCS matrix that suppress the components of the GNSS position error due to a poor geometry in the GNSS position solution in the IG position measurement constructed by the AINS Kalman filter and that multiplies the OSC matrix and the IG position measurement and measurement model matrix to suppress uncorrected component of the GNSS position error in the IG position measurement and measurement model.