Terrain database integrity monitors and terrain-referenced navigation systems are based on performing a comparison between stored terrain elevations with data from airborne sensors like radar altimeters, inertial measurement units, GPS receivers etc. This thesis introduces the concept of a spatial terrain database integrity monitor and discusses methods to improve its performance. Furthermore, this thesis discusses an improvement of the terrain-referenced aircraft position estimation for aircraft navigation using only the information from downward-looking sensors and terrain databases, and not the information from the inertial measurement unit. Vertical and horizontal failures of the terrain database are characterized. Time and frequency domain techniques such as the Kalman filter, the autocorrelation function and spectral estimation are designed to evaluate the performance of the proposed integrity monitor and position estimator performance using flight test data from Eagle/Vail, CO, Juneau, AK, Asheville, NC and Albany, OH.