Gravity gradiometer aiding of a strapdown inertial navigation system (INS) in the event of Global Navigation Satellite System (GNSS) signal loss, or as a complement to an INS/GNSS system, is proposed. Gravity gradiometry is ideal for covert military applications where a self contained, passive, spoof-free aid is desirable, and for space navigation near planetary bodies and moons where GNSS is unavailable. This dissertation provides the first comprehensive discussion on gravity gradiometry fundamentals, map modeling, and regional and altitude effects on the gravitational gradient signal for use as a navigation aid. A thorough methodology to implement strapdown and stabilized gravity gradiometer instruments (GGIs) into an autonomous extended Kalman filter is also presented in the open literature for the first time. Lastly, a brief discussion on extraterrestrial navigation using gravity gradiometry is given. To quantify the potential performance for future gravity gradiometer instruments as an INS aid, extensive Monte Carlo simulations of a hypersonic scramjet cruise missile were performed. The results for the 1000 km range mission indicate that GGI updates significantly improve the navigation accuracy of the autonomous INS. The sensitivities of the system to variations in inertial measurement unit (IMU) quality, gravity field variation, GGI noise, update rate, and type are also investigated along with a baseline INS/Global Positioning System (GPS). Given emerging technologies that have the potential to drastically decrease gradiometer noise levels, a hypothetical future grade gravity gradiometer aided INS is shown to bound root-mean-square (RMS) position errors at 0.336 m, velocity errors at 0.0069 m/s, and attitude errors at 0.00977 degrees, which is comparable to the nominal INS/GPS system with 10 sec updates. The performance of two subsonic cases is also investigated and produced impressive passive navigation accuracy. A commercial aircraft simulation using a future grade GGI provided RMS errors of 0.288 m in position, 0.0050 m/s in velocity, and 0.0135 degrees in attitude. A low altitude and velocity gravity gradiometer based survey simulation similarly showed sub-meter RMS position errors of 0.539 m, velocity errors of 0.0094 m/s, and attitude errors of 0.0198 degrees.