The increasing reliance on Global Navigation Satellite Systems (GNSS) has highlighted critical vulnerabilities to jamming and spoofing, driving demand for assured Position, Navigation and Timing (A-PNT) capabilities in GNSS-denied environments. This paper presents analytical algorithms for autonomous navigation using stellar sensors to provide GNSS-independent positioning and heading determination. Two complementary approaches are developed: sun sensor-based position determination through analytical solution of geometric equations relating measured solar vectors to ephemeris data, and star tracker-based simultaneous position and heading estimation exploiting quaternion attitude measurements. For the latter, a novel reference frame modification incorporating yaw into the Earth-to-navigation transformation enables direct extraction of latitude, longitude, and heading from quaternion data through Euler angle decomposition. Error propagation analysis via Jacobian linearization quantifies the influence of sensor noise, attitude errors, and geophysical effects. Monte Carlo simulations with realistic sensor characteristics validate the analytical error models. Results demonstrate positioning accuracies of several kilometers for sun sensors and sub-kilometer for star trackers, with the latter achieving arcsecondlevel heading precision. Latitude-dependent performance characteristics and geometric sensitivity factors are analyzed, providing design guidelines for GNSS-independent navigation systems.