An automatic celestial navigation system for navigating both night and day by observation of K-band or H-band infrared light from multiple stars. In a first set of preferred embodiments three relatively large aperture telescopes are rigidly mounted on a movable platform such as a ship or airplane with each telescope being directed at a substantially different portion of sky. Embodiments in this first set tend to be relatively large and heavy, such as about one cubic meter and about 60 pounds. In a second set of preferred embodiments one or more smaller aperture telescopes are pivotably mounted on a movable platform such as a ship, airplane or missile so that the telescope or telescopes can be pivoted to point toward specific regions of the sky. Embodiments of this second set are mechanically more complicated than those of the first set, but are much smaller and lighter and are especially useful for guidance of aircraft and missiles. Telescope optics focus (on to a pixel array of a sensor) H-band or K-band light from one or more stars in the field of view of each telescope. Each system also includes an inclinometer, an accurate timing device and a computer processor having access to catalogued infrared star charts. The processor for each system is programmed with special algorithms to use image data from the infrared sensors, inclination information from the inclinometer, time information from the timing device and the catalogued star charts information to determine positions of the platform. Direction information from two stars is needed for locating the platform with respect to the celestial sphere. The computer is also preferably programmed to use this celestial position information to calculate latitude and longitude which may be displayed on a display device such as a monitor or used by a guidance control system. These embodiments are jam proof and insensitive to radio frequency interference. These systems provide efficient alternatives to GPS when GPS is unavailable and can be used for periodic augmentation of inertial navigation systems.