Angles-Only Navigation: Position and Velocity Solution from Absolute Triangulation

Abstract

Abstract : Angles-only (or bearings-only) navigation involves determining position, velocity, or orientation information for an observer using the apparent directions or motions of objects at finite distances. Angles-only navigation covers a broad range of applications, and is generally implemented through a Kalman filter that uses imaging and other information to differentially adjust the values of the navigation parameters (state vector) at each incremental step of the observer's computed motion. This paper presents an algorithm for angles-only navigation that is a closed-form solution for both position and velocity that does not require any prior estimate of the observer's position or motion. It is least-squares-based triangulation generalized to a moving observer, involving only angular observations of objects with known coordinates. The algorithm can be applied to any situation where foreground objects are observed against background objects, so long as both foreground and background objects are identifiable and have known coordinates. It can be used for ship piloting using images of shore objects at various distances. It also has possible applications in robotics; for example, for determining the position and velocity of mobile landers on other solar system bodies, or for automated farming. A specific proposed application for open-sea ship navigation would use the angular positions of Earth satellites observed optically against a star background. Such a system could provide a supplement to ordinary GPS navigation, as well as supplying a precise absolute attitude reference.