A Topological Approach to the Analysis of Star Tracking Systems

The systems engineer, in formulating and analyzing star tracking systems, is often confronted with conversion of lengthy coordinate transformation matrices into meaningful physical data. The matrices associated with vector analysis and the equations of spherical trigonometry used in celestial and space applications often defy orderly and concise interpretation. One becomes lost in a maze of sines, cosines, and error vectors. The topological method of performing orthogonal coordinate transformations graphically illustrates the conversions and projections being attempted and serves as a map to orient our thinking. This paper discusses coordinate transformation of star tracking systems in terms of the topological and signal flow chart. The topological or signal flow diagram is briefly explained before being applied to typical star tracking problems. Star identification in space and terrestial navigation were chosen as representative problems to illustrate the usefulness of the topological analysis approach.