General Definition of Relative Misalignment

It is well known that if misalignments are modeled at all attitude sensors on a spacecraft, which may include the gyro, a linear combination of misalignments is unobservable. Typically one sensor (called the primary, master, or body reference sensor) is not parameterized with misalignments so that the remaining misalignments are fully observable. Another parameterization is to model the misalignment of two sensors as being equal and opposite in direction. In this paper we examine various misalignment models used to calibrate the alignment of spacecraft attitude sensors and gyros, and we discuss the pros and cons of each. We present a general formula for eliminating the unobservable misalignment.