Generalized attitude determination with one dominant vector observation

This paper derives an algorithm to determine the approximate attitude of a vehicle from both vector and arc-length observations, which are the most general types of attitude observa-tions. It is assumed that one of the vector observations is more accurate than the other vector and arc-length observations. The solution is found by solving a quartic polynomial equation. Then the quaternion can be determined from the polynomial solution. The attitude error-covariance is also derived using both an attitude perturbation approach and a constrained least squares approach. Both are shown to yield identical results. An optimality condition is also derived that compares the derived suboptimal error-covariance with the optimal one. Several special cases, such as a set of one direction observation and an arc-length observation, are shown. Simulation results using a Monte Carlo analysis are shown to verify the derived algorithm.