Ph.D Thesis

Ph.D StudentChoukroun Daniel
SubjectNovel Methods for Attitude Determination Using Vector
DepartmentDepartment of Aerospace Engineering
Supervisors PROF. Yaakov Oshman
PROF. Haim Weiss
PROFESSOR EMERITUS Y. Bar-Itzhack (Deceased)


In the first part of this thesis four novel optimal quaternion estimators are developed within the framework of linear least-squares estimation theory.  The first algorithm is a linear quaternion Kalman filter, where the measurement model does away with the traditional linearization procedure.  An adaptive version of that algorithm using GPS-based vector observations is presented too.  The second algorithm is an optimized REQUEST algorithm, where optimization is done with respect to the heuristic fading memory factor of the REQUEST algorithm.  A central feature of REQUEST is the so-called K-matrix.  In order to estimate that matrix, an optimal estimation strategy is proposed here by embedding the REQUEST algorithm in a Kalman filter framework.  Adaptive filtering techniques are used to enhance this optimal REQUEST algorithm.  The third algorithm is a computationally simple filter which is based on the Dynamic Programming approach that includes the quaternion unit-norm constraint.  The forth algorithm is a Kalman filter of the K-matrix, which enhances the performance of the second algorithm.  This improvement is proven by analysis and simulation.

The second part of the thesis considers the problem of state estimation in systems whose state is a stochastic matrix.  A general state-matrix Kalman filter is developed and is shown to be a generalization of previous matrix filters.  The proposed algorithm is applied to two attitude determination problems: 1) the estimation of the K-matrix, and 2) the estimation of the Direction Cosine Matrix.  Pseudo-measurement techniques are utilized to implement special constraints like symmetry, zero-trace, and orthogonality of the estimated state-matrix.  As demonstrated by simulations, combining these techniques with ad-hoc iterative procedures seems to be a promising technique for constrained Kalman filtering.

The various attitude estimators are compared via a simulation study.  Their relative merits are discussed and classified in a recapitulative table.