טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentCarmi Avishy
SubjectSequential Monte Carlo Methods for Spacecraft Attitude
and Angular Rate Estimation from Vector
Observations
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Oshman Yaakov


Abstract

The goal of this research is to derive optimal and efficient nonlinear non-Gaussian estimation algorithms for attitude and attitude-rate determination from vector observations. Contrary to the present state-of-the-art works in this field, which rely upon various assumptions related to the Kalman filtering approach, this work addresses the attitude determination problem via new nonlinear non-Gaussian filtering techniques that belong to the class of Monte Carlo sequential methods, also known as particle filters.


In the first part of this work, four novel fast particle filtering algorithms for spacecraft attitude and angular rate estimation are introduced.  The first algorithm is aimed at estimating spacecraft attitude, represented by the rotation quaternion, from vector observations. The second and the fourth filtering algorithms extend the capabilities of the first by allowing the measurement noise statistics to be captured on the fly and by permitting attitude filtering in gyroless settings,  respectively. The third filtering algorithm is aimed at estimating spacecraft angular rate independently of any attitude information.


The essential features of the new algorithms account for their fast convergence rate and high accuracy (compared to the classical state-of-the-art estimators), robustness to modeling uncertainties, and  insensitivity to the initial conditions and to the nonlinearities involved.  Innovative enhancements introduced in the basic particle filtering algorithm render the new estimators highly efficient and real-time implementable. Furthermore, and contrary to conventional attitude filters, that have to address the quaternion's unit norm constraint via special (mostly ad hoc) techniques, the new algorithms maintain the quaternion's unit norm naturally, requiring no such modification.


The last part of this work is devoted to two theoretical issues: 1) investigation of the numerical properties of  the quaternion estimation error covariance, and 2) observability analysis of the attitude and angular rate estimation problem. The former issue, which has been tackled numerous times in the past, is still at the

heart of an active and hot debate involving several of the major researchers in the field. This work sheds a new light on the nature of the covariance matrix using a rigorous asymptotic analysis. The latter issue has been  rarely studied in past works. This work provides a detailed analysis of the observability of the attitude

and angular rate estimation problem, using mathematical tools borrowed from nonlinear systems theory.

Necessary and sufficient conditions for attitude and angular rate observability are derived, and their relation  to previously published results is discussed.