טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
Ph.D Thesis
Ph.D StudentRapoport Ilia
SubjectOptimal Filtering in the Presence of Faults: Algorithms
and performance Measures
DepartmentDepartment of Aerospace Engineering
Supervisor Professor Yaakov Oshman


Abstract

This work addresses the problem of fault-tolerant estimation with special emphasis on navigation applications.  The research focuses on 1) designing computationally efficient fault-tolerant estimation techniques, and 2) developing useful tools for a priori assessment of estimation errors.

Two filtering algorithms are developed, that are suitable for systems characterized by a fault-free main dynamics and independent scalar fault-prone measurement channels. The first method is applicable to systems with highly nonlinear dynamics and fault-prone scalar measurement channels, characterized by additive measurement errors generated by scalar hybrid systems.  The method's computational efficiency is derived from its special use of the Rao-Blackwellization technique.  The second algorithm is suitable for systems that are linear with respect to the main states, with almost noise-free main dynamics.  The method's efficiency results from a decoupled processing of separate measurement channels.

Three estimation error lower bounds are proposed.  The first two are derived for linear hybrid systems with fault-prone measurements and fault-free dynamics.  Based on the Cramer-Rao bound, but circumventing its regularity conditions problem, a new bound is derived for the hybrid system's state.  Another bound, based on the Bhattacharyya distance, is derived for the fault variable estimation error.  The third bound is a sequential version of the Weiss-Weinstein lower bound, which is derived for a wide class of Markovian dynamical systems.  Like the ordinary Weiss-Weinstein bound, the novel sequential algorithm is free from regularity conditions and is, thus, suitable for hybrid systems.  However, unlike the original bound, the new one can be easily applied to dynamical systems.