טכניון מכון טכנולוגי לישראל
הטכניון מכון טכנולוגי לישראל - בית הספר ללימודי מוסמכים  
M.Sc Thesis
M.Sc StudentBenaloul Oron
SubjectA Pareto Based Comparison Approach for State
Estimation of Nonlinear Algorithms
DepartmentDepartment of Electrical Engineering
Supervisors Professor Nahum Shimkin
Dr. Ilan Rusnak
Full Thesis textFull thesis text - English Version


Abstract

State estimation is a well-established technique in control theory and signal processing. For linear systems, the Kalman filter obtains optimal estimates (with respect to the mean square error) of states from observations. For state estimation of nonlinear systems, closed-form optimal filter similar to the Kalman filter exists only in some specific cases. In practice, most of the suggested filters for state estimation of nonlinear systems refer to specific classes of systems and are suboptimal filters. There exist many suboptimal filters in the literature. Each filter has its own advantages and disadvantages. Furthermore, each filter has at least one tuning parameter which needs to be adjusted to each nonlinear problem separately. It is difficult to determine analytically which filter is most suitable for a specific problem. Our approach proposes a methodical approach for appropriate and meaningful comparison of filter performance for a given state estimation problem. The comparison is made using the Pareto front of nonlinear filters and is accordingly called the Pareto Based Comparison (PBC) approach. In order to examine the proposed approach, several nonlinear filters were simulated for the nonlinear state estimation problem of a target performing a 2-D barrel roll with a constant but unknown angular velocity. The best filter for the task is selected specifically according to user requirements. After using the PBC approach to compare between filters performances, the user can test the sensitivity of the evaluated filters to variations of different parameters of the target maneuver. Consequently, the proposed approach enables us to perform a comparison between filters performances for state estimation of nonlinear problems and to choose the best filter for the nonlinear state estimation problem.