A modified extended kalman filter as a parameter estimator for linear discrete-time system
Department of Electrical Engineering
Master of Science
Meyer, Andrew Ulrich
Oranc, Burhan Tarik
This thesis presents the derivation and implementation of a modified Extended Kalman Filter used for Joint state and parameter estimation of linear discrete-time systems operating in a, stochastic Gaussian environment. A novel derivation for the discrete-time Extended Kalman Filter is also presented. In order to eliminate the main deficiencies of the Extended Kalman Filter, which are divergence and biasedness of its estimates, the filter algorithm has been modified. The primary modifications are due to Ljung, who stated global convergence properties for the modified Extended Kalman Filter, when used as a parameter estimator for linear systems.
Implementation of this filter is further complicated by the need to initialize the parameter estimate error covariance inappropriately small, to assure filter stability. In effect, due to this inadequate initialization process the parameter estimates fail to converge. Several heuristic methods have been developed to remove the effects of the inadequate initial parameter estimate covariance matrix on the filter's convergence properties.
Performance of the improved modified Extended Kalman Filter is compared with the Recursive Extended Least Squares parameter estimation scheme.
njit-etd1988-008 (167 pages ~ 13,503 KB pdf)
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Front Matter (Title Page, Abstract, Table of Contents, etc. ~ 11 pages ~ 990 KB pdf)
Chapter 1: Introduction (6 pages ~ 823 KB pdf)
Chapter 2: Theoretical Developments (49 pages ~ 6,679 KB pdf)
Chapter 3: Implementation of the MEKF (20 pages ~ 1,399 KB pdf)
Chapter 4: Investigation and development of Various Methods to Improve Stability and rate of Convergence of the MEKF Based on Single Parameter Case (26 pages ~ 1,334 KB pdf)
Chapter 5: Comparison of an Improved MEKF with a RELS Filter (8 pages ~ 322 KB pdf)
Chapter 6: Conclusions (4 pages ~ 202 KB pdf)
Appendix A: Program Listing MEKF (39 pages ~ 1,561 KB pdf)
Appendix B: Program Listing RELS (4 pages ~ 172 KB pdf)
Appendix C: Program Listing Noise Generator (3 pages ~ 97 KB pdf)
Appendix D: Properties of the Expected Value Operator E (2 pages ~ 57 KB pdf)
Appendix E: Proof of the Matrix Inversion Lemma (3 pages ~ 72 KB pdf)
Bibliography (4 pages ~ 240 KB pdf)
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Created September 18, 2001