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Implementation of Kalman Filtering for Differential-Algebraic Equations

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Sherbak_Bogdan.pdf (2.27 MB)

Date

2020-09-28

Authors

Sherbak, Bogdan

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Volume Title

Publisher

University of Waterloo

Abstract

This thesis describes two Kalman filters which are usable on semi-explicit index-1 differential-algebraic equations, prior to which a discussion of linear and nonlinear Kalman filters is presented. Performance between differential-algebraic equation-compatible Kalman filters and their ordinary differential equation counterparts is compared in two examples. Basic existence and uniqueness theory of linear differential-algebraic equations is discussed along with the process of numerically approximating the solution. Desire to estimate the state of charge of a lithium ion cell is used as motivation. The electrochemical processes of a lithium ion cell are discussed. When discretized, the model of a lithium ion cell results in a differential-algebraic equation.

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Keywords

differential-algebraic equation, differential algebraic equation, Kalman filter, extended Kalman filter, unscented Kalman filter, DAE-compatible Kalman filter, numerical solution, lithium-ion cell, Li-ion cell, estimation, state of charge, partial differential equation, discretization, Chebyshev

LC Keywords

Differential-algebraic equations, Numerical solutions, Kalman filtering, Lithium ion batteries, Chebyshev approximation

Citation

URI

http://hdl.handle.net/10012/16388

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Theses
Applied Mathematics