Implementation of Kalman Filtering for Differential-Algebraic Equations

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.