| Since its inception in 1961 by Kalman and Bucy, the Kalman filter has become one of the most popular methods for estimation and prediction. The Kalman filter works exceptionally well when the system dynamics are known and constant. Problems arise, however, when the system dynamics are unknown or vary with time.; Adaptive Kalman filter techniques were developed to solve this problem. These techniques utilize identification algorithms to keep the Kalman filter in tune by estimating the system dynamics. Many applications of adaptive Kalman filtering have been suggested including spacecraft attitude and orbit estimation, aircraft navigation and ship steering.; This dissertation discusses an adaptive Kalman filter design that uses recursive maximum likelihood parameter identification. The approach is applicable to both linear and nonlinear dynamics. Because of the importance of identification in the adaptive Kalman filter design, much of the emphasis of this dissertation is placed in its theoretical development and implementation.; Simulated data results are shown for the second order case of {dollar}mddot x{dollar} + {dollar}kx{dollar} = 0. For this case, {dollar}omegasb{lcub}n{rcub}{dollar} = {dollar}sqrt{lcub}kover m{rcub}{dollar} is the unknown parameter. Next, the case of {dollar}mddot x{dollar} + {dollar}bdot x{dollar} + {dollar}kx{dollar} = 0 is examined. This involves the identification of both {dollar}omegasb{lcub}n{rcub}{dollar} and {dollar}zeta{dollar}, where {dollar}zeta{dollar} = {dollar}{lcub}bover2momegasb{lcub}n{rcub}{rcub}{dollar}. Use of a scaling matrix is explained for multiple parameter identification when the parameters are of different orders of magnitude.; Understanding how well the algorithm developed in this dissertation works for second order dynamics is an important issue, considering many complicated systems may be modeled as systems of multiple second order systems. Robotic arms and large flexible structures are two examples of systems that may be modeled by these methods. As a final example, an eighth order model of a flexible robotic arm at Colorado State University is investigated. This system consists of one rigid body second order system and three flexible second order systems.; In addition, analysis is provided in several identifier areas including the relationship of measurement noise to parameter convergence, the need for well-behaved partials in the identification algorithm and the algorithm's sensitivity to initial conditions of the state vector and noise covariance. |
