New variations of multiple model adaptive estimation for improved tracking and identification
Nebelecky, Christopher K.
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Multiple model adaptive estimation (MMAE) is a recursive algorithm that uses a bank of estimators, each purposefully dependent on a particular hypothesis, to determine an estimate of an uncertain system under consideration while simultaneously tracking the system state. The first generation of MMAE, introduced by Magill in 1965 considered the estimators to act independently and in parallel, determining state estimates conditional with each hypothesis. Through computation of a normalized mode-conditioned likelihood, the conditional probability that each hypothesis correctly models the system is computed. Since Magill's seminal work, many offshoots of MMAE have been developed. Modifications have been reported, but are typically on on an application specific basis which limits their versatility. In this dissertation, two variations of MMAE are considered. The first variation is based on an observed flaw which leads to degenerate tracking performance. The second variation is motivated by previous research which showed improved convergence performance by considering a generalized mode-conditioned likelihood function for determining the hypothesis conditional probabilities. Each estimator, or specifically Kalman filter, is designed around a particular system hypothesis. If the hypothesis is not sufficiently close to the true system, the resulting filter will generally produce erroneous estimates which do not track the system. This is because each filter believes that the hypothesized system is optimal. Further, the state error covariances resulting from such a suboptimal filter will be inconsistent because they have no knowledge of the incorrect hypothesized model. By explicitly accounting for the deviation of the hypothesis, recursions are developed which, when combined with MMAE are shown to provide superior tracking performance over the standard MMAE. Additionally the proposed variation, called model error MMAE, is shown to provide acceptable tracking performance for dynamically switching systems at a fraction of the computational expense of other algorithms specifically developed for that application. The second variation, referred to as generalized multiple model adaptive estimation (GMMAE), uses an augmented vector of current and past residuals to drive the recursion for the hypothesis conditional probabilities. Necessary for that recursion is evaluation of the time-domain autocovariance matrix of the residual sequence. When filtering linear (and linearized) systems, the autocovariance can be analytically expressed as a function of the system matrices, covariances and filter gain. When filtering nonlinear systems using the Unscented filter, analytic expressions for the autocovariance are not possible. Motivated to include Unscented filters within the GMMAE framework, a method for calculating the time-domain autocovariance of the residual sequence from an Unscented filter is presented. The proposed method is validated analytically on a simplified system and simulation results are presented using the algorithm for process noise estimation in a planar tracking problem.