Generalized multiple model adaptive estimation
Alsuwaidan, Badr N.
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In this dissertation a generalized multiple-model adaptive estimator (GMMAE) is presented that can be used to estimate the unknown noise statistics in filter designs. The assumed unknowns in the adaptive estimator are the process noise covariance elements. Multiple parameter elements are used to drive multiple-model parallel filters for state estimation. The current approach focuses on estimating the process noise covariance by sequentially updating weights associated with parameter elements through the calculation of the likelihood function of the measurement-minusestimate residuals, which also incorporates correlations between various measurement times. For linear Gaussian measurement processes the likelihood function is easily determined. For nonlinear Gaussian measurement processes, it is assumed that the linearized output sufficiently captures the statistics of the likelihood function by making the small noise assumption. A proof is provided that shows the convergence properties of the generalized approach versus the traditional multiple-model adaptive estimator (MMAE). Simulation results, involving a two-dimensional target tracking problem ans GPS-based position estimation problem using an extended Kalman filter, indicate that the new approach is able to correctly estimate the noise statistics.