Convergence properties of autocorrelation-based generalized multiple-model adaptive estimation

In this paper a generalized multiple-model adaptive estimator 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. Parameter elements generated from a quasi-random sequence 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 the quasi-random elements through the calculation of the likelihood function of the measurement-minus-estimate 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 standard multiple-model adaptive estimator. Simulation results, involving a two-dimensional target tracking problem using an extended Kalman filter, indicate that the new approach provides better convergence properties over a traditional multiple-model approach.