連続時間の適応推定アルゴリズムについて

概要

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The problem of estimating both states and parameters of continuous-time linear stochastic system is considered in the framework of nonlinear filtering. First, the asymptotic properties of conditional moments of states and parameters with respect to the observation are analyzed as time tends to infinity. Secondly, the nonlinear filter equations for the problem are transformed into a singular perturbed system by rescaling the conditional moments using the result of the asymptotic analysis. Finally, eliminating asymptotically negligible terms from the singular perturbed system, an adaptive estimation algorithm is obtained. Due to their contruction scheme, the estimates by the algorithm have the same asymptotic properties as those of the optimal ones.In addition, it is shown that the algorithm obtained here agrees with the continuous-time version of the Ljung's one, which was derived heuristically by the combination of the extended Kalman filter and the gradient method.
公益社団法人計測自動制御学会の論文