未知外乱を含む線形確率系の状態推定

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  • On the State Estimation of the Linear Stochastic System with the Completely Unknown Disturbance
  • ミチ ガイラン オ フクム センケイ カクリツケイ ノ ジョウタイ スイテイ

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The purpose of this paper is to derive the filtering equations for the continuous-time linear stochastic systems with completely unknown disturbance. For the discrete-time system, the filter is already well-known as the information filter. However, since the covariance matrix of the estimate error approaches infinity as the time step tends to zero, the discrete to continuous time limit fails to yield the general solution. Recently Mehra found the solution for the continuous-time Fisher model by an ingenious time-limiting procedure from the corresponding discrete-time filter.<br>In this paper the lower order filtering equations are derived by a direct procedure, rather than by a time-limiting procedure. Two different methods are attempted to derive the filtering equations. The first method is based on the partition of the state into two components; one is affected by completely unknown disturbance and the other is not. Since the only latter component is estimable, the lower order filter can be easily obtained by the direct application of the standard filtering theory. The alternate method attempted here is to let the input covariance matrix go to infinity. Thus the filter is obtained as the limiting form of the standard continuous-time Kalman filter. Then the equivalence of two filters derived from the respective approaches is examined. To facilitate the development, however, a steady state version of the solution is given for a time invariant linear model. The investigation of the stability of the filter is included.

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