The Limiting Form of Kalman Filter and the State Estimation for a Linear Stochastic System with Unknown Disturbance
Takayoshi NAKAMIZO, Nobuaki Kobayashi · Transactions of the Society of Instrument and Control Engineers · 1982
The purpose of this paper is to derive the general limiting form of the continuous-time Kalman filter in the case that the input covariance matrix tends to infinity. The only assumption for the system to be imposed is left invertible. The Silverman's inversion algorithm can be used to obtain the general limiting form. A lower order filtering equation is also derived to obtain the stable filter. It is shown here that the reduced order filter is equivalent to the partial state estimator derived previously by the present authors for a linear stochastic system with completely unknown disturbances. From this observation, a sufficient condition for the filter to be asymptotic stable is presented.