In many plants, we do not know all the component parts of the system whose state variables are to be estimated. The problem to be considered in this paper is the identification of unknown parameters and the estimation of state variables of a discrete-time noisy linear system with unknown elements in its transition matrix. The unknown elements are regarded as unknown parameters.
It is known that, for a linear system without unknown parameters, the optimal estimation process using the method of least-square fit can be replaced with a Kalman-Filter. The author suggests to utilize the performance index used in the method of least-square fit when the linear system has some unknown parameters to be identified. A parameter is identified when it gives a minimum of the performance index. The identification, therefore, is reduced to seek the minimum value of the perfomance index by changing the unknown parameters. Identifiability of unknown parameters is defined, and necessary and sufficient conditions for it are obtained, from the convergence of Kalman-Filter and from the equivalence of discrete systems.
In this method, the system with unknown parameters is treated always as a linear system, the Kalman-Filter to the system can be applied on the similar conditions as to a linear system without unknown parameters. Two examples prove the possibility of identification of unknown parameters.