A New Criterion of the Stochastic System Simplification Based on Kalman Filter

In researching the problems of stochastic system, we usually use the linearization method, the approximate decoupling method, and the truncated method etc. to simplify the system model. The traditional criterion is the ratio of the simplification part and the initial model. If the ratio is small enough or the model errors can be regarded as noise, we think the simplification method is reasonable. The shortage of the criterion is that it hasn't a very definite value or bound, and it can't combine the performance of the whole system. Therefore we propose a new criterion which calculates the errors and error covariance matrix of the state between the initial system and the simplified system based on Kalman filter. The new criterion judges the trace of the matrix and its convergence property. Because it uses the state equation and the measurement equation of the stochastic system, it is more suitable for the whole system performance.