The recursive characteristics of estimation error variance  P(K∣K) in the Kalman filter(KF) for linear random
discrete-time systems with single model and single survey is studied. Based on the recursive characteristics, a optimal
monitoring problem is presented, and the variety of issues and corresponding solutions on this problem are studied. In this
process, a series of solutions are presented which include the variable-population genetic algorithm. The problem of optimal
monitoring problem and corresponding research based on KF process are studied. So the simulation result has a significant
practical and guiding value in the measurement problem of filter with high-precision and high-cost.