The state identification model with only bounded errors is a typical constraints satisfaction problem

and variables and constraints can all be presented in the form of intervals. Thus

interval analysis can be adopted to solve this constraints satisfaction problem. The conventional interval constraints propagation method is first proposed to solve this model. However

the results are locally consistent and have conservative character to a large extent. To deal with this problem

the improved interval constraints propagation method is proposed. On one hand

monotonicity is introduced to an interval constraints propagation algorithm

which can effectively eliminate the conservative character resulting from the many times' appearance of monotone variables. On the other hand

by increasing redundant constraints

the original constraint sets are extended

which can eliminate the conservative character resulting from the local consistency of interval constraints propagation algorithm to a great extent.