This paper is concerned with state estimation problems for so-called Liu equations. These equations are counterparts of well-known Ito ones and they were introduced by B. Liu under elaboration of his uncertain theory. The Liu equations may be solved backward and they represent a more convenient object for the state estimation problem solution especially for the case when distributions of disturbances are unknown. Using the dynamic programming principle, we derive an equation for the informational set consisting of all states that are compatible with measuring data. Special cases of Liu equations and constraints for disturbances are examined. Among them the linear equations with quadratic constraints are considered in most details. Some examples are also given.