Linear minimum mean square error estimation for linear systems with stochastic state equality constraints

In the practical linear system with the state equality constraint, the constraint may exist stochastically. Considered this phenomenon, the stochastic distribution of the state equality constraint is modeled as the Bernoulli distribution, and regarded it as the perfect measurement drew into the measurement equation in this paper. A tiny noise may be subjoined on it to avoid leading the covariance of the augmented measurement noise singular. At this time, the original system can be generalized to the linear system with a part of its measurement received stochastically. Aimed at this system, the linear minimum mean square error estimator (LMMSE) is derived according to the orthogonality principle. The simulation result shows that the proposed method has a same performance with the traditional method which is used to deal with the linear system with the state equality constraint when the constraint is existed all the time. However, the performance of the proposed method is prior to that of the traditional method when the state equality constraint is existed stochastically.