When boundary mismatch occurs in state-shifting models for nonlinear and non-Gaussian systems

it is often difficult to obtain accurate state estimates by particle filtering method. Considered constraints of boundary mismatch on particles

an extended set membership particle filtering method (MAP-ESMPF) was proposed on the basis of maximum a posteriori probability criterion. First

a feasible region for real states of particles was determined by extended set membership algorithm. Then

particles outside are projected into the feasible region by an optimization equation developed from the principle of maximum posteriori probability function. As a result

the accuracy of state estimate was ensured. Applications in a numerical simulation and process simulation of continuous stirred tank reactor (CSTR) showed effectiveness of the new method.