Extended Set Membership Filtering Method For Boundary-mismatched Models

The precision of the state estimation depends on the state transition model,the measurement model and the measurement.In the real industrial process,due to the change of process or equipment condition,some parameters or model structure will change,which will result in the deviations between the model and the actual situation.The statistical properties of the deviations are often complicated,and change in real time.It is difficult to measure and evaluate accurately because of sensor technology and cost.In the long run,the operators can often determine the uncertain boundary according to the operation experience.Based on ellipsoid,the extended set membership filtering expresses the uncertain parts of the model(noise,initial state)with ellipsoid set.In this dissertation,the extended set membership filtering is proposed for the state estimation based on a mismatch model with the uncertain boundary by using the ellipsoid demarcation method.This dissertation includes the following parts:(1)The state estimation based on the model with constant mismatch.When there is a bounded deviation in the model,the prior particles will deviate from the real state value,and the credibility of the particles is low.In this dissertation,an extended set membership particle filtering(MAP-ESMPF)algorithm is proposed based on the principle of maximum a posteriori probability criterion.The algorithm employs the extended set membership to obtain the feasible domain of the real state,and then the particles falling out of the feasible region are mapped to the feasible domain based on the MAP density function criterion.As a result,the accuracy of state estimation was ensured.(2)The state estimation based on the model with varying mismatch.Because the mismatch of parameters is bounded,it leads to the varying boundary of the mismatch model.In this paper,state estimation method is proposed based on the extended set membership method.The deviation scope caused by the parameters mismatch is calculated by the interval operation and interval expansion functions,and then it is enclosed by a parameter ellipsoid set.In the prediction step,the prediction ellipsoid is obtained by the summation of the parameter deviation ellipsoid set and the interval of the priori ellipsoid.In the update step,by using the observation ellipsoid set to update the priori ellipsoid,the posterior ellipsoid set and then the state estimate are derived.(3)The joint estimation of the state and parameters under the bounded-mismatch model.The model parameters and the state estimation interact.This paper proposed a dual extension set membership filtering method.In the prediction step,the parameters are used to get the ellipsoid of the state,and the parameters are extended by a random walk model.In the update step,we update the ellipsoid by measurements to obtain the state estimation.Then we use the state estimation to update the parameters ellipsoid set.Finally,the effectiveness of the proposed method is verified in the numerical simulation and the CSTR process.