Research On System Identification And State Estimation Based On Convex Space Structure Contraction Filter

In the research of traditional system identification and state estimation methods,noise is often assumed to meet certain probability distribution conditions.However,as the complexity of the studied system becomes higher and higher,the noise that meets the probability distribution is often difficult to obtain.At this time,assuming that the noise changes within a certain interval can better meet the actual production needs.In order to reduce the amount of calculation,speed up the shrinkage rate of the feasible set of parameters,and improve the efficiency of system identification and state estimation,this paper studies the filtering algorithm based on the feasible set of convex space structure parameters based on the analysis of convex space structure shrinkage.This has forwardlooking theoretical significance and significant application value for the enrichment and development of parameter set membership filter methods.The specific work of this paper includes the following four aspects:1.For the linear system of triangular convex space structure shrinkage filtering,the polyhedron is averagely triangulated so that the difference between the area or volume of each triangulated triangle is the smallest.Based on the probability that the true value of the parameter is approximately equal in each triangle,only the polyhedron and the triangle vertices need to be stored in the calculation process,which effectively reduces the amount of calculation.During the update process,the probability of discarding or retaining each divided triangle is equal,which achieves the effect of higher efficiency and higher accuracy of parameter estimation.2.For the linear system of polyhedral cone-convex spatial structure shrinkage filtering,adding one dimension to the linear system makes the feasible set of parameters transformed from polyhedron to polyhedral cone.A four-step judgment linear programming parameter estimation method is proposed.Firstly,judge whether the constraint conditions are valid.Secondly,judge whether the vertex of the polyhedron cone is in the support plane of the constraint condition,and again judge whether the normal vector of the support plane calculation is in all the support planes of the polyhedron cone,Finally,calculate the vertices of the polyhedron cone according to the normal vector and the unique support plane of the polyhedral cone,and update the normal vector and vertices of the support plane.The linear programming is used to obtain the optimal solution to modify the parameter estimation,which achieves the effect of high system identification accuracy.3.For the linear system of orthotopic spatial structure shrinkage filtering,in the case of parameter changes,selecting the orthotope as the feasible set of parameters,using the nature of the orthotopic rule,regularly expanding the orthotope to include the change of parameters,a parameter estimation method of the orthotope transform filter is proposed.The transformation coefficients are globally optimal using linear programming,and the optimal transformation coefficients are selected so that the transformed orthotopes can accurately contain the parameters after each step.After the transformation coefficients are known,the orthotopes constraint conditions are reconstructed at each step,so that The obtained parameter feasible set is the most compact,and in the process of parameter change,it can still track the parameter change,improve the estimation accuracy and reduce the conservativeness.4.For the linear system of orthotopic double spatial structure shrinkage filtering,in the process of parameter estimation,both orthotopes and zonotopes are used,and a parameter estimation method based on double orthotopic filtering is proposed.Utilizing the correlation between the two polysomes,that is,when the zonotope is wrapped with the orthotope,the upper and lower bounds of the zonotope are not changed,it can effectively transform the zonotope into a orthotopic constraint condition,which forms a triple constraint condition with the original orthotope and the measurement equation.The increase of effective constraints must make the final feasible set of parameters contain the most compact truth values of the parameters,so the accuracy of system modeling in the convex space of the orthotope is improved under the triple constraints.In summary,this paper mainly studies system identification and state estimation based on convex space structure contraction filter algorithms,the simulation experiments verify the effectiveness of these algorithms.With the analysis of the computational costs show that the proposed algorithms have higher computational efficiency.