Fusion Filtering For Singular Systems With Time-Correlated Nois

Descriptor system has been widely applied in complex systems,circuit systems,econometrics,and other practical systems.Based on the methods of reduced-order decomposition,measurement difference and projection theory,this paper studies the fusion filtering problem for descriptor systems with time-correlated noises.The main contents are as follows:1.For descriptor system with time-correlated noise and white process noise,the original descriptor system is transformed into two reduced-order subsystems by the method of reduced-order decomposition,and the continuous measurement noises are transformed into the one-step auto-correlated measurement noises by using the method of measurement difference.Firstly,based on projection theory,the local linear optimal filters are designed,and the cross-covariance matrices between any two local estimation errors are derived.And then,based on the matrix weighted,diagonal matrix weighted and scalar weighted fusion algorithms in the linear minimum variance sense,the distributed fusion filter is given.Then,in order to improve the estimation accuracy,the distributed fusion filter with feedback and centralized fusion filter are designed,and it is proved that the two fusion filters are numerically equivalent under the condition of full rank of local gain matrices,that is,the distributed fusion filter with feedback has global optimality.Finally,the estimation performance of the three fusion algorithms is analyzed.The distributed fusion filter is globally suboptimal,but it has parallel structure and is easy to detect and isolate faults.The distributed fusion filter with feedback has global optimality,but the feedback increases the communication burden between the local sensor subsystem and the fusion center,while the centralized fusion estimation can obtain the global optimal estimation under the condition that all sensors are healthy.2.For descriptor system with time-correlated noise and one step auto-correlated process noise,the original descriptor system is transformed into two reduced-order subsystems by the method of another kind of reduced-order decomposition.Firstly,the local linear optimal filter and one step predictor in the linear minimum variance sense are designed,and then the cross-covariance matrices between any two local filtering errors are derived.Finally,the distributed fusion filter is given by using optimal fusion algorithm in the linear unbiased minimum variance sense.