Research On Filtering For Multiple Measurement Delays Systems With Correlated Noises And Nonlinear Terms

Kalman filtering is one of the core science and technology in the field of control.It is widely used in target tracking and recognition,aerospace,industrial process control,transportation and social economy.Kalman filtering is a method of estimating the state of the system by using a certain filtering criterion on the basis of the observable signal.Its purpose is to estimate or restore the real signal inside the system from the observable signal with disturbance.Due to the variability of the environment or the limitation of economic conditions,problems such as time-correlated noises,stochastic nonlinear terms,time delays,and resilient gains are caused,which inevitably lead to the performance degradation or even collapse of the system.The traditional Kalman filtering assumes that the ideal communication conditions are good and there is an accurate mathematical model,so it cannot be applied to the filtering problem of complex systems.In this paper,the filtering problem with time-correlated noises,stochastic nonlinear terms,resilient gain and multiple measurement delays is considered.The main work and research results of this paper are described as follows.1.The filtering problem of multiple measurement delays systems with time-correlated additive noises is studied.The time-correlated additive measurement noise is a linear combination of a class of stochastic noises conforming to Gaussian distribution.By introducing the difference method to process the original measurement sequence,a new measurement sequence without time-correlated noises is constructed.Furthermore,the measurement sequence without time delays is constructed by reorganizing the measurement,which effectively avoids the computational burden caused by state augmentation method.On this basis,the recursive algorithm of optimal filtering is given by using projection theorem,and the effectiveness of the algorithm design is verified by numerical simulation.2.The filtering problem for multiple measurement delays systems with time-correlated multiplicative noises is studied.The time-correlated measurement multiplicative noise is a linear combination of stochastic noises conforming to Gaussian distribution.Firstly,the original system is transformed into a time-delay-free system by reorganizing measurement to overcome the influence of time-delay measurement information.On this basis,the product of system state and time-correlated multiplicative noises is defined as a new variable,and a coupled recursive double filter is constructed.The filter gain is designed by solving a set of coupled difference Riccati equations.Finally,the effectiveness of the algorithm is proved by numerical simulation.3.The filtering problem of multiple measurement delays systems with resilient gain is studied.Stochastic nonlinear terms are characterized by its statistical properties,and the measurement attenuation phenomenon is described by a class of stochastic variables subject to a specified probability distribution.By using the method of reorganizing measurement,the original system is transformed into a delay-free system.Then,an unbiased segmented resilient filter is constructed.The upper bound of error covariance is obtained via the method of mathematical induction and stochastic analysis.And the iterative algorithm of gain is completed by optimizing the upper bound.On this basis,sufficient conditions for mean square stability of resilient filter is given.Finally,the effectiveness of the algorithm is verified by numerical analysis.