Recursive Filtering For 2-D Markov Jump Systems With Fading Channels

In recent years,the filtering problem of two-dimensional(2-D)systems is one of the research hotspots in the control field.The 2-D system changes in 2-D space,which is different from the traditional one-dimensional(1-D)state-space model.Therefore,cross terms at different times are inevitably produced while investigating the filtering estimation error covariance equation.It is urgently needed to address how to eliminate the cross-terms of the Riccati equation and develop the recursive optimal filter for 2-D systems.In addition,general2-D systems are difficult to describe when it is disturbed by various uncertainties,so the 2-D Markov jump system can be used in the modeling.This thesis systematically investigated the centralized and distributed recursive filtering problems for 2-D stochastic linear systems and 2-D random Markov jump systems under multiparallel fading channels and Rice fading channels.The 2-D centralized and distributed recursive estimation algorithms are designed based on the complete square method,the innovation analysis method,the lifting technology,the state augmentation method,and the distributed estimation fusion method.The main work is as follows:1.The recursive filtering problem for the 2-D multi-rate system and Markov jump system under multi-parallel fading channels are studied.The lifting technique is used to convert a multi-rate system into a single-rate system.The appropriate transition probability constraints need to be introduced for Markov systems.The complete square method is applied to minimize the estimated error variance array to derive 2-D recursive filters for the multi-rate system and Markov jump system,respectively,where the filter gains are derived by solving the 2-D generalized difference Riccati equation and the 2-D coupled difference Riccati equation.The main innovations include the following: 1)Eliminating the cross-terms in the expressions of the estimation error variance matrix and determining the recursive form of the Ricatti equation for the minimum variance filter of the 2-D system.2)The transition probability constraint is introduced to overcome the correlation of transition probability.A 2-D recursive filter with jump parameters is proposed.3)The phenomenon of multi-parallel channel fading is considered to correlate with the 2-D recursively coupled differential Riccati equation both the transfer probability and the packet loss probability.2.The optimal recursive filtering problems for 2-D systems with Rice channel fading and2-D Markov jump systems are studied.The 2-D recursive filtering problem under Rice channel fading is essentially a 2-D system filtering problem with both packet loss and time delay.The appropriate transition probability constraints are introduced for Markov systems.The state augmentation method is applied to eliminate impact from the time-delay terms,converting the time-delay packet loss system into a delay-free general 2-D system and 2-D Markov jump system.In this case,the gain of the minimum variance filter corresponding to the two kinds of systems and the corresponding 2-D recursive Riccati equation and coupled difference Riccati equation is obtained by using the new information analysis method and the complete square method respectively to minimize the estimated error variance matrix.The main contributions of this paper are as follows: 1)For the 2-D Markov system with Rice channel fading,the appropriate transition probability constraint condition is introduced to determine the optimal filter estimation error variance matrix expression due to the simultaneous existence of delay,packet loss and jump parameters.2)The time-delay system is transformed into a time-delay system with no time delay via the state extension method and filters with relatively high accuracy are designed,accounting for time-delay and packet loss simultaneously in the 2-D system with jump parameters.3.The distributed recursive filtering problem for multi-rate 2-D stochastic linear systems with fading channels and 2-D Markov jump systems are studied.Firstly,the multi-rate multisensor system is transformed into a single-rate multi-sensor system with the lifting technique for the multi-rate 2-D system under the multi-parallel fading channel.For the 2-D Markov jump system,an appropriate transition probability constraint is introduced.Secondly,the local recursive optimal filters of the two kinds of systems are designed respectively based on the method mentioned in the first part,minimizing local estimation error at each moment,and the filter gain is obtained by the complete square method.Furthermore,the distributed filter is designed based on a sequential fusion algorithm and CI fusion algorithm,and the obtained filter has relatively high estimation accuracy.The main innovations are as follows: 1)The sequential fusion algorithm is applied to 2-D systems,proposing a novel 2-D distributed filter with higher estimation accuracy and lower computational burden than the centralized filter.2)The proposed CI fusion algorithm for the 2-D Markov jump system avoided the calculation of the estimated error covariance matrix and relieved the computational burden.