TAILIEUCHUNG - Robot Arms 2010 Part 6

Tham khảo tài liệu 'robot arms 2010 part 6', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Distributed Nonlinear Filtering Under Packet Drops and Variable Delays for Robotic Visual Servoing 91 Thus in the case of packet losses the discrete time Kalman Filter recursion that was described in Eq. 5 measurement update is modified as K k YkP k CT CP k CT R 1 63 where Yks 0 1 . This modification implies that the value of the estimated state vector x k remains unchanged if the a packet drop occurs . when Yk 0. It is assumed that the system A C is observable. Next the following time sequences Tk and Pk are defined T1 inf k k 1 Yk 0 . Time T1 denotes the first time instant when the transmission over the communication channel is interrupted loss of connection . On the other hand time sequence Pk is defined as P1 inf k k T1 Yk 1 . Time Pk denotes the k-th time instant in which the transmission over the communication channel is restored reestablishment of connection . Therefore for time sequences Tk and Pk it holds 1 T1 p1 T2 P2 Tk pk . Thus 1 is the beginning of tranmission T1 is the time instant at which the connection is lost for the first time P1 is the time instant at which the connection is re-established after first interruption T2 is the time instant at which the connection is lost for second time P2 is the time instant at which the connection is re-established after second interruption etc. The following variable is also defined P Pk 1 where P is the last time instant in a period of subsequent packet losses. Time P is useful for analyzing the behavior of the Kalman Filter in case of a sequence of packet losses deterioration of the estimation error covariance matrix . It is noted that in the case of the filtering procedure over the communication network the sequence of covariance matrices PPk is stable if supk 1 E pPk II TO Xia et al. 2009 . Equivalently it can be stated that the networked system satisfies the condition of peak covariance stability Xia et al. 2009 . Fig. 4. Distributed filtering over sensors network with communication delays and packet .

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