The Recursive Form of Error Bounds for RFS State and Observation with Pd<1

In the target tracking and its engineering applications, recursive state estimation of the target is of fundamental importance. This paper presents a recursive performance bound for dynamic estimation and filtering problem, in the framework of the finite set statistics for the first time. The number of tracking algorithms with set-valued observations and state of targets is increased sharply recently. Nevertheless, the bound for these algorithms has not been fully discussed. Treating the measurement as set, this bound can be applied when the probability of detection is less than unity. Moreover, the state is treated as set, which is singleton or empty with certain probability and accounts for the appearance and the disappearance of the targets. When the existence of the target state is certain, our bound is as same as the most accurate results of the bound with probability of detection is less than unity in the framework of random vector statistics. When the uncertainty is taken into account, both linear and non-linear applications are presented to confirm the theory and reveal this bound is more general than previous bounds in the framework of random vector statistics.In fact, the collection of such measurements could be treated as a random finite set (RFS)

The Strain Energy Release Rate for Stack of Coated Conductors with Interface Crack in Perpendicular Magnetic Field

Due to the ability of transporting huge current in the stack of high-temperature superconducting conductors, the electromagnetic body force generated by the interaction of magnetic field and current may affect the mechanical stability of structure. In this paper, the fracture behavior of the stack of coated conductors which contains an interface crack is studied for increasing field and decreasing field. The body forces are obtained with variational formulation for the Bean’s critical state model. Based on the virtual crack closure technique (VCCT), the strain energy release rate of the stack of coated conductors with an interface crack is determined. The strain energy release rates are compared for different crack positions, crack lengths, magnetic fields and the thicknesses of substrate, respectively. These results may be useful for the practical application