Scaling parameters selection principle for the scaled unscented Kalman filter

The paper deals with the state estimation of the widely used scaled unscented Kalman filter（UKF）. In particular, the stress is laid on the scaling parameters selection principle for the scaled UKF. Several problems caused by recommended constant scaling parameters are highlighted. On the basis of the analyses, an effective scaled UKF is proposed with self-adaptive scaling parameters,which is easy to understand and implement in engineering. Two typical strong nonlinear examples are given and their simulation results show the effectiveness of the proposed principle and algorithm.

Selection Principles and Sierpinski Sets

We show that a set of real numbers is a Sierpinski set if, and only if, it satisfies a selection property similar to the familiar Menger property.

A Sparse Kernel Approximate Method for Fractional Boundary Value Problems

In this paper,the weak pre-orthogonal adaptive Fourier decomposition(W-POAFD)method is applied to solve fractional boundary value problems(FBVPs)in the reproducing kernel Hilbert spaces(RKHSs)W_(0)^(4)[0,1] and W^(1)[0,1].The process of the W-POAFD is as follows:(i)choose a dictionary and implement the pre-orthogonalization to all the dictionary elements;(ii)select points in[0,1]by the weak maximal selection principle to determine the corresponding orthonormalized dictionary elements iteratively;(iii)express the analytical solution as a linear combination of these determined dictionary elements.Convergence properties of numerical solutions are also discussed.The numerical experiments are carried out to illustrate the accuracy and efficiency of W-POAFD for solving FBVPs.

Parameter design of a liquid-filled sloshing system

The nonlinear governing equations of the liquid sloshing modals in a cylindrical storage tank are established. Through analytical analysis, the analytical expressions of the solutions of this kind of system are obtained. With different parameters, the dynamical behaviors of the solutions are different from the trivial ones. To prevent system instability, two selection principles that the stiffness equations are positive-definite and the nonlinear terms of the system are not regenerative elements are given. Meanwhile, numerical simulations are also given, which confirm the analytical results.

Site occupation of doping La^(3+) cations and phase transition in Na_(0.5)Bi_(0.5)TiO_3-BaTiO_3 solid solution

The effects of La doping on the ferroelectric properties of 0.92Na0.5Bi0.5TiO3-0.08BaTiO3（NBT-BT） solid solution have been studied both experimentally and theoretically.The experimental results show that an abnormal ferro-toantiferroelectric phase transition is induced by La doping in NBT-BT.The first-principles calculations indicate that La3＋ cations selectively substitute for the A site in NBT-BT as donors.Furthermore,the computed binding energy reveals that La cations is most likely to substitute Ba^ 2＋or Na^＋,not Bi^3＋,at A site as donors in NBT-BT,as supported by our Raman spectra.The ferro-to-antiferroelectric phase transition of La-doped NBT-BT is believed to originate from the lattice aberrance and redistribution of valence electrons,thus strengthening the bonding of A-O,enhancing the hybridization between the A cation d orbital and O 2p orbital,and resulting in the deflection of the polar direction of NBT-BT lattice.

Applications of k-covers

We investigate a role of k-covers in selection principles theory. Some results about relationships between Ramsey theory and game theory and selection principles that involve k-covers are also given.