On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering （EKF）, the unscented K...On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering （EKF）, the unscented Kalman filtering （UKF） and the Gaussian particle filtering （GPF） to the case in which there is a positive probability that the observation in each time consists of noise alone and does not contain the chaotic signal （These generalized novel algorithms are referred to as GEKF, GUKF and GGPF correspondingly in this paper）. Using weights and network output of neural networks to constitute state equation and observation equation for chaotic time-series prediction to obtain the linear system state transition equation with continuous update scheme in an online fashion, and the prediction results of chaotic time series represented by the predicted observation value, these proposed novel algorithms are applied to the prediction of Mackey-Glass time-series with additive and multiplicative noises. Simulation results prove that the GGPF provides a relatively better prediction performance in comparison with GEKF and GUKF.展开更多
In this study,we extend traditional(single-target)hybrid systems to multi-target hybrid systems with a focus on the multi-maneuvering-target tracking system.This system consists of a continuous state,a discrete and sw...In this study,we extend traditional(single-target)hybrid systems to multi-target hybrid systems with a focus on the multi-maneuvering-target tracking system.This system consists of a continuous state,a discrete and switchable state,and a discrete,time-constant,and unique state.By defining a new generalized labeled multi-Bernoulli density,we prove that it is closed under the Chapman-Kolmogorov prediction and Bayes update for multi-target hybrid systems.In other words,we provide the exact derivation of a solution to this system,i.e.,the multi-model generalized labeled multi-Bemoulli filter,which has been developed without strict proof.展开更多
In this paper,we characterize all generalized low pass filters and MRA Parseval frame wavelets in L 2 （R n ） with matrix dilations of the form （Df）（x） =√ 2f（Ax）,where A is an arbitrary expanding n × n ma...In this paper,we characterize all generalized low pass filters and MRA Parseval frame wavelets in L 2 （R n ） with matrix dilations of the form （Df）（x） =√ 2f（Ax）,where A is an arbitrary expanding n × n matrix with integer coefficients,such that ｜det A｜ = 2.We study the pseudo-scaling functions,generalized low pass filters and MRA Parseval frame wavelets and give some important characterizations about them.Furthermore,we give a characterization of the semiorthogonal MRA Parseval frame wavelets and provide several examples to verify our results.展开更多
基金supported by the National Natural Science Foundation of China (Grant No 60774067)the Natural Science Foundation of Fujian Province of China (Grant No 2006J0017)
文摘On the assumption that random interruptions in the observation process are modelled by a sequence of independent Bernoulli random variables, this paper generalize the extended Kalman filtering （EKF）, the unscented Kalman filtering （UKF） and the Gaussian particle filtering （GPF） to the case in which there is a positive probability that the observation in each time consists of noise alone and does not contain the chaotic signal （These generalized novel algorithms are referred to as GEKF, GUKF and GGPF correspondingly in this paper）. Using weights and network output of neural networks to constitute state equation and observation equation for chaotic time-series prediction to obtain the linear system state transition equation with continuous update scheme in an online fashion, and the prediction results of chaotic time series represented by the predicted observation value, these proposed novel algorithms are applied to the prediction of Mackey-Glass time-series with additive and multiplicative noises. Simulation results prove that the GGPF provides a relatively better prediction performance in comparison with GEKF and GUKF.
基金Project supported by the National Natural Science Foundation of China(No.61601510)the Young Talent Support Project of China Association for Science and Technology(No.18-JCJQ-QT-008)。
文摘In this study,we extend traditional(single-target)hybrid systems to multi-target hybrid systems with a focus on the multi-maneuvering-target tracking system.This system consists of a continuous state,a discrete and switchable state,and a discrete,time-constant,and unique state.By defining a new generalized labeled multi-Bernoulli density,we prove that it is closed under the Chapman-Kolmogorov prediction and Bayes update for multi-target hybrid systems.In other words,we provide the exact derivation of a solution to this system,i.e.,the multi-model generalized labeled multi-Bemoulli filter,which has been developed without strict proof.
基金Supported by the National Natural Science Foundation of China (Grant No. 60774041)the Natural Science Foundation for the Education Department of Henan Province of China (Grant No. 2010A110002)
文摘In this paper,we characterize all generalized low pass filters and MRA Parseval frame wavelets in L 2 （R n ） with matrix dilations of the form （Df）（x） =√ 2f（Ax）,where A is an arbitrary expanding n × n matrix with integer coefficients,such that ｜det A｜ = 2.We study the pseudo-scaling functions,generalized low pass filters and MRA Parseval frame wavelets and give some important characterizations about them.Furthermore,we give a characterization of the semiorthogonal MRA Parseval frame wavelets and provide several examples to verify our results.
