We consider filtering for a continuous-time, or asynchronous, stochastic system where the full distribution over states is too large to be stored or calculated. We assume that the rate matrix of the system can be compactly represented and that the belief distribution is to be approximated as a product of marginals. The essential computation is the matrix exponential. We look at two different methods for its computation: ODE integration and uniformization of the Taylor expansion. For both we consider approximations in which only a factored belief state is maintained. For factored uniformization we demonstrate that the KL-divergence of the filtering is bounded. Our experimental results confirm our factored uniformization performs better than previously suggested uniformization methods and the mean field algorithm.
Quantum Filtering (Quantum Trajectories) for Systems Driven by Fields in Single Photon States and Superposition of Coherent States
Aberystwyth University（阿伯里斯特威斯大学）；ARC Centre for Quantum Computation and Communication Technology（量子计算与通信技术ARC中心）；Research School of Engineering, Australian National University（澳大利亚国立大学工程研究学院）；School of Electrical Engineering and Telecommunications, The University of New South Wales（新南威尔士大学电气工程和电信学院）；Department of Physics and Astronomy, University of New Mexico（新墨西哥大学物理与天文学系）
Intelligent Sensor-Actuator-Systems Laboratory (ISAS)（智能传感器-执行器系统实验室（ISAS））；Institute for Anthropomatics（人体工程学研究所）；Karlsruhe Institute of Technology (KIT)（卡尔斯鲁厄理工学院（KIT））
Mitigating Error Accumulation in Continuous Navigation via Memory-Augmented Kalman Filtering
Big Data Institute, Central South University, Changsha, China. Work done while working at CityUHK as a visiting scholar.；Department of Computer Science \& Institute of Digital Medicine, City University of Hong Kong, Hong Kong, China；School of Computer Science, Central South University, Changsha, China
