TY - GEN
T1 - Generalized Jacobi Spectral Method in Solving Nonlinear Filtering Problems
AU - Luo, Xue
AU - Wang, Fang
N1 - Publisher Copyright:
© 2018 IEEE.
PY - 2018/7/2
Y1 - 2018/7/2
N2 - The on-and off-line algorithm for the nonlinear filtering (NLF) problems was developed by Yau and the first author, and the Hermite spectral method (HSM) has been implemented to serve as the off-line computations. Notice that the true states in real applications can always be assumed to be bounded. In this paper, we shall investigate the Jacobi spectral method (JSM) instead to numerically solve the forward Kolmogorov equation (FKE) arising in NLF problems. The convergence rate of JSM to FKE is analyzed in the suitable function space, which is twice as fast as that in HSM. The formulation has been detailed for an essentially infinite-dimensional NLF problem, the 1-d cubic sensor problem. Compared with HSM, the JSM yields more accurate result.
AB - The on-and off-line algorithm for the nonlinear filtering (NLF) problems was developed by Yau and the first author, and the Hermite spectral method (HSM) has been implemented to serve as the off-line computations. Notice that the true states in real applications can always be assumed to be bounded. In this paper, we shall investigate the Jacobi spectral method (JSM) instead to numerically solve the forward Kolmogorov equation (FKE) arising in NLF problems. The convergence rate of JSM to FKE is analyzed in the suitable function space, which is twice as fast as that in HSM. The formulation has been detailed for an essentially infinite-dimensional NLF problem, the 1-d cubic sensor problem. Compared with HSM, the JSM yields more accurate result.
UR - https://www.scopus.com/pages/publications/85062191919
U2 - 10.1109/CDC.2018.8619484
DO - 10.1109/CDC.2018.8619484
M3 - 会议稿件
AN - SCOPUS:85062191919
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 7206
EP - 7212
BT - 2018 IEEE Conference on Decision and Control, CDC 2018
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 57th IEEE Conference on Decision and Control, CDC 2018
Y2 - 17 December 2018 through 19 December 2018
ER -