Log-Concave Posterior Densities Arising in Continuous Filtering and a Maximum A Posteriori Algorithm
Nonlinear filtering is fundamental to many engineering problems, as it involves inferring the
state of a system given complicated dynamics and noisy observations. Some approaches to …
state of a system given complicated dynamics and noisy observations. Some approaches to …
Finite-dimensional filters with nonlinear drift. II: Brockett's problem on classification of finite-dimensional estimation algebras
WL Chiou, SST Yau - SIAM journal on control and optimization, 1994 - SIAM
The idea of using estimation algebras to construct finite-dimensional nonlinear filters was
first proposed by Brockett and Mitter independently. It turns out that the concept of estimation …
first proposed by Brockett and Mitter independently. It turns out that the concept of estimation …
Recurrent neural networks are universal approximators with stochastic inputs
In this article, we investigate the approximation ability of recurrent neural networks (RNNs)
with stochastic inputs in state space model form. More explicitly, we prove that open …
with stochastic inputs in state space model form. More explicitly, we prove that open …
The estimation algebra of nonlinear filtering systems
WS Wong, SST Yau - Mathematical control theory, 1999 - Springer
The concept of an estimation algebra, introduced independently by Mitter and Brockett,
provides an important research direction for nonlinear filtering theory. By interpreting the …
provides an important research direction for nonlinear filtering theory. By interpreting the …
Finite-dimensional filters with nonlinear drift, VI: Linear structure of Ω
J Chen, SST Yau - Mathematics of Control, Signals and Systems, 1996 - Springer
Ever since the concept of estimation algebra was first introduced by Brockett and Mitter
independently, it has been playing a crucial role in the investigation of finite-dimensional …
independently, it has been playing a crucial role in the investigation of finite-dimensional …
Finite dimensional estimation algebras with state dimension 3 and rank 2, I: Linear structure of Wong matrix
J Shi, SST Yau - SIAM Journal on Control and Optimization, 2017 - SIAM
In this paper we study the structure of finite dimensional estimation algebras with state
dimension 3 and rank 2 arising from a nonlinear filtering system by using the theories of the …
dimension 3 and rank 2 arising from a nonlinear filtering system by using the theories of the …
Finite-dimensional filters with nonlinear drift. III: Duncan-mortensen-zakai equation with arbitrary initial condition for the linear filtering system and the benes filtering …
ST Yau, SST Yau - IEEE transactions on aerospace and …, 1997 - ieeexplore.ieee.org
We consider the Duncan-Mortensen-Zakai (DMZ) equation for the Kalman-Bucy filtering
system and Benes filtering system. We show that this equation can be solved explicitly with …
system and Benes filtering system. We show that this equation can be solved explicitly with …
Classification of finite-dimensional estimation algebras of maximal rank with arbitrary state–space dimension and Mitter conjecture
SST Yau*, GQ Hu - International Journal of Control, 2005 - Taylor & Francis
In the late seventies, the concept of the estimation algebra of a filtering system was
introduced. It was proven to be an invaluable tool in the study of non-linear filtering …
introduced. It was proven to be an invaluable tool in the study of non-linear filtering …
Finite-dimensional filters with nonlinear drift IV: Classification of finite-dimensional estimation algebras of maximal rank with state–space dimension 3
J Chen, SST Yau, CW Leung - SIAM journal on control and optimization, 1996 - SIAM
The idea of using estimation algebras to construct finite-dimensional nonlinear filters was
first proposed by Brockett and Mitter independently. It turns out that the concept of estimation …
first proposed by Brockett and Mitter independently. It turns out that the concept of estimation …
Complete classification of finite-dimensional estimation algebras of maximal rank
SST Yau - International Journal of Control, 2003 - Taylor & Francis
The idea of using estimation algebras to construct finite-dimensional non-linear filters was
first proposed by Brockett and Clark, and Mitter independently. In his famous talk at the …
first proposed by Brockett and Clark, and Mitter independently. In his famous talk at the …