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 …

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 …

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 …

The concept of an estimation algebra, introduced independently by Mitter and Brockett,
provides an important research direction for nonlinear filtering theory. By interpreting the …

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 …

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 …

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 …

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 …

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 …

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 …