Related papers: An Approach to Duality in Nonlinear Filtering
This article presents an up-to-date tutorial review of nonlinear Bayesian estimation. State estimation for nonlinear systems has been a challenge encountered in a wide range of engineering fields, attracting decades of research effort. To…
This paper is concerned with a partially observed hybrid optimal control problem, where continuous dynamics and discrete events coexist and in particular, the continuous dynamics can be observed while the discrete events, described by a…
This report provides a brief historical evolution of the concepts in the Kalman filtering theory since ancient times to the present. A brief description of the filter equations its aesthetics, beauty, truth, fascinating perspectives and…
Recursive estimation of nonlinear dynamical systems is an important problem that arises in several engineering applications. Consistent and accurate propagation of uncertainties is important to ensuring good estimation performance. It is…
We consider a continuous-time linear-quadratic Gaussian control problem with partial observations and costly information acquisition. More precisely, we assume the drift of the state process to be governed by an unobservable…
Linear Quadratic Gaussian (LQG) control is a framework first introduced in control theory that provides an optimal solution to linear problems of regulation in the presence of uncertainty. This framework combines Kalman-Bucy filters for the…
Kalman filters provide a straightforward and interpretable means to estimate hidden or latent variables, and have found numerous applications in control, robotics, signal processing, and machine learning. One such application is neural…
Contemporary data assimilation often involves millions of prediction variables. The classical Kalman filter is no longer computationally feasible in such a high dimensional context. This problem can often be resolved by exploiting the…
In this article, we introduce decentralized Kalman filters for linear quadratic deep structured teams. The agents in deep structured teams are coupled in dynamics, costs and measurements through a set of linear regressions of the states and…
We address the problem of determining optimal sensor precisions for estimating the states of linear time-varying discrete-time stochastic dynamical systems, with guaranteed bounds on the estimation errors. This is performed in the Kalman…
Nonlinear state estimation under noisy observations is rapidly intractable as system dimension increases. We introduce an improved Yau-Yau filtering framework that breaks the curse of dimensionality and extends real-time nonlinear filtering…
Novel nonlinear damping control is proposed for the second-order systems. The proportional output feedback is combined with the damping term which is quadratic to the output derivative and inverse to the set-point distance. The global…
A Markovian model for a quantum automata, i.e. an open quantum dynamical discrete-time system with input and output channels and a feedback, is described. A dynamical theory of quantum discrete-time adaptive measurements and multi-stage…
In this article, we consider a stochastic linear quadratic control problem with partial observation. A near optimal control in the weak formulation is characterized. The main features of this paper are the presence of the control in the…
We analyze the Ensemble and Polynomial Chaos Kalman filters applied to nonlinear stationary Bayesian inverse problems. In a sequential data assimilation setting such stationary problems arise in each step of either filter. We give a new…
For a primal-dual pair of conic linear problems that are described by convex cones $S\subset X$, $T\subset Y$, bilinear symmetric objective functions $\langle\cdot,\cdot\rangle_X$, $\langle\cdot,\cdot\rangle_Y$ and a linear operator…
The Ensemble Kalman filter is a sophisticated and powerful data assimilation method for filtering high dimensional problems arising in fluid mechanics and geophysical sciences. This Monte Carlo method can be interpreted as a mean-field…
One of the most common misconceptions made about the Kalman filter when applied to linear systems is that it requires an assumption that all error and noise processes are Gaussian. This misconception has frequently led to the Kalman filter…
System identification poses a significant bottleneck to characterizing and controlling complex systems. This challenge is greatest when both the system states and parameters are not directly accessible leading to a dual-estimation problem.…
The Kalman filter is the most powerful tool for estimation of the states of a linear Gaussian system. In addition, using this method, an expectation maximization algorithm can be used to estimate the parameters of the model. However, this…