Related papers: An Approach to Duality in Nonlinear Filtering
Concurrent observation technologies have made high-precision real-time data available in large quantities. Data assimilation (DA) is concerned with how to combine this data with physical models to produce accurate predictions. For…
This paper studies the distributed state estimation problem for a class of discrete time-varying systems over sensor networks. Firstly, it is shown that a networked Kalman filter with optimal gain parameter is actually a centralized filter,…
This paper studies the distributed state estimation in sensor network, where $m$ sensors are deployed to infer the $n$-dimensional state of a linear time-invariant (LTI) Gaussian system. By a lossless decomposition of optimal steady-state…
The Kalman-Bucy filter is extensively utilized across various applications. However, its computational complexity increases significantly in large-scale systems. To mitigate this challenge, a low-rank approximated Kalman--Bucy filter was…
The purpose of this paper is to review and highlight some connections between the problem of nonlinear smoothing and optimal control of the Liouville equation. The latter has been an active area of recent research interest owing to work in…
This paper is concerned with the problem of state estimation for discrete-time linear systems in the presence of additional (equality or inequality) constraints on the state (or estimate). By use of the minimum variance duality, the…
This paper deals with a nonlinear filtering problem in which a multi-dimensional signal process is additively affected by a process $\nu$ whose components have paths of bounded variation. The presence of the process $\nu$ prevents from…
Motivated by the maneuvering target tracking with sensors such as radar and sonar, this paper considers the joint and recursive estimation of the dynamic state and the time-varying process noise covariance in nonlinear state space models.…
Common filters are usually based on the linear approximation of the optimal minimum mean square error estimator. The Extended and Unscented Kalman Filters handle nonlinearity through linearization and unscented transformation, respectively,…
We derive the dual variational principle (principle of minimal complementary energy) for the nonlocal nonlinear scalar diffusion problem, which may be viewed as the nonlocal version of the $p$-Laplacian operator. We establish existence and…
This paper studies the question of filtering and maximizing terminal wealth from expected utility in a partially information stochastic volatility models. The special features is that the only information available to the investor is the…
This paper presents an adaptive Kalman filter for a linear dynamic system perturbed by an additive disturbance. The objective is to estimate both of the state and the unknown disturbance concurrently, while learning the disturbance as a…
The possible methodologies to handle the uncertain parameter are reviewed. The core idea of the desensitized Kalman filter is introduced. A new cost function consisting of a posterior covariance trace and trace of a weighted norm of the…
We study finite-horizon quadratic control of linear systems with bilinear observations, in which the control input affects not only the state dynamics but also the partial observations of the state. In this setting, the separation principle…
The measure timetable plays a critical role for the accuracy of the estimator. This article deals with the optimization of the schedule of measures for observing a random process in time using a Kalman filter, when the length of the process…
This paper introduces a novel approach to the optimal control of linear discrete-time systems subject to bounded disturbances. Our approach is based on the newly established duality between ellipsoidal approximations of reachable and hardly…
Bayesian linear inverse problems aim to recover an unknown signal from noisy observations, incorporating prior knowledge. This paper analyses a data-dependent method to choose the scale parameter of a Gaussian prior. The method we study…
Quantum mechanical systems exhibit an inherently probabilistic nature upon measurement. Using a quantum noise model to describe the stochastic evolution of the open quantum system and working in parallel with classical indeterministic…
The aim of this paper is to provide a variational interpretation of the nonlinear filter in continuous time. A time-stepping procedure is introduced, consisting of successive minimization problems in the space of probability densities. The…
We provide a continuous time limit analysis for the class of Ensemble Square Root Filter algorithms with deterministic model perturbations. In the particular linear case, we specify general conditions on the model perturbations implying…