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In this paper, we explore the embedding of nonlinear dynamical systems into linear ordinary differential equations (ODEs) via the Carleman linearization method. Under dissipative conditions, numerous previous works have established rigorous…
In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold…
We study a distributed Kalman filtering problem in which a number of nodes cooperate without central coordination to estimate a common state based on local measurements and data received from neighbors. This is typically done by running a…
An optimal estimator of quantum states based on a modified Kalman's Filter is proposed in this work. Such estimator acts after state measurement, allowing obtain an optimal estimation of quantum state resulting in the output of any quantum…
This paper studies detectability for switched linear differential-algebraic equations (DAEs) and its application to the synthesis of observers, which generate asymptotically converging state estimates. Equating detectability to asymptotic…
Nonlinear filtering problems are encountered in many applications, and one solution approach is the extended Kalman filter, which is not always convergent. Therefore, it is crucial to identify conditions under which the extended Kalman…
This manuscript develops a general purpose inner-product norm for the Kendall \(\tau\) and Spearman's \(\rho\), which operates as an unbiased MLE even in the presence of ties. We derive and prove the strict sub-Gaussianity of the Kemeny…
Inspired by the work done by Belavkin [Belavkin V. P., Stochastics, 1, 315 (1975)], and independently by Mochon, [Phys. Rev. A 73, 032328, (2006)], we formulate the problem of minimum error discrimination of any ensemble of $n$ linearly…
This paper investigates the state estimation problem for a class of complex networks, in which the dynamics of each node is subject to Gaussian noise, system uncertainties and nonlinearities. Based on a regularized least-squares approach,…
This paper examines the problem of state estimation in power distribution systems under low-observability conditions. The recently proposed constrained matrix completion method which combines the standard matrix completion method and power…
In this paper, we propose a new framework for solving state estimation problems with an additional sparsity-promoting $L_1$-regularizer term. We first formulate such problems as minimization of the sum of linear or nonlinear quadratic error…
This paper considers estimation and inference in semiparametric econometric models. Standard procedures estimate the model based on an independence restriction that induces a minimum distance between a joint cumulative distribution function…
This paper studies the convergence of the estimation error process and the characterization of the corresponding invariant measure in distributed Kalman filtering for potentially unstable and large linear dynamic systems. A gossip network…
Fueled by applications in sensor networks, these years have witnessed a surge of interest in distributed estimation and filtering. A new approach is hereby proposed for the Distributed Kalman Filter (DKF) by integrating a local covariance…
We consider the problem of parameter estimation in a partially observed linear Gaussian system with small noises in the state and observation equations. We describe asymptotic properties of the MLE and Bayes estimators in the setting with…
We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…
This paper presents a framework on minimal-order appointed-time unknown input observers for linear systems based on the pairwise observer structure. A minimal-order appointed-time observer is first proposed for the linear system without the…
An optimal estimator of quantum states based on a modified Kalman Filter is presented in this work. Such estimator acts after state measurement, allowing to obtain an optimal estimation of quantum state resulting in the output of any…
General Probabilistic Theories provide the most general mathematical framework for the theory of probability in an operationally natural manner, and generalize classical and quantum theories. In this article, we study state-discrimination…
This letter proposes a new method for joint state and parameter estimation in uncertain dynamical systems. We exploit the partial errors-in-variables (PEIV) principle and formulate a regression problem in the sense of weighted total least…