Related papers: Spatial discretization error in Kalman filtering f…
In this paper, a new filter model called set-membership Kalman filter for nonlinear state estimation problems was designed, where both random and unknown but bounded uncertainties were considered simultaneously in the discrete-time system.…
Input estimation is a signal processing technique associated with deconvolution of measured signals after filtering through a known dynamic system. Kitanidis and others extended this to the simultaneous estimation of the input signal and…
This paper addresses the synthesis of an optimal fixed-gain distributed observer for discrete-time linear systems over wireless sensor networks. The proposed approach targets the steady-state estimation regime and computes fixed observer…
We propose a partition-based state estimator for linear discrete-time systems composed by coupled subsystems affected by bounded disturbances. The architecture is distributed in the sense that each subsystem is equipped with a local state…
State estimation in stochastic dynamical systems with noisy measurements is a challenge. While the Kalman filter is optimal for linear systems with independent Gaussian white noise, real-world conditions often deviate from these…
For linear and Gaussian state space models parametrized by $\theta_0 \in \Theta \subset \mathbb{R}^r, r \geq 1$ corresponding to the vector of parameters of the model, the Kalman filter gives exactly the solution for the optimal filtering…
Kalman filtering is a cornerstone of estimation theory, yet learning the optimal filter under unknown and potentially singular noise covariances remains a fundamental challenge. In this paper, we revisit this problem through the lens of…
This paper presents a novel Wasserstein distributionally robust control and state estimation algorithm for partially observable linear stochastic systems, where the probability distributions of disturbances and measurement noises are…
This paper introduces a spatio-temporal resonator model and an inference method for detection and estimation of nearly periodic temporal phenomena in spatio-temporal data. The model is derived as a spatial extension of a stochastic harmonic…
This paper proposes a new framework for constructing interval-valued state estimators for discrete-time linear and switched linear systems. Our main results are (i) the derivation of the tightest interval-valued estimator for linear…
Dynamic discrete choice models often discretize the state vector and restrict its dimension in order to achieve valid inference. I propose a novel two-stage estimator for the set-identified structural parameter that incorporates a…
We propose a new recursive estimator for linear dynamical systems under Gaussian process noise and non-Gaussian measurement noise. Specifically, we develop an approximate maximum a posteriori (MAP) estimator using dynamic programming and…
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…
Motivated by optimization with differential equations, we consider optimization problems with Hilbert spaces as decision spaces. As a consequence of their infinite dimensionality, the numerical solution necessitates finite dimensional…
Stochastic models in biomolecular contexts can have a state-dependent process noise covariance. The choice of the process noise covariance is an important parameter in the design of a Kalman Filter for state estimation and the theoretical…
We demonstrate optimal state estimation for a cavity optomechanical system through Kalman filtering. By taking into account nontrivial experimental noise sources, such as colored laser noise and spurious mechanical modes, we implement a…
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,…
We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…
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…
We consider optimal signalling and control of discrete-time nonlinear partially observable stochastic systems in state space form. In the first part of the paper, we characterize the operational {\it control-coding capacity}, $C_{FB}$ in…