Related papers: Bellman filtering and smoothing for state-space mo…
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…
Using results from quantum filtering theory and methods from classical control theory, we derive an optimal control strategy for an open two-level system (a qubit in interaction with the electromagnetic field) controlled by a laser. The aim…
Simultaneous state and parameter estimation arises from various applicational areas but presents a major computational challenge. Most available Markov chain or sequential Monte Carlo techniques are applicable to relatively low dimensional…
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,…
A set of N independent Gaussian linear time invariant systems is observed by M sensors whose task is to provide the best possible steady-state causal minimum mean square estimate of the state of the systems, in addition to minimizing a…
Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we…
In this work, we explore finite-dimensional linear representations of nonlinear dynamical systems by restricting the Koopman operator to an invariant subspace. The Koopman operator is an infinite-dimensional linear operator that evolves…
Traditional filtering algorithms for state estimation -- such as classical Kalman filtering, unscented Kalman filtering, and particle filters - show performance degradation when applied to nonlinear systems whose uncertainty follows…
Complex systems are often described with competing models. Such divergence of interpretation on the system may stem from model fidelity, mathematical simplicity, and more generally, our limited knowledge of the underlying processes.…
UltimateKalman is a flexible linear Kalman filter and smoother implemented in three popular programming languages: MATLAB, C, and Java. UltimateKalman is a slight simplification and slight generalization of an elegant Kalman filter and…
We propose a Dynamical Low-Rank Ensemble Kalman Filter (DLR-ENKF) for efficient joint state-parameter estimation in high-dimensional dynamical systems. The method extends the DLR-ENKF formulation of arXiv:2509.11210 to the augmented…
This paper proposes a novel convex optimization framework for designing robust Kalman filters that guarantee a user-specified steady-state error while maximizing process and sensor noise. The proposed framework simultaneously determines the…
Bayesian filtering serves as the mainstream framework of state estimation in dynamic systems. Its standard version utilizes total probability rule and Bayes' law alternatively, where how to define and compute conditional probability is…
We consider a general form of the sensor scheduling problem for state estimation of linear dynamical systems, which involves selecting sensors that minimize the trace of the Kalman filter error covariance (weighted by a positive…
Particle filters contain the promise of fully nonlinear data assimilation. They have been applied in numerous science areas, but their application to the geosciences has been limited due to their inefficiency in high-dimensional systems in…
The purpose of this tutorial is to give a brief introduction to linear quantum control systems. The mathematical model of linear quantum control systems is presented first, then some fundamental control-theoretic notions such as stability,…
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…
This letter shows that the following three classes of recursive state estimation filters: standard filters, such as the extended Kalman filter; iterated filters, such as the iterated unscented Kalman filter; and dynamically iterated…
We consider the discrete-time filtering problem in scenarios where the observation noise is low or degenerate. We focus on the case where the observation equation is a linear function of the state and the data involve additive noise.…
The design and analysis of optimal control policies for dynamical systems can be complicated by nonlinear dependence in the state variables. Koopman operators have been used to simplify the analysis of dynamical systems by mapping the flow…