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This paper considers the simultaneous state and unknown input estimation for continuous-discrete stochastic systems. Two types of approaches (with and without modeling of unknown inputs) which can address this issue are investigated. A…
We consider the dynamic large deviation behaviour of Kac's collisional process for a range of initial conditions including equilibrium. We prove an upper bound with a rate function of the type which has previously been found for kinetic…
In this paper, a distributed Kalman filtering (DKF) algorithm is proposed based on a diffusion strategy, which is used to track an unknown signal process in sensor networks cooperatively. Unlike the centralized algorithms, no fusion center…
A stable filter has the property that it asymptotically `forgets' initial perturbations. As a result of this property, it is possible to construct approximations of such filters whose errors remain small in time, in other words…
A summary of the relationship between the Langevin equation, Fokker-Planck-Kolmogorov forward equation (FPKfe) and the Feynman path integral descriptions of stochastic processes relevant for the solution of the continuous-discrete filtering…
Collaborative filtering (CF) is a popular technique in today's recommender systems, and matrix approximation-based CF methods have achieved great success in both rating prediction and top-N recommendation tasks. However, real-world…
A hybrid particle ensemble Kalman filter is developed for problems with medium non-Gaussianity, i.e. problems where the prior is very non-Gaussian but the posterior is approximately Gaussian. Such situations arise, e.g., when nonlinear…
The Kalman-Bucy filter is the optimal state estimator for an Ornstein-Uhlenbeck diffusion given that the system is partially observed via a linear diffusion-type (noisy) sensor. Under Gaussian assumptions, it provides a finite-dimensional…
We provide a generic way of deducing non-asymptotic error bounds for Sequential MCMC methods from suitable stability properties of Feynman-Kac propagators. We show how to derive this type of stability from mixing conditions for the MCMC…
We say that an algorithm is stable if small changes in the input result in small changes in the output. This kind of algorithm stability is particularly relevant when analyzing and visualizing time-varying data. Stability in general plays…
State estimation in the presence of uncertain or data-driven noise distributions remains a critical challenge in control and robotics. Although the Kalman filter is the most popular choice, its performance degrades significantly when…
Predictive safety filters provide a way of projecting potentially unsafe inputs, proposed, e.g. by a human or learning-based controller, onto the set of inputs that guarantee recursive state and input constraint satisfaction by leveraging…
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 papers shows that nonlinear filter in the case of deterministic dynamics is stable with respect to the initial conditions under the conditions that observations are sufficiently rich, both in the context of continuous and discrete time…
In this paper, we consider a new framework for particle filtering under model uncertainty that operates beyond the scope of Markovian switching systems. Specifically, we develop a novel particle filtering algorithm that applies to general…
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…
The success of the ensemble Kalman filter has triggered a strong interest in expanding its scope beyond classical state estimation problems. In this paper, we focus on continuous-time data assimilation where the model and measurement errors…
Stability analysis of the Kalman filter under randomly lost measurements has been widely studied. We revisit this problem in a general continuous-time framework, where both the measurement matrix and noise covariance evolve as random…
Preserving stability is a central problem in data-driven model order reduction of dynamical systems. For linear systems whose dynamics depend on geometric or physical parameters, multivariate rational approximation algorithms such as the…
The ensemble Kalman filter (EnKF) is a popular technique for performing inference in state-space models (SSMs), particularly when the dynamic process is high-dimensional. Unlike reweighting methods such as sequential Monte Carlo (SMC, i.e.…