Related papers: Mathematically equivalent approaches for equality …
Matrix factorization from a small number of observed entries has recently garnered much attention as the key ingredient of successful recommendation systems. One unresolved problem in this area is how to adapt current methods to handle…
State estimation that combines observational data with mathematical models is central to many applications and is commonly addressed through filtering methods, such as ensemble Kalman filters. In this article, we examine the signal-tracking…
Angular path integration is the ability of a system to estimate its own heading direction from potentially noisy angular velocity (or increment) observations. Non-probabilistic algorithms for angular path integration, which rely on a…
In this work we propose a framework to address the issue of state dependent nonlinear equality-constrained state estimation using Bayesian filtering. This framework is constructed specifically for a linear approximation of Bayesian…
The Ensemble Kalman Filter method can be used as an iterative numerical scheme for parameter identification or nonlinear filtering problems. We study the limit of infinitely large ensemble size and derive the corresponding mean-field limit…
In this paper, we propose a class of efficient, accurate, and general methods for solving state-estimation problems with equality and inequality constraints. The methods are based on recent developments in variable splitting and partially…
In this paper we investigate the performance of projection-based low-rank approximations in Kalman filtering. For large-scale gas pipeline networks structure-preserving model order reduction has turned out to be an advantageous way to…
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…
Target tracking using observations from multiple sensors can achieve better estimation performance than a single sensor. The most famous estimation tool in target tracking is Kalman filter. There are several mathematical approaches to…
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…
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…
In this paper, we first review the theory of symmetry-preserving observers and we mention some recent results. Then, we apply the theory to Extended Kalman Filter-based Simultaneous Localization and Mapping (EKF SLAM). It allows to derive a…
Weighted and controlled frames have been introduced recently to improve the numerical efficiency of iterative algorithms for inverting the frame operator. In this paper we develop systematically these notions, including their mutual…
We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…
In this paper, we propose a robust Kalman filtering framework for systems with probabilistic uncertainty in system parameters. We consider two cases, namely discrete time systems, and continuous time systems with discrete measurements. The…
The Kalman filter (KF) and the extended Kalman filter (EKF) are well established techniques for state estimation. However, the choice of the filter tuning parameters still poses a major challenge for the engineers [1]. In the present work,…
In this paper we provide novel closed-form expressions enabling differentiation of any scalar function of the Kalman filter's outputs with respect to all its tuning parameters and to the measurements. The approach differs from the previous…
The estimation of spatiotemporal data from limited sensor measurements is a required task across many scientific disciplines. The sensor selection problem, which aims to optimize the placement of sensors, leverages innovations in greedy…
In this work, we present methods for state estimation in continuous-discrete nonlinear systems involving stochastic differential equations. We present the extended Kalman filter, the unscented Kalman filter, the ensemble Kalman filter, and…
This paper presents a new filter for state-space models based on Bellman's dynamic-programming principle, allowing for nonlinearity, non-Gaussianity and degeneracy in the observation and/or state-transition equations. The resulting Bellman…