Related papers: Kinetic Methods for Inverse Problems
This paper develops an efficient implementation of the ensemble Kalman filter based on a modified Cholesky decomposition for inverse covariance matrix estimation. This implementation is named EnKF-MC. Background errors corresponding to…
Inverse kinematic (IK) methods recover the parameters of the joints, given the desired position of selected elements in the kinematic chain. While the problem is well-defined and low-dimensional, it has to be solved rapidly, accounting for…
We propose an ensemble score filter (EnSF) for solving high-dimensional nonlinear filtering problems with superior accuracy. A major drawback of existing filtering methods, e.g., particle filters or ensemble Kalman filters, is the low…
We propose a method to account for model error due to unresolved scales in the context of the ensemble transform Kalman filter (ETKF). The approach extends to this class of algorithms the deterministic model error formulation recently…
In this paper, we study in detail various solutions, especially kink ones, in different nonlocal scalar field theories, whose kinetic term is described by an arbitrary non-polynomial analytic function of the d'Alembertian operator, and the…
Many modern algorithms for inverse problems and data assimilation rely on ensemble Kalman updates to blend prior predictions with observed data. Ensemble Kalman methods often perform well with a small ensemble size, which is essential in…
It has been proposed that classical filtering methods, like the Kalman filter and 3DVAR, can be used to solve linear statistical inverse problems. In the work of Iglesias, Lin, Lu, & Stuart (2017), error estimates were obtained for this…
The ensemble Kalman inversion (EKI), as a derivative-free methodology, has been widely used in the parameter estimation of inverse problems. Unfortunately, its cost may become moderately large for systems described by high dimensional…
The general inverse kinematics (IK) problem of a manipulator, namely that of acquiring the self-motion manifold (SMM) of all admissible joint angles for a desired end-effector pose, plays a vital role in robotics modeling, planning and…
In this paper an optimal control problem for a large system of interacting agents is considered using a kinetic perspective. As a prototype model we analyze a microscopic model of opinion formation under constraints. For this problem a…
We show how one can obtain kink solutions of ordinary differential equations with polynomial nonlinearities by an efficient factorization procedure directly related to the factorization of their nonlinear polynomial part. We focus on…
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…
The paper proposes a new recursive filter for non-linear systems that inherently computes a valid bound on the mean square estimation error. The proposed filter, bound based extended Kalman, (BEKF) is in the form of an extended Kalman…
We show how to compute globally optimal solutions to inverse kinematics (IK) by formulating the problem as an indefinite quadratically constrained quadratic program. Our approach makes it feasible to solve IK instances of generic redundant…
Ensemble Kalman Inversion (EnKI) and Ensemble Square Root Filter (EnSRF) are popular sampling methods for obtaining a target posterior distribution. They can be seem as one step (the analysis step) in the data assimilation method Ensemble…
We present a novel sampling-based method for estimating probabilities of rare or failure events. Our approach is founded on the Ensemble Kalman filter (EnKF) for inverse problems. Therefore, we reformulate the rare event problem as an…
Both constrained and unconstrained optimization problems regularly appear in recursive tracking problems engineers currently address -- however, constraints are rarely exploited for these applications. We define the Kalman Filter and…
In the process of reproducing the state dynamics of parameter dependent distributed systems, data from physical measurements can be incorporated into the mathematical model to reduce the parameter uncertainty and, consequently, improve the…
The objective is to investigate the advantages and performance of Extended Kalman Filter for the estimation of non-linear system where linearization takes place about a trajectory that was continually updated with the state estimates…
Convergence of the ensemble Kalman filter in the limit for large ensembles to the Kalman filter is proved. In each step of the filter, convergence of the ensemble sample covariance follows from a weak law of large numbers for exchangeable…