Related papers: Nonlinearity and Uncertainty Informed Moment-Match…

Accurate propagation of orbital uncertainty is essential for a range of applications within space domain awareness. Adaptive Gaussian mixture-based approaches offer tractable nonlinear uncertainty propagation through splitting mixands to…

Uncertainty propagation in non-linear dynamical systems has become a key problem in various fields including control theory and machine learning. In this work we focus on discrete-time non-linear stochastic dynamical systems. We present a…

A method is presented to solve a stochastic, nonlinear optimal control problem representative of spacecraft trajectory design under uncertainty. The problem is reformulated as a chance constrained nonlinear program, or what is known as a…

The paper studies the optimal density steering problem for nonlinear continuous-time stochastic systems. To accurately capture nonlinear dynamics in high-uncertainty regions that deviate significantly from a nominal linearization point, we…

This paper presents a novel approach for propagating uncertainties in dynamical systems building on high-order Taylor expansions of the flow and moment-generating functions (MGFs). Unlike prior methods that focus on Gaussian distributions,…

A new multifidelity method is developed for nonlinear orbit uncertainty propagation. This approach guarantees improved computational efficiency and limited accuracy losses compared to fully high-fidelity counterparts. The initial…

This paper introduces a novel method for the automatic detection and handling of nonlinearities in a generic transformation. A nonlinearity index that exploits second order Taylor expansions and polynomial bounding techniques is first…

Gaussian mixtures are a common density representation in nonlinear, non-Gaussian Bayesian state estimation. Selecting an appropriate number of Gaussian components, however, is difficult as one has to trade of computational complexity…

In this paper, we study the finite-horizon optimal density steering problem for discrete-time stochastic linear dynamical systems. Specifically, we focus on steering probability densities represented as Gaussian mixture models which are…

In this paper, we address the problem of uncertainty propagation through nonlinear stochastic dynamical systems. More precisely, given a discrete-time continuous-state probabilistic nonlinear dynamical system, we aim at finding the sequence…

The Bayesian smoothing equations are generally intractable for systems described by nonlinear stochastic differential equations and discrete-time measurements. Gaussian approximations are a computationally efficient way to approximate the…

A multifidelity method for the nonlinear propagation of uncertainties in the presence of stochastic accelerations is presented. The proposed algorithm treats the uncertainty propagation (UP) problem by separating the propagation of the…

This paper develops a probabilistic anticipation algorithm for dynamic objects observed by an autonomous robot in an urban environment. Predictive Gaussian mixture models are used due to their ability to probabilistically capture continuous…

In highly nonlinear systems such as the ones commonly found in astrodynamics, Gaussian distributions generally evolve into non-Gaussian distributions. This paper introduces a method for effectively controlling non-Gaussian distributions in…

Gaussian mixture filters for nonlinear systems usually rely on severe approximations when calculating mixtures in the prediction and filtering step. Thus, offline approximations of noise densities by Gaussian mixture densities to reduce the…

We have previously reported a Bayesian algorithm for determining the coordinates of points in three-dimensional space from uncertain constraints. This method is useful in the determination of biological molecular structure. It is limited,…

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…

Advances in information technology have led to extremely large datasets that are often kept in different storage centers. Existing statistical methods must be adapted to overcome the resulting computational obstacles while retaining…

Deep learning offers promising new ways to accurately model aleatoric uncertainty in robotic state estimation systems, particularly when the uncertainty distributions do not conform to traditional assumptions of being fixed and Gaussian. In…

In object tracking and state estimation problems, ambiguous evidence such as imprecise measurements and the absence of detections can contain valuable information and thus be leveraged to further refine the probabilistic belief state. In…