3 citations · 4 across the 7 of their papers we have counts for
7 papers
Covariance Square Root Second-Order Mapping
Keith A. LeGrand, Braden Hastings, Jackson Kulik
In recursive state estimation, numerical error can play a major role in an algorithm's overall performance and reliability. Roundoff errors due to finite precision arithmetic can v…
Bayesian hypergraph inference from scarce and noisy dynamical observations
Katerina Tang, Vivek Srikrishnan, Jackson Kulik
Inferring higher-order interaction structure from observations of dynamics is a central challenge in complex systems, particularly when data are scarce, noisy, or concentrated in l…
Unscented and Higher-Order Linear Covariance Fidelity Checks and Measures of Non-Gaussianity
Jackson Kulik, Braden Hastings, Keith A. LeGrand
Linear covariance (LinCov) techniques have gained widespread traction in the modeling of uncertainty, including in the preliminary study of spacecraft navigation performance. While…
Optimal Rank-1 Directional State Transition Tensors
Grace E. Calkins, Jay W. McMahon, Jackson Kulik
An optimal rank-1 approximation of state transition tensors was developed as an efficient alternative to state transition tensors for nonlinear uncertainty quantification. While pr…
Higher-Order Tensor-Based Deferral of Gaussian Splitting for Orbit Uncertainty Propagation
G. Andrew Siciliano, Keith A. LeGrand, Jackson Kulik
Accurate propagation of orbital uncertainty is essential for a range of applications within space domain awareness. Adaptive Gaussian mixture-based approaches offer tractable nonli…
Robust computation of higher-dimensional invariant tori from individual trajectories
Maximilian Ruth, Jackson Kulik, Joshua Burby
We present a method for computing invariant tori of dimension greater than one. The method uses a single short trajectory of a dynamical system without any continuation or initial…
Nonlinearity and Uncertainty Informed Moment-Matching Gaussian Mixture Splitting
Jackson Kulik, Keith A. LeGrand
Many problems in navigation and tracking require increasingly accurate characterizations of the evolution of uncertainty in nonlinear systems. Nonlinear uncertainty propagation app…