Unscented and Higher-Order Linear Covariance Fidelity Checks and Measures of Non-Gaussianity

TL;DR

This paper introduces advanced computational techniques using higher-order statistics, constrained optimization, and the unscented transform to evaluate the accuracy of linear covariance methods in nonlinear uncertainty modeling, crucial for spacecraft navigation.

Contribution

It presents novel LinCov fidelity measures that improve assessment of linearization accuracy in nonlinear systems, addressing limitations of traditional methods.

Findings

New LinCov fidelity measures formulated with higher-order statistics

Techniques incorporate constrained optimization and the unscented transform

Enhanced ability to detect when linear covariance approximations are inadequate

Abstract

Linear covariance (LinCov) techniques have gained widespread traction in the modeling of uncertainty, including in the preliminary study of spacecraft navigation performance. While LinCov methods offer improved computational efficiency compared to Monte Carlo based uncertainty analysis, they inherently rely on linearization approximations. Understanding the fidelity of these approximations and identifying when they are deficient is critically important for spacecraft navigation and mission planning, especially when dealing with highly nonlinear systems and large state uncertainties. This work presents a number of computational techniques for assessing linear covariance performance. These new LinCov fidelity measures are formulated using higher-order statistics, constrained optimization, and the unscented transform.