Applying Gaussian distributed constraints to Gaussian distributed variables

TL;DR

This paper presents an analytical method for truncating Gaussian variables with Gaussian constraints, improving Kalman filtering performance under uncertain constraints by over 40% compared to unconstrained methods.

Contribution

It introduces a moment-based Gaussian approximation technique for uncertain constraint truncation, advancing beyond existing hard or numerical constraint handling methods.

Findings

Outperforms unconstrained Kalman filtering by over 40%

Outperforms hard-constrained Kalman filtering by over 17%

Applicable to various problems involving Gaussian constraints

Abstract

This paper develops an analytical method of truncating inequality constrained Gaussian distributed variables where the constraints are themselves described by Gaussian distributions. Existing truncation methods either assume hard constraints, or use numerical methods to handle uncertain constraints. The proposed approach introduces moment-based Gaussian approximations of the truncated distribution. This method can be applied to numerous problems, with the motivating problem being Kalman filtering with uncertain constraints. In a simulation example, the developed method is shown to outperform unconstrained Kalman filtering by over 40% and hard-constrained Kalman filtering by over 17%.