Application of PIV and Delaunay Triangulation Method for Satellite Angular Velocity Estimation Using Star Tracker

Abstract

The main objective of this paper is to apply a particle image velocimetry technique accompanied by Delaunay triangulation and spatial angles to consecutive images of star tracker in order to estimate the angular velocity of spacecraft. This method is independent of star identification or attitude matrix and can be performed parallel to conventional star tracker algorithms. It is computationally light and consumes a reasonable time to perform. An interrogation window containing two or more stars in the first image is selected and based on the peak of normalized cross correlation matrix, the same window in the second image is matched. In order to make sure that the matched windows are indeed the same, local recognition features, such as spatial angles for windows with two stars and Delaunay triangle planar angles for three or more stars, are compared. When matched, window center angular displacement is calculated in a fixed imaging time interval, and eventually, an angular rate is estimated. In order to evaluate the performance of the proposed method, Monte Carlo simulation of random night sky images is used. It is shown that for angular rates, about 1°/s accuracies better than 7e−5°/s are achieved. Accuracy decreases to 1e−3°/s for the rates of about 12°/s in 0.1-s time interval.