Dual Quaternion Kalman Filtering and Observability Analysis for Satellite Relative Navigation With Line-of-Sight Measurements

Yigal Zivan, Daniel Choukroun

Research output: Contribution to journalArticlepeer-review

Abstract

This article is concerned with the development of two novel Kalman filters for satellite relative pose estimation. The relative pose, which is represented by a dual quaternion, is estimated from noisy lines-of-sight via a single camera, along with biases of linear velocity and angular rate measurements. The constraints on the dual quaternion are handled by brute-force and virtual measurement techniques. The partial reset analysis shows how to propagate the estimation error biases and covariances. Closed-form expressions for the Jacobians are provided. A quantitative observability analysis for the position states is provided. Compared with traditional representations, the dual quaternion model increases the position observability by a factor of four for each line-of-sight. The additive dual quaternion model enhances the observability of the rotation states thanks to a specific coupling term in the pose dynamics. Extensive Monte-Carlo simulations of a flight formation case verify that the proposed novel filters are asymptotically unbiased and statistically consistent for all practical purposes. They outperform the other candidate estimators in particular during the transient phase. The numerical simulations validate the observability analysis.

Original languageEnglish
Pages (from-to)754-765
Number of pages12
JournalIEEE Transactions on Aerospace and Electronic Systems
Volume58
Issue number2
DOIs
StatePublished - 1 Apr 2022

Keywords

  • Dual quaternion
  • kalman filtering
  • line-of-sight (LOS) measurements
  • observability analysis
  • satellite relative pose

ASJC Scopus subject areas

  • Aerospace Engineering
  • Electrical and Electronic Engineering

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