GNSS Processing Using Kalman Filter on Lie Groups

EasyChair Preprint no. 8920

Abstract

This paper explores the problem of position and speed estimation of a target using satellite-based measurements in a Lie Group Kalman-like filter. The filter employs an intrinsic formulation of a nearly constant velocity model based on the Frenet-Serret frame, embedded in a Lie Group structure. It stands as a more suitable model for the kinematics of a target in space than the usual Euclidean model, since it induces a banana-shaped distribution instead of the typical ellipsoidal provided by Gaussian schemes. The paper presents numeric experiments using a real application dataset to evaluate the performance of the proposed filtering scheme against the standard approach in Euclidean representation. A differential GNSS solution provided by commercial software furnishes the ground truth. The results indicate a better performance of the proposed Lie Groups filtering scheme.

Keyphrases: Kalman filter, Lie groups, Satellite-based navigation

@Booklet{EasyChair:8920,
  author = {Marcos Rogério Fernandes and Giorgio M. Magalhães and Yusef Cáceres and João B. R. Do Val},
  title = {GNSS Processing Using Kalman Filter on Lie Groups},
  howpublished = {EasyChair Preprint no. 8920},

  year = {EasyChair, 2022}}