Nonlinear Filter for Simultaneous Localization and Mapping on a Matrix Lie Group Using IMU and Feature Measurements

Hashim A. Hashim, Abdelrahman E.E. Eltoukhy

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


Simultaneous localization and mapping (SLAM) is a process of concurrent estimation of the vehicle's pose and feature locations with respect to a frame of reference. This article proposes a computationally cheap geometric nonlinear SLAM filter algorithm structured to mimic the nonlinear motion dynamics of the true SLAM problem posed on the matrix Lie group of SLAMn(3). The nonlinear filter on manifold is proposed in continuous form and it utilizes available measurements obtained from group velocity vectors, feature measurements, and an inertial measurement unit (IMU). The unknown bias attached to velocity measurements is successfully handled by the proposed estimator. Simulation results illustrate the robustness of the proposed filter in discrete form, demonstrating its utility for the six-degrees-of-freedom (6 DoF) pose estimation as well as feature estimation in three-dimensional (3-D) space. In addition, the quaternion representation of the nonlinear filter for SLAM is provided.

Original languageEnglish
Pages (from-to)2098-2109
Number of pages12
JournalIEEE Transactions on Systems, Man, and Cybernetics: Systems
Issue number4
Publication statusPublished - 1 Apr 2022


  • special orthogonal group [SO(3)]
  • Inertial measurement unit (IMU)
  • inertial vision system
  • nonlinear observer algorithm for SLAM
  • simultaneous localization and mapping (SLAM)
  • special Euclidean group [SE(3)]

ASJC Scopus subject areas

  • Software
  • Control and Systems Engineering
  • Human-Computer Interaction
  • Computer Science Applications
  • Electrical and Electronic Engineering


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