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Peer-reviewedCC BYApplied Sciences

A Matrix-Based Sensor Fusion Algorithm for Nine-D.o.F. IMU Attitude Estimation

  • Alessandro Muccichini1
  • Davide Camponeschi1
  • Pietro Pennestrì2
  • Alessandro Neri3
  • Nicola Pio Belfiore1
  1. 1Department of Industrial, Electronic and Mechanical Engineering, Roma Tre University, 00146 Rome, Italy
  2. 2Benchmark Electronics, 7602 EA Almelo, The Netherlands
  3. 3Radiolabs Research Center, 00198 Rome, Italy
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Abstract

The orientation of a body in space can be conveniently determined through the fusion of different and redundant sensors; for example, as in Inertial Measurement Units (IMUs) and Magnetic, Angular Rate, and Gravity (MARG). Although this problem has been already addressed by many authors, and many relevant algorithms are available nowadays, this paper explores the possibility of improving their computational efficiency and reliability by suggesting some alternative refinements: (a) A matrix-based reformulation that speeds up the code by avoiding quaternion library operations, exploiting the well-established correspondence between quaternion algebra and linear matrix operators; (b) the use of a necessary condition between Euler parameters and their time derivatives as a kinematic-consistency residual; (c) the minimization of this norm; and (d) the possibility of decoupling the accelerometer sensor data in case the acceleration is higher than the gravity intensity. The matrix-based reformulation significantly improves the execution time of the original algorithms, while the optional refinement steps trade most of this saving for a consistency norm with machine precision. The algorithms are compared on a publicly available benchmark dataset and validated experimentally against a goniometric mechanical reference.

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Cite

BibTeXRIS
BibTeX
@article{muccichini2026matrixbased,
  title = {{A Matrix-Based Sensor Fusion Algorithm for Nine-D.o.F. IMU Attitude Estimation}},
  author = {Alessandro Muccichini and Davide Camponeschi and Pietro Pennestrì and Alessandro Neri and Nicola Pio Belfiore},
  journal = {Applied Sciences},
  year = {2026},
  month = oct,
  doi = {10.3390/app162010101},
  url = {https://doi.org/10.3390/app162010101},
  note = {CC BY},
}
RIS
TY  - JOUR
TI  - A Matrix-Based Sensor Fusion Algorithm for Nine-D.o.F. IMU Attitude Estimation
AU  - Alessandro Muccichini
AU  - Davide Camponeschi
AU  - Pietro Pennestrì
AU  - Alessandro Neri
AU  - Nicola Pio Belfiore
PY  - 2026
DA  - 2026/10/26
JO  - Applied Sciences
DO  - 10.3390/app162010101
UR  - https://doi.org/10.3390/app162010101
AB  - The orientation of a body in space can be conveniently determined through the fusion of different and redundant sensors; for example, as in Inertial Measurement Units (IMUs) and Magnetic, Angular Rate, and Gravity (MARG). Although this problem has been already addressed by many authors, and many relevant algorithms are available nowadays, this paper explores the possibility of improving their computational efficiency and reliability by suggesting some alternative refinements: (a) A matrix-based reformulation that speeds up the code by avoiding quaternion library operations, exploiting the well-established correspondence between quaternion algebra and linear matrix operators; (b) the use of a necessary condition between Euler parameters and their time derivatives as a kinematic-consistency residual; (c) the minimization of this norm; and (d) the possibility of decoupling the accelerometer sensor data in case the acceleration is higher than the gravity intensity. The matrix-based reformulation significantly improves the execution time of the original algorithms, while the optional refinement steps trade most of this saving for a consistency norm with machine precision. The algorithms are compared on a publicly available benchmark dataset and validated experimentally against a goniometric mechanical reference.
SN  - 2076-3417
ER  -