An RNS-Based Initial Absolute Position Estimator for Electrical Encoders

Gian Carlo Cardarilli, Luca Di Nunzio, Rocco Fazzolari, Daniele Giardino, Marco Re, Alberto Nannarelli, Seergio Spanò

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In digital systems, the Residue Number System (RNS) represents an interesting alternative to the traditional two’s complement representation. Its performance and low-power properties have attracted significant research interest over the years. In this paper, RNS is used to estimate the angular position of a multi-trace electrical encoder (EE), an electro-mechanical device to measure angles at high precision widely used, for example, in antennas on-board satellites. The model of this system presents cyclic characteristics and, consequently, allows efficient use of modular arithmetic for its description. The RNS is applied to EEs equipped with more than two plates, and the absolute angle reconstruction is performed by using the Chinese Remainder Theorem (CRT). Furthermore, the use of RNS allows detection and mitigation solutions for errors due to encoders’ non-idealities and electrical noise. In this noisy context, we provide a detailed analysis of the performance of the system and propose a more robust, flexible, and easy-to-implement solution compared with the traditional methods. The results show that the RNS-based system can attenuate the noise, measure accurately the angles, and improve the overall performance.
Original languageEnglish
JournalIEEE Access
Pages (from-to)98586-98595
Publication statusPublished - 2023


  • Angle measurement
  • Chinese reminder theorem (CRT)
  • Electrical encoder
  • Error detection
  • Modular arithmetic
  • Residue Number System (RNS)


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