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New Fast Arctangent Approximation Algorithm for Generic Real-Time Embedded Applications

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journal contribution
submitted on 2024-03-05, 08:13 and posted on 2024-03-05, 08:14 authored by Mohieddine Benammar, Abdulrahman Alassi, Adel Gastli, Lazhar Ben-Brahim, Farid Touati

Fast and accurate arctangent approximations are used in several contemporary applications, including embedded systems, signal processing, radar, and power systems. Three main approximation techniques are well-established in the literature, varying in their accuracy and resource utilization levels. Those are the iterative coordinate rotational digital computer (CORDIC), the lookup tables (LUTs)-based, and the rational formulae techniques. This paper presents a novel technique that combines the advantages of both rational formulae and LUT approximation methods. The new algorithm exploits the pseudo-linear region around the tangent function zero point to estimate a reduced input arctangent through a modified rational approximation before referring this estimate to its original value using miniature LUTs. A new 2nd order rational approximation formula is introduced for the first time in this work and benchmarked against existing alternatives as it improves the new algorithm performance. The eZDSP-F28335 platform has been used for practical implementation and results validation of the proposed technique. The contributions of this work are summarized as follows: (1) introducing a new approximation algorithm with high precision and application-based flexibility; (2) introducing a new rational approximation formula that outperforms literature alternatives with the algorithm at higher accuracy requirement; and (3) presenting a practical evaluation index for rational approximations in the literature.

Other Information

Published in: Sensors
License: https://creativecommons.org/licenses/by/4.0/
See article on publisher's website: https://dx.doi.org/10.3390/s19235148

Funding

Open Access funding provided by the Qatar National Library.

History

Language

  • English

Publisher

MDPI

Publication Year

  • 2019

License statement

This Item is licensed under the Creative Commons Attribution 4.0 International License.

Institution affiliated with

  • Qatar University
  • College of Engineering - QU