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

• Published in: Sensors (Basel, Switzerland) Vol. 19; no. 23; p. 5148
• Main Authors: Benammar, Mohieddine, Alassi, Abdulrahman, Gastli, Adel, Ben-Brahim, Lazhar, Touati, Farid
• Format: Journal Article
• Language: English
• Published: Switzerland MDPI AG 25.11.2019; MDPI
• Subjects: Accuracy; Algorithms; Approximation; Digital signal processors; Field programmable gate arrays; Optimization; arctangent approximation; signals processing; minimax optimization; rational approximations; look-up-tables; CORDIC; novel algorithm; position sensors
• ISSN: 1424-8220; 1424-8220
• DOI: 10.3390/s19235148

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.