Quaternion-Based Attitude Update Calculations Using the Cordic Algorithm

Jeanette F. Arrigo and Paul M. Chau

Abstract:	We describe a digital hardware system for real-time updating of vehicular attitude information. The system yields significantly improved data for large angle rotations when compared with standard methods for attitude updating. The hardware system computes a quaternion-based closed form solution of the kinematic equation for rotation. The system architecture incorporates processing elements that implement the CORDIC algorithm. The processing elements perform logical shifts and adds that are basic to the CORDIC algorithm and require only standard digital registers and gates. The system is used efficiently when calculating such functions as sine, cosine, multiply, square root, etc. that are standard functions involved in CORDIC calculations. A 32 bit fixed point version of the system has been implemented using a hardware description language capable of synthesis into either field programmable gate arrays (FPGAs) or application specific integrated circuits (ASICs). Simulation results and comparisons to floating point Taylor series and Runge Kutta calculations are described. Simulation results using the hardware language indicate an improved accuracy over the third order floating point Taylor Series approximation calculation for angular disturbances greater than 20 degrees. When compared with a fourth order Taylor Series approximation the accuracy is improved above 30 degrees. A set of one thousand uniformly random normalized quaternion inputs was used. At 60 degrees angular disturbance the 32-bit fixed point CORDIC implementation is as much as 60 times more accurate than the fourth order floating point Taylor series approximation. A brief review of quaternion mathematics, the attitude update procedure and CORDIC algorithm are presented. This review is followed by the system design and resulting error analysis.
Published in:	Proceedings of the 2001 National Technical Meeting of The Institute of Navigation January 22 - 24, 2001 Westin Long Beach Hotel Long Beach, CA
Pages:	458 - 464
Cite this article:	Arrigo, Jeanette F., Chau, Paul M., "Quaternion-Based Attitude Update Calculations Using the Cordic Algorithm," Proceedings of the 2001 National Technical Meeting of The Institute of Navigation, Long Beach, CA, January 2001, pp. 458-464.
Full Paper:	ION Members/Non-Members: 1 Download Credit Sign In