Title :
Improved accelerometer and magnetometer-based solution to solve quaternion
Author :
Zhou, Feng ; Wu, Yanxuan ; Fan, Ningjun
Author_Institution :
Sch. of Electromech., Beijing Inst. of Technol., Beijing, China
Abstract :
Light overloaded small aircraft, such as ducted fan MAV, could use accelerometer and magnetometer to measure acceleration and earth magnetic field in the body coordinate frame. There is a quaternion that relates the measured accelerations and earth magnetic field in the body coordinate frame to calculated values in the earth coordinate frame. An overdetermined nonlinear equations which could get the quaternion need to be solved. So far, the Gauss-Newton iteration algorithm was being used most commonly to solve the overdetermined equations. However, when the inverse of Jacobian matrix is singular or conditioned, the iteration would be diverge. To overcome the problem, first, transferring the overdetermined problem to determined one by a premultiply transposition of Jacobian matrix, then using Correctional Newton with Parameter iteration algorithm to solve the determined equations. Compared to Gauss-Newton iteration algorithm, this method not only could converge more fast, but also could overcome the situation which Jacobian matrix is singular or conditioned.
Keywords :
Jacobian matrices; Newton method; acceleration measurement; accelerometers; aircraft; autonomous aerial vehicles; magnetic field measurement; magnetometers; acceleration measurement; accelerometer; body coordinate frame; conditioned Jacobian matrix; correctional Newton; ducted fan MAV; earth magnetic field measurement; light overloaded small aircraft; magnetometer-based solution; micro aerial vehicle; overdetermined nonlinear equations; parameter iteration algorithm; quaternion; singular Jacobian; singular Jacobian matrix; Earth; Jacobian matrices; Magnetic field measurement; Magnetometers; Mathematical model; Nonlinear equations; Quaternions; Correctional Newton; Correctional Newton with Parameter; attitude estimation; quaternion;
Conference_Titel :
Control, Automation and Systems (ICCAS), 2012 12th International Conference on
Conference_Location :
JeJu Island
Print_ISBN :
978-1-4673-2247-8