Improved formulation of the IMU and MARG orientation gradient descent algorithm for motion tracking in human-machine interfaces

Wearable motion tracking systems are becoming increasingly popular in human-machine interfaces. For inertial measurement, it is vital to efficiently fuse inertial, gyroscopic, and magnetometer data for spatial orientation. We introduce a new algorithm for this fusion based on using gradient descent to correct for the integral error in calculating the orientation quaternion of a rotating body. The algorithm is an improved formulation of the well-known estimation of orientation using a gradient descent algorithm. The new formulation ensures that the gradient descent algorithm uses the steepest descent, resulting in a five order of magnitude increase in the precision of the calculated orientation quaternion. We have also converted the algorithm to use fixed point integers instead of floating point numbers to more than double the speed of the calculations on the types of processors used with Inertial Measurement Units (IMUs) and Magnetic, Angular Rate and Gravity sensors (MARGs). This enables the corrections to not only be faster than the original formulations, but also remain valid for a larger range of inputs. The improved efficiency and accuracy show significant potential for increasing the scope of inertial measurement in applications where low power or greater precision is necessary such as very small wearable or implantable systems.