TABLE OF CONTENTS Attitude and heading reference system (AHRS) is the avionic system that enables the aircraft pilot to establish an artificial horizontal and bearing. Its function is to measure the attitude pitch and roll and trajectory heading for an aircraft. The legacy AHRS was built with vertical and directional gyros technology. More recently, modern AHRS uses micro electro-mechanical sensors (MEMS) gyros. Although with this technology gyro drifts could be so high that they are rendered unsuitable for navigation and alignment. And for this reason, an AHRS is usually aided with external navigational sensors like GPS, air data systems or magnetometers, even though there are some standalone AHRSs.
Since the attitude and heading data are inherent in 
or 
, they must be properly initialized. On the ground, craft attitude is typically determined from accelerometer sensor data. Heading can be initialized from magnetic sensors or, when flying, from GPS. In the meantime, for reliable operation, gyro drifts must be accounted for and should be continually estimated.
Herein we address the initialization procedure and provide the means for the detection and estimation of the low-grade gyro drifts.
As before, we assume that each of the gyro and accelerometer triads comprise mutually orthogonal sensors that are perfectly aligned with the craft's principal body axes.
Here, 
is considered the product of the Euler angle rotations
In the following, we describe the procedure for initializing the Euler angles ( 
, ?, ?). In contrast to the alignment...
