The IMU is a single unit in the electronics module which collects
angular velocity and linear acceleration data which is sent to the
main processor. The IMU housing actually contains two separate
sensors. The first sensor is the accelerometer triad. It generates
three analog signals describing the accelerations along each of its
axes produced by, and acting on the vehicle. Due to thruster system
and physical limitations, the most significant of these sensed
accelerations is caused by gravity. The second sensor is the angular
rate sensor triad. It also outputs three analog signals. These
signals describe the vehicle angular rate about each of the sensor
axes. Even though the IMU is not located at the vehicle center of
mass, the angular rate measurements are not effected by linear or
angular accelerations. The data from these sensors is collected by
the IMU 6811 microprocessor through a 12 bit ADC board. The sensor
information is then returned to the main processor via a RS422 serial
communications interface at a rate of about 200 Hz.
The accelerometer triad, and angular rate sensors within the IMU are
mounted such that their sensor coordinate axes are not aligned with
those of the vehicle. This is due to the fact that the two sensors in
the IMU are mounted in two different orientations in the housing,
along with the fact that the axes of the IMU are not aligned with the
vehicle axes.
The Figure 215 shows two pictures of the IMU, and depicts the
direction of the axes of each of the two sensors each with respect to
the IMU housing.
Figure 215 Initial IMU sensor coordinate axes
The accelerometer triad was manufactured using a left handed coordinate system. The transformation algorithm first uses (2.1) to align the coordinate axes of the two sensors.

_{} 
(2.1) 
These simple transformations align the axes of the two sensors so
that they appear axes then appear as shown in Figure 216.
Figure 216 Transformed IMU sensor coordinate axes
Notice that the coordinate systems are now aligned and right
handed.
Once the sensor axes are aligned with the axes of the IMU, they must
be aligned with the vehicle reference frame. The unit is mounted on
the wall of the electronics module, and is also rotated 45° with
respect to the horizontal. The wall of the electronics module is also
angled inward at
from the vehicle axes. This was calculated by using the fact that
over the 30 inches from the back to the front of the electronics
module the sides move inward 4 inches.
Using this information, along with knowledge of the orientation with
which the IMU is mounted to the wall of the EM allows the formation
of a direction cosine matrix that is used to convert the measurements
from the IMU coordinate frame to the vehicle coordinate frame. Figure
217 illustrates the orientation with which the IMU is mounted in the
electronics module.
Figure 217 Transformed IMU coordinate axes compared to vehicle coordinate axes
Following is the order of transformations:
1) Rotate alpha + 90° about the xaxis to align the IMU zaxis
with the Vehicle zaxis.

(2.2) 
2) Rotate beta + 90° about the zaxis to align IMU and vehicle coordinate frames.

(2.3) 
So the complete transformation from IMU to vehicle coordinates is given by

(2.4) 


. 
(2.5) 
Inserting numerical values for the angles ([alpha] = 45°, [beta] = 7.5946°), produces:

(2.6) 
In order to transform the sensor data from the individual sensor frames into the vehicle frame, first use the simple sign/axis transformations shown in (2.1), then premultiply the modified sensor data by the transformation matrix given in (2.6). It would also be possible to combine the initial transformations from (2.1) into the transformation in (2.6), however since the initial axes are different for each of the two sensors in the IMU, there would be a different transformation matrix for each sensor. In interest of simplicity, the software first aligns the sensor axes using (2.1), and then uses the transformation matrix from (2.6) to transform the data of the accelerometer and angular rate sensors from IMU to vehicle coordinates.