Instrument Reference system:
This is at centre of laser output mirror with Z axis along path of laser beam at centre of laser swath and X in the direction of aircraft nose while Y is as per right hand coordinate system. This is shown by black colour in Figure 15. This reference system will move and rotate with aircraft.
Scanning reference system:
The red lines in Figure 15 indicate the laser pulse and corresponding time-variable axis system with z being in the direction of laser pulse travel. The x axis is coincident with instrument reference X axis. The direction of z axis is fixed as per the instantaneous scan angle η.
INS reference system (Body) :
INS is aligned initially to local gravity and True North when switched on. It works by detecting rotation of earth and gravity. The origin of INS reference system is at INS with X, Y, Z defined as local roll, pitch, and yaw axes of airplane. Here X is along nose and Y along right wing of aircraft in a RH coordinate system. The INS gives the roll, pitch, and yaw values w.r.t. to the initially aligned system at any moment.
The above three reference systems are related to each other. Blue dotted lines are INS body axis with origin at instrument while black lines are instrument axis. These differ due to mounting errors which are referred to as mounting biases in roll, pitch, and yaw and determined by calibration process. They also differ due to translation between INS and the laser head. The red lines indicate the laser pulse and corresponding time-variable axis system with z being in the direction of laser pulse travel. This is due to scan angle h. This reference system is related to instrument reference system with rotation angle h.
Earth tangential (ET) reference system
It has its origin at onboard GPS antenna with X axis pointing in the direction of True north and Z axis pointing towards mass centre of Earth in a right handed system. This is variable for each shot in flight and can be conceptualized and realized computationally with the attitude measurements (Figure 16).
ET reference system is related to INS reference system by roll, pitch, and yaw measurements about X, Y, and Z, respectively, at the time of each shot. ET is also related to Instrument System by the GPS vector measured in INS reference system. WGS-84 is related to ET by location of GPS antenna at the time of each laser shot.