Command Generation

A principal requirement for the command generation is to maintain the LOS position on the earth’s surface at constant earth-fixed coordinates for the duration of one sensor integration period. Command generation decides the antenna gimbal commands to stabilize antenna LOS. Most of the inputs required for command generation are provided by Inertial Measurement Unit (IMU).

2.4.1 Inertial Rate Generator

The inertial rate generator analytically computes angular rate commands as a function of time to transfer the antenna LOS from an initial state to a final desired state. During scan, this is accomplished by closing the inertial rate loops to control the antenna earth-fixed rates. The inertial rate loops attenuate aircraft angular motion sensed by the on-gimbal inertial rate sensor and compensate for any unobserved angular motion induced by aircraft linear motion.

To meet coverage requirements, the sensor must be scanned with respect to an earth-fixed target at a constant rate. The mechanism for performing a slew maneuver of the LOS is described graphically in Figure 2.10. The typical maneuver requires the LOS to be repositioned from its present earth-fixed position to the next desired earth-fixed position. This problem is partitioned such that inertial rate generator analytically generates the reposition commands while the aircraft-induced rate compensation is numerically integrated.

At the inception of a transfer, two target and aircraft positions are located in EF coordinate frame. The scan is from target positon1 to target postion2 when aircraft flies a path from postion1 to positon2. To compensate for aircraft and target motion, antenna LOS inertial rate can be partitioned into two parts. is the angular rate assuming antenna scan from target1 to target2 and aircraft is stationary. is the angular rate assuming antenna scan the same point target1 and aircraft is under motion.

ef

where , , and are target and aircraft position vectors represented in EF coordinates. is frame time which scan bar moves from one FOV to the next. is length from target to aircraft.

Therefore, antenna LOS inertial rate is equated to

is comprised of three distinct rates :

where is the angular rate of S frame with respect to AC frame, and this rate is the necessary gimbal rate command while radar mapping. is the angular rate of the aircraft with respect to LL frame, and this angular rate vector is determined from gyroscope by sensing aircraft angular velocity. is the LL frame angular rate vector with respect to the EF frame. This frame is rotated to maintain the down axis aligned with geodetic vertical. It is determined from GPS by sensing aircraft position resolved in EF coordinates.

/ 1

At the conclusion of the transfer, equation (2-9) generates the appropriate antenna gimbal rate commands to control the LOS with respect to an EF frame.

The LOS is at the desired earth-fixed location and rate that exactly cancels the linear and angular aircraft motion.

2.4.2 Gimbal Angle Generator

The radar antenna is servo to the unit vector by the antenna driving system.

Its stabilization involves a series of coordinate rotations. The antenna LOS unit vector in antenna frame is defined by

0

First, the target vector should be defined which is the direction we attempt to keep antenna toward. The target unit vector in LL frame is defined by two angles, one is azimuth and the other is elevation. The azimuth angle is called the map heading angle HM, and it is the angle from the inertial reference north to the ground point being imaged, measured in a plane parallel to the Earth’s surface.

The elevation angle ES, is measured from the horizontal plane of the aircraft to the ground point in a vertical plane. These angles are illustrated in Figure 2.11.

Then the transformation from S frame to LL frame is

( , ) ( , )

cos( ) 0 sin( )

When aircraft rotated in the inertial reference, the included angles between LL frame and AC frame are roll, pitch, and yaw angles, with notation are α, β, and γ respectively, called aircraft Euler angles. The transformation sequence is in the Z-Y-X Euler angles form, and it is obtained by the gyroscope measurement. Therefore, the transformation from LL to AC frame is a rotation matrix

To get final antenna gimbal angle commands, we should transform the antenna LOS vector in S frame into AC frame using the direction cosine matrices. Combining equation (2-11) and (2-13) the antenna LOS unit vector in AC coordinate is

AC AC LL S

LOS LL s LOS

u

C

C u

Since the Euler angles are in Cartesian coordinate space, but in our radar roll axis:

gimbal mechanism is defined in sphere coordinates, we will transform from the Cartesian space to the sphere space or from the sphere space to the Cartesian space. And we assumed that the unit vector in radar antenna coordinates by following servo errors should be zero when the antenna is aligned to the unit vector. In our radar gimbal mechanism, there are only two axes to stabilize the aircraft body rotation which has three rotation degrees of freedom. There, the final commands order to antenna gimbals can be written in arctangent form by

(2

During antenna pointing a target on the ground, the position loops are closed to remove gyro drift and servo position biases accumulated during the scan bar. The gimbal angle commands are continually updated according to the above process when the position loops are closed.