| Version 31 (modified by mark1, 12 years ago) (diff) |
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Lever arm offset details
This page gives details of how the lever arm offset is calculated.
All nav is transformed back to the master antenna on the rear of the cabin roof, and then aznav transforms nav from there to each sensor as required when the individual sensor data is processed. AT4 nav is already wrt this antenna, and the IMU data is transformed back to the antenna during Applanix processing.
The distance is from the phase centre of the master (rear) antenna to each sensor's "prime" point; so for the ATM it is the scan mirror centre, for the Eagle, Hawk and CASI ideally the focus point of the lens.
The angles (as used in aznav) are: gamma is the positive angle from the vertical through the antenna to the sensor prime point and delta is positive to starboard from the centre line direction of the aircraft.
Initially it is necessary to make sure you have the correct sensor prime point coords as observed.
Then aznav sorts out what axis system has been used by the surveyors and swaps the coordinates around until it gets it in the NASA Standard Aircraft system [ Y+ port, X+ tail to nose, Z+ up ]. Then do the angle calcs.
2011
Aircraft was surveyed by Sterling Surveys in March 2011.
LiDAR
The LiDAR measurements are made from the antenna to a reference point, then transformed from that reference point to an internal point (PAV 80). The reference point is the front left corner of the LIDAR sensor unit casing.
Measured antenna to reference point numbers:
- X = 0.173 ; Y = 0.073 ; Z = -1.412
LiDAR lever arm values are:
| X | Y | Z | |
| GNSS | -0.144 | -0.029 | -1.672 |
| IMU | -0.411 | 0.206 | -0.192 |
| User Frame | -0.142 | -0.001 | -0.188 |
Hyperspectral sensors
The hyperspectral measurements are made from the antenna to a reference point, then transformed from that reference point to the Eagle/Hawk lens. The reference point is the forward port corner of the Eagle/Hawk base plate.
Measured antenna to reference point numbers:
- X = 0.864 ; Y = 0.300 ; Z = 1.569
Eagle and Hawk lever arm values are:
| X | Y | Z | |
| Eagle | 0.559 | -0.015 | -1.543 |
| Hawk | 0.729 | -0.015 | -1.543 |
2010
Where unspecified, the measurements are as in the previous year.
LIDAR
Internal measurements provided by Leica:
- PAV80 rotation point to RCD lens (no spacer): X= 0.112 ; Y = 0.061 ; Z = -0.060
Axes are:
- X = increasing towards the front of the plane
- Y = increasing to port
- Z = increasing downwards
Note that to get to PAV80 from reference point we apply: X = -0.14 ; Y = 0 ; Z = -0.17 (see email March 2010 from Leica)
Hyperspectral sensors
We're told these are the same as end of 2008. Note: These are xyz co-ords, not gam-del-dst
| X | Y | Z | |
| Eagle | 0.408 | 0.001 | -1.548 |
| Hawk | 0.578 | 0.001 | -1.548 |
2009
Hyperspectral sensors
We're told these are the same as end of 2008. Note: These are xyz co-ords, not gam-del-dst
| X | Y | Z | |
| Eagle | 0.408 | 0.001 | -1.548 |
| Hawk | 0.578 | 0.001 | -1.548 |
TABI
Measured by ARSF-Ops relative to Hawk (numbers converted below to relative to the GPS antenna), not surveyed. Should be accurate enough though.
| X | Y | Z |
| 0.858 | 0.001 | -1.548 |
Applanix IMU
Use 2006/7 numbers?
Leica LIDAR + IMU
The LIDAR survey measurements are made from the antenna to a reference point, then transformed from that reference point to internal points (the IMU and mirror center). The reference point is the front left corner of the LIDAR sensor unit casing. Survey was in late 2008.
Measured antenna to reference point numbers:
- X = 0.010 ; Y = 0.078 ; Z = -1.432
Internal measurements provided by Leica:
- reference point to mirror center: X = 0.169 ; Y = 0.102 ; Z = 0.090
- reference point to IMU: X = -0.269 ; Y = 0.207 ; Z = -0.004
- laser mirror centre to RCD lens (no spacer): X= 0.239 ; Y = 0.062 ; Z = -0.060
Axes are:
- X = increasing towards the front of the plane
- Y = increasing to port
- Z = increasing upwards
2008
18th Dec. 2008: Due to confusion about angle directions, the originally computed gamma angles are incorrect. The error caused should be of similar magnitude to the previous, similar error (ie ~1.5m along-track for ATM, other sensors will have a smaller error). Because the error will be partially compensated for by boresight angles depending on flight altitude, the "wrong" numbers should be used anyway unless you re-calculate the boresight angles.
Jan 2008 numbers (Wrong but use anyway, or we have to redo boresights):
| Gam | Del | Dst | |
| ATM | 1.2258 | 0.0051 | 1.7380 |
| Eagle | 1.0748 | -0.0036 | 1.7441 |
| Hawk | 0.9705 | -0.0049 | 1.7985 |
Jan 2008 numbers (Corrected for reference but use "wrong" numbers above, unless you've redone boresights):
| Gam | Del | Dst | |
| ATM | 0.3450 | 0.0051 | 1.7380 |
| Eagle | 0.4960 | -0.0036 | 1.7441 |
| Hawk | 0.6003 | -0.0049 | 1.7985 |
VOCALS
Use these numbers for VOCALS flights from autumn 2008. Note: These are xyz co-ords, not gam-del-dst (ie use -acx, not -acv)
| X | Y | Z | |
| Eagle | 0.2302 | 0.001 | -1.548 |
| Hawk | 0.4002 | 0.001 | -1.548 |
Applanix IMU
Use 2006/7 numbers?
Leica LIDAR + IMU
The LIDAR survey measurements are made from the antenna to a reference point, then transformed from that reference point to internal points (the IMU and mirror center). The reference point is the front left corner of the LIDAR sensor unit casing. Survey was in late 2008.
Measured antenna to reference point numbers:
- X = 0.010 ; Y = 0.078 ; Z = -1.522
Internal measurements provided by Leica:
- reference point to mirror center: X = 0.169 ; Y = 0.102 ; Z = 0.090
- reference point to IMU: X = -0.269 ; Y = 0.207 ; Z = -0.004
Axes are:
- X = increasing towards the front of the plane
- Y = increasing to port
- Z = increasing upwards
2007
Use 2006 numbers..
2006
Obs and results as follows:
v:200601 may 2006
2006 D-CALM instrument coords from SJR 9th May
------------------------------------------------------------------------------------------
z x y Z offset X offset Y offset dst gam del
ATM 8.991 96.9065 99.9881 -1.68 0.4565 -0.0029 1.741 0.2655 0.006353
CASI 9.156 97.22509 99.98485 -1.515 0.775092 -0.00615 1.702 0.4732 0.007934
Eagle 9.143 97.7307 99.99 -1.528 1.2807 -0.001 1.994 0.6977 0.000781
Hawk 9.143 97.9155 99.99 -1.528 1.4655 -0.001 2.117 0.7644 0.000682
IMU 9.182 97.5181 99.8089 -1.489 1.0681 -0.1821 1.841 0.6287 0.1689
560 -1.476 1.4831 -0.0061 2.092 0.8264 0.004113
Pant 10.945 100.001 95.095 0.274 3.551 -4.815
Sant 10.906 100.000 104.91 0.235 3.550 5.000
Fant 10.843 101.661 99.989 0.172 5.211 0.079
------------------------------------------------------------------------------------------
Aant 10.671 96.450 99.991 0.0 0.0 0.0
------------------------------------------------------------------------------------------
Axes: Y+ port, X+ tail to nose, Z+ up
Antennas: name, postion, AT4 name, survey name
Aant = aft = master = GPS4
Fant = fore = slave_1 = GPS3
Pant = port = slave_2 = GPS1
Sant = starboard = slave_3 = GPS2
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Sensor offset vector paras allowing for this coordinate system
dx == X offset, dy = Y offset, dz = Z offset
dst = sqrt( dx * dx + dy + dy + dz + dz )
gam = acos( abs(dz) / dst )
del = atan( dy / (-dx) )
Units: dst: metres, gam, del: radians
-----------------
Verification test
p = r = h = 0
ant1: lat: 52.0 lng: -3 hgt: 1000
IMU is at: lat: 52.00000959 lng: -2.99999734 hgt: 998.511013
==========================================================================================
Applanix IMU Lever arm offsets
| Year | X | Y | Z |
| 2006 | 1.068 | 0.182 | 1.489 |
| 2007 | Use 2006 :S | Use 2006 :S | Use 2006 :S |
N.B. Some of the 2006, 2007 data has a preset IMU lever arm offset of 0.907, 0.190, 1.783 - not sure where this comes from, perhaps coords noted on the plane? Dave Davis has said to use the 1.068, 0.182, 1.489 offsets.