| Version 3 (modified by benj, 17 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 horizontal 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 cooridnates around until it gets it in the NASA Standard Aircraft system [ Y+ port, X+ tail to nose, Z+ up ]. Then do the angle calcs.
Jan 2008 numbers:
| Gam | Del | Dst | |
| ATM | 1.2258 | 0.0051 | 1.7380 |
| Eagle | 1.0748 | -0.0036 | 1.7441 |
| Hawk | 0.9705 | -0.0049 | 1.7985 |
2006 obs and results as follows:
11th Mar. 2008: Note that the email below were the numbers as originally received, but calculation of the Gamma angle contains an error - "gam = acos( abs(dz) / dst )" should use asin, not acos. Del and Dst are unaffected. Investigation of this suggests this causes an along-track error of approx. 1.5m in all 2006/2007 delivered data for ATM, which may be partially corrected by boresight correction (since these numbers were computed using the incorrect lever-arm numbers) depending on flight altitude. Other sensors have smaller errors, since the effect of the original calculation error is smaller for the offset angles of these sensors. Correct lever-arm numbers are below for reference, new boresight numbers would need to be computed to use these.
Corrected 2006/7 lever-arm numbers
| Gam | Del | Dst | |
| ATM | 1.306 | 0.006353 | 1.741 |
| Casi | 1.098 | 0.007934 | 1.702 |
| Eagle | 0.873 | 0.000781 | 1.994 |
| Hawk | 0.806 | 0.000682 | 2.117 |
v:200601 may 2006
2006 D-CALM instrument coords from SJR 9th May
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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
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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
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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
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