Version 3 (modified by benj, 11 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

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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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