Magnetic Declination and Inclination: A writeup on their use and calculation

(image from http://www.ngdc.noaa.gov/geomag/WMM/image.shtml)

Hi folks!

I decided to implement an on-board declination calculator based on geographic location and I'd love to get some feedback. It takes up about 1400 flash bytes in total for a 3 degree declination error anywhere that people live (permanently - sorry Vostok!) and using a compass is reasonable. It's not going to be flight tested until it stops raining here, so use at your own risk! See the paper for more details :)

-John

Paper:

Lightweight%20Computation%20of%20the%20Earths%20Magnetic%20Field.pdf

APM Code - check under AP_GPS for AP_Declination_Lookup.*

ArduPilot.zip

LUT/IDW C# Calculator:

Geomag.zip

Footprint:

COMPASS_DECLINATION_LUT == DISABLED

113268 bytes, Free RAM: 1351, using 2061 bytes of memory

COMPASS_DECLINATION_LUT == ENABLED, COMPASS_DECLINATION_LUT_ACCURACY_LEVEL == 0

114692 bytes, Free RAM: 1351, using 2061 bytes of memory

Accuracy:
Scalable with table size

Table size: 89 entries (COMPASS_DECLINATION_LUT_ACCURACY_LEVEL == 0)
-------------------------------
Error 0 percentile: 0

Error 10 percentile: 0.1098926

Error 20 percentile: 0.2223369

Error 30 percentile: 0.3377705

Error 40 percentile: 0.4542923

Error 50 percentile: 0.5770731

Error 60 percentile: 0.7134132

Error 70 percentile: 0.8671622

Error 80 percentile: 1.072514

Error 90 percentile: 1.401104

Error 91 percentile: 1.447367

Error 92 percentile: 1.495352

Error 93 percentile: 1.551685

Error 94 percentile: 1.611044

Error 95 percentile: 1.676226

Error 96 percentile: 1.764013

Error 97 percentile: 1.864101

Error 98 percentile: 1.988347

Error 99 percentile: 2.208701

Error 100 percentile: 2.987068

Great feedback, Doug! I am re-running the table creation with a 0.1 degree grid this time. Also, could you share the coordinates of such a disturbance? I'd be interested if either the IGRF11 or the WMM2010 take these into account. You can try out both models here: http://www.ngdc.noaa.gov/geomagmodels/IGRFWMM.jsp?defaultModel=WMM. Obviously, the accuracy of this method is limited by the accuracy of the model - GIGO as they say :) That said, I don't want anyone thinking that I am claiming the worst case error will scale linearly with the number of points. In other words, 100% < 1 degree error will take *lots* of points. And by the sound of these disturbances, it's likely infeasible with this model in general.

I also wanted to explain some more more caveats: 1) 1400 bytes is cheating a little bit (I briefly mention this in the write-up); I have the user-configurable declination code disabled when this is enabled, so I'd estimate it's closer to 2-3k, but I have not specifically calculated this. 2) By limiting the area of applicability, I'm making a difficult problem much more tractable 3) I'm not taking into account either elevation or time. In my area, declination is changing at 0.2 degrees/year. I don't know what worst cases are for this though.

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Comments

John Erickson March 18, 2011 at 10:23am

Jack- Could you elaborate? Errors are not necessarily bad as long as they are quantifiable, right? What I think we want to avoid is treating tilt-compensated yaw values from small and high inclinations with the same level of confidence in their accuracy.

Regarding Doug's comments, I re-ran at 0.1 degree resolution. Here I should clarify that the error is based on deviation from the IGRF model. Here are the results:

Size:114952
Table: 114 entries * 5 bytes

Error 0 percentile: 0
Error 10 percentile: 0.1202459
Error 20 percentile: 0.241147
Error 30 percentile: 0.366117
Error 40 percentile: 0.4916201
Error 50 percentile: 0.6215248
Error 60 percentile: 0.7635632
Error 70 percentile: 0.9314415
Error 80 percentile: 1.148144
Error 90 percentile: 1.463516
Error 91 percentile: 1.508278
Error 92 percentile: 1.557454
Error 93 percentile: 1.611344
Error 94 percentile: 1.671692
Error 95 percentile: 1.740637
Error 96 percentile: 1.819055
Error 97 percentile: 1.909616
Error 98 percentile: 2.026399
Error 99 percentile: 2.20524
Error 100 percentile: 2.983333
Jack Crossfire March 16, 2011 at 12:21am

With the errors introduced by acceleration, GPS, & shifting poles, there is a point of overdoing the magnetometer.
bcr March 15, 2011 at 8:42pm

Great work, thanks for posting this John. To improve accuracy, we could store the high res data on a PC or cellphone and send relevant sections to the UAV as needed. Perhaps a MAVLink/QGC extension is in order.
John Erickson March 15, 2011 at 2:16pm

Great feedback, Doug! I am re-running the table creation with a 0.1 degree grid this time. Also, could you share the coordinates of such a disturbance? I'd be interested if either the IGRF11 or the WMM2010 take these into account. You can try out both models here: http://www.ngdc.noaa.gov/geomagmodels/IGRFWMM.jsp?defaultModel=WMM. Obviously, the accuracy of this method is limited by the accuracy of the model - GIGO as they say :) That said, I don't want anyone thinking that I am claiming the worst case error will scale linearly with the number of points. In other words, 100% < 1 degree error will take *lots* of points. And by the sound of these disturbances, it's likely infeasible with this model in general.

I also wanted to explain some more more caveats: 1) 1400 bytes is cheating a little bit (I briefly mention this in the write-up); I have the user-configurable declination code disabled when this is enabled, so I'd estimate it's closer to 2-3k, but I have not specifically calculated this. 2) By limiting the area of applicability, I'm making a difficult problem much more tractable 3) I'm not taking into account either elevation or time. In my area, declination is changing at 0.2 degrees/year. I don't know what worst cases are for this though.
Developer

Doug Weibel March 15, 2011 at 10:20am

Hi John,

Interesting approach, but I am skeptical. For this approach to truly have a 100 percentile error of only 3 degrees the grid of points you weight from would have to be fine enough to catch areas of local geological disturbance. For example there are several locations here in Colorado where the declination can vary by more than a degree over a kilometer near point areas of high disturbance due to mineral deposits. For your approach to catch these localized phenomena I think you would need a lot more data points than would fit in 1400 bytes.

This reply was deleted.