Via Geometric Algebra: Direction and Distance between Two Points on a Spherical Earth

[@IBHunter]

Man! I have to dig in the old memory banks for this one. When we were working on developing corrections for GPS, I spent a lot of time doing time series plots over known positions. I ended up writing a simple program to parse the RS233 NMEA data log the raw data, calculate the deviation and bearing from the known point real time and provide a RMS error value. In the decades since, I haven’t had to dig into the raw calculations very often. Elevations have been the biggest issue since not all standards have a direct conversion. That only raises a problem when dealing with RTK accuracy in the vertical axis. Another real wrinkle in vertical measurements is due to the fact that some differential GPS corrections are not localized and are not referencing a local position near the receiver. This causes the GPS to pick up earth tides. The actual ground rises and falls with the tide, but it is to small for no corrected GPS, and local referenced GPS has its reference affected the same as the receiver. Global differential networks such as C-Nav correct GPS position by individually correcting the sources of errors. It corrects clock errors by using reference stations. It corrects orbit errors by using the same reference stations. The biggest error is ionospheric and tropospheric delays due to changes in the atmosphere. This is corrected using a duel frequency receiver and measuring phase delays between the two frequencies to determine how the atmosphere is affecting the signals. A workaround has been employed you filter out the tidal heave, but it is a user configurable option.

[@JimSmithInChiapas]

That's really interesting! Thanks.

[@FlatEarthMath]

Excellent! I'm going to have to learn what this Geometric Algebra stuff is all about... :-)

[@JimSmithInChiapas]

Thanks. You'd be very welcome in the LinkedIn group "Pre-University Geometric Algebra". I started it as a place where students, experts, and self-learners (like myself) can collaborate in developing materials for teaching the subject at the HS level.

[@FlatEarthMath]

@@JimSmithInChiapas Thanks for the encouragement! I'm not in LinkedIn, but it appears there are other resources also. 🙂

[@Voidsworn]

I see you made one crucial error...you used math.

[@JimSmithInChiapas]

Rats. I was hoping no one would notice.