# standard for generating a geolocation error ellipse from lines of position/bearing

Given SEVERAL points, where each point is a line of bearing (LOB)/line of position, and thus each point consists of a (1) latitude & (2) longitude position on the Earth's globe that this LOB is received from and (3) an angle of arrival in degrees from true north measured clockwise that this LOB was received from, as well as (4) a fixed length of each of these LOBs in nautical miles

From these SEVERAL points, I want to compute ONE location error ellipse consisting of one (1) latitude & (2) longitude coordinate which is the center of the error ellipse, (3) a semimajor and (4) semiminor distance in nautical miles of the ellipse, and (5) a orientation angle in degrees from true north to the semimajor axis of the ellipse.

I've been trying to look for the most commonly accepted/most popular method to do this, since this has definitely been done several times before.

I've seen this link: Standard Deviational Ellipse with Open Source Python (GDAL/OGR etc) and read a lot about the standard deviational ellipse, but I have a qualm with it.

If I were to use that standard deviation ellipse, I would probably compute all the points of intersection between each LOB, and then take all the intersection points (lat, long) and use those as (x, y) values as input to those equations to generate that ellipse.

My problem with this is that would assume that our (lat, long) pairs are in Cartesian space - which they aren't. If I were to assume so anyway (which I believe is invalid), then the resulting standard deviational ellipse would be in cartesian space, yet converting that to the earth's geocoordinates polar space wouldn't make sense to me.

If I were to NOT assume that they are in cartesian space, then I would convert the (lat, long) to (x, y, z), and the use this (x, y, z) to compute an error ellipsoid using those equations, then project the resultant ellipsoid on the earth's ellipsoid to get back to (lat, long) geocoordinate polar space, giving me a 2D (curved) error ellipse on the surface of the Earth. I don't have an altitude at each point necessary to compute the (x, y, z), but theoretically I can just use sea level so when I project the (x, y, z) ellipsoid back into (lat, long) geocoordinates, it can be altitude-agnostic. I can see this method making sense to me, but it seems a little too elongated for something that I believe is already solved.

I've looked at other papers as well, specifically those that generate an error ellipse just from two (a pair of) LOBs: https://www.ngs.noaa.gov/PUBS_LIB/AlgorithmsForConfidenceCirclesAndEllipses_TR_NOS107_CGS3.pdf and then papers that combine error ellipses together so I can get a final single error ellipse: https://calhoun.nps.edu/bitstream/handle/10945/32273/96Sep_Orechovesky.pdf;sequence=1 but I've only scratched the surface on these in favor of looking for a less complex solution.

TL;DR what generally is the standard in this field to generate a geocoordinate error ellipse from several lines of bearing/position?