I am trying to write code to parse the NMEA strings coming from survey-grade RTK/GNSS receivers. The requirements I have are to calculate the 3DRMS (distance RMS at 97.5% probability), VRMS (vertical RMS) and HRMS (horizontal RMS) values (amongst others).
3DRMS = 3 * Math.sqrt(Math.pow(dx,2) + Math.pow(dy,2))
dx is Latitude error and
dy is Longitude error.
So, for example, if the GST message string is:
3DRMS = 3 * Math.sqrt(Math.pow(0.023,2) + Math.pow(0.020,2)) = 0.091
However, I'm struggling to find a definition or formula to calculate the VRMS and HRMS values, and therefore which NMEA strings I need to parse to calulate them.
I've also found a PhD thesis which contains some equations, but I'm having trouble understanding how to abstract them into a generic formula. However, it looks like PDOP is involve, so I would assume I need to parse the GSA message in addition to the GST.
Where can I find the relevant formulas or how to calculate these values?