# Are latitude and longitude observations independent of each other or correlated?

I want to develop a bivariate gaussian kernel in order to handle the random noise in my GPS tracks where each point has three parameters (lat, long and time stamp).

I was wondering if latitude and longitude errors are correlated or independent of each other?

My common sense says they are independent because no causal relationship exists between them.

• are you really asking if the lat error and lon error in your GPS readings are correlated? Jul 24, 2014 at 2:21
• This question totally depends on the movement of the GPS device, not on longitude/latitude per se - surely you want to know about the actual space in which the thing is moving, longitude/latitude are just one way to represent that. (See the "Moving objects, trajectories" section in this CRAN Task View for a few pointers to software in R: cran.at.r-project.org/web/views/SpatioTemporal.html) KDE is a poor way to handle noise in tracks imo, how to deal with the temporal dimension and serial autocorrelation? Also, use map projections for a real world space rather than ellipsoid angles. Jul 24, 2014 at 4:07
• So by noise you mean GPS positions/points within your track that you've noticed aren't as accurate as other positions? This would be mainly dependant on your GPS unit that you are using for recording these points. This would be were you're question would lead. Also this is horizontal accuracy, note the vertical z component will be greater in it's inaccuracy. Now if it's just the trail it's self then type of movement and what's reasonable for change of speed and direction will allow filtering of these points. PLUS you may have a accuracy value from the GPS unit too? Jul 24, 2014 at 9:24
• I think folks are misunderstanding the intended but slightly mis-stated question: are the quoted observations (or their errors) of lat, long correlated? It is an important issue in rigorous least-squares analysis. Apr 25, 2015 at 21:04
• Have you considered that there may be a correlation between the time and the error in either the Lat or Long observation? Jun 12, 2015 at 12:15