- #1

Frank Einstein

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- TL;DR Summary
- I have two points which represent geographical positions whose coordinates are given in spherical coordinates and also have an associated uncertainty. I can calculate the distance between said points in cartesian coordinates, but I don't know how to translate the uncertainty.

Hello everyone.

I have two points in space (on the surface of the earth) represented using spherical coordinates (in this case there is no z axis since both are assumed to be at the same height). These points have an associated standard deviation in lambda and in phi, which are longitude and latitude respectively. I can calculate the distance between the mean position of both points using the haversine as

ζ=sin^2[(φ1-φ2)/2]+cos(φ1)cos(φ2)sin^2[(λ1-λ2)/2] and then

d=2*R*atan2(√ζ, √1-ζ) where R is the Earth radius and d is the distance in meters between the points defined by (λi,φi) where i=1,2.

However, I have no idea on how to find out the uncertainty of d. I have a standard deviation for the values of (λi,φi), I was wondering if someone can tell me how to incorporate this data to the haversine to be able to calculate the standard deviation of the distance d.

Can someone please tell me of a way to do this?

Any help is appreciated.

Regards.

Frank.

I have two points in space (on the surface of the earth) represented using spherical coordinates (in this case there is no z axis since both are assumed to be at the same height). These points have an associated standard deviation in lambda and in phi, which are longitude and latitude respectively. I can calculate the distance between the mean position of both points using the haversine as

ζ=sin^2[(φ1-φ2)/2]+cos(φ1)cos(φ2)sin^2[(λ1-λ2)/2] and then

d=2*R*atan2(√ζ, √1-ζ) where R is the Earth radius and d is the distance in meters between the points defined by (λi,φi) where i=1,2.

However, I have no idea on how to find out the uncertainty of d. I have a standard deviation for the values of (λi,φi), I was wondering if someone can tell me how to incorporate this data to the haversine to be able to calculate the standard deviation of the distance d.

Can someone please tell me of a way to do this?

Any help is appreciated.

Regards.

Frank.