# How to calculate the slope from geopraphical coordinates?

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Serbring 2020년 1월 18일
댓글: Jeremy Salerno 2022년 6월 21일
Hi all,
I have installed a GPS logger on a vehicle, so I have extracted the geographcal coordinates in degree (longitude, latitude and elevation). I need to calculate the slope encountered by the vehicle. I came up with the following code, that is far from being good as you can see in the attached plot. How may I improve the results?
wgs84 = wgs84Ellipsoid('meters');
[gpsx,gpsy,gpsz] = geodetic2ecef(wgs84,Latitude,Longitude,Altitude);
slope=atand(diff(gpsz)./sqrt(diff(gpsx).^2+diff(gpsy).^2));
Thank you.
Best regards.

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### 채택된 답변

Jim Riggs 2020년 1월 19일
편집: Jim Riggs 2020년 1월 19일
First of all, you should consider the relationship between the WGS84 lat/lon/alt and the ECEF frame. Altitude is perpendicular to the reference ellipsoid, so it is effectively parallel to "down". I would assume that if you want to know the slope encounrered by a vehicle, that implies the rate of change of "down" over the horizontal displacement. So when you tranform your data to ECEF, you lose the "down" reference.
Rather, you should be working in a local level frame, such as North/East/Down (NED).
You can transform ECEF to NED using;
In this (NED) frame, X points to the north, Y points east, and Z points down (i.e positive z is down) . Now if you calculate delta Z over the X-Y distance (in the NED frame), it should come out as the parameter you are seeking; the change in height over the change in horizontal distance. This would be the tangent of the local slope angle.
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Jeremy Salerno 2022년 6월 21일
If you have lat/lon in degrees with height in meters, are you still able to use the geodetic2ned or geodetic2enu the same way? Can my input be in lat, lon for x, y and meters for z, or do conversions need to be made beforehand?

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