How do you convert velocity given a heading and speed to ECEF coordinates? If you are given positional data in latitude, longitude, altitude along with a given velocity and heading, how do you convert the velocity into Earth Centered Earth Fixed (ECEF) based values?
In this specific problem the altitude is fixed. I currently have an idea of how to solve this problem, but I feel that there is probably a simpler way.
Hypothesized idea steps:


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*Convert the lat/long/altitude into ECEF coordinates.

*Convert heading and speed to deltas of latitude & longitude, bearing in mind that these are dependent on positional data. (I figure it's some type of differential equation, in which I am a bit rusty)

*Add the deltas to the initial LLA coordinates and convert to ECEF again. 

*Use the change of position in ECEF coordinates to calculate the velocity.


The roadblock that I have hit in my approach is step #2. Trying to determine the delta values when the value of the longitude and latitude deltas vary on position so far has gotten the better of me....  Everything I find in this area always start with being given 2 coordinates. However in this case, I don't have that luxury.
 A: I ended up changing a little of my methodology after getting a little recommendation; my brain does not like traveling into spherical coordinate land. After following these steps I was able to get a satisfactory result.

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*Started by converting the given Latitude/Longitude/Altitude into ECEF.


*Computed the Geocentric radius for each point.


*Break the speed into component vectors of using the heading into vectors of longitude and latitude.


*By treating these vectors as arc length of their given directions. I used the equation solving for theta:
Arc length = Geocentric radius * theta


*I took the computed thetas and added them to my givens of latitude and longitude and changed this new value into ECEF.


*Once converted I subtracted the values converted in step 1 to find my component velocities.
After these steps I found my answers to be consistent and somewhat more accurate than the values that were expected. I believe that they used a method by which a flat plane was used to compute velocities at the given points rather than factoring in the curvature of the vector if holding a constant altitude.
