Let's assume a ground receiver RX has the geocentric coordinates (X, Y, Z) and geodetic coordinates (Φ, λ, h_ellispoid). The topocentric coordinate system at RX denoted by (N,E,U) is defined as follows

• the origin of the topocentic coordinate system is at the ground station RX
• N-axis pointing to the North direction (tangent to the local meridian) at RX
• E-axis pointing to the East direction (tangent to local parallel circle) at RX
• U-axis pointing upwards along the vertical of RX

There is a VERY important thing to remember about a topocentric system (defined as above): it does not constitute a right-handed system while (-N,E,U) does.

Based on above mentioned things, the topocentric coordinates (N,E,U) of a satellite (SV) with respect to a ground receiver can be derived from the corresponding satellite geocentric coordinates (X_SV, Y_SV, Z_SV) following these steps (the order is very important):

1. a translation of coordinate origin from the geocentre to the ground receiver
2. a rotation of Z-axis by λ at RX (align Y-axis along East direction)
3. a rotation of Y-axis by 90⁰-Φ at RX (align Z-axis along Up direction and X-axis along South direction)
4. change a sign of the N-component (align X-axis along North direction)

The mathematical formulas can be found in the attached document.

-- OctavianAndrei - 14 Jul 2009