Theory of the local scale parameter method for EDM

The determination of a representative refractive index for the wave path is the main limitation of the attainable accuracy in electronic distance measurement. To overcome this limitation the length ratio method was initially proposed and later developed into the local scale parameter (LSP) method. In this paper, the mathematical model of the LSP method is derived for electro-optical distance measurement from first principles based on the physics of the atmospheric boundary layer. The model does not rely on standard atmospheres. It is shown that atmospheric temperatures and pressures must be observed at instrument stations but not at reflector stations. Appropriate LSP field procedures and the results of some field experiments are summarized. The method consistently produces accuracies of better than ±1 ppm. Use of the method is recommended for high precision (trilateration) networks, which need to be measured repeatedly and where absolute scale is not relevant.