An optimal algorithm for multi-carrier range combination

An algorithm for optimal processing of multi-carrier ranging measurements developed in this work. It takes into account both noise errors and errors associated with the troposphere and multipath. Algorithm derivation is based on the maximum likelihood method. It is shown that the proposed algorithm completely coincides with the Iono-free algorithm in the particular case when non-ionospheric errors are assumed to be zero. At the same time, optimal weighing leads to the fact that the combined range error under no circumstances is higher than the error of the original measurements. The use of the synthesized algorithm in comparison with the well-known Iono-free algorithm, firstly, does not lead to increased errors at a low signal-to-noise ratio, and secondly, it allows to combine ranges from an arbitrary number of carrier frequencies.