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High-energy neutrino physics offers a unique way to investigate the most violent phenomena in our universe. The detection of energies above E > 10¹⁷ eV is most efficient using the Askaryan effect, where a neutrino-induced particle shower produces coherent radio emission that is detectable with radio antennas. By using radio techniques large volumes can be covered with few stations at moderate cost exploiting the large attenuation length of radio in cold ice. Key to the reconstruction of the neutrino properties visa precise and continuous monitoring of the firn properties. In particular the snow accumulation (changing the absolute depth of the antennas thus the propagation path of the signal) and the index-of-refraction profile are crucial for the neutrino energy and direction reconstruction. This work presents an in-situ calibration design that acts as an detector extension by adding additional emitter antennas to the station design to continuously monitor the firn properties by measuring the direct and reflected signals (D’n’R). In a simulation study the optimal station layout is determined and the achievable precision is quantified. Furthermore 14 months of data from an ARIANNA station at the Ross Ice Shelf, Antarctica, are presented where a prototype of this calibration system has been successfully installed to monitor the snow accumulation with unprecedented precision of 1 mm. Several algorithms, including deep learning algorithms, to compute the D’n’R time difference from radio traces are considered.