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This work analyzes the performance of a mutual impedance probe used to measure the complex permittivity of a soil, and detect the presence of water ice buried in the subsurface. The sensor consists of four electrodes deployed above the ground, equally spaced along a straight line array. The quadrupole accuracy has been evaluated through a suitable error analysis which considered the errors associated with the electronics used to measure the mutual impedance of the system, and the position uncertainties of the electrode array. It has been found that the quadrupole accuracy is mainly limited by the electrode positioning. In particular, the electrode vertical misplacements perturb the measurements much more than the horizontal ones. As a case study, a two-layers soil with the deeper stratum containing 20% of water ice at 190 K, which could represent a realistic Martian soil scenario, has been analyzed. It was found that the ice detection requires an electrode vertical position accuracy better than 0.001 times the interelectrode distance. This requirement is far too difficult to be achieved in a fully automated rover mission. Such a conclusion poses significant doubts about the feasibility of projects which foresee the use of electric quadrupoles to detect water ice in the Martian subsoil. [ABSTRACT FROM AUTHOR]