An innovative high-precision digital instrument for position measurement of particle accelerators collimators is proposed. The instrument relies on Linear Variable Differential Transformer by exploiting the three-parameter sine fit to estimate the amplitudes of their secondary signals. Moreover, the crucial problem of interfering magnetic fields is thoroughly analyzed by means of two different models: an analytical one aimed at capturing the main physics of the phenomenon and a predictive one based on Finite Elements Method. Both models have been validated by means of simulations and...