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This paper aims to investigate the optimal placement and/or orientation of individual sensor elements within integrated angular position sensors, in particular magnetic sensors based on the Hall effect or magnetoresistive effects under consideration of random deviations (variations in the production process, environmental influences, noise) and correlations of these influences.

The authors utilize methods from optimal design of experiments to consider random deviations in a system-level model. In this sensor model, they include spatial dependencies of random deviations by means of a Gaussian random field. Based on this, an approach for fast determination of D-optimal designs is presented.

The results show that the intuitive and commonly used distributions of magnetic field sensors are actually optimal for the determination of in-phase and quadrature signals in the presence of spatial correlations, provided that the number of field sensors is higher or equal to three. However, in the uncorrelated case, the intuitive solutions are not the only optimal solutions or even not optimal at all. It is found that a restriction to symmetric designs is not necessary; thus, the design space can be extended to allow for further improvements, e.g. miniaturization, of such angular position sensors.

The proposed approach allows for the fast optimization based on a system model. Correlated random influences are considered by means of a Gaussian random field, which can be obtained either from measurements or from field simulations, e.g. using the finite element method. As this is done before the actual simulation, such evaluations are not needed during the optimization, which allows for very fast solution of the optimization problem. Therefore, the approach is well suited for application-dependent adjustment of sensor designs.