Mathematical Model and Calibration Procedure of a PSD Sensor Used in Local Positioning Systems

Here, we propose a mathematical model and a calibration procedure for a PSD (position sensitive device) sensor equipped with an optical system, to enable accurate measurement of the angle of arrival of one or more beams of light emitted by infrared (IR) transmitters located at distances of between 4 and 6 m. To achieve this objective, it was necessary to characterize the intrinsic parameters that model the system and obtain their values. This first approach was based on a pin-hole model, to which system nonlinearities were added, and this was used to model the points obtained with the nA currents provided by the PSD. In addition, we analyzed the main sources of error, including PSD sensor signal noise, gain factor imbalances and PSD sensor distortion. The results indicated that the proposed model and method provided satisfactory calibration and yielded precise parameter values, enabling accurate measurement of the angle of arrival with a low degree of error, as evidenced by the experimental results.