Erratum: Rodríguez-Navarro, D., et al. Mathematical Model and Calibration Procedure of a PSD Sensor Used in Local Positioning Systems. Sensors 2016, 16, 1484.

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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.

Optimization of the Coverage and Accuracy of an Indoor Positioning System with a Variable Number of Sensors.

This paper focuses on optimal sensor deployment for indoor localization with a multi-objective evolutionary algorithm. Our goal is to obtain an algorithm to deploy sensors taking the number of sensors, accuracy and coverage into account. Contrary to most works in the literature, we consider the presence of obstacles in the region of interest (ROI) that can cause occlusions between the target and some sensors. In addition, we aim to obtain all of the Pareto optimal solutions regarding the number of sensors, coverage and accuracy. To deal with a variable number of sensors, we add speciation and structural mutations to the well-known non-dominated sorting genetic algorithm (NSGA-II). Speciation allows one to keep the evolution of sensor sets under control and to apply genetic operators to them so that they compete with other sets of the same size. We show some case studies of the sensor placement of an infrared range-difference indoor positioning system with a fairly complex model of the error of the measurements. The results obtained by our algorithm are compared to sensor placement patterns obtained with random deployment to highlight the relevance of using such a deployment algorithm.