In this paper, an innovative grid-based approach to optimize the sensor arrangement in a sensor array is presented. Such an optimized sensor arrangement involving low-cost sensors finds its use in a variety of areas as in automotive safety applications. The potential cost-savings achievable through the use of such sensor systems makes them attractive for car makers.
The presented approach is based on an array of N sensors located in a horizontal plane. The sensors that are being used are low-cost infrared sensors, which provide an output voltage depending on the presence of an object inside the sensor's field of view (FOV). Since every sensor has a limited FOV and range-of-sight, several sensors with overlapping FOV's are necessary to cover any specific region of interest (ROI) satisfactorily.
The goal of the presented approach is to identify an optimal sensor arrangement for object localization within the ROI. Since only the signal changes are used for processing and not their absolute values, it is imperative that FOV's of at least two sensors should overlap for object position estimation. In addition, the accuracy of the estimation depends on the size of the overlapping area. To solve this (multi-faceted) optimization problem there were no convenient analytic solutions available. Therefore a numerical grid-based solution to compute the best sensor arrangement was developed in this approach. The ROI is represented by a regular grid. Every cell in the grid has a determined weighting function. The formulation of the weighting function is the key to the optimization problem and it is based on the following parameters: number of sensors that cover the cell, dimensions of the overlapping areas and the complete coverage of the ROI. The sum over all cell-weights within the grid is the cost function to be optimized. Due to the high computational effort several algorithms are considered and the final implementation with a simulated annealing approach is chosen because of its ability to find a global minimum in reasonable time.