Optimal Design and Simulation of Sensor Arrays for Solar Motion Estimation

Modern sensors consist of arrays of detectors specially arranged to enhance precision, capabilities, and field of view (FOV). Sensor arrays can have multiple functionalities, such as the simultaneous detection of position and motion. We use a linear sensor model and develop an optimization method to design an array of photodiodes. Our objective function minimizes bias and variance estimations. We introduce a maximum likelihood technique to approximate and determine the bias caused by measurement errors, and verify our theory by statistically complete simulations. We apply our theory to design an optimal sun sensor. The sensor has a predefined conical FOV, and its accuracy is controlled by a set of directionally variable weighting parameters. This enables us to compute the optimal placements of photodiodes under various operational conditions. It is found that for a uniform accuracy distribution, both the variance and bias estimations can be exactly minimized for a given array configuration. For non-uniform accuracy distributions with rotational symmetries, when a higher accuracy is required around the centerline of the FOV, both errors attain their minima when the array configuration becomes inclined toward the center. In non-uniform and non-axisymmetric distributions, when a higher accuracy is imposed along a line or a path, the bias and variance errors differ significantly, while the variance minimization implies the concentration of the cells toward the path, the bias minimization yields a uniform distribution. The method presented in this paper can be used in the optimal design of sun sensors for space systems and solar power plants.