A Biologically Inspired Compound-Eye Detector Array—Part II: Statistical Performance Analysis

Abstract

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> This is the second part of our paper. In this paper, we propose, model, and analyze the performance of a detector array for localizing far-field particle-emitting sources, which is inspired by but generalizes the compound eye of insects. The array consists of multiple eyelets, each having a conical module with a lens on its top and an inner subarray containing multiple particle detectors. Using a parametric measurement model introduced for the array in Part I, in this part we analytically and numerically analyze the statistical performance of the array. First, we compute the statistical CramÉr–Rao bounds (CRBs) on the errors in estimating the direction of arrival of the incident particles; then we derive a lower bound on the mean-square angular error (MSAE) of source localization for any specific array configuration; thirdly, we consider two source-direction estimators, the maximum likelihood estimator (MLE) and the weighted direction estimator (WDE), and analyze their MSAE performance. In the numerical examples, we quantitatively compare the performance of the proposed array with the biological compound eye; show the array performance as a function of the array configuration variables; optimally design the array configuration; illustrate that the MLE asymptotically attains the performance bound, whereas the WDE is nearly optimal for sufficiently large SNR; and analyze the hardware efficiency by comparing the two MSAE bounds. Potential applications of this work include artificial vision in medicine or robotics, astronomy assisted, security, and particle communications. </para>