Techniques for selecting pose algorithms

Abstract

A technique for selecting one pose algorithm from m algorithms containing zero mean Gaussian errors is derived. The procedure consists of a two stage analysis. First, the joint entropy of each algorithm is found. The algorithm with minimum entropy is shown to possess the greatest possible lower bound reliability of meeting any quadratic specification of the pose error. Hence it is the best pose algorithm to select without further analysis. In addition, the entropy of pose measurements is shown to be invariant with respect to homogeneous coordinate transformations, so the analysis is simplified for physically distributed robotic systems. To guarantee a minimum reliability, a second stage of analysis is necessary. Methods of calculating reliability bounds for a given quadratic specification are derived. The resulting bounds require three orders of magnitude less computations than the alternative, Monte Carlo simulations. Entropy analysis requires another order of magnitude less computations than reliability analysis, so the computations are reduced by a total of four orders of magnitude. The concepts are simulated using a visual pose measurement system developed by NASA, where each viewpoint of the camera is considered to be a separate pose algorithm (accuracy depends upon viewpoint). The results indicate that entropy is very effective for selecting pose algorithms, and the reliability greatest lower bound is close to the actual reliability.