Envelopes and waves: safe multivehicle collision avoidance for horizontal non-deterministic turns

International Journal on Software Tools for Technology Transfer - We present an approach to analyze the safety of asynchronous, independent, non-deterministic, turn-to-bearing horizontal maneuvers...     

A formally verified hybrid system for safe advisories in the next-generation airborne collision avoidance system

The Next-Generation Airborne Collision Avoidance System (ACAS X) is intended to be installed on all large aircraft to give advice to pilots and prevent mid-air collisions with other aircraft. It is currently being developed by the Federal Aviation Administration (FAA). In this paper, we determine the geometric configurations under which the advice given by ACAS X is safe under a precise set of assumptions and formally verify these configurations using hybrid systems theorem proving techniques. We consider subsequent advisories and show how to adapt our formal verification to take them into account. We examine the current version of the real ACAS X system and discuss some cases where our safety theorem conflicts with the actual advisory given by that version, demonstrating how formal hybrid systems proving approaches are helping to ensure the safety of ACAS X. Our approach is general and could also be used to identify unsafe advice issued by other collision avoidance systems or confirm their safety.     

The Bayesian hierarchical classifier (BHC) and its application to short vegetation using multifrequency polarimetric SAR

Given an image of a scene comprised of a number of distinct terrain classes, the optimum Bayesian classifier (OBC) provides the highest possible classification accuracy of the imaged scene, provided we have a priori knowledge of the probability density function (pdf) of the sensor's output for each terrain class. If the imaging sensor consists of multiple channels, application of OBC requires knowledge of the joint pdf of the observations made by all the channels. In practice, the volume of data needed in order to generate an accurate multidimensional pdf far exceeds the size of available datasets. The data-size requirement may be relaxed by assuming the pdfs to be Gaussian in form, but such an assumption leads to suboptimum classification performance. This paper addresses the data size issue by (1) taking advantage of the maximum-entropy density estimation (MEDE) technique introduced in a companion paper and (2) using marginal pdfs in a hierarchical approach. Using multidate synthetic aperture radar observations, it was shown that the Bayesian hierarchical classifier introduced in this paper can classify short vegetation classes with an accuracy of 93%, without retraining, compared with an accuracy of 84% for the maximum-likelihood estimator (with Gaussian assumption) and only 74% with ISODATA.     

A computationally efficient multivariate maximum-entropy density estimation (MEDE) technique

Density estimation is the process of taking a set of multivariate data and finding an estimate for the probability density function (pdf) that produced it. One approach for obtaining an accurate estimate of the true density f(x) is to use the polynomial-moment method with Boltzmann-Shannon entropy. Although rigorous mathematically, the method is difficult to implement in practice because the solution involves a large set of simultaneous nonlinear integral equations, one for each moment or joint moment constraint. Solutions available in the literature are generally not easily applicable to multivariate data, nor computationally efficient. In this paper, we take the functional form that was developed in this problem and apply pointwise estimates of the pdf as constraints. These pointwise estimates are transformed into basis coefficients for a set of Legendre polynomials. The procedure is mathematically similar to the multidimensional Fourier transform, although with different basis functions. We apply this technique, called the maximum-entropy density estimation (MEDE) technique, to a series of multivariate datasets.