Particle swarm optimization and uncertainty in Dempster-Shafer fusion

Recent investigations into multi-sensor fusion have yielded a variety of data fusion algorithms. Some fuse imagery from multiple sensors at the pixel level, while others fuse outputs of detection algorithms-such as radar prescreeners or hyperspectral anomaly detectors-at the feature level. Many of the feature-level fusion algorithms build upon the foundation of Bayesian probability, and they assign probability to the event that a certain feature value is due either to a target or to clutter. A few of the feature-level fusion algorithms, however, exploit tools developed within the framework of the Dempster-Shafer (DS) theory of evidence. In these formulations some of the probability can be assigned to a third hypothesis representing uncertainty, and the algorithm developer must specify an uncertainty function that maps feature values to probability "mass" for this third hypothesis. Unfortunately, the DS paradigm lacks a standard method for assignment of mass to the "don't know" hypothesis for a particular input feature. In this paper we define a feature-level DS fusion algorithm and determine a method for specifying its uncertainty function. We begin by developing and describing a measure of performance based on the area under the receiver operating characteristic (ROC) curve. We then incorporate this measure of performance into a training procedure that exploits the dynamics of the particle swarm and is capable of discovering locally optimal uncertainty functions. We exercise the training algorithm using simulated data, and analyze the performance of its hypothesized optimal uncertainty function. Next we apply the newly developed training techniques to data produced by separate prescreener algorithms operating on measured Hyperspectral Imager (HSI) and synthetic aperture radar (SAR) data from the same scene. Finally, we quantify the performance of the entire DS fusion procedure using ROC curves.