Particle Filtering of Two Targets (March 2010)
In theory, a good particle filter allows to approximate an exact Bayesian filter solution arbitrarily well. This has motivated a strong and successful development of particle filtering approaches towards target tracking. In this presentation we pose the question whether this theory also applies to problems of tracking two targets that maneuver in and out a formation flight, and where the observations may include false measurements, missed detections and limited sensor resolution.
Probabilistic safety verification of future air traffic (March 2010)
Despite advances in formal and probabilistic verification approaches, fault and event trees are still the dominant techniques used for safety risk analysis in aviation. However, the combination of concurrent, dynamic, and random effects that appear in air traffic cannot properly be captured by these classical techniques. In this lecture, it will be explained how safety risk modeling and analysis can be formulated as a problem of estimating the rare event probability of a large scale stochastic hybrid system. Subsequently it is explained how rare event estimation theory for diffusions can be extended to a large scale stochastic hybrid system (SHS), in which a large number of rare discrete modes may contribute significantly to the rare event estimation. Essentially, the approach taken is to develop a compositional model of the air traffic operation considered in the form of a large scale SHS; then to introduce a suitable aggregation of the discrete modes of this large scale SHS; and then to develop importance sampling and Rao-Blackwellization relative to these aggregations. The practical use of this approach will be demonstrated for the estimation of the mid-air collision probability for an advanced air traffic application.
Information Fusion and Performance Modeling with Distributed Sensor Networks
Multi-sensor fusion is founded on the principle that combining information from multiple sources will enable a better understanding of the surroundings. However, it would be desirable to evaluate how much one gains by integrating different sensors in a fusion system, even before implementing it. This presentation describes our latest research on fusion performance modeling. Specifically, we have developed a framework for quantifying the classification performance of a set of sensors with varying qualities based on local confusion matrix and global confusion matrix using the Bayesian network model. We have developed a theoretical model to analyze the convergence property of the methodology. We have also developed a software tool based on UnBBayes open source environment (http://unbbayes.sourceforge.net/index.html) to validate the performance modeling. A demonstration with an example model for air target tracking and classification using the developed tool will be given.
In recent years Mahler’s Finite Set Statistics (FISST) approach to multi-target tracking has
attracted substantial interest mainly through the developments of the PHD/cardinalized PHD (CPHD)
filters. However, FISST is much more powerful and extends beyond the PHD/CPHD filters. This talk
explores a number of tractable tracking solutions derived from FISST, including, joint detection and
tracking (of a single target) using Bernoulli random sets, multi-target tracking using multi-Bernoulli random
sets, and multi-target smoothing with the PHD.
Nonnegative Matrix Factorization (NMF) has attracted much attention during the past decade as
a dimension reduction method in machine learning and data mining. NMF is considered for high
dimensional data where each element has a nonnegative value, and it provides a lower rank
approximation formed by factors whose elements are also nonnegative. Numerous success
stories were reported in application areas including text clustering, computer vision, and
chemometrics.