We address the problem of characterizing uncertainty for multisensor data fusion in a classification problem. To achieve this goal, we model the joint density of given multivariate data using copula functions while allowing the ability to incorporate any desired marginal distributions, i.e., any desired modalities. The proposed model is data driven in that the corresponding copula functions and their parameters are learned from the data. Our results show that the proposed framework can capture the uncertainties more accurately than current state of the practice, and lead to robust and improved classification performance compared to traditional classifiers.
Development of the novel homotopy, or particle-flow, nonlinear filters1-10 has recently been quite rapid. There
is actually a whole family of such methods, so we will refer to these collectively in this paper as "DH" filters,
after their developers, the third and fourth authors of this manuscript. Unlike a particle filter, a DH filter does
not resample; instead, the particles are moved in a smooth way, from a space that reflects prior (predicted)
knowledge to one that is updated according to the measurements. Working versions of several DH filters now
exist, and the purpose of this paper is to attempt to provide some perspective on them. We stress that this paper
discusses the efforts of the first two authors to learn about and to explain in their own terms these these filters
that others might benefit from that. The latter pair of authors - these are the developers of the DH filter family
- have been instrumental in this effort. But it must be noted that they continue to develop their algorithms,
and that this paper represents a snapshot of a rapidly changing landscape.
We present a target tracking system for a specific sort of passive radar, that using a Digital Audio/Video
Broadcast (DAB/DVB) network for illuminators of opportunity. The system can measure bi-static range and
range-rate. Angular information is assumed here unavailable. The DAB/DVB network operates in a single
frequency mode; this means the same data stream is broadcast from multiple senders in the same frequency
band. This supplies multiple measurements of each target using just one receiver, but introduces an additional
ambiguity, as the signals from each sender are indistinguishable. This leads to a significant data association
problem: as well as the usual target/measurement uncertainty there is additional "list" of illuminators that must
be contended with.
Our intention is to provide tracks directly in the geographic space, as opposed to a two-step procedure of
formation of tracks in (bi-static) range and range-rate space to fuse these onto a map. We offer two solutions:
one employing joint probabilistic data association (JPDA) based on an Extended Kalman Filter (EKF), and the
other a particle filter. For the former, we explain a "super-target" approach to bring what might otherwise be
a three-dimensional assignment list down to the two dimensions the JPDAF needs. The latter approach would
seem prohibitive in computation even with these; as such, we discuss the use of a PMHT-like measurement model
that greatly reduces the numerical load.