Communication Networks Applications

Our new corporate partner, Optovation of Ottawa, is paying us to investigate fibre optic signal properties.  In particular, they are building a product that tests the quality of optic signals at various frequencies, using a lot of proprietary hardware and software.  One of the most difficult problems left for them is the accurate simultaneous estimation of optical signal to noise ratios, peak powers, and bit rates for all the carrier frequencies on a fibre.  In the Ordered Multi-Target Tracking problem, we are solving a simplified version of this problem for them.  In early September 2002, Hailes and Kouritzin visited Optovation's lab to learn the characteristics of this problem and collect some data.  Since then, we have built a first model for their problem including the targets, their interactions, the optical noise, and the electrical noise.  The problem and model are naturally addressed by filtering theory.  However, due to the huge size of this problem (up to eighty interacting targets), we will have to make significant advances in multi-target tracking and applying REST to such tracking in order to help them.  Even with knowledge of problem specific simplifications that can be made, the problem seems too large for anything but possibly REST.  There is also a necessary parameter estimation that must be done to characterize the optical noise in this problem.  We may try to do this within REST or else using our recursive-combined algorithm.

Michael Kouritzin established a new class of models described by a nonlinear stochastic parabolic equation with arbitrary cádlág noise and arbitrary order elliptic operators.  The noise sources in these models include long-range dependent processes, heavy-tailed Lévy processes, and composite processes like iterated Brownian motion.  It is believed that these models are a reasonable starting point for modeling such events as the flow of information through a complicated communication network.  Filtering would then be used to determine more ?x201c;internal?x201d; quantities.