**Sensor Vibration Neutralization**

One of Lockheed Martin Naval Electronics and Surveillance Systems' and Lockheed Martin Canada's most vital concerns is to improve the onboard performance of the Canadian Wescam sensor. This sensor has been installed in several U.S. military aircraft and would be installed in many more if its performance were more satisfactory. The most practical methods of improving performance are via software-implemented mathematical algorithms. There are three separate problem areas in which nonlinear filtering can improve the performance of the Wescam filter. In simplification, they are: initialization, remote pod neutralization, and low observable tracking of vessels. We have essentially provided our sponsors with their most promising methods of improving the low observable tracking performance of the Wescam sensor through our work on SERP and REST filters. Our convolutional filter appears ideal for problems like remote pod movement neutralization. This Wescam filter enhancement is part of the realistic and quite technical motivation for our previously mentioned Search and Rescue problem.

To explain the Pod Tracking problem further, we mention that the sensor must be mounted externally to be effective and this external sensor pod is subject to random vibrations and forces. Our goal is to neutralize the effect of the first sensor movement from the first sensor readings. This is done by a filtering algorithm and a second sensor in the craft, whose only task is to estimate the pod. Depending upon the choice for this second sensor different observation models are appropriate. Due to the distances involved small errors in the pod location estimate have a dramatically amplified effect on the first sensor's readings. Therefore, we wanted to avoid the extra approximations of particle or space-discretization methods and use IDEX. Currently, we believe we have a workable explicit solution for the stochastic movement of the pod in terms of a small number of multiple Wiener integrals in the sense that the corresponding Stratonovich equation should adequately model the pod movement and the explicit solution is computer workable. Most likely, we will have to modify our solution later to account for the pole behaviour more fully. However, the explicit solution method has the highly desirable properties that the solution is forced to stay on the manifold even in the presence of numeric error and the evolution is in two dimensions (the dimension of the manifold), not three as direct particle or space discretization methods would do.

The mathematics behind this solution is reasonably involved but general enough to accommodate more general manifolds. Basically, we prove such things as that there are explicit solutions involving the one and two-parameter stochastic integrals if and only if the vector fields corresponding to the columns of the dispersion coefficient in the Stratonovich equation are two step nilpotent and the ?x201c;drift?x201d; vector field satisfies some more general condition. Then, we study the class of such explicit solutions and show that it is large and contains many suitable models for this problem. In particular, we show that there are solutions that stay on the desired manifold and have the desired drift and diffusion properties on this manifold. The work is being done by Kouritzin, Remillard, and Van Weelden. Kouritzin and Wiersma are implementing the solution.

We
are also talking with Lockheed about the possibility of combining the Pod
Tracking problem with the Search and Rescue problem to better reflect reality
and produce one large problem.