Differential geometry measures of nonlinearity for the video tracking problem
Mahendra K. Mallick, Barbara F. La Scala · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 2006
Tracking people and vehicles in an urban environment using video cameras onboard unmanned aerial vehicles has drawn a great deal of interest in recent years due to their low cost compared with expensive radar systems. Video cameras onboard a number of small UAVs can provide inexpensive, effective, and highly flexible airborne intelligence, surveillance and reconnaissance as well as situational awareness functions. The perspective transformation is a commonly used general measurement model for the video camera when the variation in terrain height in the object scene is not negligible and the distance between the camera and the scene is not large. The perspective transformation is a nonlinear function of the object position. Most video tracking applications use a nearly constant velocity model (NCVM) of the target in the local horizontal plane. The filtering problem is nonlinear due to nonlinearity in the measurement model. In this paper, we present algorithms for quantifying the degree of nonlinearity (DoN) by calculating the differential geometry based parameter-effects curvature and intrinsic curvature measures of nonlinearity for the video tracking problem. We use the constant velocity model (CVM) of a target in 2D with simulated video measurements in the image plane. We have presented preliminary results using 200 Monte Carlo simulations and future work will focus on detailed numerical results. Our results for the chosen video tracking problem indicate that the DoN is low and therefore, we expect the extended Kalman filter to be reasonable choice.