Differential geometry measures of nonlinearity for the video filtering problem

Mahendra Mallick; Barbara F. La Scala

doi:10.1117/12.781537

16 April 2008 Differential geometry measures of nonlinearity for the video filtering problem

Mahendra Mallick, Barbara F. La Scala

Proceedings Volume 6969, Signal and Data Processing of Small Targets 2008; 69690M (2008) https://doi.org/10.1117/12.781537
Event: SPIE Defense and Security Symposium, 2008, Orlando, Florida, United States

Abstract

Video cameras onboard multiple unmanned aerial vehicles (UAVs) can provide effective and inexpensive tracking and surveillance functions for ground targets. In our previous work, we quantified the degree of nonlinearity (DoN) of the video filtering problem by considering the perspective transformation for the video measurement model and constant velocity motion for the target dynamic model. In this paper, we generalize the formulation by using a more realistic video measurement model which is based on the perspective transformation, radial and tangential lens distortions, scale, offset, and skew. The centroid pixel coordinates of a target in the digital image represent the sensor measurement for this model. This measurement model is commonly used in photogrammetry, computer vision, and video tracking, where significant height variation can occur. Since the measurement model is a nonlinear function of the target state, the filtering problem is nonlinear. We quantify the DoN of the video filtering problem by calculating the differential geometry based parameter-effects curvature and intrinsic curvature. These measures help a filter designer to select an appropriate nonlinear filtering algorithm for the video filtering problem so that tracking accuracy and computational load requirements are satisfied. Our results show that the DoN of the video filtering problem is quite low and hence a computationally simple filter such as the extended Kalman filter (EKF) is a better choice than the particle filter (PF) which has a much higher computational cost. The state estimation accuracies of the EKF and PF are nearly the same.

Citation Download Citation

Mahendra Mallick and Barbara F. La Scala "Differential geometry measures of nonlinearity for the video filtering problem", Proc. SPIE 6969, Signal and Data Processing of Small Targets 2008, 69690M (16 April 2008); https://doi.org/10.1117/12.781537

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