Tracking of a Mobile Target Using Generalized Polarization Tensors

In this paper we consider the inverse conductivity problem in two dimensions. We apply an extended Kalman filter to track both the location and the orientation of a small target in motion from multistatic response measurements. We also analyze the effect of the limited-view aspect on the stability and the efficiency of our tracking approach. Our algorithm is based on the use of the generalized polarization tensors, which can be reconstructed from the multistatic response measurements by simply solving a linear system. The reconstruction problem of generalized polarization tensors from multistatic response measurements has the remarkable property that low order generalized polarization tensors are not affected by the error caused by the instability of higher orders in the presence of measurement noise.

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