Correcting for Target Motion in Time-Reversal Spectral Focusing

It is well-known that an iterative time-reversal (TR) process, applied via a distributed sensing system, can be used to produce a space-time waveform that maximizes the energy scattered from a stationary target back to the sensors. The TR process accomplishes this by automatically focusing energy, both spatially and spectrally, on the stationary target. When scatterers are moving, however, the TR focusing can break down. This article shows how to modify the TR process so that it automatically focuses energy on a moving target. This new TR process automatically generates a distributed beam that: 1) follows the target as it moves and 2) enhances the target resonances by concentrating the energy spectrally. This focusing occurs without a priori knowledge of the target’s location or spectral response. The new TR algorithm is derived through a careful analysis of the idealized case of a single isotropic moving point scatterer. This article includes simulations that compare the TR focus both with and without the new modification. Although the simulations are carried out for the electromagnetic case, the theory applies equally well to the acoustic case when the target speed is significantly less than the ambient sound speed. Appendices are included with details of the calculations and with analysis of the range of relative velocities for which the modified TR process should be used.