Statement of Objectives

The objective of this project is to exploit a powerful signal-processing tool called the fractional Fourier transform (FRFT), suitable for representing chirped signals common to radar, to design a novel exploitation of synthetic-aperture-radar (SAR) that yields a spatial map of the vibration frequencies present in and co-mapped with high-resolution SAR imagery. Modeling and initial validations have been completed and the project is now scheduled for a wider range of verifications and extensions in collaboration with the Sandia National Laboratories (SNL) and General Atomics Aeronautical Systems, Inc (GA-ASI).

 Background and Research

Vibrations of structures during surveillance efforts for national security, such as buildings and underground facilities that may contain concealed machinery or generators, tanks, personnel carriers and their decoy counterparts, bear vital characteristic signatures about these objects. Presently, no single sensing platform exists to simultaneous image an area and co-register vibration information. SAR is a natural fit to this problem because (1) it is a proven highly effective imaging technology; and (2) it is inherently capable of capturing vibration-induced Doppler shifts in the electromagnetic returns from objects. The instantaneous Doppler shift associated with returned electromagnetic waves reflected off vibrating objects is proportional to the component of the object’s instantaneous velocity along the microwave-pulse propagation (range direction), and can be approximated by a harmonic-motion model. We are able to reliably estimate the center frequencies and the associated chirp rates in each pulse with the FRFT (Figure 1), and then we concatenate these estimates over the series of SAR pulses and construct a piecewise-linear approximation of the instantaneous acceleration and velocity track, and consequently determine an object’s vibration frequency spectrum.

 Outcomes

The vibrometry method developed in this project has been modeled mathematically and its performance has been characterized in terms of required deflections, range of vibration frequencies, and required SNR. It has also been tested with basic simulations to prove its performance in SAR broadside stripmap and spotlight modes. Simulation results show that the algorithm has better performance in estimating multi-component vibrations when compared to state-of-the-art bilinear time-frequency transforms. For example, a resolution of at least 1 mm in deflection at 10 Hz can be achievable for realistic SNR scenarios. Major accomplishments in the last year include: (1) testing using real SAR experiments; (2) testing in the RF laboratory at UNM; and (3) exploitation of pseudo-subspace approach and up-sampling to improve the robustness of the vibrometry method.

Since May 2010, collaboration with GA-ASI and the liaison from SNL helped evaluate the performance of the proposed method using real SAR data. Two vibrating corner reflectors with different vibration signatures were built and deployed on the ground during SAR imaging (Figure 2). The first vibrating corner reflector bears a 1 Hz harmonic motion with a 3-cm peak-to-peak amplitude and the second vibrates at 5 Hz with a 3 mm peak-to-peak amplitude. SAR image data of the vibrating corner reflectors was collected with the Lynx SAR (K_u-band) built by GA-ASI. Our method successfully extracted the vibration signatures of both targets, as shown in Figure 3. Up-sampling (interpolation) has further improved performance in estimating high vibrating frequency without increasing the pulse repetition frequency (expensi...

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