Shape- and motion-reconstruction is inherently ill-conditioned such that estimates rapidly degrade in the presence of noise, outliers, and missing data. For moving-target radar imaging applications, methods which infer the underlying geometric invariance within back-scattered data are the only known way to recover completely arbitrary target motion. We previously demonstrated algorithms that recover the target motion and shape, even with very high data drop-out (e.g., greater than 75%), which can happen due to self-shadowing, scintillation, and destructive-interference effects. We did this by combining our previous results, that a set of rigid scattering centers forms an elliptical manifold, with new methods to estimate low-rank subspaces via convex optimization routines. This result is especially significant because it will enable us to utilize more data, ultimately improving the stability of the motion-reconstruction process.
Since then, we developed a feature- based shape- and motion-estimation scheme based on newly developed object-image relations (OIRs) for moving targets collected in bistatic measurement geometries. In addition to generalizing the previous OIR-based radar imaging techniques from monostatic to bistatic geometries, our formulation allows us to image multiple closely-spaced moving targets, each of which is allowed to exhibit missing data due to target self-shadowing as well as extreme outliers (scattering centers that are inconsistent with the assumed physical or geometric models). The new method is based on exploiting the underlying structure of the model equations, that is, far-field radar data matrices can be decomposed into multiple low-rank subspaces while simultaneously locating sparse outliers.