Jointly estimating 3D target shape and motion from radar data

Abstract

A novel hybrid 3D radar imaging technique is presented that jointly estimates both target shape and motion using range, range-rate, and phase. This work expands on research done by the author as an intern at MIT Lincoln Laboratory. It builds on and combines the work of two papers: Phase-Enhanced 3D Snapshot ISAR Imaging and Interferometric SAR (Joseph Mayhan) and Shape and Motion Reconstruction from 3D-to-1D Orthographically Projected Data via Object-Image Relations (Matthew Ferrara). The second paper is a modification to work first presented in Derivation and Estimation of Euclidean Invariants of Far Field Range Data (Mark Stuff). The phase-enhanced 3D snapshot imaging algorithm solves for shape using known motion and uncorrelated range, range-rate, and phase data. The second method uses an SVD to jointly solve for shape and motion using correlated range data. Key features from each of these methods are incorporated in to the novel hybrid phase-enhanced 3D SVD method.

Two algorithms are presented that eliminate the need for scatterer correlation so that the hybrid method can be used on uncorrelated radar data. One algorithm, applicable to targets with a small number of scatterers, methodically determines the optimal correlation for a set of data using continuity and slope conditions. This algorithm can be used in the presence of noise and phase ambiguities. The other algorithm, applicable to targets with a large number of scatterers, iterates on an optimally chosen set of possible correlations and chooses the ``best" one based on a condition on the resulting singular values. This algorithm can also be used in the presence of noise and phase ambiguities. A mathematical proof is presented to show that a matrix of radar observables data is uncorrelated if and only if it has more than three nonzero singular values. This proof justifies the use of the iterative algorithm.