This article describes an algorithm for reconstructing the motion of a radar platform relative to a scene, given video phase history and an estimate of the sensor’s average speed and altitude. This algorithm is a more robust alternative to previous geometric-invariant-based approaches, capable of producing motion estimates accurate enough for the formation of backprojection imagery. The algorithm is modular. In the first phase, the algorithm estimates the range to fixed locations in the scene as a function of time. In the second phase, these range tracks are used by a specialized solver to recover the relative positions of the tracked locations in the scene, along with the relative position of the sensor platform as a function of time. We demonstrate the effectiveness of the algorithm by forming an image from the large-scene Gotcha data set, without the use of GPS or inertial measurement unit data. The results are compared to those from another invariant-based algorithm.

Typical synthetic aperture radar imaging techniques neglect the dispersive nature of the so-called image “reflectivity” function over the bandwidth of the transmitted waveform. In this paper, we form an image of the complex scene reflectivity as it depends on (x, y, and frequency), or equivalently (x, y, and time delay), a technique we refer to as hyperspectral synthetic aperture radar (HSAR). Our approach is based on a signal model that allows arbitrary flight trajectories and arbitrary waveforms (including continuously transmitting signals such as noise waveforms), and incorporates the causal, dispersive nature of the scene reflectivity without resorting to resolution-degrading frequency-domain sub-banding as others have previously proposed. We describe the resulting joint time-space resolution of HSAR in terms of the imaging point spread function for a selection of geometries and waveform bandwidths, and provide numerical examples to illustrate the approach.

The linear sampling method (LSM) offers a qualitative image reconstruction approach, which is known as a viable alternative for obstacle support identification to the well-studied filtered backprojection (FBP), which depends on a linearized forward scattering model. Of practical interest is the imaging of obstacles from sparse aperture far-field data under a fixed single frequency mode of operation. Under this scenario, the Tikhonov regularization typically applied to LSM produces poor images that fail to capture the obstacle boundary. In this paper, we employ an alternative regularization strategy based on constraining the sparsity of the solution's spatial gradient. Two regularization approaches based on the spatial gradient are developed. A numerical comparison to the FBP demonstrates that the new method's ability to account for aspect-dependent scattering permits more accurate reconstruction of concave obstacles, whereas a comparison to Tikhonov-regularized LSM demonstrates that the proposed approach significantly improves obstacle recovery with sparse-aperture data.

This paper describes an invariant-based shape- and motion reconstruction algorithm for 3D-to-1D orthographically projected range data taken from unknown viewpoints. The algorithm exploits the object-image relation that arises in echo-based range data and represents a simplification and unification of previous work in the literature. Unlike one proposed approach, this method does not require uniqueness constraints, which makes its algorithmic form independent of the translation removal process (centroid removal, range alignment, etc.). The new algorithm, which simultaneously incorporates every projection and does not use an initialization in the optimization process, requires fewer calculations and is more straightforward than the previous approach. Additionally, the new algorithm is shown to be the natural extension of the approach developed by Tomasi and Kanade for 3D-to-2D orthographically projected data and is applied to a realistic inverse synthetic aperture radar imaging scenario, as well as experiments with varying amounts of aperture diversity and noise.

This paper presents a new approach for reconstructing both shape and motion from data collected by echo-based ranging sensors. The approach is based on geometric invariant theory and exploits object-image relations for near-field (spherical-wavefront) range data. These object-image equations relate the data to a unique matrix of Euclidean invariants that completely describe the object shape. The object-image relations can be used to determine the shape of a scene viewed from unknown vantage points. Specifically, the object-image equations form a linear system of equations whose solution determines the relevant shape parameters for a configuration of features within the scene. Once the shape parameters are estimated, a single shape exemplar from the point in shape space can be used to determine the relative motion (up to an arbitrary rotation) between the sensor and the object. One advantage of this motion-estimation approach is that the geometric-invariant-based strategy allows us to uniquely solve the optimization problem without the need to introduce coordinate-system-dependent “nuisance” parameters. The theorems stated in this paper hold for any range-measurement sensor scenario. As an example of the utility of the given theorems, the object-image relations are used to augment noisy GPS measurements in a circular synthetic aperture radar geometry.