Two-Dimensional ESPRIT With Tracking for Radar Imaging and Feature Extraction

Abstract

ESPRIT processing appears to be the best of the known spectral-analysis techniques. It provides the highest resolution and has no spectral splatter. By applying matrix eigenstructure analysis, it gives a direct answer to the direct question "What frequencies, real or complex, are present in the data and what are their amplitudes?" Conventional Fourier techniques, as well as some of the other higher-resolution methods, answer the less direct question "What amplitudes, applied to a set of regularly-spaced real frequencies, best represent the data?" Then comes the problem of interpreting the amplitudes.These attributes of ESPRIT, in the two-dimensional version described here, make it a natural for radar signal processing, where it answers the need for high-resolution imaging, free of sidelobes in range and Doppler, and for high-fidelity target feature extraction. For example, the uncertainty in the scatterering-center locations in an ESPRIT image extracted from high-quality static-range radar data collected over a bandwidth of 1 GHz is just a few millimeters; for conventional Fourier processing of the same data the uncertainty is many centimeters. The signature of the base edge of a perfectly conducting cone extracted from static-range data by ESPRIT agrees accurately with the signature predicted by edgediffraction theory.This report starts with a mathematical model for the radar data, describes a technique for "resampling" the data to achieve a more perfect fit with the ESPRIT data model, summarizes the twodimensional ESPRIT algorithm itself, and presents examples of its performance. The appendix covers the details of this least-mean-square version of ESPRIT, including an enhancement that allows the scatterers to be tracked individually. The algorithm properly distinguishes between target locations having one coordinate in common, and it automatically associates correctly in pairs each entry in the list of ranges with the corresponding entry in the list of range rates. 1The Fourier and ESPRIT X-band radar images of an aluminum round-nosed cone target at nose-on aspect derived from measured static-range data of 1 GHz bandwidth. The target's rotation axis and the radar's magnetic-field polarization on transmit and receive were vertical (HH polarization); the target's body-axis of symmetry and the radar line of sight were horizontal. 2 2 The complex diffraction coefficient of the base edge extracted by ESPRIT processing, from the same measured static-range HH-polarization data used for Figure 1, compared with the coefficient predicted by the geometric theory of diffraction. 3 3 ESPRIT X-band images from different aspects and 360-composite images, both in B&W and, to include amplitude information, in false color. The images were extracted from the same measured static-range X-band HH-polarization radar data used for the previous figures. 9 4 Narrow-angle imaging with ESPRIT, including zoom views showing the smaller location uncertainty that greater signal-to-noise ratio provides. 11 5 360° trajectories of t...

A GTD model and state space approach based method for extracting the UWB scattering center of moving target

“…(14); therefore (j nΔf fc ) αs j αs e αs n Δf fc . That means the frequency-dependent factor has no effect on the phase of the system poles and does not affect the solution of the range and the range rate.…”

“…As shown in eqs. (38) and (14), the range matrix Λ ri of each scattering center in each echo of one time window remains unchanged, while the range rate factor Λṙ im,n is changing over time…”

“…Current extraction methods of scattering center focus on spectral estimation methods based on parametric model, such as Prony method, matrix pencil method, ARMA model, ESPRIT method, MUSIC method, Cauchy method [2,[9][10][11][12][13][14][15][16] and so on. These methods are based on DE model assumption and used to calculate the location, the intensity and the damped factor of the scattering center, but cannot reflect the frequency-dependent characteristics of different scattering centers.…”

State-space spectral estimation of characteristic electromagnetic responses in wideband data

“…The objective in this letter is to derive the state matrix , from which the model parameters, and , can be calculated. A finite-size Hankel or forward prediction matrix is formed from the data samples, as described by (4), and its singular value decomposition (SVD) is computed to derive . The parameter that appears in denotes the correlation window.…”

“…The basis behind these spectral estimation techniques is that the electromagnetic (EM) response of any scattering object can be adequately represented as a sum of complex sinusoids, whose amplitude and phase relate to the parameters of interest (e.g., complex propagation constants and their modal responses). Pencil of functions [3], ESPRIT [4], MUSIC [5], Prony's method [6], and decoupled optimal method [7] all fall into this category. A significant constraint in these approaches is that the model parameters are assumed to be independent of time or frequency, as the case may be, in order to limit the model order, and ensure stability and convergence.…”