Radio Science Bulletin 313 - June 2005 - URSI

Quantitative Comparison BetweenMatrix Pencil Method and State-Space-Based Methods for RadarObject IdentificationS. JangW. ChoiT. K. SarkarE. L. MokoleAbstractApproximating a function by a sum of complexexponentials to identify the nature of electromagneticscatterers is treated with three model-based parameterestimationmethods. In particular, the Matrix Pencil Methodand two State-Space-Based Harmonic-Retrieval methodsare compared quantitatively. It is known that these methodsgenerate very similar results in the absence of noise in thedata and have only minor differences between them whenthe data is contaminated by noise. Since a quantitativecomparison of the three methods has not been reported inthe literature, this paper compares them by determininghow accurately and quickly they predict the poles of thetransient impulse responses of five electromagnetic systems:thin wire; perfectly conducting sphere; finite closed cylinder;dielectric sphere; composite metallic-dielectric sphere. It isimportant to note that these techniques are applied directlyto the data and not to the covariance matrix, as noisestatistics require additional information that is not availableand the noise in electromagnetic scenes is generated typicallyby undesired signals in the form of a base-line shift in themeasurement hardware instead of thermal background noise.1. Introductioninterest. The natural resonances are the poles of the impulseresponse of an object, which correspond to the generalizedeigenvalues of a pertinent Hankel matrix for the MatrixPencil Method (MPM) and to the zeroes of an appropriatedeterminant for the State-Space Methods.The accuracies of the methods vary with the amountof noise in the data. To ascertain the speed and accuracy ofthe methods, scattering data from three types of objects(three perfect conductors, a dielectric, a composite metallicdielectric) are simulated with a known electromagneticscode. Each method approximates the real time-domainscattered field with a finite sum of complex exponentials.An essential question is how many sinusoids are needed tocharacterize the scatterer accurately.These Matrix Pencil and State-Space Methods,sometimes called direct-data-domain (DDD) methods,derive the resonances from the transfer function of a discretetimerepresentation of the impulse response. Approximatinga function by a sum of complex exponentials has beenfrequently used for identification. Usually, the kth sampley()k of the time-domain electromagnetic scattered field isrepresented by a finite sum of damped sinusoidsy() k = x() k + n()kIn this paper, methods that directly estimate radarsignals from scattered data, as opposed to methods that usea covariance matrix, are compared. The key discriminatorsin the comparisons are the speed and accuracy of themethods. In particular, three model-based parameterestimationtechniques, the Matrix Pencil [1-6] and twoState-Space Harmonic-Retrieval Methods [7,8], are selectedfor analysis. The fundamental parameters to be estimatedare the natural resonances of the scattering structure ofM[( αm+ jωm) kTs+jφm]∑ cme n()k (1)= +m=1M∑m=1km m()= R z + n kSeongman Jang, Wonsuk Choi, and Tapan K. Sarkar arewith the Department of Electrical Engineering andComputer ScienceS yracuse University, 121 Link Hall,Syracuse,NY 13244 USA; E-mail: sejang@syr.edu;wchoi01@syr.edu; tksarkar@syr.edu.Eric L. Mokole is with the Naval Research Laboratory,Radar Division, 4555 Overlook Avenue SW, Washington,DC 20375 USA; E-mail: mokole@radar.nrl.navy.mil.TheRadio Science Bulletin No 313 (June, 2005) 27