xxii Adaptive Radar Detection of Extended Gaussian Targets

We have addressed the derivation and the analysis of an adaptive decision scheme to detect possible extended targets modeled as Gaussian vectors known to belong to a given subspace; noise returns from the cells under test are modeled as independent and identically-distributed Gaussian vectors with one and the same covariance matrix; a set of secondary data, free of signal components is also available; secondary data are Gaussian-distributed and share the same covariance matrix of noise in the cells under test but for a possible different power level. The proposed detector relies on a two-step design procedure: first we derive the GLRT assuming that the noise covariance matrix is known up to a scale factor; then, we come up with a fully adaptive detector by replacing the structure of the covariance matrix of the noise with the sample covariance matrix based upon the secondary data. The first step requires the maximum likelihood (ML) estimate of the covariance matrix of the useful signal (under the signal-plus-noise hypothesis) which, in turn, has a known structure. That ML estimate has been firstly proposed by Bresler in [3]; a different derivation is also proposed herein. The performance assessment is conducted resorting to the method proposed in [4–5] to model extended targets: therein an exponential model for fully-polarized returns has been used assuming that each scattering center can be characterized by its (relative) range, amplitude, and polarization elipse. [1] E. Conte, A. De Maio, and G. Ricci, "GLRT-Based Adaptive Detection Algorithms for Range Spread Targets," IEEE Trans. on Signal Processing, Vol. 49, No. 7, pp. 1336–1348, July 2001. [2] T. McWhorter and M. Clark, "Matched Subspace Detectors and Classifiers," Mission Research Technical Report: MRC/MRY-R-073, August 2001. [3] Y. Bresler, "Maximum Likelihood Estimation of a Linearly Structured Covariance with Application to Antenna Array Processing," Fourth Annual ASSP Workshop on Spectrum Estimation and Modeling, 1988. [4] W.M. Steedly and R.L. Moses, "High-Resolution Exponential Modeling of Fully Polarized Radar Returns," IEEE Trans. on Aerospace and Electronic Systems, Vol. 27, No. 3, pp. 459–469, May 1991. [5] K.M. Cuomo, J.E. Piou, and J.T. Mayhan, "Ultra-Wideband Coherent Processing," The Lincoln Laboratory Journal, Vol. 10, No. 2, pp. 203–221, 1997. Giuseppe Ricci Università di Lecce Via Monteroni 73100 Lecce, Italy phone: 39-0832-297205 email: giuseppe.ricci@unile.it Louis L. Scharf Electrical and Computer Engineering Campus Delivery 1373 Colorado State University Fort Collins, CO 80523-1373 email: scharf@engr.colostate.edu Report Documentation Page Form Approved OMB No. 0704-0188 Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden, to Washington Headquarters Services, Directorate for Information Operations and Reports, 1215 Jefferson Davis Highway, Suite 1204, Arlington VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to a penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number. 1. REPORT DATE 20 DEC 2004 2. REPORT TYPE N/A 3. DATES COVERED 4. TITLE AND SUBTITLE Adaptive Radar Detection of Extended Gaussian Targets 5a. CONTRACT NUMBER