Array Calibration for Circular-Array STAP using Clutter Scattering and Projection Matrix Fitting
Daniel R. Fuhrmann and David W.Rieken
Electronic Signals and Systems Research Laboratory
Department of Electrical Engineering
St. Louis MO 63130
Abstract We consider the problem of estimating an array manifold, either from calibration data or from a known set of response vectors sampled on a sparse grid in direction space. It is argued that, since one cannot observe the array response directly due to the influence of an unknown multiplicative scale factor, the proper mathematical object to estimate, at each direction, should be the space spanned by the direction vector, rather than the direction vector itself. That is, the array manifold is viewed as a sub-manifold of complex projective space rather than complex Euclidean space. Furthermore, it is argued that the deviation of the array manifold from the nominal array manifold determined by array geometry should be a smooth function. For computational purposes we take rank-one projection matrices as representations of points in projective space.
The proposed estimation algorithm comprises five steps: 1) Each data vector is Hadamard-multiplied by the complex conjugate of the associated nominal steering vector. This is referred to as free-space phase compensation.; 2) Each data vector is used to compute a rank-one sample projection matrix; 3) The sequence of sample projection matrices is smoothed using weighted least-squares fitting, using a set of basis functions appropriate to the space of directions. The weights in the weighted LS fit are determined by the magnitudes of the individual data vectors; 4) Eigenvector analysis is used to determine the principal component of each of the projection matrices after smoothing; and 5) The free-space phase is restored again by Hadamard vector multiplication.
A simulation example will be presented showing how this technique might apply to the calibration of an airborne circular radar array, such as the one currently in development for STAP applications on the U.S. Navy E-2C. Here the data arise from stationary ground clutter resolved in range and Doppler, and the basis functions used for projection matrix fitting are spherical harmonics. It is shown that calibration can be achieved over a large region in azimuth-elevation space covered by the range-Doppler sampling grid.
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