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GAMMA: A Fast Adaptive
Parameter Estimation
Algorithm for
Multidimensional Arrays

Gary F. Hatke
MIT Lincoln Laboratory
244 Wood Street
Lexington, MA 02173-9108
tel: (781) 981-3364
email: hatke@ll.mit.edu

The problem of adaptive detection using multidimensional array structures, such as planar arrays, polarization diverse arrays, and space-time arrays, has been discussed thoroughly in the literature. Various sub-optimal methods have been proposed to decrease the computation of the optimal detection test statistic. However, the problem of estimating the parameters of the detected signal in an efficient manner has only recently been addressed. Specifically, when the dimensionality of the target parameters becomes larger than two, there have been no algorithms proposed which do not require a computationally intensive manifold search for parameter estimation. This talk introduces a method for adaptively estimating signal parameters in the presence of non-white noise. The technique couples the multidimensional rooting aspects of elimination theory with a generalized form of adaptive monopulse to produce an algorithm which can estimate a signal parameter set of arbitrary dimension. The algorithm projects the error vector between the measured whitened steering vector and a candidate whitened steering vector taken from a multivariate polynomial manifold onto a space which has dimension equal to the number of unknown parameters to be estimated. Hence, the elements of the error vector constitute a set of multivariate polynomial equations which have a finite set of homogeneous solutions, one of which corresponds to the desired solution. Simulation results are shown for a simple planar array used to estimate target azimuth, elevation, and polarization state of the target. In all cases, comparison of the simulation results with Cramer-Rao bounds for estimate uncertainty show that the new estimator, although generally sub-optimal, achieves the lower bound.



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