TY - JOUR
T1 - Polarimetric Detection in Compound Gaussian Clutter with Kronecker Structured Covariance Matrix
AU - Wang, Yikai
AU - Xia, Wei
AU - He, Zishu
AU - Li, Hongbin
AU - Petropulu, Athina P.
N1 - Publisher Copyright:
© 1991-2012 IEEE.
PY - 2017/9/1
Y1 - 2017/9/1
N2 - In this paper, we consider polarimetric adaptive detection in compound Gaussian clutter whose covariance matrix (CM) has a Kronecker structure. We derive the Cramér-Rao bound of a Kronecker structured CM estimate and analyze the constant false alarm rate property of the adaptive subspace matched filter detector that uses Kronecker structured estimates. We provide a general expression for the average signal-to-clutter ratio loss (SCRL) as a function of the mean square error of the covariance estimate. The aforementioned expression is helpful in determining how many samples are required in order to achieve a desired average SCRL level in practical scenarios. Based on that expression, we show that the required sample size can be effectively reduced by exploiting the Kronecker structure of the clutter CM. We also derive the asymptotic detection performance of the adaptive subspace matched filter. The analysis of SCRL and detection performance can be extended to more general scenarios, especially when the maximum-likelihood estimate of the structured CM involves solving fixed point equations. Numerical simulations validate the merits of the proposed methods.
AB - In this paper, we consider polarimetric adaptive detection in compound Gaussian clutter whose covariance matrix (CM) has a Kronecker structure. We derive the Cramér-Rao bound of a Kronecker structured CM estimate and analyze the constant false alarm rate property of the adaptive subspace matched filter detector that uses Kronecker structured estimates. We provide a general expression for the average signal-to-clutter ratio loss (SCRL) as a function of the mean square error of the covariance estimate. The aforementioned expression is helpful in determining how many samples are required in order to achieve a desired average SCRL level in practical scenarios. Based on that expression, we show that the required sample size can be effectively reduced by exploiting the Kronecker structure of the clutter CM. We also derive the asymptotic detection performance of the adaptive subspace matched filter. The analysis of SCRL and detection performance can be extended to more general scenarios, especially when the maximum-likelihood estimate of the structured CM involves solving fixed point equations. Numerical simulations validate the merits of the proposed methods.
KW - Cramér-Rao bound
KW - Kronecker structure
KW - Polarimetric detection
KW - SCR loss
KW - asymptotic performance
KW - compound Gaussian clutter
KW - constant false alarm rate
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U2 - 10.1109/TSP.2017.2716912
DO - 10.1109/TSP.2017.2716912
M3 - Article
AN - SCOPUS:85023205036
SN - 1053-587X
VL - 65
SP - 4562
EP - 4576
JO - IEEE Transactions on Signal Processing
JF - IEEE Transactions on Signal Processing
IS - 17
M1 - 7950961
ER -