Signal Processing 152 (2018) 340–349
Contents lists available at ScienceDirect
Signal Processing
journal homepage: www.elsevier.com/locate/sigpro
Persymmetric adaptive detection of distributed targets in
compound-Gaussian sea clutter with Gamma texture
Jun Liu
a , b
, Sha Liu
a
, Weijian Liu
c , ∗
, Shenghua Zhou
a
, Shengqi Zhu
a
, Zi-Jing Zhang
a
a
National Laboratory of Radar Signal Processing, Xidian University, Xi’an 710071, China
b
Department of Electronic Engineering and Information Science, University of Science and Technology of China, Hefei 230027, China
c
Wuhan Electronic Information Institute, Wuhan 430019, China
a r t i c l e i n f o
Article history:
Received 16 January 2018
Revised 23 May 2018
Accepted 4 June 2018
Available online 15 June 2018
Keywords:
Distributed target detection
Compound-Gaussian clutter
Gamma distribution
Rao test
Wald test
Generalized likelihood ratio test
a b s t r a c t
We consider the problem of detecting a distributed target in compound-Gaussian sea clutter with Gamma
distributed texture components. We design the Rao, Wald, and generalized likelihood ratio test (GLRT) de-
tectors according to the two-step method: the first step is to obtain the Rao, Wald tests and GLRT on the
assumption that the texture or/and covariance matrix structure are known; then the maximum a posteri-
ori probability estimate of the clutter texture and the fixed point estimate of covariance matrix exploiting
persymmetry are employed to replace the known texture and covariance matrix in the tests derived in
the first step. Remarkably these proposed detectors ensure constant false alarm rate with respect to the
covariance matrix structure. The effectiveness of the proposed detectors is verified by using simulated
and real sea clutter data.
©2018 Published by Elsevier B.V.
1. Introduction
The problem of detecting distributed targets has received con-
siderable attention in the literature [1–6] . Much work has been
done for this problem in Gaussian clutter (see [7,8] , and references
therein). Nevertheless, the Gaussian model is not suitable for clut-
ter in many practical scenarios, e.g., in sea clutter or high reso-
lution radars. As an alternative, a compound-Gaussian model for
rational physical interpretation mechanism, is widely used to de-
scribe the statistical properties of clutter [9–15] . In this model,
clutter can be expressed as the product of two mutually inde-
pendent components: texture and speckle. The texture component
varies slowly, which describes the reflectivity of illuminated areas
and is a non-negative real random process; the speckle component
varies more rapidly, which accounts for the local backscattering
and has a complex, zero-mean, possibly correlated Gaussian dis-
tribution due to the central limit theorem [16] .
Recently, many studies have been done for distributed target
detection in compound-Gaussian clutter. In [17–20] , the general-
ized likelihood ratio test (GLRT), Rao and Wald tests were designed
for the distributed target detection in the compound-Gaussian clut-
ter with deterministic but unknown texture components. In [21] , a
subspace model was used for target returns, and a two-step adap-
∗
Corresponding author.
E-mail address: liuvjian@163.com (W. Liu).
tive subspace detector was designed for detecting distributed tar-
gets. The authors in [22] derived a GLRT for adaptively detecting
range and Doppler-distributed targets in compound-Gaussian clut-
ter whose texture is range dependent. The problem of detecting
a distributed target in compound-Gaussian clutter in polarimetric
multiple input multiple output radar was addressed in [23] , where
a two-step GLRT was proposed. In [24] , the speckle component in
the compound-Gaussian clutter was described by an autoregressive
(AR) process, and an AR-based GLRT was developed for the dis-
tributed target detection.
It is known that compound-Gaussian distribution is referred to
as K -distribution and t -distribution, when the texture component
is subject to Gamma and inverse Gamma distributions, respec-
tively. In the compound-Gaussian clutter with inverse Gamma tex-
ture, three adaptive detectors (one-step, a-posteriori, and two-step
GLRTs) were derived in [25] for detecting distributed targets. In
[26] , the persymmetric Rao and Wald tests were developed for the
problem of detecting a distributed target in compound-Gaussian
clutter with unknown covariance matrix, where the texture com-
ponent is assumed to follow an inverse-Gamma distribution. The
choice of a Gamma distribution for texture is widely accepted and
verified [27,28] . In compound-Gaussian clutter with Gamma dis-
tributed texture, the detection problem of a point-like (instead of
distributed) target was investigated in [29–33] . Bandiera et al. de-
veloped a Bayesian GLRT detector without using secondary data
for the distributed target detection problem in compound-Gaussian
https://doi.org/10.1016/j.sigpro.2018.06.006
0165-1684/© 2018 Published by Elsevier B.V.