Chinese Journal of Electronics
Vol.19, No.3, July 2010
Fast Converging Estimator for Covariance Matrix
Structure of Compound-Gaussian Clutter
∗
JIAN Tao, HE You, SU Feng, PING Dianfa and GU Xinfeng
(Research Institute of Information Fusion, Naval Aeronautical and Astronautical University, Yantai 264001, China)
Abstract — In order to estimate the covariance matrix
structure of compound-Gaussian clutter, a Fast converg-
ing estimator (FCE) is proposed. Moreover, for the match
case, the FCE is independent of the clutter power levels.
Furthermore, the simulation results show that the estima-
tion accuracy of FCE improves as the one-lag correlation
coefficient or the number of secondary data increases, but
it is degraded as the number of pulses increases. In ad-
dition, the FCE is very robust with respect to different
subsets. Compared to the existing estimators, the FCE
accelerates convergence rate and improves estimation ac-
curacy with moderate computational burden.
Key words — Radar target detection, Compound-
Gaussian, Covariance matrix estimate, Convergence rate.
I. Introduction
Adaptive detection is important for modern radar sys-
tems, where the unknown clutter covariance matrix or its
p ower spectral density usually needs to be estimated. In low-
resolution radar systems, the clutter statistics can be modeled
as Gaussian distribution
[1]
. However, in situations such as low
grazing angles or high-resolution radars, the background clut-
ter may no longer be modeled accurately as a Gaussian ran-
dom variable
[2−4]
. On-field measurements have shown that,
as viewed by high-resolution radars, the radar system receives
target-like spikes that result in non-Gaussian observations. It
has been found that the spiky clutter returns can be suit-
ably modeled by compound-Gaussian
[5,6]
. Nevertheless, the
covariance matrix structure of compound-Gaussian are usu-
ally not known and need to be estimated. A possible solution
is resorting to a set of secondary data collected from cells sur-
rounding the one being tested. Since a closed-form solution
for the maximum likelihood estimation of the covariance ma-
trix structure in compound-Gaussian clutter does not exist
[7,8]
,
some simplified estimators are derived and evaluated
[9,10]
. Un-
der the assumption that the secondary data can be clustered
into groups of cells sharing one and the same value of the
texture, Conte proposes a covariance matrix Estimator based
on clustered-clutter (for short, ECC), which is independent of
the clutter power levels
[9]
. Nevertheless, The ECC degrades
for mismatch between the estimated clutter group size and the
actual one. Therefore, an Iterative estimator based on clutter-
clustered (IECC) is proposed, by only utilizing the real parts
of secondary data in the iterations
[10]
. However, the IECC still
brings forth estimation loss to a certain extent.
In this work, we propose a Fast converging estimator
(FCE), which introduces a constraint that the trace of the es-
timated covariance matrix is equal to the number of integrated
pulses, and furthermore exploits all secondary data fully, not
only the real parts of those. The proposed FCE improves es-
timation accuracy and accelerates convergence rate. Further-
more, the performance evaluation of FCE is also given.
II. Fast Converging Estimator
In this section, the ECC and IECC are introduced firstly,
and then the FCE is derived.
In the radar target detection applications, let z
t
s and c
t
s,
t = 0, ···, R denote the N-dimensional complex sampled vec-
tors of the received signal and the clutter in all range cells, re-
sp ectively; N denotes the number of pulses in a coherent train;
the subscript t implies different range cells, more precisely,
t = 0 denotes the range cell under test, while t = 1, ···, R de-
note those surrounding that being tested. It is assumed that
each of the secondary data set z
t
s, t = 1, ···, R does not con-
tain any useful target echo and includes the same compound-
Gaussian clutter as the primary data
[1]
. It is also imposed that
R > N, which can ensure the estimated matrix based on the
secondary data is nonsingular with probability one (wp1)
[11]
.
The clutter returns are modeled as a compound-Gaussian
distribution
[5]
, hence c
t
can be given by
c
t
=
√
τ
t
· η
t
, t = 0, ···, R (1)
where η
t
s and τ
t
s, t = 0, ···, R are supposed to be each
other independent. The texture component τ
t
is a semi-
p ositive real random variable with unknown probability dis-
tribution f
τ
, which is called mixing distribution. Whereas
η
t
= (η
t
(1), η
t
(2), ···, η
t
(N))
T
; η
t
(n)s, n = 1, ···, N are zero-
mean complex circular Gaussian random variables with vari-
ance equal to one, and η
t
s, t = 0, ···, R are independent and
∗
Manuscript Received Jan. 2009; Accepted May 2008. This work is supported in part by Program for New Century Excellent Talents in
University (No.NCET-05-0912), the National Natural Science Foundation of China (No.60672140) and the Scientific Research Foundation
of Naval Aeronautical and Astronautical University for Young Scholars (No.01C3).