A Novel Tracking Method for Fast Varying
Subspaces in Impulsive Noise Environments
Jinfeng Zhang
Shenzhen Key Laboratory of Antennas and Propagation
Shenzhen University
Shenzhen, China
zhangjf@szu.edu.cn
Tianshuang Qiu
Faculty of Electronic Information and Electrical
Engineering
Dalian University of Technology
Dalian, China
qiutsh@dlut.edu.cn
Abstract
—
By employing the MCC (maximum correntropy
criterion) based cost function in projection approximation
subspace tracking (PAST) algorithm, the MCC-PAST algorithm
is deduced which can be utilized for the subspace tracking under
impulsive noise environments. The Gaussian transformation
technique is combined to further enhance the tracking
performance. To handle the fast varying subspaces
circumstances, the variable forgetting factor (VFF) technique is
developed and incorporated into the algorithm. Simulation
results show the robustness of the proposed nonlinear MCC-
PAST with VFF algorithm, especially when the GSNR
(generalized signal to noise ratio) is fairly low or the underlying
noise is extremely impulsive
.
I. I
NTRODUCTION
Subspace tracking, which aims to derive a selected subset
of eigenvectors of a Hermitian matrix, has been developed as a
valuable tool in array signal processing in the few past decades
[1-2]. Different from the traditional subspace-based algorithms
which exploit the whole eigenstructure of the data
autocorrelation matrix, a number of fast subspace tracking
algorithms were developed by only updating the signal or noise
subspace so as to lower the computational complexity and
reduce the storage requirements. One very efficient subspace
tracking algorithm is the project approximation subspace
tracking (PAST) approach [2]. By employing the recursive
least-squares (RLS) technique, the PAST algorithm recursively
estimates the signal subspace by minimizing the least square
errors between the observation and a “projection
approximation” obtained from previously estimated subspace.
Unfortunately, the conventional PAST method has two
distinct shortcomings. First, the RLS technique is vulnerable to
impulsive noise in nature. As a matter of fact, in some
scenarios, sudden bursts or spikes, are exhibited at the array
outputs which can be characterized as impulsive. In such cases,
the PAST algorithm degrades its performance substantially.
The second defect of the conventional PAST is also traced
back to the RLS technique. That is, the RLS with a constant
forgetting factor (FF) is not suitable for tracking fast varying
subspaces. In fact, both of the drawbacks of the conventional
PAST have been studied [3-4]. In [3], Chan derived a robust
subspace tracking method by incorporating the M-estimate
technique into PAST to suppress the impulsive noise. In [4], an
extension of the Kalman filter-based algorithm with variable
number of measurements (KFVNM) is developed to handle the
tracking of time varying subspaces. That is, when the subspace
substantially varies, a small number of past measurements are
employed in the recursion and vice versa. In addition, to deal
with the impulsive noise, the M-estimate technique is also
incorporated into the KFVNM algorithm. To distinguish, it is
called the robust KFVNM algorithm.
However, as we noticed, the robust KFVNM algorithm still
suffers from two limitations. First, the computation complexity
may increase considerably when the signal subspace varies
slowly since a relative large number of past measurements
need to be utilized for computation. Second, due to the
employed M-estimate technique, the approach against the
impulsive noise is to withdraw the impulsive noise
contaminated measurements from computation. It is easily to
deduce that, for the scenario the impulses significantly
increase, the estimation error of the algorithm will increase
considerably because of the excessive withdrawn of the
measurements in the computation.
To overcome the defect of the M-estimate technique in the
robust KFVNM, in this paper, the correntropy, which has been
proposed as a new statistics that can quantify both the time
structure and the statistical distribution of two stochastic
random processes,
is employed to deal with the impulsive
noise. Motivated by the “mix norm” property of CIM
(correntropy induced metric), the maximum correntropy
criterion (MCC) is applied as a substitute for the MSE (mean
square error) criterion in the cost formulation in the PAST
algorithm. Based on the RLS-technique, the MCC based PAST
algorithm is developed.
To extend the tracking capability of the MCC-PAST,
guided by the measure of subspace variations [5], a variable
forgetting factors (VFF) technique is developed and employed
in the recursion. More precisely, when the subspace varies
rapidly, a relative small FF should be used to gain a fast
tracking behavior. On the other hand, when the subspace varies
slowly, a relative large FF should be utilized to achieve a good
convergence property.
978-1-5090-0941-1/16/$31.00 ©2016 IEEE