A COMPUTATIONALLY EFFICIENT SOURCE LOCALIZATION METHOD FOR A
MIXTURE OF NEAR-FIELD AND FAR-FIELD NARROWBAND SIGNALS
Weiliang Zuo
†
, Jingmin Xin
†∗
, Jiasong Wang
‡
, Nanning Zheng
†
, and Akira Sano
§
†
Institute of Artificial Intelligence and Robotics, Xi’an Jiaotong University, Xi’an 710049, China,
‡
State Key Laboratory of Astronautic Dynamics, Xi’an 710043, China
§
Department of System Design Engineering, Keio University, Yokohama 223-8522, Japan
ABSTRACT
In this paper, we consider the source localization for a mixed
near-field (NF) and far-field (FF) narrowband signals im-
pinging on a uniform linear array (ULA) with the symmet-
rical geometric configuration. A computationally efficient
direction-of-arrivals (DOAs) and range estimation method
for the mixed NF and FF signals is proposed, where the
DOAs of the NF and FF signals are estimated separately,
and the computationally burdensome eigendecomposition is
avoided. Comparing to some existent methods, the proposed
method can separate the NF signals from the FF signals more
efficiently, and consequently the estimation performance is
improved. The effectiveness of the proposed method is veri-
fied though numerical examples.
Index Terms— Source localization, far-field, near-field,
uniform linear array, direction-of-arrival.
1. INTRODUCTION
The source localization is a fundamental problem in radar,
sonar, wireless communication, seismic exploration and so
on (e.g., [1] and references therein), and many algorithm-
s have been developed to deal with either the far-field (FF)
signals [2, 3] or the near-field (NF) signals [4, 5], respective-
ly. In many application scenarios of sources localization such
as speaker localization using microphone arrays [6,7], the NF
and FF signals may coexist. Hence the source localization and
classification of the mixed NF and FF signals have received
considerable attention recently.
By utilizing the properties of the higher-order statistics
(HOS) (i.e., cumulant), and some methods were develope-
d to localize the mixed NF and FF of non-Gaussian signal-
s [8–11]. In these methods, the main step is to form a special
cumulant matrix, which only contains the direction-of-arrival
(DOA) information of mixed signals, and from this result-
ing cumulant matrix, the DOA estimates are obtained firstly.
Then the range estimation is easily obtained, where an addi-
tional DOA association procedure is needed. However, the
HOS-based methods require high computational complexity
This work was supported in part by the National Natural Science Foun-
dation of China under Grant 61172162.
for constructing cumulant matrix. A new second-order statis-
tics (SOS) based differencing method was developed in [12],
where the crux is to eliminate the contribution of the FF sig-
nals and additive noise for localizing NF signals. Unfortu-
nately, the structure property of the covariance matrix of inci-
dent signals is required, which is only valid for large number
of snapshots. By utilizing the advantage of a symmetric uni-
form linear array (ULA), some SOS-based methods [13, 14]
were proposed to localize the mixed NF and FF signals. These
methods have low computational burden and use a subjective
criterion, which distinguishes the NF and FF signals by DOAs
or ranges estimation, to determine the type (i.e., NF or FF) of
the incident signals. Additionally, the oblique projection [15],
which projects the measurement onto a low-rank subspace a-
long a non-orthogonal subspace, was used to separate the in-
cident signals [13]. Although it outperforms the differenc-
ing one, it possesses a “saturation behavior” for localizing
the NF signals. Moreover these SOS-based methods afore-
mentioned require a computationally intensive procedure of
eigendecomposition.
Therefore, we propose a more computationally efficient
method for localizing the mixed NF and FF incident signals
impinging on the ULA with the symmetrical geometric con-
figuration. By taking the advantage of the oblique projector, a
new covariance matrix which only contains the information of
the NF signals is formed, then the anti-diagonal elements of
this resulting matrix are used to estimate the DOA of the NF
signals. Although the oblique projector was used for separat-
ing the mixed signals in [13], in this paper, we present a more
efficient way to calculate it. Furthermore in order to over-
come the “saturation behavior” encountered by the differenc-
ing and the oblique projection based methods for localizing
the NF signals, an alternating iterative method is developed.
Finally, the effectiveness of the proposed method is verified
through some numerical examples.
2. DATA MODEL AND BASIC ASSUMPTIONS
As shown in Fig. 1, we consider K noncoherent narrow-
band signals {s
k
(n)} impinging on the ULA consisting
of 2M +1omnidirectional sensors with spacing d, and
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