A Hybrid BP-VMP-EP Localization Algorithm for
Passive MIMO Radar Networks
Dan Wu
†
, Yuan Feng
‡
, Jianfeng Wang
‡
and Nan Wu
†
†
School of Information and Electronics, Beijing Institute of Technology, Beijing, China, 100081
‡
China Research and Development Academy of Machinery Equipment, Beijing, China, 100089
Abstract—A passive multiple-input multiple-output (MIMO)
radar (PMR) network is an efficient system to detect and track
targets, which consists of multiple distributed receivers and
illuminators of opportunity. Conventional two-step localization
first estimates the distance based on signal time delay mea-
surements, then the location is obtained by using least square
or maximum likelihood estimator. Recently, several works show
that through direct localization, performance can be significantly
improved. For a better balance between accuracy and complexity,
in this paper, we propose a hybrid message passing localization
algorithm. Derived from a Bayesian inference framework, the
proposed method can be regarded as an iterative version of
two-step methods. Simulations show that the proposed algorithm
outperforms conventional two-step localization, and provides a
trade-off between position accuracy, communication overhead
and computational costs.
Index Terms—Passive MIMO radar, factor graph, message
passing, localization
I. INTRODUCTION
A passive multiple-input multiple-output (MIMO) radar net-
work consists of multiple distributed receivers. The receivers
have no prior knowledge of the timing or instantaneous shape
of the transmitted signals. Due to the advantages of low
cost, anti-interference and anti-electronic support measures
(ESM), passive MIMO radar (PMR) networks have attracted
widespread attention in recent years [1]–[3].
The conventional positioning approach is to estimate the
target location in two-steps: first estimating signal time delay
measurements, then the location is obtained from time delay.
A two-stage tracking algorithm is proposed in [4]. In [5],
a least square (LS) method is proposed based on time-
difference-of-arrival (TDOA) measurement. Recently, several
researches have demonstrated that the direct localization on the
signals perform better than two-step localization in traditional
networks [6]–[10]. In [6], it is shown that the localization
accuracy of direct positioning method is superior at low SNRs.
In [7] and [10], it is further demonstrated that the variance of
direct localization is closed to the CRB analytically. However,
all the above methods assume that the transmitted signal is
known. For unknown signal, although surveillance signal can
still be used for localization, this will lead to significant
performance loss in localization accuracy.
To jointly process all available information in the situation
of unknown signals, a direct target detection method based on
Corresponding author: Nan Wu (E-mail: l: wunan@bit.edu.cn). T). This
work is supported by National Science Foundation of China (NSFC) (Grant
Nos. 61471037, 61571041, 61471360).
generalized likelihood ratio test for PMR networks is proposed
in [11]. This idea is further extended to target localization in
[12], where a ML estimator is derived from the generalized
likelihood ratio test. Simulations show the direct detection
and localization for PMR networks are prominently improved
by using all information. Unfortunately, in [12], receivers are
required to broadcast all the signals it received to fusion
center. Because of the communication overhead, this algorithm
is unrealistic in practical application. An iterative algorithm
based on time-of-arrival (TOA) localization is proposed in
[13], which shows that the iterative algorithm perform is closed
to the direct localization. By analogy to [13], it is reasonable
to propose an algorithm bridging the direct localization and
two-step localization for PMR networks.
In this paper, we develop a mathematical framework for
positioning in PMR networks localization and introduce a
hybrid message passing localization algorithm on factor graph
(FG). Considering the product between time delay operators
and transmitted signal is infeasible by using belief propagation
(BP), we propose to perform variational message passing
(VMP) instead on surveillance factor nodes. Moreover, expec-
tation propagation (EP) is used to update the message from
position by Gaussian distribution. The proposed hybrid BP-
VMP-EP algorithm can be regarded as an iterative version
of two-step method, and enables effective Gaussian message
approximation, which allows low-complexity implementation.
Simulations show that the proposed algorithm outperforms
conventional two-step algorithm, and provides a trade-off
between position accuracy, communication over head and
computational complexity.
II. S
YSTEM MODEL
We consider a PMR network with N
t
transmitters and N
r
receivers. For the ijth bistatic pair, where i and j denote
the ith transmitter and jth receiver. Only target-path and
direct-path signals are considered here, with clutter-path signal
being mitigated through other techniques. By beamforming,
target-path and direct-path are isolated into surveilliance
and reference channels. Assume the transmitted signals are
emitted with a common bandwith of B Hertz, and the receivers
sample at each channels of a rate f
s
≥ B for T seconds.
Considering a static target with position state y
k
at time k,
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