Please
cite
this
article
in
press
as:
Liang-qun
L,
et
al.
Bearings-only
maneuvering
target
tracking
based
on
truncated
quadrature
Kalman
filtering.
Int
J
Electron
Commun
(AEÜ)
(2014),
http://dx.doi.org/10.1016/j.aeue.2014.09.013
ARTICLE IN PRESS
G Model
AEUE-51289;
No.
of
Pages
9
Int.
J.
Electron.
Commun.
(AEÜ)
xxx
(2014)
xxx–xxx
Contents
lists
available
at
ScienceDirect
International
Journal
of
Electronics
and
Communications
(AEÜ)
j
ourna
l
h
om
epage:
www.elsevier.com/locate/aeue
Bearings-only
maneuvering
target
tracking
based
on
truncated
quadrature
Kalman
filtering
Li
Liang-qun
∗
,
Xie
Wei-xin,
Liu
Zong-xiang
ATR
Key
Laboratory,
Shenzhen
University,
Shenzhen
518060,
PR
China
a
r
t
i
c
l
e
i
n
f
o
Article
history:
Received
20
May
2014
Accepted
19
September
2014
Keywords:
Maneuvering
target
tracking
Truncated
quadrature
Kalman
filtering
Least
square
method
a
b
s
t
r
a
c
t
In
this
paper,
a
novel
bearings-only
maneuvering
target
tracking
algorithm
based
on
truncated
quadrature
Kalman
filtering
(TQKF)
is
proposed.
In
the
proposed
method,
when
the
target
maneuvers,
in
order
to
reduce
the
effect
on
performance
duo
to
the
increasing
variance
of
the
prior
distribution,
a
modified
prior
distribution
based
on
the
current
measurement
is
proposed.
In
the
update
step,
the
first
two
moments
of
the
modified
prior
distribution
is
approximately
estimated
based
on
the
least
square
estimation
method
and
Gauss–Hermite
quadrature
rule,
and
the
posterior
distribution
is
jointly
updated
by
using
the
prior
distribution
and
the
modified
prior
distribution.
Moreover,
in
order
to
adaptively
choose
the
estimated
results
obtained
by
the
prior
PDF
and
the
truncated
prior
PDF,
a
fuzzy
logic
approach
in
which
a
Gaussian
membership
function
is
employed
is
proposed
to
determine
the
weight
˛.
Finally,
the
experiment
results
show
that
the
proposed
algorithm
results
in
more
accurate
tracking
than
the
existing
one,
namely,
the
unscented
Kalman
filter
(UKF),
the
quadrature
Kalman
filter
(QKF),
interact
multiple
model
extended
Kalman
filter
(IMMEKF)
and
multiple
model
Rao–Blackwellized
particle
filter
(MMRBPF).
©
2014
Elsevier
GmbH.
All
rights
reserved.
1.
Introduction
Bearing-only
maneuvering
target
tracking
by
multiple
passive
sensors
is
a
problem
of
considerable
importance
in
a
variety
of
fields
including
radar,
sonar
and
oceanography.
Source
localization
and
tracking
has
therefore
received
considerable
attention
in
the
liter-
ature,
and
has
resulted
in
many
different
estimation
schemes
[1,2].
In
many
applications
the
tracking
problem
is
further
complicated
because
the
motion
and/or
location
of
the
sensors
is
uncertain
[2].
The
bearings-only
tracking
(BOT)
problem
is
unobservable
without
sensor
maneuvers
for
a
passive
sensor,
the
azimuth
and
elevation
measurements
do
not
allow
an
instantaneous
range
determination.
To
solve
this
problem,
two
solutions
have
been
considered.
First,
if
the
passive
sensor
platform
is
allowed
to
move
freely
[3],
it
is
possible
to
recover
range
observability
by
selecting
an
appropriate
path
for
the
platform.
The
problem
of
a
passive
tracking
using
a
single
sensor
of
uncertain
location
is
discussed
in
[4].
However,
in
some
applications,
the
sensor
platforms
have
very
slow
mobility
compared
with
the
target
dynamics,
so
this
solution
is
not
feasi-
ble.
A
possible
solution
is
to
use
several
passive
sensors
and
fuse
their
information
in
some
way
to
estimate
the
range
[5,6].
In
this
∗
Corresponding
author.
Tel.:
+86
755
26732055;
fax:
+86
13510572278.
E-mail
address:
lqli@szu.edu.cn
(L.
Liang-qun).
paper
we
are
focused
on
the
problem
of
bearings-only
maneuvering
target
tracking
by
multiple
passive
sensors.
For
the
bearings-only
maneuvering
target
tracking,
many
algo-
rithms
have
been
presented
in
the
literature,
including
the
probabilistic
multi-hypothesis
tracking
(PMHT)
algorithm
[7],
Markov
Chain
Monte
Carlo
(MCMC)
methods
[8],
and
particle
filter-
ing
[9,10].
A
promising
approach
is
the
interacting
multiple
model
(IMM)
algorithm,
originally
developed
by
Blom
[11],
which
is
based
on
a
hybrid
system
description
of
the
maneuver
scenarios,
the
occurrence
of
target
maneuvers
is
explicitly
included
in
the
kine-
matics
equations
through
regime
jumps.
In
the
presence
of
clutter,
the
integration
of
the
IMM
and
PDAF
is
an
efficient
solution
to
the
uncertainty
of
measurement
origins.
Li
et
al.
[12]
proposed
a
multiple
model
Rao–Blackwellized
particle
filter
(MMRBPF)
based
algorithm
for
maneuvering
target
tracking
in
a
cluttered
environ-
ment.
Rao-Blackwellization
allows
the
algorithm
to
be
partitioned
into
target
tracking
and
model
selection
sub-problems,
where
the
target
tracking
can
be
solved
by
the
probabilistic
data
association
filter,
and
the
model
selection
by
sequential
importance
sampling.
The
main
shortcoming
of
their
method
is
its
heavy
computational
load.
Another
difficulty
with
BOT
is
that
it
is
a
nonlinear
problem.
The
usual
approach
for
recursive
estimation
is
to
employ
an
extended
Kalman
filter
(EKF)
[13].
Because
the
LOS
is
an
incomplete
position
observation,
it
cannot
be
converted
into
Cartesian
coordinates
to
allow
for
linear
filtering.
In
recursive
bearings-only
tracking,
the
use
http://dx.doi.org/10.1016/j.aeue.2014.09.013
1434-8411/©
2014
Elsevier
GmbH.
All
rights
reserved.