a
Corresponding author: Shi_xiao_fei_57@163.com
A Target Tracking Algorithm based on Fractional Ambiguity
Function in Impulsive Noise Environment
Xiaofei Shi
1,a
, Li Li
2
1
Information Science and Technology College, Dalian Maritime University, Dalian, 116026, China
2
Information Engineering College, Dalian University, Dalian, 116622, China
Abstract. This paper proposes an airplane tracking algorithm based on study of the problem of interference
localization. Firstly, a novel signal model to accurately estimate parameters of the airplane is proposed in impulsive
noise environment. A method of instantaneous Doppler frequency estimation based on peak searching of the
fractional lower-order ambiguity function based on the fractional Fourier transform (FLOS_FAF) is proposed, and a
method of projection approximation subspace tracking using robust m-estimation method based on fractional lower-
order ambiguity function in fractional Fourier transform domain (FF-RLM_PAST) is proposed to estimate the
azimuth angle and elevation angle. As a result, the airplane tracking is achieved in bistatic radar, laying the
foundations for interference localization. The correctness and effectiveness of the proposed method are verified with
the computer simulation.
1 Introduction
With increase of radio stations quantity, the interfered
probability of civil aviation radio frequency increases. It
is key point how to make it safe operation of civil
aviation radio frequency. Interference localization is
realized by utilizing Doppler frequency shifts of the
scattered signals from civil airplane in the receiver
[1],[2]
. If
real-time state information of airplane is not obtained,
interference localization is not realized. It is shown that
accurate estimation of airplane state information is very
important.
Studies and experimental measurements have shown
that a class of
D
-stable distributions is more appropriate
for modeling impulsive noise than Gaussian distribution
in signal processing applications
[3]
. Since the stable
distribution does not have finite second-order moments
(
12d
D
), or even first-order moment ( 1
D
) due to
the heavy tails, the performance of the existing parameter
estimation and target tracking methods based on second-
order will degrade severely.
In research background of the problem of interference
localization, this paper addresses the problem of
parameter estimation and target tracking in the presence
of impulsive noise. With combination of the fractional
ambiguity function with the fractional lower order
statistics, a parameter estimation and airplane tracking
algorithm is presented in this paper.
2 The Proposed Signal Model
In this paper, the airplane tracking and localization is
realized by employing the principle of parameter
estimation in bistatic Multiple-Input Multiple-Output
radar system. Fig.1 illustrates a bistatic MIMO radar
system. The considered bistatic MIMO radar is composed
of
M transmit antennas and N receive antennas with an
interelement spacing of
2
O
. D is the base line distance
between the transmit reference element and the receive
reference element.
t
t
T
,
t
t
M
and
r
t
T
,
r
t
M
are
azimuth angle and elevation angle correspond to the
transmit array and receive array, respectively. The
transmitting antennas emit orthogonal waveforms
m
t
for
1,...,mM . The received signals contain time-
variant Doppler due to the three dimension motion of
airplane. If the cubic phase is ignored, the performance of
parameter estimation and airplane tracking will degrade.
This paper presents a new signal model for the bistatic
MIMO radar system. The echo of the n th receiving
antenna is
23
1
exp 2
,,
M
nm
m
tm t t rn r r n
st x t j t t t
aa wt
¦
SK P N
TM TM
(1)
where
,
, and
N
are Doppler frequency parameters.
,exp 1sincos
tm t t t t
ajmtt
TM S T M
is the
mth element of the transmitter steering vector,
, exp( ( 1 2 )sin (t)cos (t))
rn r r r r
ajnD
TM S S O T M
is the steering vector of the nth element of the receiver.
DOI: 10.1051/
07011 (2016)
,
matecconf/2016MATEC Web of Conferences
61
610
2016
APOP
7011
© The Authors, published by EDP Sciences. This is an open access article distributed under the terms of the
Creative
Commons
Attribution
License 4.0 (http://creativecommons.org/licenses/by/4.0/).