Aerospace and Electronic Systems Magazine December 2017 - 73
in real time is added to determine whether the traditional IMM
algorithm is replaced by the IMMASTF algorithm. In order to
evaluate the performance of the proposed algorithm theoretically,
the Cramer-Rao lower bound (CRLB) for the system is derived
for analyzing the speed and position estimation errors. CRLB
shows the minimum estimation variance of the nonlinear filter,
which is an important factor when applying the algorithm [22].
Finally, simulation results show the effectiveness of the proposed
IMMASTF algorithm.
where A and B represent the state transition matrix and the transition matrix of the process noise, respectively. The process noise is
described as W (k ) = [ wx (k ), wy (k ), ww (k )] T , in which each element
is zero mean Gaussian white noise.
For constant velocity (CV) model, the state equation is
X (
k 1) ACV X (k ) BCV W (k )
where the transition matrices are
SYSTEM MODEL
The principle of HFSWR is that it can detect maneuvering targets
based on the Doppler frequency shift. The frequency of HFSWR is
usually between 3-30 MHz, so the wavelength is between 10∼100
meters. Since HFSWR has long surface wave length, the wave can
transmit across the barriers even if the maneuvering target is behind the island or near a sea-land border. When the targets and the
islands are in the same range cell, the moving targets can still be
detected by calculating the Doppler shift, while the islands and the
sea border are static with no Doppler shift.
The 2-HFSWR multisensor surveillance system is shown in
Figure 1, in which two radars are installed on one side of the coast
and the distance between two radars is known. The maneuvering
vessel target is detected independently by two radars and the echo
data can be obtained respectively.
ACV
BCV
1
0
= 0
0
0
0 0
0
0
0
0
0
T 2 / 2
0
0
T
0
T 2/ 2
T
0
0
0
0
0
0
0
0
T
0 0
1 0 0
0 1 T
0 0 1
0
with the sampling period T.
STATE SPACE MODEL OF THE SYSTEM
For maneuvering targets, the motion state may change at any time
during the whole process. At time point k, the state is described as
X (k ) = [ x(k ), vx (k ), y (k ), v y (k ), ω (k )] T
where x(k) and y(k) describe the position of the target; vx(k) and
vy(k) represent the target velocity along x and y direction, respectively; ω(k) denotes the angular velocity of the turning motion. The
state model of the system is given as
X (k + 1) = AX (k ) + BW (k )
DECEMBER 2017
Figure 1.
Schematic diagram of the 2-HFSWR multisensor surveillance system.
IEEE A&E SYSTEMS MAGAZINE
71
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