A Direction Tracking Algorithm Based on the
Repulsive Force Model with Low SNR in MIMO HF
Sky-wave Radar
Yuguan Hou
School of Electronics and Information Engineering
Harbin Institute of Technology
Harbin, China,
yuguanhou@qq.com
Hongyan Liu
School of Electronics and Information Engineering
Harbin Institute of Technology
Harbin, China
496634023@qq.com
Abstract—In MIMO HF sky-wave radar, the spatial spectrum
estimation technology is used to obtain the estimates of the
Direction-Of-Departure (DOD) and the Direction-Of-Arrival
(DOA) of signals of interest and the “undesired” signals for
suppressing the multipath clutter of the instability ionosphere
layer. However, in the case of low Signal-to-Noise Ratio (SNR),
the biases of the estimates of the direction of the signals and
clutter are relatively large. And the biases could not be
calibrated by the conventional Particle Filter (PF) algorithm.
Therefore, in this paper, a direction tracking algorithm based on
the repulsive force model with low SNR in MIMO HF sky-wave
radar is proposed to improve the accuracy of the direction
tracking. Firstly, the MUSIC algorithm based on the Toeplitz
approximation is used to obtain the directions of the signals,
which are most often taken as the coherent sources for better
resolution performance. Secondly, we develop the repulsive force
model with Stochastic Differential Equations (SDE), and add it
to the Markov Chain Monte Carlo Particle Filter (MCMC-PF)
algorithm. We compare the azimuth estimates obtained by the
MUSIC algorithm based on the Toeplitz approximation method
using the PF algorithm with the repulsive force model and the
PF algorithm without the repulsive force model. The simulation
results demonstrate the effectiveness of this algorithm. The
algorithm can be applied to DOD and DOA estimates of the
azimuth and the elevation with the proper antenna array.
Index Terms—MIMO HF sky-wave radar, Repulsive Force
Model, Particle Filter.
I. INTRODUCTION
In HF sky-wave radar, the propagation of HF
electromagnetic wave by the reflection of the instability
ionosphere layer will broaden the clutter spectra in the
Doppler domain. The MIMO HF sky-wave radar combines
transmitting and receiving adaptive beam forming to suppress
the multipath clutter, which mitigates the adverse situation
effect
[1-4]
. When suppressing the clutter, the spatial spectrum
estimation technology is used to obtain the estimates of the
Direction-Of-Departure (DOD) and the Direction-Of-Arrival
(DOA) of the signals of interest and the “undesired” signals.
While, in the case of low SNR, there are always some biases
in the estimates. The PF technology is very successful for
solving non-linear and non-Gaussian estimation problems
[5]
. It
had been developing since 1960s, but there were some fatal
problems, such as particle degradation, computational
constraints and so on, which made people ignore it. Until
early 1990s, Gordon et al. proposed resampling in the process
of recursion, which contributed to the practicability of PF. So
far, there has been many PF algorithms, including the
Sequential Importance Sampling (SIS), Sampling Importance
Resampling (SIR), Likelihood Particle Filter (LPF),
Regularized Particle Filter (RPF), Markov Chain Monte Carlo
Particle Filter (MCMC PF), etc.
[6,7]
. In addition, Kronander et
al. proposed Robust auxiliary particle filters. This method
uses mixture sampling techniques to derive robust and
efficient particle filters, which performs on par with or better
than the best of the standard importance densities
[8]
. Li et al.
proposed Gaussian sum quadrature particle filter (GSQPF)
which utilizes the Gaussian sum particle filter and
Gauss-Hermite quadrature to approximate the posterior
distributions. It can outperform both Gaussian sum particle
filter (GSPF) and quadrature particle filter (QPF)
[9]
. However,
in the case of low SNR, the biases of the estimates of the
direction of the signals are relatively large, which could not be
calibrated by the PF algorithm mentioned above. Therefore, in
this paper, a direction tracking algorithm based on the
repulsive force model with low SNR in MIMO HF sky-wave
radar is proposed to improve the accuracy of the direction
tracking.
II. REPULSIVE FORCE MODEL
Consider the MIMO HF sky-wave radar with
a uniform linear array (ULA). Assume
it,
(i=1, 2, …, D) is
the DOA of the ith signal at time t, where D is the number of
the signals. The biases of the DOA estimation of the multiple
signals are not independent from each other in the low SNR
case. There should be an interaction among them. If two
signals approach too closely, it prevents them from being too
close or colliding. Therefore, we introduce the spatial
repulsive force, which is similar to that of particle physical