Auxiliary Gaussian Sum Quadrature
Particle Filtering
Liangqun Li, Sheng Luo, Zhenglong Yi
ATR Key Laboratory, Shenzhen University, Shenzhen, China
lqli@szu.edu.cn, luosheng5@email.szu.edu.cn
Abstract—For the nonlinear non-Gaussian filtering problem
of observation data in sparseness sampling environment, a novel
auxiliary Gaussian sum quadrature particle filter (AGSQPF)
based on target characteristics is proposed. In the proposed
algorithm, the predicted and the posterior probability density
function of target state are approximated by finite Gaussian
mixtures based on Gauss-Hermite quadrature and the particle
filtering. Moreover, the proposed algorithm can incorporate
target speed, time interval and the latest observation information
into the importance density function, which can effectively
improve the performance. The simulation results show that the
performance of the proposed algorithm is much better than
Gaussian sum quadrature particle filter (GSQPF) for sparseness
sampling environment.
Keywords-Gaussian Sum; Gauss-Hermite quadrature;
Quadrature particle filtering; target characteristics.
I. INTRODUCTION
Nonlinear non-Gaussian filtering problem of observation data is
widely used in the field of Large-Scale passive sensor system, such as
visual tracking, navigation and guidance, automatic control, signal
processing, fault diagnosis and analysis, etc. To address this problem,
the researchers have proposed the Gaussian sum filter (GSF) [1, 2] and
Gaussian sum quadrature Kalman filter (GSQKF) [3, 4].These filters
approximated the posterior probability density function of the target
state as single Gaussian by finite Gaussian mixture. However, for the
highly nonlinear non-Gaussian systems, these filters perform badly [5].
Particle filter is a kind of Bayesian state estimation algorithm
based on Monte Carlo [6] simulation method, which can approximates
the posterior probability density by using a finite set of weighted
samples. Because of particle filter is a nonlinear estimation method, it
can achieve good results for nonlinear non-Gaussian filter problems
[7]. Kotecha et al [8, 9] proposed the Gaussian sum particle filter
(GSPF), which approximate the filtering and predictive distributions
by weighted Gaussian mixtures. However, after several iterations, the
variance of the Gaussian density weights increased gradually with
time .Li et al [10] proposed the Gaussian sum quadrature particle filter
(GSQPF), which introduce a set of quadrature point probability
densities to approximate the importance density function, and the
posterior probability density function are approximated as finite
Gaussian mixtures. In [10], the particle sampling have adopted its state
transition function based on updates in time. The posterior probability
distribution cannot effectively represented by each sample of the set
based on changes in time interval of the target observation or target
motion model is not accurate. In order to improve the adaptive ability
of the importance density function for aperiodic sparseness sampling
environment, based on GSQPF, an auxiliary Gaussian sum quadrature
particle filter (AGSQPF) is proposed, which can simultaneously
incorporate current measurement information and target characteristic
information, and effectively improve the diversity and accuracy of
particles.
II. AUXILIARY GAUSSIAN SUM QUADRATURE PARTICLE
FILTER
There exists the same drawback that the particles are sampled
based on target posterior probability density function
,
where is between GSPF and traditional PF. However, this method is
accurately estimated on the premise of target motion model [11].
When time interval of target observation is increasing and target state
don’t update in a long time, the target motion model is difficulty
estimated by using several observation information. For the sparseness
sampling environment, the particles are merely sampled from the prior
probability density function
, and the sampling particle
seriously deviates from the actual of the target. Then the prediction
accuracy of mean
and covariance
is reduced. In order
to enhance the filtering ability of the PF for observation data in
sparseness sampling environment, we have adopted a set of quadrature
point probability densities to approximate the importance density
function [4], and effectively improve the diversity and accuracy of
particles.
A. Time Update
Assume at time that the posterior probability density
(
) is Gaussian with mean
and covariance
.
Considering the effect of target characteristics
to the
predicted probability density function, and the predictive distribution
is given by
ICWMMN2015 Proceedings
129
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