Distributed Fusion Filter for Asynchronous Multi-rate
Multi-sensor Non-uniform Sampling Systems
Jing Ma, Honglei Lin
School of Mathematics science
Heilongjiang University
Harbin, Heilongjiang Province, China
majing427@gmail.com, linhonglei0810@163.com
Shuli Sun
Department of Automation
Heilongjiang University
Harbin, Heilongjiang Province, China
sunsl@hlju.edu.cn
Abstract—This paper is concerned with the distributed fusion
filtering problem for a class of asynchronous multi-rate multi-
sensor non-uniform sampling discrete stochastic systems, where
the state is updated at the highest sampling rate and different
sensors may have different lower measurement sampling rates.
Furthermore, the state is updated uniformly and the
measurement is sampled non-uniformly. The non-augmented
state models at each sensor are established by considering the
system noises. The local filters at measurement sampling points
of each sensor are designed based on the established state space
models by an innovation analysis approach. Further, the local
filters at state update points are proposed. The corresponding
filtering error covariance matrices are derived. Using the
covariance intersection fusion algorithm, the distributed fusion
filter is given based on the local filters and the local filtering
error covariance matrices. The proposed algorithm can
significantly improve the estimation accuracy compared to the
previous modeling method which ignores the system noise. The
simulation research verifies the effectiveness of the proposed
algorithm.
Keywords-multi-rate, multi-sensor, non-uniform sampling,
covariance intersection, distributed fusion filter
I. INTRODUCTION
Recently, the state estimation problem for multi-sensor
multi-rate systems has attracted lots of attention due to the
impossibility to sample all the physical signals at one single
rate in many complicated practical systems. Generally
speaking, there are two cases for it. The first case is the
estimation problem for single sensor system [1-2], which
includes two rates or four rates as follows: the state updating
rate, the measurement sampling rate, the estimation updating
rate and the estimation output rate. The difficulty is how to
obtain the state estimation values at no measurement times. The
linear minimum variance optimal state filter is presented by
state augmentation approach [2]. However, the proposed filter
has expensive computational cost due to the high dimension
augmented state. The other case is the estimation problem for
multi-sensor system [3-16], where the state is updated at the
fastest rate and different sensors have different measurement
sampling rates. Further, there is at least one sensor with the
sampling rate same with updating rate. The difficulty is how to
transform the fusion estimation problem for multi-rate systems
to the equivalent fusion estimation problem for a single rate
system. Generally, there are two methods: multiscale theory [3-
7] and Kalman filter [8-16]. Based on multiscale theory, using
wavelet transformation, Hong [3-4], Zhang [5] and Wen [6-7]
et al propose some fusion strategies for different sensors with
the ratio of the sampling rates being a power of two. However,
the white noise is converted into colored noise in the state
decomposition [3-4], which results in the suboptimal state
estimators. The state augmentation method is used in [5-7],
which results in the high dimension computational cost. Based
on Kalman filter, Ge [8], Yan and Zhou [9-13] propose some
fusion algorithms for different sensors with the ratio of the
sampling rates being any positive rational. However, the filters
in [8-9] have expensive computational cost, the filter in [10] is
suboptimal since some available sensor information is ignored
at some instants and the filters in [11-13] are also suboptimal
since the system noise is ignored. Moreover, the centralized
and distributed asynchronous fusion algorithms are presented
for continuous stochastic system [14]. The
∞
filtering
problem is also investigated for multi-rate system [15-16].
Motivated by the above discussion, we consider the
distributed fusion filtering problem for an asynchronous multi-
rate multi-sensor non-uniform sampling discrete stochastic
system. Firstly, the non-augmented state models at each sensor
are established by considering the system noises. Then, based
on the established state space models, the local filters at the
measurement sampling points and at the state update points are
obtained, respectively. Further, the distributed fusion filter is
given by the covariance intersection fusion algorithm [17]. The
local filtering error covariance matrices are derived to compute
the fusion weights.
II.
PROBLEM FORMULATION
Consider the following asynchronous multi-rate multi-
sensor non-uniform sampling discrete time invariant linear
stochastic system with L sensors
(1) () ()xt xt wt
ΦΓ
+= + (1)
() () (), 1,2, ,
iiii
yk Hxk vk i L=+ =" (2)
This work was supported by National Natural Science Foundation o
China, NSFC-61174139, and Program for New Century Excellent Talents in
University under Grant NCET-10-0133.
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