Shu-Li Sun
e-mail: sunsl@hlju.edu.cn
Zi-Li Deng
Department of Automation,
Heilongjiang University,
Harbin 150080,
People’s Republic of China
Multi-Sensor Information Fusion
Kalman Filter W eighted by
Scalars for Systems with Colored
Measurement Noises
An optimal information fusion criterion weighted by scalars is presented in the linear
minimum variance sense. Based on this fusion criterion, a scalar weighting information
fusion decentralized Kalman filter is given for discrete time-varying linear stochastic
control systems measured by multiple sensors with colored measurement noises, which is
equivalent to an information fusion Kalman predictor for systems with correlated noises.
It has a two-layer fusion structure with fault tolerant and robust properties. Its precision
is higher than that of each local filter. Compared with the fusion filter weighted by
matrices and the centralized filter, it has lower precision when all sensors are faultless,
but has reduced computational burden. Simulation researches show the effectiveness.
关DOI: 10.1115/1.2101844兴
1 Introduction
The information fusion Kalman filtering theory has been further
studied and widely applied in integrated navigation systems for
maneuvering targets, for example, airplane, ship, automobile, and
robot, etc. When multiple sensors measure the states for the same
stochastic system, generally we have two different types of meth-
ods to process the measured sensor data. The first method is the
centralized filter 关1兴, where all measured sensor data are commu-
nicated to the central site for processing. The advantage of this
method is that there is a minimal information loss. However, the
centralized filter may be unreliable or suffer from poor accuracy
and stability when there is severe data fault. The second method is
the decentralized filter, where the information from local estima-
tors can yield the global optimal or suboptimal state estimator
according to some information fusion criterion. The advantages of
this method are that the requirement of memory space to the fu-
sion center is broadened, and the parallel structures can increase
the input data rates, furthermore, the decentralization makes for
easy fault detection and isolation. However, the precision of the
decentralized filter is generally lower than that of the centralized
filter when there is not data fault. Recently, various decentralized
and parallel versions of the Kalman filter have been reported
关2–11兴. Bar-Shalom 关2兴 studies the correlation between two sen-
sors and gives the cross-covariance matrix between two sensors
where the process noise is independent of the measurement
noises. Carlson 关3兴 presents the famous federated square root fil-
ter. But to some extent, it has the conservatism because of using
the upper bound of the process noise variance matrix instead of
the process noise variance matrix itself. Roy et al. 关4兴 give a
parallel algorithm for Kalman filtering using a band of reduced-
order local filters, which yields higher input data rates and com-
putation speeds. The decentralized estimator is also given for the
linear observation model with correlated measurement noises 关5兴.
Saha et al. 关6,7兴 discusses the steady-state fusing problem for
linear systems with two sensors, and gives the necessary and suf-
ficient conditions for positive definiteness of the filtering error
cross-covariance matrix between two sensors. Kim 关8兴 and Chen
et al. 关9兴, respectively, extend the results in 关2兴 and give the mul-
tisensor optimal information fusion estimator in the maximum
likelihood sense under the assumption of normal distributions.
Chen et al. 关9兴 indicate that it is also the weighted least squares
estimator under the assumption of normal distributions. Vorobyov
et al. 关10兴 give the fusion estimator for a scalar signal as a special
case of 关8,9兴. Deng et al. 关11兴 give a fusion criterion weighted by
scalars for systems with multiple sensors. But the assumption for
the state estimation errors between any two sensors to be uncor-
related does not accord with the general case. So it can only
obtain the suboptimal fusion estimation.
In this paper we present an information fusion criterion
weighted by scalars in the linear minimum variance sense. It con-
siders the correlation among local estimation errors, and only re-
quires the computation of the scalar weights but avoids the com-
putation of matrix weights and the assumption of normal
distributions of 关8,9兴 also avoids the assumption of local estima-
tion errors to be uncorrelated of 关11兴. It has a reduced computa-
tional burden. Based on this fusion criterion, an optimal informa-
tion fusion decentralized Kalman filter with scalar weights is
given for discrete time-varying linear stochastic control systems
with colored measurement noises, which is equivalent to an opti-
mal information fusion decentralized Kalman predictor for sys-
tems with correlated noises. A two-layer fusion structure with
fault tolerant and robust properties is given. The first-step predic-
tion error cross-covariance between any two sensors is given for
systems with correlated noises.
2 Problem Formulation
Consider the discrete time-varying linear stochastic control sys-
tem with multiple sensors
x共t +1兲 = ⌽共t兲x共t兲 + B共t兲u共t兲 + ⌫共t兲w共t兲共1兲
y
i
共t兲 = H
¯
i
共t兲x共t兲 +
i
共t兲, i =1,2,… ,l 共2兲
i
共t +1兲 = C
i
共t兲
i
共t兲 +
i
共t兲, i =1,2,… ,l 共3兲
where x共t兲苸 R
n
is the state, y
i
共t兲苸 R
m
i
, i =1,2,… , l, are the mea-
surements, u共t兲苸 R
p
is the known control input,
i
共t兲苸 R
m
i
, i
=1,2,… ,l, are the colored measurement noises that satisfy the
Markov processes, ⌽共t兲, B共t兲, ⌫共t兲,H
¯
i
共t兲,C
i
共t兲 are the time-
varying matrices with compatible dimensions, and l is the number
of sensors.
Contributed by the Dynamic Systems Division of ASME for publication in the
J
OURNAL OF DYMANIC SYSTEMS,MEASUREMENT, AND CONTROL. Manuscript received
August 12, 2003; final manuscript received February 21, 2005. Assoc. Editor: Fathi
H. Ghorbel.
Journal of Dynamic Systems, Measurement, and Control DECEMBER 2005, Vol. 127 / 663
Copyright © 2005 by ASME
Downloaded 17 Feb 2009 to 219.217.235.175. Redistribution subject to ASME license or copyright; see http://www.asme.org/terms/Terms_Use.cfm