Research Article
Distributed Fusion Estimation for Multisensor Multirate
Systems with Stochastic Observation Multiplicative Noises
Peng Fangfang and Sun Shuli
School of Electronics Engineering, Heilongjiang University, Harbin 150080, China
Correspondence should be addressed to Sun Shuli; sunsl@hlju.edu.cn
Received August ; Accepted December ; Published February
Academic Editor: Wendong Xiao
Copyright © P. Fangfang and S. Shuli. is is an open access article distributed under the Creative Commons Attribution
License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly
cited.
is paper studies the fusion estimation problem of a class of multisensor multirate systems with observation multiplicative noises.
e dynamic system is sampled uniformly. Sampling period of each sensor is uniform and the integer multiple of the state update
period. Moreover, dierent sensors have the dierent sampling rates and observations of sensors are subject to the stochastic
uncertainties of multiplicative noises. At rst, local lters at the observation sampling points are obtained based on the observations
of each sensor. Further, local estimators at the state update points are obtained by predictions of local lters at the observation
sampling points. ey have the reduced computational cost and a good real-time property. en, the cross-covariance matrices
between any two local estimators are derived at the state update points. At last, using the matrix weighted optimal fusion estimation
algorithm in the linear minimum variance sense, the distributed optimal fusion estimator is obtained based on the local estimators
and the cross-covariance matrices. An example shows the eectiveness of the proposed algorithms.
1. Introduction
In networked systems or sensor networks, there oen exist
various uncertainties during the transmission process of sig-
nals due to the imperfection of the communication channels.
It makes impossible to use linear model to describe some sys-
tems.euncertaintiescanbeapproximatedmathematically
by an additive noise or a multiplicative noise [–]. ese
systems are widely used in petroleum seismic exploration,
target detection, speech processing, and other areas; thus,
the research on systems with multiplicative noise has the
important practical signicance. In the early references [],
the optimal linear lters have been proposed for systems with
uncertain observations described by the multiplicative noise.
For more general case with stochastic parameters, the optimal
linear estimation is designed in []. References [–]study
thepolynomiallters;however,theproposednonlinearlters
have expensive computational cost. For networked systems
with multiplicative noises and packet dropouts, optimal
linear estimators including lter, predictor, and smoother
have been proposed in []. However, the above-mentioned
literatures are all concerned with single sensor case but do
nottakemultiplesensorsintoaccount.
As the sensor technology is widely used in military, civil-
ian, scientic research, and many other elds, single sensor
hasfailedtomeettheperformancerequirementsinmany
aspects. Moreover, as the development of electronics tech-
nologies, various sensors have been developed and applied to
many practical elds such as target tracking since they can
provide more information than any single sensor. erefore,
multisensor information fusion has received considerable
research attention in recent years []. For systems with a
single sampling rate, the optimal state weighted fusion lter
in the linear minimum variance sense []andtheself-tuning
fusion lter with unknown noise variances []havebeen
presented. Recently, the multirate multisensor asynchronous
fusion algorithms have been studied in [–]. References
[, ] adopt the state augmentation approach to give the
estimators with the expensive computational cost. ough
[, ] adopt the nonaugmented approach to design the
lters, a modeling error is made by ignoring the process
noise. erefore, there is the accuracy loss. By considering
Hindawi Publishing Corporation
Mathematical Problems in Engineering
Volume 2014, Article ID 373270, 8 pages
http://dx.doi.org/10.1155/2014/373270