J Control Theory Appl 2009 7 (4) 438–444
DOI 10.1007/s11768-009-7154-y
A new information fusion white noise
deconvolution estimator
Xiaojun SUN, Shigang WANG, Zili DENG
(
Department of Automation, University of Heilongjiang, Harbin Heilongjiang 150080, China)
Abstract: The white noise deconvolution or input white noise estimation problem has important applications in
oil seismic exploration, communication and signal processing. By the modern time series analysis method, based on the
autoregressive moving average (ARMA) innovation model, a new information fusion white noise deconvolution estimator
is presented for the general multisensor systems with different local dynamic models and correlated noises. It can handle
the input white noise fused filtering, prediction and smoothing problems, and it is applicable to systems with colored
measurement noises. It is locally optimal, and is globally suboptimal. The accuracy of the fuser is higher than that of each
local white noise estimator. In order to compute the optimal weights, the formula computing the local estimation error
cross-covariances is given. A Monte Carlo simulation example for the system with Bernoulli-Gaussian input white noise
shows the effectiveness and performances.
Keywords: Multisensor information fusion; Weighted fusion; White noise estimator; Deconvolution; Modern time
series analysis method
1 Introduction
Input estimation or decovolution has wide applications
in many areas such as oil exploration, image restoration,
fault detection, communication, signal processing and so on
[1∼6]. Mendel [1∼3], and Mendel and Kormylo [4] pre-
sented an optimal input white noise estimator with appli-
cation to the oil seismic exploration based on the Kalman
filter. Deng et al. [7] presented a unified white noise es-
timation theory based on the modern time series analysis
method, which not only includes input noise estimator but
also includes measurement noise estimator.
In order to improve the estimation accuracy based on a
single sensor, the multisensor information fusion has re-
ceived great attention in recent years. For Kalman filtering-
based fusion, two basic fusion methods are the central-
ized and distributed fusion methods. The centralized fusion
method can give the globally optimal state estimation by di-
rectly combing local measurement data, but its disadvantage
is that it may admit a larger computational burden. The dis-
tributed fusion method can give globally suboptimal state
estimation by weighting the local state estimators, but it can
reduce the computational burden, and can facilitate fault de-
tection and isolation more conveniently.
The optimal fusion rules weighted by matrices, diago-
nal matrices, and scalars were presented in linear minimum
variance sense in [8], which gave three globally suboptimal
Kalman fusers compared with the centralized Kalman fuser.
So far, the information fusion is mainly focused on the state
estimation problem, but the white noise fusion problem is
seldom reported [9, 11].
Recently, Deng et al. [9] presented an optimal informa-
tion fusion white noise estimator using the modern time se-
ries analysis method, and Sun [10, 11], and Sun et al. [12]
presented an optimal information fusion white noise filter
and smoother based on the Kalman filtering method, re-
spectively, but all of them cannot handle the white noise de-
convolution fusion problem for systems with colored mea-
surement noises. Sun et al. [13] gave an information fusion
white noise deconvolution smoother for systems with col-
ored measurement noises. However, all the above references
are only applicable to systems with the same local dynamic
models, and cannot handle the white noise deconvolution
fusion problem for the systems with different local dynamic
models.
In order to overcome the above drawback and limita-
tion, using the modern time series analysis method, a new
weighted fusion white noise deconvolution estimator is pre-
sented for the linear discrete time-invariant stochastic sys-
tems with different local models in this paper, which is
different from the white noise estimator obtained by the
Kalman filtering method in [14]. It can handle the white
noise fused filtering, smoothing and prediction problems,
and it is applicable to systems with colored measurement
noises. In order to compute the optimal weights, the for-
mula computing the local estimation error covariances is
presented.
2 Problem formulation
Consider the linear discrete time-invariant stochastic sys-
tem with different local dynamic models
x
i
(t +1)=Φ
i
x
i
(t)+Γ
i
w
i
(t), (1)
y
i
(t)=H
i
x
i
(t)+v
i
(t),i=1, ··· ,L, (2)
w
c
(t)=C
i
w
i
(t), (3)
where t is the discrete time, x
i
(t) ∈ R
n
i
is the state, y
i
(t) ∈
R
m
i
is the measurement, w
i
(t) ∈ R
p
i
and v
i
(t) ∈ R
m
i
are
Received 16 July 2007; revised 6 October 2008.
This work was supported by the National Natural Science Foundation of China (No.60874063), Science and Technology Research Foudation of
Heilongjiang Education Department (No.11523037) and Automatic Control Key Laboratory of Heilongjiang University.