IET Signal Processing
Research Article
Optimal distributed Kalman filtering fusion for
multirate multisensor dynamic systems with
correlated noise and unreliable
measurements
ISSN 1751-9675
Received on 15th August 2017
Revised 28th November 2017
Accepted on 2nd January 2018
E-First on 28th March 2018
doi: 10.1049/iet-spr.2017.0389
www.ietdl.org
Liping Yan
1
, Lu Jiang
1
, Jun Liu
1
, Yuanqing Xia
1
, Mengyin Fu
1
1
Key Laboratory of Intelligent Control and Decision of Complex Systems, School of Automation, Beijing Institute of Technology, Beijing 100081,
People's Republic of China
E-mail: ylp@bit.edu.cn
Abstract: An optimal distributed fusion estimation problem is concerned in this study for a kind of linear dynamic multirate
sensors systems with correlated noise and stochastic unreliable measurements. The system is formulated at the finest scale
with multiple sensors at different scales observing a common target independently with different sampling rates. The noise
between different sensors is relevant, moreover, is also correlated with the system noise. The authors derive the local state
estimation algorithms under the circumstance of total reliable measurements and stochastic unreliable measurements occur
occasions, and the optimal distributed Kalman filter fusion algorithm, respectively. The authors provide a simulation example to
illustrate the effectiveness and feasibility of the proposed algorithm.
1 Introduction
In recent years, sensor networks have shown to be a persistent
focus of research due to the rapid development of technology and
its wildly use in multiple industries including military, law
enforcement, agricultural and forestry-based projects, surveillance,
and even information collection. Accordingly, considerable
research attention has been devoted to state estimation techniques
over sensor networks, not only due to a large number of potential
applications but also because they provide more information than
traditional communication systems with a single sensor. By using
different research methods, a large number of research results on
the design of fusion estimation algorithms in multi-sensor systems
have been reported [1, 2].
For state estimation of multi-sensor systems, the existing
researches rarely take into account the correlation of the noise [3,
4] which is widely existed in reality because different sensors
usually observe the same target in a common noisy environment [5,
6]. The existed multisensor fusion estimation algorithms that
consider the correlation of noises seldom consider the multirate
sampling of sensors. For example, when the fusion centre is not fed
back to the local sensor and sensor noise is cross-correlated, a
distributed fusion formula is proposed in [7] where the sensors are
observing the single target with single sampling rate. When the
error cross-correlation matrix between local estimates is
unavailable, the distributed fusion approach is addressed in [8].
The performance of the Kalman filter with the mismatched process
and measurement noise covariance is studied in [9]. For non-linear
systems with two kinds of noise correlations, the non-linear
information filters and the decentralised fusion algorithms on the
basis of square-root cubature Kalman filter and cubature Kalman
filter are researched in [10]. With correlated and autocorrelated
noise, a distributed weighted robust Kalman filter fusion algorithm
is derived for uncertain systems with multiple sensors in [11]. In
consideration of the correlation of the process noise and the system
noise, the optimal distributed fusion and sequential fusion
algorithms are derived in [12].
The literatures mentioned above seldom take consideration of
the measurements randomly lose or unreliable that occur possibly
in practical applications because of sensor intermittent faults or
communication limitations. When the packet dropping
phenomenon or outlier of the sensor measurement occurs in multi-
sensor fusion systems, the centralised and the distributed fusion
estimation algorithms were developed in [13, 14]. To deal with the
packet dropouts and delays simultaneously, an optimal distributed
fusion Kalman filter is designed in [15]. Based on a packet dropout
model, the optimal linear estimators for the discrete-time system
are developed in [16], and a linear-minimum-variance filter is
proposed using the orthogonality principle in [17]. When the
missing of data is Bernoulli distributed, the algorithms presented
by the team of Wang [18], Sinopoli [19] and Kal [20] are
promising in that they have proper computation complexity and
can generate nearly optimal state estimations. Huang presents a
Kalman filtering algorithm for a class of linear dynamic systems
where the measurements packet loss obeys Markov distribution
[21]. When there are multi-step transmission delays, multiple
packet dropouts and correlated noises are concerned, a recursive
non-linear estimator is given in [22]. There are quite a few
literatures concerned about multisensor data fusion for the
networked system. As an example, Sun et al. present optimal
filtering algorithm for systems with multiple packet dropouts [23].
A networked federated filter algorithm with variable delays and
packet losses is presented by Xia et al. [24]. A multisensor
distributed weighted Kalman filter with stochastic uncertainties,
network delays, autocorrelated and cross-correlated noises is put
forward in [25].
For fusion of unreliable measurements, the problem of multirate
or multiscale multisensor state estimation are seldom considered.
The multirate sensor sampling problem is widely existed in
applications, e.g. in Global Position System/Inertial Navigation
System (GPS/INS) integrated navigation. In fact, it is often
unrealistic to sample all physical signals uniformly at one single
rate in practice [26]. In [27], the multi-rate estimation model with
four rates is constructed, and the state estimator in the multi-rate
linear minimum mean square error is designed. In [28, 29], the
multismart, multirate sensors state estimation problem is studied.
However, the above literatures do not consider unreliable
measurements. The optimal state estimation with unreliable
measurements and multirate sensors is researched in [4, 30]
without consideration of the noise correlation. For multirate
dynamic systems, an optimal sequential fusion estimation
algorithm with correlated noise and unreliable measurements is
presented in [31], where the correlation of the measurement noise
and the system noise at the same time step is not considered, and
the distributed fusion of the observations is not considered. The
IET Signal Process., 2018, Vol. 12 Iss. 4, pp. 522-531
© The Institution of Engineering and Technology 2018
522