IET Control Theory & Applications
Brief Paper
Fault detection for multi-rate sensor fusion
under multiple uncertainties
ISSN 1751-8644
Received on 14th July 2014
Accepted on 5th December 2014
doi: 10.1049/iet-cta.2014.1134
www.ietdl.org
Hang Geng
1,2
,Yan Liang
1,2
, Linfeng Xu
1,2
1
School of Automation, Northwestern Polytechnical University, Xi’an, People’s Republic of China
2
Key Laboratory of Information FusionTechnology, Ministry of Education, Xi’an, People’s Republic of China
E-mail: liangyan@nwpu.edu.cn
Abstract: In multi-sensor fusion, it is hard to guarantee that all sensors have an identical sampling rate, especially in the
distributive and/or heterogeneous case. Meanwhile, system modelling may face the coexistence of multiple uncertainties
including stochastic noise, unknown input (UI) and faults in complex environment. To this end, the authors propose the
problem of fault detection for multi-rate sensor fusion systems subject to UI, stochastic noise with known covariance, and
faults imposed on the actuator and sensors. Furthermore, the new form of multi-rate observer (MRO) is presented and lifted
to the single-rate one with causality constraint for parameter design. Observer parameters are determined optimally in
pursuit of the UI decoupling and maximum noise attenuation under the causality constraint. Differing from the traditional
observer, the proposed MRO is time varying, that is, its parameters need recursive computation and hence has better
adaptability to the effect of uncertainties. Finally, a multi-rate residual generator is constructed via a hypothesis test in
which the threshold is adaptively designed. A numerical example is given to show the effectiveness of their proposed
method.
1 Introduction
In some complex systems, it is often unrealistic or sometimes
impossible to guarantee that all physical signals operate at one sin-
gle rate [1]. For example, for signals with different bandwidths,
better trade-offs between performance and implementation cost
can be obtained using A/D and D/A converters at different rates.
On the other hand, for processed/estimated quantities, sometimes
users may specify rates which are different from the sampling
rates of sensors. Therefore researches on multi-rate sensor fusion
arise.
State estimation approach based on dual-rate sensor measure-
ments was proposed in [2] and extended to deal with the asyn-
chronous multi-rate sensor measurements, where the ratio between
the sampling rates of different sensors was allowed to be any pos-
itive integer [3]. Accounting for out of sequence data and latent
data, general asynchronous fusion estimation methods were put
forward for multi-sensor systems [4, 5]. Since different dynamic
models always have different frequency properties in multiple
model systems, the fast-rate sensor measurement was thus com-
pressed to a slow rate sub-situation with little or no accuracy
degradation in low-frequency models, and hence results in multi-
rate interacting multiple model estimators [6] and its target-tracking
application with out-of-sequence GMTI data [7] or distributed
fusion [8]. In the case that the updating rate of state estimates
is different from the measurement sampling rate, the wavelet-
transform-based and the optimal H
2
/H
∞
-based estimation schemes
were proposed in [9, 10], respectively. For a four-rate estimation
problem including the state updating rate, measurement sampling
rate, estimate updating rate and the estimate output rate, Liang
et al. [11] presented a linear minimum variance (LMV) estima-
tor. For systems existing measurement missing or packet losses,
Liang et al. [12] and Zhang et al. [13] presented a multi-rate
H
∞
method and a two-stage distributed fusion estimation method,
respectively. When such packet dropouts are multiple, the optimal
LMV centralised and decentralised fusion estimators are designed
in [14]. In addition, Zhang et al. [15] concerned the multi-sensor
fusion estimation scheme for wireless sensor networks with non-
uniform estimation rates and provided two fusion algorithms that
can fuse available local estimates generated at different time
scales, allowing estimation rates at different sensors to be different
from each other. In general, no fault is considered in the above
research.
Concerning the fault detection (FD) problem in multi-rate sen-
sor systems with unknown input (UI) in the state equation, the
lifting technique was used to convert the multi-rate system into a
linear time-invariant (LTI) model with slow sampling rate, based
on which residual generators were designed using state observers
[16, 17], but the residual can only be updated at the same rate as
the LTI model resulting in a slow-rate FD scheme. For fast-rate
residual generation, an observer was designed for each set of syn-
chronous measurements resulting in a bank of observers that run
simultaneously at different rates [18]. For multi-rate systems with
UI both in the state equation and output equation, by optimising a
performance index which maximises the effect of the fault on the
residual, at the same time, minimises the influence of the UI on the
residual, Izada et al. [19] presented a parity-space-based residual
generator, and Izada et al. [20] proposed different H
∞
optimal and
causal residual generators. For the case of norm-bounded UI [21],
an observer-based FD filter (FDF) was considered as a residual
generator and the residual was obtained by solving an H
∞
/H
∞
or
H
∞
/H
−
optimisation problem.
However, all the above researches are limited to the scope of
deterministic systems, that is, the stochastic noise is not considered
either in the state equation or output equation although random
noise is common to state evolvement and sensor sampling in com-
plex environment. In other words, an interesting but still open
problem is FD of multi-sensor fusion in the presence of UI and
noise.
In this paper, the FD problem for the multi-rate sensor fusion
system with both UI and noise is proposed. First, we proposed a
new multi-rate observer (MRO) to generate the multi-rate resid-
ual, and the MRO parameters are determined through decoupling
the residual with the UI and minimising the effect of the noise
on the residual in the minimum-mean-square error (MMSE) sense.
The disturbance decoupling and noise attenuation conditions are
found to be closely related with sensor rates and the causality con-
straint because of the multi-rate nature. The residual is evaluated
via a hypothesis test in which the detection threshold is adaptively
determined.
IET Control Theory Appl., 2015, Vol. 9, Iss. 11, pp. 1709–1716
© The Institution of Engineering and Technology 2015 1709