Robust Distributed Estimation Using Efficient Sensor ...

Robust Distributed Estimation Using Efficient Sensor-Fault Detection in Sensor Networks Pei-Yin Chen, Member, IEEE, Li-Yuan Chang, Yi-Ming Lin, Chih-Yuan Lien, and Ching-Sung Chen

placed. Furthermore, the sensors are generally deployed in outdoor or similarly harsh environments, and thus the occur­ rence of sensor failures or malfunctions is almost inevitable. To solve the problem, we have proposed a collaborative fault detection (CSFD) scheme [9] to detect the faulty nodes within the network such that their quantized messages can be ex­ cluded from the parameter estimation process. It considers the problem of enhancing the estimation performance of a WSN in which a set of local sensor nodes and a remote fusion center collaborate to estimate a local parameter of interest, theta.

Abstract-A robust distributed estimation scheme for fusion center in the presence of sensor faults via collaborative sensor fault detection (CSFD) was proposed in our previous research [91. The scheme can identify the faulty nodes efficiently and improve the accuracy of the estimates significantly. It achieves very good performance at the expense of such extensive computations as logarithm and division in the detecting process. In many real-time WSN applications, the fusion center might be implemented in an ASIC and included in a standalone device. Therefore, a simple and efficient distributed estimation scheme requiring lower com­ putational complexity is extremely desired for fusion center. In this paper, we propose the efficient collaborative sensor fault de­

Some related works about variants of enhancing the fault to­ lerant capability of decentralized estimation systems have been considered in the following literature. [10] addressed the prob­ lem of sensor fault detection and estimation in dynamic sys­ tems using an a priori sensor-fault model. Meanwhile, De­ louille et al. [11] used an embedded sub-graphs algorithm to design a robust distributed estimation scheme for sensor net­ works in which the sensors observe different physical pheno­ mena. The scheme considers only temporary communication faults such as failing links and sleeping nodes, whereas the robust CSFD estimation scheme proposed considers all man­ ner of possible sensor failures. Ishwar et al. [12] utilized a packet-erasure model to examine various aspects of distributed estimation in WSN, including its robustness toward sensor unreliability, its power-cycling characteristics, and the effects of uncertainties in the wireless transmissions. However, the estimation problem assumes that the fusion center requires the ability to discriminate between the local messages received from normally-operating nodes and those messages received from faulty nodes. Ertin et al. [13] proposed a Bayesian-based distributed estimation scheme in which the probability of the sensors failing to detect a source signal was modeled with a Bernoulli distribution whose characteristics depended on the particular parameter under estimation. In performing the esti­ mation process, the scheme simply excluded the information received from any nodes which failed to take a measurement of the parameter of interest. In many cases, a faulty node con­ tinues to transmit messages to the fusion center. In this case, the sensor faults may range from random sensor faults or stuck-at faults to arbitrary behavior pattern faults. In other words, faulty nodes exhibit a variety of different misbehaviors, and thus the assumption that the faults within a WSN are li­ mited to the simple case in which nodes cease to transmit their information to the fusion center is overly simplistic. In [9], CSFD takes the concept of collaborative signal processing to perform robust distributed estimation. Specifically, this work employs the homogeneity test [14] to implement CSFD scheme to detect the faulty nodes within the network such that

tection (ECSFD) scheme. A simple method for measuring faulty weight of sensors is designed in ECSFD. Given the low computa­ tional complexity, it is suitable for hardware implementation. Simulation results indicate the accuracy of the estimates obtained from the ECSFD better than that obtained from a conventional approach when applied in sensor networks.

Index terms-distributed estimation, wireless sensor networks, sensor fault detection, fusion.

I.

INTRODUCTION

As wireless communications technology and micro-electro­ mechanical systems (MEMS) techniques have matured in re­ cent years, wireless sensor networks (WSN) have emerged as a promising solution for a variety of remote sensing applications, including battlefield surveillance, environmental monitoring, intruder detection systems, weather forecasting, and so on. Irrespective of their purpose, all WSN are characterized by the requirement for energy efficiency, scalability and fault toler­ ance [1]. These requirements are particularly crucial in sensor networks designed to perform an estimation function based upon the information received from the local nodes. In such networks, the estimation performance is critically dependent upon the availability and reliability of the local information, and substantial errors are induced if the nodes become unavail­ able (e.g. as a result of consuming all their energy) or unrelia­ ble (e.g. as a result of intermittent malfunctions). Hence, the design of a robust distributed estimation for fusion center in WSN is essential. The problem of distributed estimation systems have at­ tracted significant interest in recent years [2]-[8], the research focuses principally on the problem of developing energy­ efficient and bandwidth-constrained designs. By contrast, the problem of enhancing the fault tolerance capability of decen­ tralized estimation systems has attracted relatively little atten­ tion. In practical networks, fault tolerance is a critical concern since the sensor nodes are invariably battery-powered and ran­ domly deployed, and are therefore not easily recharged or re-

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38

their quantized messages can be excluded from the parameter estimation process. Utilizing the proposed CSFD mechanism, the fusion center identifies the faulty nodes with the WSN and then excludes theirs information when estimating the parame­ ter of interest. With the aid of CSFD scheme, different sensor faults can be tolerated to improve the performance of estimat­ ing the parameter of interest. As predicted, CSFD performs better than the conventional approach in estimating theta in terms of different sensor faulty types and faulty number.

.//1

node

node

Figure

output

82

1.

r-- B

rh}.,

Sensor

x-

8N

channel elTor

System model for distributed estimation fusion scheme.

nodes because of random deployment in a harsh environment. The second error is the channel transmission error due to interference or noise. In the situation, the received m� at the fusion center may not be equal to E

for all t and n.

m� and we denote Pr[b:lj -:f. b:lj] by

Consider the case where the fusion center estimates B at some arbitrary time T. Note that in performing this estimation process, all the messages received from the local nodes up to

time T, i.e. m! = {{m�};=1'"''{m� };=1} are available at the fu­ sion center. If sensor faults exist within the network, the esti­ mated value of B is liable to deviate significantly from the true value. To solve the problem, CSFD adopts the concept of collaborative signal processing to identify the faulty nodes {Sn}EFr' where Fr is the set of faulty nodes at time T. Then, the fusion center can eliminates the local message associated with these nodes {sn}Eh.' and makes the final estimate BT at time

T,

where

based only on the censored messages, nE

S\ F, denotes

nE

Sand

n

E

F;..

T {{mnt h=l}nEsIFr '

The following sensor faults models are considered in order to include different misbehavior. Given M partition levels {qk=l, ... , M} for the quantizer, then we denote PilO =

is the time

E very sensor node quantizes its own observations

rh� x-

x:

Figure I illustrates the basic structure of the distributed es­ timation network considered in the present study. The Baye­ sian formulation is considered here. Let S= {sJ, ..., SN} be a finite set corresponding to the N sensor nodes observing sensor measurement sequences generated from a common status of phenomenon BEe, the parameter under estimation. It is as­ sumed that the distribution of B is known and is denoted by p(B). The observation sequences taken by sensor Sn are det

�

Center

node

OVERVIEW OF CSFD

is the node index and

x-

Fusion

, .t 'VN

In the prior work [9], we have proposed an collaborative sensor fault detection (CSFD) scheme for isolating faulty nodes and eliminating unreliable quantized messages when performing distributed estimation. The system model, sensor fault models and CSFD scheme are described in the following.

n

m

• t ml

e

The remainder of the paper is organized as follows. Section II presents the system model, sensor fault models and the overview of CSFD scheme. The details of ECSFD are de­ scribed in Section III. Section IV presents the performance of ECSFD and compares it with CSFD. Conclusions are finally drawn in Section V.

noted by {X�}�=I' where index.

t

81

Sensor

In the detecting process, CSFD requires such extensive computations as logarithm and division though it achieves very good performance. In many real-time WSN applications, the fusion center might be implemented with the ASIC and in­ cluded in a standalone device, so a simple and good distributed estimation scheme of lower computational complexity is ex­ tremely desired. This motivation makes us modify CSFD and propose an efficient collaborative sensor fault detection (ECSFD) scheme. Compared with CSFD, ECSFD performs slightly better and requires only about 55% of computations. Therefore, it does qualify as a good candidate for hardware implementation.

II.

m

Sensor

Pr[ m� = qi I B) when node Sn operates in a fault-free manner. In one fault model, the output of local quantizers is indepen­ dent of the parameter B. For example, a stuck-at fault may occur in which the output of the affected node is frozen at a fixed quantization level. Alternately, a random fault may arise in which the distribution of the output of a faulty node is dif­ ferent from the normal situation and equals a particular value regardless of the true parameter. By contrast, some nodes may exhibit a B -dependent error in which a sensor offset bias transforms the sensor measurement uniformly to a certain value and therefore alters the value of Pr[ m� I B).

x� to

m� and send it to the fusion center. The local messages

m� are mapped to a binary signal vector b! =( b:'P".,b:'c), where G= flog2 M l is the number of bits used to represent the local message and M is the number of partition levels at the local sensors. In the distributed estimation network shown in Fig. 1, two types of errors may affect the received quantized messages at the fusion center. The first error is caused by the faulty node. The considered WSN herein is very possible to contain faulty

39

The process of CSFD can be divided into three stages. The first stage is to measure the faulty weights of all N nodes. Then, the faulty nodes are determined. The final distributed estimate is generated in the last stage. The detail of each stage is de­ scribed as follows.

Utilizing the statistic H(S \ Fr), the binary hypothesis testing problem given in (4) can be set as follows. Ho : H(S \

'ir) < XLX,(N-ll�l- l)(M-l); �

This stage consists of two steps and its aim is to decide the faulty weight of each node. In the first step, we compute the number of qi received from sensor Sn and denote it as 0ni'

r

Oni= Il{m;, == qJ, 1=1 where

where

(1)

r

sensor faults search policy, i.e. I F I� NF. The step of deter­ mining faulty nodes of CSFD scheme can be summarized as follows:

As mentioned in [15], the Kullback-Leibler (K-L) distance between distributions can be used to measure sensor-fault dev­ iation. In CSFD, we use K-L distance to estimate the faulty weights of all sensors. According to the local decisions

CSFD-l: Set k=O and assign the required significance level a. In addition, choose suitable value of NF in ac­ cordance with the network requirements and/or any prior information regarding the failure cha­ racteristic of the network.

{{m�};=I}nEs, the K-L distance EDn for node Sn is employed to measure the distribution distance from average sensor

weight (1/ N) I.�=l m;, to faulty sensor weight fined as

m�, and is de­

CSFD-2: Perform (6) for the candidate set F(k)' If Ho is ac­ cepted, terminate the CSFD process and deter­

' M ED,,( Vi II �,J == L Vi log r:i , Vj j=l

mine the final decision

(2)

FeZ) = F(k)'

If Ho is re­

jected, increase the value of k by 1. CSFD-3: If k=Nr, terminate the CSFD process and deter­ mine F(z)

F(NF)' If k=N-l, accept hypothesis Ho and decide F(z) == F(N-1 )' Otherwise, rerun to Step

_

•

Determining Faulty Nodes

ratively until F(z) is determined.

Making distribution estimation

order based on their magnitude of {EDn}�=l to get the faulty­ weight-oriented sequence, F == {sell' S(2) ... , SeN) }' After F is

Once the set of faulty nodes

number of faulty nodes. In order to determine the value of z, the following homogeneity testing problem can be formulated to test for the existence of a set of sensor nodes Fr at time T. E

S \ F6

HI : otherwise.

is determined, the fusion

(7) More details of CSFD can be found in [9].

(3)

III.

Then, the following statistics is utilized for homogeneity test­ ing to determine whether or not a candidate set

Fe Z)

center removes the quantized messages of the faulty nodes and performs the parameter estimation. Then, the estimate obtained by minimum mean square error (MSE) criterion is adopted and is given by

determined, we can obtain the candidate set of faulty sensors, denoted as F(z) == {sell' S(2) . . . , s(z)} where z is the possible

q; 18] == PilB for all sn

==

CSFD-2 and repeat Steps CSFD-2 to CSFD-3 ite­

The aim of this stage is to decide the faulty sensor nodes ac­ cording to the faulty weight of each node obtained in the pre­ vious stage. First, all sensor nodes are sorted in descending

==

is a threshold indicating the critical

In CSFD, the maximum value of I 1; I is constrained to the

{-} is the indicator function.

Ho : Pr[m�

ZLa,(N-lhil-I)(M-I)

(6)

value of the chi-square distribution with (N - F, -1)(M -1) degrees of freedom at a significance level a.

1

°ni and'V - L:=loni where 'rni i T NT

2

Hl : H(S \ Fr) > Zl-a, (N-li'; l- l)(M-l)'

Measuring Faulty Weight

Fr is Fr.

EFFICIENT CSFD

CSFD performs better than the conventional approach with regard to fault tolerance. However, it required larger computa­ tional complexity and is not suitable for hardware implementa­ tion. The main problem is that it requires some extensive and complex computations, such as logarithm and division, in the detecting process (see (2)-(6)). In order to overcome the diffi­ culty, we modity CSFD and propose an efficient collaborative sensor fault detection (ECSFD) scheme in this paper. ECSFD is simple and requires lower computational complexity, thus lower hardware cost and power consumption can be achieved.

where

40

Furthermore, ECSFD achieves better performance than CSFD. The details of ECSFD are described in the following.

TABLE I The computing time of ECSFD for Pentium 4.

To avoid the logarithm and division operations required in (2), a simple and efficient sensor faulty weight estimate me­ thod is provided. We take advantage of collaborative signal processing. More concretely, without knowing the true distri­ bution of B, most nodes in the networks can be reasonably assumed to normally report their decisions inferring the true distribution of B to the fusion center. If the sensor behavior more obviously, the sensor Sn has larger faulty sensor weight. Hence, the faulty weight of the sensor nodes can be estimated by the sum of the absolute differences between Vi and �'i ' M =

N = O"i L... . = ,, I I. L... NT i=1 "

ani . ) T

ED;,,)

affecting the decided

F;z).

Finally, the

ED;,,)

without

can be estimated

IV.

with less computational complexity and is given as

EDr,,)

N = II I "=lo"i - NO"i I· i=l

(9)

In the stage of determining the faulty nodes, we must calcu�

late H(S \ FT) first. The computation of H(S \ FT) suffer from the problem of massive division which needs large com­ putational complexity. In order to overcome the problem, the hypothesis testing can be rewritten in the following formation by mUltiplying (6) with a constant.

Fr)Il�1 ei < 2'Lx,(N'I1:rl'1)(M.l) Il�1 ei; M M HI : H(S \ Fr) Il i=1 ei > 2'1-a,(N.IFrl.I)(M.I) Il i=1 ei·

Ho : H(S \

Z

�

PERFORMANCE EVALUATION

The section presents the results of a series of simulations designed to evaluate the performance of the CSFD and ECSFD mechanisms in WSN in which the number of faulty sensors and the type of sensor faults are unknown in advance. This simulation results obtained for the MSE s of both estima­ tion schemes are also compared with those obtained using a conventional distributed Bayesian estimation system in which the unreliable local messages are included within the parame­ ter estimation. The evaluation trials consider a WSN with eight sensor nodes, i.e. N=8. The sensor measurements are processed us­ ing an additive noise model, and thus the sensor observations are given by

M

�

0.0000922 s

to obtain the B. By implementing (9), (1 I), and (7), ECSFD requires less computation than CSFD, and can achieve quite good performance with regard to fault tolerance as demon­ strated in section IV. Moreover, ECSFD is suitable for hard­ ware implementation. To verify the computational complexity, both CSFD and ECSFD are implemented in C language on the 2.8 GHz Pen­ tium 4 processor with 512 MB memory. Table I shows the computing time (in the unit of second). ECSFD requires about 55% of CSFD's computing time on Pentium 4 processor.

(8)

ED;,,)

ECSFD

After deciding F(z)' ECSFD using the same operation in (7)

with a constant simultaneously, we can

further reduce the computational complexity of

0.0001672 s

according to the step of determining faulty nodes of CSFD scheme listed in section II.

Besides, the final purpose of this stage is to calculate the ED;,,) for obtaining the faulty-weight-oriented sequence F. By

multiplying all

CSFD

can be reduced. Using (9) and (11), we can choose the F(z)

Ilvi - �'i I j.:::l::

�

Computing Time (Pentium 4)

The required division operation in (4) is replaced with multip­ lication and the corresponding computational complexity cost

m:, deviates from the average sensor behavior (1/ N)L�=I m:,

ED;,,)

Scheme

(10)

(12) where B is drawn from a Gaussian distribution with zero­

Substituting (4) to (10) gives

mean and a variance

�

(J"

=

0.5, and

w�, i.e. the additive noise

at node Sn at time t, also has a Gaussian distribution with zero­ mean and a variance

�

(J"

=

0.5. It is assumed that all the local

nodes apply the Lloyd-Max quantizer [16] with M=4. The corresponding partitions are given by

(11)

ql =-1.5104, -DO < x :, �-0.9816 >

z

", (N·!FTI·I)(M·I) N ' AI-a, _

M

Ili=1

qz =-0.4528, - 0.9816