Localization in Wireless Sensor Networks - Semantic Scholar

IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 61, NO. 6, MARCH 15, 2013

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Localization in Wireless Sensor Networks: Byzantines and Mitigation Techniques Aditya Vempaty, Student Member, IEEE, Onur Ozdemir, Member, IEEE, Keshav Agrawal, Hao Chen, Member, IEEE, and Pramod K. Varshney, Fellow, IEEE

Abstract—Wireless Sensor Networks (WSNs) are vulnerable to Byzantine attacks in which malicious sensors send falsified information to the Fusion Center (FC) with the goal of degrading inference performance. In this paper, we consider Byzantine attacks for the location estimation task in WSNs using binary quantized data. Posterior Cramér-Rao Lower Bound (PCRLB) is used to characterize the performance of the network. Two kinds of attack strategies are considered: Independent and Collaborative attacks. We determine the fraction of Byzantine attackers in the network that make the FC incapable of utilizing sensor information to estimate the target location. Optimal attacking strategies for given attacking resources are also derived. Furthermore, we propose two schemes for the mitigation of Byzantine attacks. The first scheme is based on a Byzantine Identification method under the assumption of identical local quantizers. We show with simulations that the proposed scheme identifies most of the Byzantines. In order to improve the performance, we propose a second scheme in conjunction with our identification scheme where dynamic non-identical threshold quantizers are used at the sensors. We show that it not only reduces the location estimation error but also makes the Byzantines ‘ineffective’ in their attack strategy. Index Terms—Byzantine attacks, malicious sensors, posterior Cramér-Rao lower bound, target localization, wireless sensor networks.

I. INTRODUCTION

W

IRELESS Sensor Networks (WSNs) are increasingly being used both in military and civilian applications. One such application is to monitor, detect and/or estimate the

Manuscript received June 01, 2012; revised September 14, 2012 and November 07, 2012; accepted November 19, 2012. Date of publication December 24, 2012; date of current version February 26, 2013. The associate editor coordinating the review of this manuscript and approving it for publication was Prof. Huaiyu Dai. This work was supported in part by the U.S. Air Force Office of Scientific Research Contracts FA 9750-10-C-0221, FA 9550-10-C-0179 and by CASE at Syracuse University. Some related preliminary work was presented at the Asilomar Conference on Signals, Systems and Computers, Pacific Grove, CA, USA, November 2011, and the Annual Conference on Information Sciences and Systems (CISS), Princeton, NJ, USA, March 2012. A. Vempaty and P. K. Varshney are with the Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY 13244 USA (e-mail: [email protected]; [email protected]). O. Ozdemir is with the Andro Computational Solutions, Rome, NY 13440 USA (e-mail: [email protected]). K. Agrawal is with the Electrical Engineering Department, University of California, Los Angeles, CA 90095 USA (e-mail: [email protected]). H. Chen is with the Department of Electrical and Computer Engineering, Boise State University, Boise, ID 83725 USA (e-mail: haochen@boisestate. edu). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TSP.2012.2236325

location of a target or object in an area of interest. Secure localization is extremely important in situations where malicious sensors attempt to disrupt the network and diminish its capability. Several algorithms have been developed for secure localization in WSNs [1]–[3]. Localization techniques proposed in the literature for sensor networks include Direction of arrival (DOA), time of arrival (TOA) and time-difference of arrival (TDOA) based methods [4], [5]. Recent research has focused on developing techniques which do not suffer from imperfect time synchronization. For example, in [6], [7], the authors propose localization in WSNs by “dumb sensors” which are cheap and do not require time synchronization or extensive local processing. Received signal strength) based methods, which do not suffer from imperfect synchronization and/or extensive processing, have also been proposed which employ least-squares or maximum-likelihood (ML) based source localization techniques [8], [9]. Due to resource constraints such as energy and bandwidth, it is often desirable that sensors only send binary or multi-bit quantized data to limit the communication requirements. RSS based target localization using quantized data in a sensor network has been investigated in the literature [10], [11], but no malicious sensors or attackers in the network have been considered. One kind of attack in a WSN is by Byzantines [12] where an adversary takes over some sensors of the WSN and forces them to send falsified information to the Fusion Center (FC). The main goal of Byzantine attackers is to undermine the network such that the FC is unable to estimate the correct location of the target. A related work was carried out for distributed detection by Marano et al. [12] and for primary user detection for cognitive radio networks by Rawat et al. in [13]. Previously, we proposed a Byzantine identification scheme in a distributed detection problem [14], where the Byzantines are identified in an adaptive fashion and their information is used adaptively to improve the system’s detection performance. The problem of Byzantines has also been investigated in the context of network coding and information theory in [15] and [16]. In our previous work [17], we developed a maximum likelihood (ML) estimator for target localization in a WSN using binary quantized data, where we analyzed the effects of Byzantine attacks. In such a scenario, the performance metric is the Fisher Information [18]. We numerically designed optimal strategies for the Byzantines and the network for the localization process. In [19], we considered the same ML based target location scenario and proposed a Byzantine identification method along with a dynamic non-identical threshold design scheme to mitigate the effects of Byzantines. Building on these works [17], [19] that employ ML estimation, in our current

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work, we investigate the target localization problem in a WSN under a Bayesian framework and develop a Monte Carlo based approach for target localization. We assume the target location to be random and evaluate the performance of a minimum mean square error (MMSE) estimator in the presence of Byzantines. The appropriate performance metric for the Bayesian framework is Posterior Fisher Information or Posterior Cramér-Rao lower bound (PCRLB) which makes the analysis more difficult. We define the minimum fraction of Byzantines as the fraction of Byzantines required to make the network non-informative to the FC. Unlike our previous work [17], where we derived numerically, in this paper we analytically derive this value by modeling the effect of Byzantines as a binary symmetric channel (BSC). We design the optimal strategies for both the Byzantines and the network by modelling their behavior as a zero-sum game. We use PCRLB as the utility function and find the Nash-Equilibrium as the saddle point. We also investigate new techniques to make the network robust to the presence of Byzantines. Specifically, we propose an adaptive learning scheme to identify the Byzantines in the network which is shown to be highly effective. Moreover, in order to improve the performance further, we propose a dynamic iterative quantization scheme at the local sensors. Although the non-identical threshold design proposed in this work is similar to our previous work [19], the derivation of such a design is more rigorous here and is derived using Calculus of Variation [20]. We formulate the problem in a game theoretic framework and derive the optimal quantizers for both the honest sensors and the Byzantines. We show that the proposed quantization scheme not only improves the estimation performance significantly but also makes the Byzantines ‘ineffective’ when combined with our adaptive learning scheme. We also extend our work to include collaborative attacks by the Byzantines. The rest of the paper is organized as follows. In Section II, we introduce the system model and lay out the assumptions made. We also develop the estimation process and define the performance metrics used. In Section III, we analyze the performance of the estimation process in the presence of independent attacks. We also find the optimal strategies for both the honest and the Byzantine sensors. We analyze the problem from the network’s perspective in Section IV and Section V, where we propose Byzantine mitigation schemes which make the Byzantines ‘ineffective’ and benefit the network. In Section VI, we introduce collaborative attacks of Byzantines and perform analysis similar to the analysis of independent attacks. We present numerical results that support our theoretical analyses of Byzantines and the effectiveness of our proposed mitigation schemes in the respective sections. We conclude with further discussions in Section VII. II. PRELIMINARIES A. System Model sensors are deployed in a We consider a scenario where WSN to estimate the location of a target present at where and denote the coordinates of the target location in the 2-D Cartesian plane as shown in Fig. 1. Although the sensors in Fig. 1 are shown to be deployed on a regular grid, the schemes

Fig. 1. The target in a grid deployed sensor field with anchor sensors.

proposed in this paper are capable of handling any kind of sensor deployment as long as the location information for each sensor is available at the FC. We assume that the target location has a prior distribution . For simplicity, we assume that is a Gaussian distribution, i.e., , where the mean is the center of Region of Interest (ROI) and is very large such that the ROI includes the target’s 99% confidence region. We assume that the signal radiated from this location follows an isotropic power attenuation model given as (1) where is the signal amplitude received at the sensor, is the power measured at a reference distance , is the pathloss exponent, and is the distance between the target and the sensor. We assume here that , i.e., the target is not on a sensor. This assumption is valid as the probability of a target being on a sensor is zero, therefore, is almost surely not unbounded. In this paper, without loss of generality, we assume and . The signal amplitude is corrupted by additive white Gaussian noise (AWGN) at each sensor: (2) sensor and the noise where is the corrupted signal at the follows . We assume this noise to be independent across sensors. Note that the signal model given in (1) and (2) has been verified experimentally for acoustic signals in [8] and it results from averaging time samples of the received acoustic energy. The interested reader is referred to [8], [9], [21] for details. Due to bandwidth and energy limitations, each sensor uses binary quantizers and sends its quantized binary measurement to the FC. We assume that the FC knows the sensor locations and the sensors use threshold quantizers because of their simplicity [22] in terms of both implementation and analysis: (3) is the quantized binary measurement and is the where quantization threshold at the sensor. The FC receives the binary vector from all the sensors in the network. After collecting , the FC estimates the location by using the Minimum Mean Square Error (MMSE) , where denotes estimator as in [23], i.e.,

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the expectation with respect to the posterior probability density function (pdf) . Since cannot be calculated in closed from, we compute it using an importance sampling based Monte Carlo method described in detail below. We also assume the presence of anchor nodes in the network similar to [23]. These anchor nodes are assumed to be secure and are used to obtain an initial estimate of the target location, .

where is the gradient operator defined as . and represent the contributions of data and the prior to respectively. The elements of are:

(12)

B. Monte Carlo Method Based Target Localization With the recent advances in computation power, Monte Carlo based methods have become useful tools for inference problems. In this paper, we use an importance sampling based Monte Carlo method [24] to approximate the posterior pdf, , as

(13)

(4) where the approximation is obtained as a weighted sum of particles. The particles are drawn from the prior distribution . The weights are calculated using the data and are proportional to the likelihood function (5) . where the initial weights are set as identical, i.e., The updated weight of each particle is the original weight multiplied by the likelihood function of the data. Since the sensors’ data are conditionally independent, we have for . The particle weights are then normalized as (6)

(7)

This results in the location estimate

given by (8)

C. Performance Metrics In this paper, we use PCRLB and posterior Fisher Information Matrix (FIM) as the performance metrics to analyze the estimation performance [18], [25]. Let be an estimator of the target location . Then, the covariance matrix of the estimation error is bounded below by the PCRLB, ,

(14) where sends strategy.

for is the probability that a sensor . This value depends on Byzantines’ attacking

III. LOCALIZATION IN THE PRESENCE OF BYZANTINE SENSORS A. Independent Attack Model For a major part of this work, we assume that the Byzantines attack the network independently. In an independent attack, each Byzantine sensor attacks the network by relying on its own observation without any knowledge regarding the presence of other Byzantines or their observations. Let the number of Byzantines present in the network be . For an honest sensor, , whereas for the Byzantines, we assume that they flip their quantized binary measurements with probability . Therefore, under the Gaussian noise assumption, the probability that is given by (15)

(16) where is the complementary cumulative distribution function of a standard Gaussian distribution defined as

(9) In (9),

The probability of a sensor sending a quantized value ‘1’ is given by

is the posterior FIM [18] given as (10) (11)

(17)

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Proposition 3.1: Under independent attack, the PCRLB is given by , where is the posterior FIM whose elements are given by

(18)

(19)

(20) where is given in (17). Proof: The proof follows from the definition of (10)–(14) and using the following

given in

(21) (22)

It can be observed that when , i.e., when all the sensors are honest, the above expression simplifies to the special case of where is the Fisher information matrix derived by Niu et al. in [11] for the case of target localization using quantized data in the absence of Byzantines. B. Blinding the Fusion Center The goal of Byzantines is naturally to cause as much damage to the functionality of the FC as possible. We call the event of causing the maximum possible damage as ‘Blinding’ the FC which refers to making the FC incapable of using the data from the local sensors to estimate the target location. This is clearly the case when the data’s contribution to posterior Fisher Information matrix, , approaches zero. In this scenario, the best the FC can do is to use the prior to estimate the location. In other words, approaches the prior’s contribution to posterior Fisher Information, or the PCRLB approaches . Since PCRLB and FIM are matrix-valued and are functions of , the blinding condition corresponds to the trace of PCRLB tending to or the determinant of FIM tending to . That is, is defined as (23) or (24) A closed form expression for can be derived and further analysis of the localization process in the presence of Byzantines can be carried out if all the honest sensors are

identical and similarly all the Byzantines are identical. In this case, all the honest sensors use the same local threshold and all the Byzantines use . 1) Byzantines Modeled as a Binary Symmetric Channel (BSC): From the FC’s perspective, the binary data received from the local sensor is either a false observation of the local sensor with probability or a true observation with probability . Therefore, the effect of Byzantines, as seen by the FC, can be modelled as a Binary Symmetric Channel (BSC) with transition probability . It is clear that this virtual ‘channel’ affects the PCRLB at the FC, which is a function of . It has been shown in the literature [26] that the Cramér-Rao Lower Bound (CRLB) of the localization process approaches infinity when this transition probability approaches irrespective of the true location of the target . This result means that the data’s contribution to posterior Fisher Information approaches 0 for . Observe that higher the probability of flipping of the Byzantines , the lower the fraction of Byzantines required to ‘blind’ the FC. So, the minimum fraction of Byzantines, , is corresponding to . In order to bring down the network, the Byzantines need to be at least 50% in number and should flip their quantized local observations with probability . Another interpretation of this problem can be made from the Information Theoretic perspective. Since the Byzantines’ effect is modeled as a BSC, the capacity of this channel is where is the Binary Entropy Function given by (25) The FC receives non-informative data from the sensors or becomes ‘blind’, when the capacity approaches 0 which happens or . Following the discussion above, we when have and . It can also be observed that the data’s contribution to and elements of given by (18) and (20) become 0 when . Once again, we get and as the optimal attack strategy to blind the FC. Due to this observation, in the remainder of the section, we assume that the Byzantines flip their observations with probability 1, i.e., . C. Best Honest and Byzantine Strategies: A Zero-Sum Game When , the fraction of Byzantine sensors in the network, is greater than or equal to , attackers will be able to ‘blind’ the FC completely. But when is not large enough to ‘blind’ the FC, the Byzantine sensors will try to maximize the damage by making either as large as possible or as small as possible. In contrast, the FC will try to minimize or maximize . This will result in a game between the FC and each Byzantine attacker where each player has competing goals. Each Byzantine sensor will adjust its threshold to maximize or minimize while the FC will adjust the honest sensor’s threshold to minimize or maximize . Thus, it is a zero-sum game where the utility of the FC is (or ) and the utility of the Byzantine sensor is (or ) [27]. More formally, let us consider and denote as the cost function adopted by the honest sensors. Let and denote the best threshold


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(strategy) of the honest and the Byzantine sensors, respectively. For a given , is computed as (26) Similarly, for a given

,

is computed as (27)

The solutions to (26) and (27) characterize the Nash equilibria which are defined as follows [27]. Definition: A (pure) strategy for the honest sensor is a Nash equilibrium (NE) if (28) Similarly, a (pure) strategy equilibrium (NE) if

for the Byzantine sensor is a Nash

Fig. 2. Plot of

versus .

(29) In a zero-sum game, the best strategy for both players is the saddle point, at which none of the players has the incentive to change their strategy. The saddle point for this problem given by (26) and (27) can be found using traditional methods. First, we find the set of stationary points of defined by , (30) , is the one at which the Hessian maThe saddle point, trix is indefinite, i.e., the determinant of the Hessian matrix is negative,

Fig. 3. Plot of

versus .

(31) Note that the above expressions are with respect to . Similar analysis can be carried out when is replaced with as the performance metric. D. Numerical Results In this subsection, we present simulation results in support of our analysis of Byzantines in a localization problem. We consensors are randomly sider the WSN model where deployed in a square region of interest where the target is located. The target’s location is randomly generated from the prior with such that its 99% confidence region covers the entire ROI. There are Byzantine sensors present in the network who try to manipulate the data and send falsified information to the FC. We assume that the power at the reference point is . The signal amplitude at the local sensor is corrupted by AWGN with standard deviation . In Figs. 2 and 3, we plot the values of and against in the case of an independent attack with . The figures show that when , the approaches and approaches . This shows

that is equal to 1/2, i.e., unless the number of Byzantine sensors is greater or equal to 50 percent of the total number of sensors, the FC can not be made blind under independent attack. This supports our theoretical analysis regarding the PCRLB approaching when , which is the transition probability of the BSC model, approaches . These results can be reproduced for different values of and . We omit them for the sake of brevity. Fig. 4 shows the increase in Mean Square Error (MSE) of the target estimate with . As the fraction of Byzantines increase, the MSE increases as illustrated in Fig. 4. Since the MSE is lower bounded by , the plot in Fig. 4 is always above the plot of versus in Fig. 2. As discussed in Section III-C, when , there exists a zero-sum game between the FC and Byzantine sensors, in which the optimal strategies are given by the saddle points (equilibrium points). In Figs. 5 and 6, we plot with varying thresholds for and we observe that there exists a saddle point which provides optimal strategies for both types of sensors. The saddle point , in this particular example, is at . This result is intuitive as Byzantines flip their decision with probability 1. Therefore, the best

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Fig. 7. Plot of versus honest and Byzantine sensor’s threshold, The existence of a saddle point is clear.

Fig. 4. Plot of MSE versus .

Fig. 5. Surface plot of versus honest and Byzantine sensor’s and . The existence of a saddle point is clear. threshold,

Fig. 8. Plot of contour of the surface of

and

.

shown in Fig. 7.

that the two objective functions used in the anlaysis ( and ) need not always result in the same operational point in general. However, in this particular example, this value turns out to be the same, irrespective of the performance metric. IV. BYZANTINE IDENTIFICATION

Fig. 6. Contour plot of the surface of

shown in Fig. 5.

strategy for the Byzantines would be to use the same best response of the Honest sensors and then flip them with probability 1. Similar results can be obtained for different values of . Figs. 7 and 8 show similar game theoretic analysis results for the case of as the performance metric. The optimal values for this case are the same . Thus, there exist saddle points which yield the optimal strategies for both the FC and Byzantine attackers. We would like to point out

The first scheme proposed for the mitigation of independent Byzantine attacks is to identify the Byzantines by observing their behavior over time. In the preceding sections, we have shown how the optimal identical thresholds are designed based on the PCRLB for the target location estimation error. We assumed that all the Byzantines use an identical threshold and all the honest sensors use an identical threshold . It can be seen in the numerical results presented in Section III-D that the optimal strategy for the Byzantines and the honest sensors is to use . Here, we propose a scheme to identify the Byzantines present in the network. This scheme is similar to our work in [14] for the cooperative spectrum sensing problem. The basic idea of this identification scheme is to observe a sensor’s behavior over time and decide on whether it behaves closer to an honest or a Byzantine sensor [14]. This is done by comparing the observed values of to the or expected values of . We estimate


in an iterative manner where calculated as

at the

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iteration is

(32) and can be calculated using (15) and (16). The values of It is important to observe here that these values require the location which is unknown. These values in our scheme are initialized by using a coarse estimate of the location, . In order to obtain an initial coarse estimate, , we follow a procedure similar to the one proposed by Masazade et al. in [23]. In this procedure, it is assumed that there are anchor nodes in the network that have a higher level of security and thereby treated as honest nodes. The initial data is collected at the FC (at time ) from these anchor nodes and the MMSE estimate is obtained using the procedure described in Section II-B. For the remainder of this section, we assume the following model. At every iteration of the algorithm, the sensors send their 1-bit data using the pre-designed identical threshold value. Using these sensors’ data of previous time instants, the FC iteratively updates . The estimate is computed at every iteration and a sensor is declared honest or Byzantine based on the test statistic

Fig. 9. Number of wrongly identified sensors with time.

(33) which is the ratio of the deviations between the estimated behavior of the sensor and the expected behavior of an honest sensor, to the estimated behavior of the sensor and the expected behavior of a Byzantine sensor. The FC declares a sensor as a Byzantine at time instant if is greater than 1. This would mean that the sensor behaves closer to a Byzantine than an honest sensor. The advantage of this scheme is that it is adaptive such that the sensor’s declaration regarding the sensor being honest or Byzantine is based on data from previous time instants. It is important to note that the above formulation (33) is purely heuristic and no optimality is claimed. It is a suboptimal and an easy to implement formulation. The rationale behind such a formulation is that in traditional classification/pattern recognition problems, the decision regarding the type (of a sensor) is made by observing the behavior (of the sensor). A sensor is declared as Type A, if it behaves closer to the expected behavior of Type A. In our problem, the behavior is characterized by and we make a decision by comparing the closeness of this behavior to the expected behavior ( or ). It is important to note that, in this section, we propose a Byzantine identification scheme but do not discuss the estimation procedure. The estimation is done after a final decision is made regarding the identity of the Byzantines. The time instant when a final decision is made depends on the particular scenario and is a design criterion. Once, the final decision is made, the data from the sensors identified as Byzantines can be re-flipped and used in the estimation process similar to the adaptive fusion rule designed in [14] for the problem of distributed spectrum sensing in the presence of Byzantines. In the following sub-section, we show with numerical simulations that, for our particular

Fig. 10. Estimate of

with time.

example, most of the Byzantines can be identified in around 100 iterations using the proposed Byzantine Identification Scheme. A. Numerical Results We present the effectiveness of our identification scheme through numerical results. For this scenario, we use the same sensors uniformly deployed in a network with 11 11 area as shown in Fig. 1. The fraction of the Byzantines is , i.e., 40 out of 100 sensors are malicious. We assume that there are anchor nodes as shown in Fig. 1. Each sensor measures , the signal amplitude corrupted by AWGN with . The power at the reference distance is . The Byzantines and honest sensors use thresholds , which are the optimum thresholds found in Section III-D assuming that the prior distribution of the target location is a normal distribution such that the region of interest (ROI) includes confidence region. Each Byzantine flips its binary observation with probability 1, before sending it to the FC. The results of our proposed Byzantine identification scheme for a specific target location realization can be seen in Figs. 9 and 10. In Fig. 9, the number of wrongly identified sensors (an Honest sensor wrongly identified as a Byzantine and vice-versa) is plotted as a function of time for different

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TABLE I MISMATCHES VERSUS MSE OF THE INITIAL COARSE ESTIMATE FOUND USING ANCHOR NODES.

values of , the number of anchor nodes. The value of has been varied to observe the effect of the roughness of the coarse estimate on the Byzantine Identification scheme. The graph shows that most of the sensors are correctly identified with time. The number of wrongly identified sensors is maximum for and minimum for as expected since the coarse estimate is more accurate when the number of anchor nodes is larger. For , the number of wrongly identified sensors converges to the value of 14 (out of a total of 100 sensors). From this figure, it can be inferred that is a reasonable number of anchor nodes to be used. In Fig. 10, the estimated given by , where is the number of sensors identified as Byzantines, is plotted as a function of time for a network with anchor nodes placed in star formation as shown in Fig. 1. As can be seen from Fig. 10, converges to the value of 0.42. From these figures, it can be inferred that 8 honest nodes (out of 60 honest nodes in the network) have been falsely identified as Byzantines and 6 Byzantines (out of 40 Byzantines present in the network) have been mis-identified as honest nodes. It is important to note that the performance of the proposed scheme depends on the MSE of the initial coarse estimate. In all the simulations performed, the MSE of the initial coarse estimate is sq units and in Table I, we show the effect of MSE of the estimate on the performance of the identification scheme when anchor nodes are used.

Fig. 11. Boundary around which the sensors are ‘ambigious’.

Since, the Byzantines flip their decision with probability 1, it cannot be inferred if it was an honest sensor genuinely sending 1 with probability 0.5 or a Byzantine sensor sending 1 with probability 0.5 after flipping its decision. Furthermore, since the received amplitude is constant for sensors, they happen to form a circle around the true target location. This ‘hard’ decision regarding the type of sensor results in a high probability of misidentification of the sensors in the region shown in Fig. 11. These sensors can, therefore, be categorized as . The ratio of the number of these ambiguous sensors on the boundary region to the total number of sensors in a network may be small in practice. In this case, they have negligible impact on estimation performance. However, this number depends on the relative positioning of the target with the local sensors and on the threshold used for quantization at the local sensors. The width of the uncertain zone also depends on sensor noise variance. If this ratio is high, then the estimation performance might be severely degraded. Therefore, we need to design a scheme where the information from these sensors can be utilized for localization. This problem of boundary sensors can be alleviated if we use non-identical quantizers discussed in the following section, in conjunction with our identification scheme.

B. Discussion The proposed scheme does not depend on the fraction of present in the network and, therefore, the Byzantines scheme performs well for all possible values of . It detects most of the Byzantines in the network. A major limitation of this scheme is that some sensors can not be identified reliably as Byzantine or honest. It can be observed that the sensors for which this scheme fails are the sensors for which the test statistic is close to 1. This happens when or is close to 0.5. These are the sensors for which corresponding to some constant . These sensors lie on the boundary region as shown in Fig. 11. These sensors evade the identification process due to the following reason. An sensor is defined as the sensor , for which the quantization threshold is approximately equal to its received amplitude . Therefore, for the Gaussian noise model assumed in the paper, for an sensor irrespective of whether it is an honest sensor or a Byzantine. This implies that these sensors send 1 with approximate probability 0.5.

V. DYNAMIC NON-IDENTICAL QUANTIZERS MITIGATION OF BYZANTINES

FOR THE

In this section, we introduce our non-identical quantizer design scheme to tackle the ambiguity caused by boundary sensors when identical quantizers are used. The estimation model in this section is sequential and described as follows. At every iteration , all the N sensors send their one-bit data regarding the location of the target using their local thresholds. At time , the local sensors use the optimal identical thresholds designed in Section III-C for quantization. The FC estimates the target location at every time instant using Monte-Carlo based MMSE estimation described in Section II-B and broadcasts this estimate information to the local sensors. The essential difference between this new scheme and the previous one is the feedback between the FC and the local sensors. In other words, according to this new scheme, local sensors update their quantizers based on the feedback information (location estimate) they receive from the FC. In order to understand the design, we first


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investigate the case where there are no Byzantines and all the sensors are honest.

Proposition 5.1: The posterior Fisher Information about the signal amplitude, , at a given sensor is given by

A. Honest Nodes Only

(40)

Niu et al. in [11] analyzed the location estimation problem and proposed a threshold design method by minimizing the CRLB on the location estimation error, where the optimal thresholds are found by

where and

is the pdf of the signal amplitude

at the sensor

(34) (41) where is the trace of the CRLB matrix. In our paper, since PRCLB is the performance metric, our optimization problem can be written as (35) This minimization problem is a non-convex vector minimization problem over variables. Here, we simplify this problem by making every threshold a function of signal amplitude at the sensor and assuming that all the sensors follow the same functional dependence, i.e, (36) where is some function and is the amplitude of the observation at the sensor. Since the value of is not known, we update each threshold iteratively as (37) where is the expected amplitude at the previous time instant which is estimated by using the location estimate of the iteration, . The minimization problem now becomes a variational minimization problem (38) This is still a difficult problem as is a function of the target’s location which is unknown. Therefore, we propose a heuristic approach similar to the one used in [11] which is explained next. 1) Heuristic Approach for Non-Identical Quantizer Design: It is important to observe that all the required information about the target location is completely available in the signal amplitudes ’s. Therefore, intuitively, if we can accurately estimate from for , then we can accurately estimate the target location. At any given sensor, this estimation problem is to estimate using the log-likelihood function given by

(39) where is the signal amplitude at that sensor, is the estimate of the amplitude and is the corresponding quantized bit-value.

is the data’s contribution to posterior FI and is a constant representing prior’s contribution to the posterior FI which is given by (42) Proof: We defer the proof of Proposition 5.1 to Appendix A which is the proof of Proposition 5.3. Proposition 5.3 is a more general result such that when , we get the result of Proposition 5.1. We skip further details for the sake of brevity of the paper. Now the threshold function can be designed such that it maximizes the posterior Fisher information. Proposition 5.2: The posterior Fisher Information is maximized when the threshold function is . Proof: Since the second term on the right hand side of (40) is not a function of , we can only consider the first term. The maximization of the first term with respect to is a functional maximization problem and it can be solved using the Euler-Lagrange equation from variational calculus [20] given by (43) where

is the first derivative of with respect to . Since is independent of , the Euler-Lagrange equation reduces to or with respect to . From for to be a constant (41), this gives the result that with respect to .1 Such an analysis was also carried out numerically by Ribeiro et al. in [22], where the authors plotted the CRLB against to show that minimizes the CRLB or in other words maximizes the Fisher information. Therefore, the thresholds are designed such that, which means that the threshold of the sensor at time is the estimated amplitude at this sensor at the previous time instant . This amplitude is estimated by using the previous time instant’s location estimate, , which is broadcast by the FC to the local sensors. It is important to note that this result is expected as such a threshold design will ideally yield the maximum entropy as it results in . 1Interested reader is referred to Section II.2 of [20] for further information on Euler-Lagrange Equation and Variational Calculus.

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B. Game Between Honest and Byzantine Nodes The situation changes when there are honest nodes as well as Byzantine nodes present in the system. Since the Byzantines’ aim is to deteriorate the system performance, they do not necessarily use the threshold design specified by the FC. Instead, Byzantines use their own threshold function and they flip their decisions with probability . Let the threshold function of the honest sensors be . Proposition 5.3: The posterior Fisher Information about the signal amplitude, , at a given sensor in the presence of Byzantines is given by (44) where the constant is given in (42), signal amplitude at the sensor, and

is the pdf of the

(45) with is defined as the probability of the sensor sending 1 as seen by the FC

(46) Proof: The proof is given in Appendix A. In this case, the problem can again be modeled as a zero-sum game where the objective of the FC is to maximize the posterior Fisher Information whereas the objective of the Byzantine sensor is to minimize . This problem can be solved by examining the expression of in (44). Under the scenario that each sensor behaves independently, it can be shown that the Fisher Information (FI) given by (45) is maximized when honest nodes set their thresholds as regardless of the value of . For Byzantines, there are two cases to be considered: and . For , the Byzantines, who try to minimize this posterior FI, achieve the minimization similarly by setting regardless of the value of . This result is expected as the Byzantines flip their observations with a probability . It is important to observe that when , it implies that the honest nodes send with probability approximately equal to . Also, observe that if the Byzantines also use this thresholding scheme, the probability of a Byzantine sending 1 is

(47)

, irrespective of the value which becomes , when of . Similar to the honest nodes, the Byzantines as well maximize the entropy and eventually benefit the network in the localization task as discussed earlier. This result can also be interpreted by using the BSC modeling of Byzantines. In this model, the honest sensors try to transmit the data (0/1) such that the capacity is achieved. The capacity is achieved when the input follows uniform distribution. Our threshold scheme makes , thereby achieving capacity of this ‘Byzantine’ BSC. For , the Byzantines need to use , always send a 0 or 1. However, in this case, the network would again eventually overcome the actions of Byzantines as the FC can easily identify the Byzantines using our proposed Byzantine identification scheme explained in Section IV. We would like to point out here that we do not propose any final strategies for the Byzantines in this paper. Instead, we show that any non-honest strategy used by the Byzantines can be identified by the FC and, therefore, the effect of Byzantines can be mitigated. Therefore, utilizing dynamic non-identical quantizers ensures that the Byzantines become ‘ineffective’ in their attack strategy and the network eventually mitigates the actions of Byzantines. It is also important to observe that this particular framework ensures that the network is robust for any fraction of the Byzantines in the system. The trade-off is that the FC needs to broadcast the target location estimate at each iteration which would increase the system complexity and consume more system resources compared to using static identical quantizers. Static thresholds are set only once in the beginning and they stay constant throughout the estimation process. In the identification procedure, the FC tries to identify sensors based on their observed behavior over time, which requires each sensor to send their decisions to the FC in a continuous manner. In contrast, dynamic thresholds are adjusted dynamically at each sensor using the feedback from the FC. As one would expect, feedback not only improves estimation performance but it also makes the network more robust to Byzantine attacks. C. Numerical Results We now show how the proposed dynamic non-identical quantizer design is superior to the static identical quantizer design. For this scenario, we use a network with sensors uniformly deployed in a 11 11 area same as before (refer to Fig. 1). The power at the reference distance is again set as . This set-up yielded an optimal identical threshold as . During the first iteration, the location is estimated using identical thresholds. After obtaining , the estimates in the next iterations are calculated by using the proposed dynamic non-identical threshold design scheme as . MMSE estimators are implemented using the importance sampling method as described in Section II-B with particles. Fig. 12 shows the mean squared error (MSE) values of the estimators for 1000 Monte-Carlo realizations of compared to the MSE of those using identical thresholds. As can be seen from Fig. 12, the estimation error reduces significantly (by around 70% in 3 iterations) when non-identical dynamic threshold quantizers are used as compared to the identical threshold quantizers. This motivates the


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sensor as possible. However, target is as far away from the if the same sensor behaved as a Byzantine it is reasonable to assume that a sensible Byzantine would send a 1 to the FC with as high a probability as possible, i.e., . Similarly, if the sensor was honest and , then it would mean that the target is as close to the sensor as possible and if the same sensor behaved as a Byzantine, under similar assumption as before, it would send a 1 to the FC with as low a probability as possible, i.e., . This gives us two equations in two unknowns, and : (49) and Fig. 12. MSE comparison of the two schemes: Identical Threshold scheme and Non-Identical Dynamic Threshold scheme.

(50) After solving (49) and (50), we get

honest sensors to use the designed non-identical thresholds. As discussed above, the Byzantines are ineffective in this proposed scheme. VI. COLLABORATIVE ATTACK Next, we consider the case of Byzantine attacks where all the malicious sensors communicate with each other and attack the network in a coordinated fashion. In a collaborative attack, Byzantines collaborate to deteriorate the network’s estimation performance and attack the network after colluding with others. Here again, we assume to be the fraction of Byzantines present in the network. Analysis of the collaborative attack is significantly more complicated than the independent case. Here, we provide a reasonable lower bound for , namely , for this case. In order to find the lower bound for , we assume that the exact location of target can be perfectly learned by Byzantine sensors due to collaboration. Thus, we consider the case where Byzantine attackers know the location of the target and use this information collaboratively to improve their attack on the network. Let us first consider the case where each sensor uses identical thresholds. In such a case, the optimal strategy for the Byzantine sensors will be to send based on the true value and their locations. For a given sensor , its location , its observation model, and its threshold , the probability of the sensor sending a quantized value 1 as seen by the FC is:

(51) where is the fraction of malicious sensors required to make sensor non-informative to the FC. In this case, we have the following at the FC,

(52) which is a constant independent of . Thus, when for a particular honest sensor , the attackers can have fraction of Byzantine sensors act like honest nodes and have the rest Byzantine sensors send 1 with probability as below:

This causes the FC to become incapable of utilizing the received sensor to estimate the target location. information from the In order to guarantee that the FC cannot obtain any useful information from any of its sensors, the minimum required is given as (53)

The Byzantines would like to so that the FC mation received from this received from the sensor mate the target location. This the value a spect to . Let was honest and

(48) design their variables and becomes ‘blind’ to the inforsensor, i.e., the information does not help the FC estican be achieved by making constant value with reand the . Then for the sensor, if it , it would mean that the

, for the collabThis provides us with a lower bound, orative case under the identical threshold scheme. For the Collaborative Attack case, it can be observed that given by which implies that which is (51) is always the obtained in the Independent Attack case. This shows that if a strategy exists to obtain this lower bound, then the fraction of sensors required to blind the FC would decrease in the Collaborative Attack case as compared to the Independent Attack case. A similar observation was made by Rawat et al. in

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[13] for the primary user detection for cognitive radio networks in the presence of Byzantines. When each sensor uses the dynamic non-identical quantizer design scheme proposed earlier, the analysis is extremely difficult, however, we can conjecture the following. The largest deviation in the current estimate caused by the Byzantines is limited to the confidence interval of the previous estimate since, otherwise, they would be easily identified as outliers at the FC. This limits the attacking power of each Byzantine and hence, more number of Byzantines are required to cause the same blinding effect at the FC. We conjecture that , where denotes the fraction of Byzantines required to blind the FC under dynamic non-identical quantizer scheme.

protection of Byzantines from being identified. This analysis is more difficult to formulate and will be investigated in our future work. This would be an interesting problem as it is a more realistic scenario where malicious nodes would try to hide their malicious behavior. We would also like to extend this work to target tracking where the target is no longer stationary and the goal is to track its trajectory using Bayesian sequential estimation methods [28] in the presence of Byzantine attacks. APPENDIX PROOF OF PROPOSITION 5.3 as

Let the probability of a sensor sending a bit value 1 be defined .

VII. DISCUSSION In this paper, we investigated the problem of Byzantine attacks on a wireless sensor network whose task is target localization using binary quantized data in a Bayesian framework. For the independent attack case, we proposed an optimal strategy for both the Byzantines and the FC for the target localization task. We also defined and calculated the fraction of Byzantine sensors needed to completely ‘blind’ the FC. In addition, we analyzed the situation when the Byzantines do not have enough resources to ‘blind’ the FC . In such a case, we formulated the problem as a zero-sum game and obtained the optimal strategies using numerical techniques. Furthermore, we proposed Byzantine mitigation schemes to make the network robust to such Byzantine attacks. Under the first framework where each sensor uses an identical local quantizer, we showed that our proposed Byzantine Identification scheme is able to identify most of the Byzantines regardless of their number. In order to further improve the performance, we considered a different framework where each sensor uses a non-identical local quantizer. Under this framework, we have developed a dynamic quantizer design scheme which not only improves the estimation performance significantly but also makes the Byzantines ‘ineffective’ when used in conjunction with our identification scheme. It is also important to notice that our proposed frameworks do not depend on the fraction of malicious sensors, i.e; they are robust to the number of Byzantines in the network. For the collaborative attack case where all the Byzantine sensors communicate with each other to have the maximum damage, we found the lower bound on the number of Byzantine sensors required to completely ‘blind’ the FC. In this paper, the Byzantines’ sole aim is to bring down the network and make the FC blind to the information sent by the local sensors. This formulation results in a mathematical utility function which only contains the condition that approaches 0. For this formulation, it has been found that the optimal attack for the Byzantines is to always flip their local result with probability 1. One interesting problem is the analysis of ‘Smart’ Byzantines which, besides aiming at bringing down the network, also aim at protecting themselves from being detected. This analysis needs a mathematical formulation, where along with the utility function containing the ‘blinding’ aspect of Byzantines, there is an additional constraint defining the

(54) where is the probability that the sensor is a Byzantine, and similarly, is the probability that the sensor is honest. Here, denotes the probability of flipping by the Byzantines. The data’s contribution to the posterior Fisher Information is given by (55) where

. Let . Then

and (56) Note the fact that ,

has been used in (56). Since

(57) where the relation (58) has been used. From (55), (56) and (57), we get the desired result.


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Note that when , the data’s contribution to posterior Fisher Information in (45) becomes

(59) which is the result of Proposition 5.1. ACKNOWLEDGMENT The authors are grateful for the valuable comments and suggestions made by the reviewers which helped improve the presentation of the paper. REFERENCES [1] A. Boukerche, H. A. B. Oliveira, E. F. Nakamura, and A. A. F. Loureiro, “Secure localization algorithms for wireless sensor networks,” IEEE Commun. Mag., vol. 46, no. 4, pp. 96–101, Apr. 2008. [2] Z. Li, W. Trappe, Y. Zhang, and B. Nath, “Robust statistical methods for securing wireless localization in sensor networks,” in Proc. Int. Workshop Inf. Process. Sens. Netw., Apr. 2005, pp. 91–98. [3] Y. Zhang, W. Liu, and Y. Fang, “Secure localization in wireless sensor networks,” in Proc. IEEE Military Commun. Conf. (MILCOM), Oct. 2005, pp. 3169–3175. [4] L. M. Kaplan, L. Qiang, and N. Molnar, “Maximum likelihood methods for bearings-only target localization,” in Proc. Int. Conf. Acoust., Speech, Signal Process. (ICASSP), Salt Lake City, UT, USA, May 2001. [5] J. Chen, R. Hudson, and K. Yao, “A maximum likelihood parametric approach to source localization,” in Proc. Int. Conf. Acoust. Speech, Signal Process. (ICASSP), Salt Lake City, UT, USA, May 2001, vol. 5, pp. 3013–3016. [6] S. Marano, V. Matta, P. Willett, and L. Tong, “DOA estimation via a network of dumb sensors under the SENMA paradigm,” IEEE Signal Process. Lett., vol. 12, no. 10, pp. 709–712, 2005. [7] S. Marano, V. Matta, P. Willett, and L. Tong, “Support-based and ML approaches to DOA estimation in a dumb sensor network,” IEEE Trans. Signal Process., vol. 54, no. 4, pp. 1563–1567, Apr. 2006. [8] D. Li and Y. H. Hu, “Energy-based collaborative source localization using acoustic micro-sensor array,” EURASIP J. Appl. Signal Process., vol. 2003, no. 4, pp. 321–337, 2003. [9] X. Sheng and Y. H. Hu, “Maximum likelihood multiple-source localization using acoustic energy measurements with wireless sensor networks,” IEEE Trans. Signal Process., vol. 53, no. 1, pp. 44–53, Jan. 2005. [10] N. Patwari and A. Hero, “Using proximity and quantized RSS for sensor localization in wireless networks,” in Proc. 2nd Int. ACM Workshop Wireless Sens. Netw. Appl., San Diego, CA, USA, Sep. 2003, pp. 20–29. [11] R. Niu and P. K. Varshney, “Target location estimation in sensor networks with quantized data,” IEEE Trans. Signal Process., vol. 54, no. 12, pp. 4519–4528, Dec. 2006. [12] S. Marano, V. Matta, and L. Tong, “Distributed detection in the presence of Byzantine attacks,” IEEE Trans. Signal Process., vol. 57, no. 1, pp. 16–29, Jan. 2009. [13] A. Rawat, P. Anand, H. Chen, and P. K. Varshney, “Collaborative spectrum sensing in the presence of Byzantine attacks in cognitive radio networks,” IEEE Trans. Signal Process., vol. 59, pp. 774–786, Feb. 2011. [14] A. Vempaty, K. Agrawal, H. Chen, and P. K. Varshney, “Adaptive learning of Byzantines’ behavior in cooperative spectrum sensing,” in Proc. IEEE Wireless Commun. Netw. Conf. (WCNC), Cancun, Mexico, Mar. 2011, pp. 1310–1315. [15] O. Kosut and L. Tong, “Distributed source coding in the presence of byzantine sensors,” IEEE Trans. Inf. Theory, vol. 54, no. 6, pp. 2550–2565, Jun. 2008.

[16] O. Kosut, L. Tong, and D. Tse, “Nonlinear network coding is necessary to combat general Byzantine attacks,” in Proc. 47th Ann. Allerton Conf. Commun., Contr., Comput., Urbana, IL, USA, Oct. 2009, pp. 593–599. [17] K. Agrawal, A. Vempaty, H. Chen, and P. K. Varshney, “Target localization in sensor networks with quantized data in the presence of Byzantine attacks,” in Proc. Asilomar Conf. Signals, Syst. Comp., Pacific Grove, CA, USA, Nov. 2011, pp. 1669–1673. [18] H. L. V. Trees and K. L. Bell, Bayesian Bounds for Parameter Estimation and Nonlinear Filtering/Tracking. Hoboken, NJ, USA: WileyIEEE , 2007. [19] A. Vempaty, O. Ozdemir, and P. Varshney, “Mitigation of Byzantine attacks for target location estimation in wireless sensor networks,” in Proc. 46th Ann. Conf. on Inf. Sci. Syst. (CISS), Princeton, NJ, USA, Mar. 2012. [20] B. Van Brunt, The Calculus of Variations. New York, NY, USA: Springer, 2004. [21] C. Meesookho, U. Mitra, and S. Narayanan, “On energy-based acoustic source localization for sensor networks,” IEEE Trans. Signal Process., vol. 55, no. 1, pp. 365–377, Jan. 2008. [22] A. Ribeiro and G. B. Giannakis, “Bandwidth-constrained distributed estimation for wireless sensor networks—Part I: Gaussian case,” IEEE Trans. Signal Process., vol. 54, no. 3, pp. 1131–1143, Mar. 2006. [23] E. Masazade, R. Niu, and P. K. Varshney, “Energy aware iterative source localization schemes for wireless sensor networks,” IEEE Trans. Signal Process., vol. 58, no. 9, pp. 4824–4835, Sep. 2010. [24] A. Doucet and X. Wang, “Monte Carlo methods for signal processing: A review in the statistical signal processing context,” IEEE Signal Process. Mag., vol. 22, no. 6, pp. 152–170, Nov. 2005. [25] H. V. Trees, Detection, Estimation and Modulation Theory. New York, NY, USA: Wiley, 1968, vol. 1. [26] O. Ozdemir, R. Niu, and P. K. Varshney, “Channel aware target localization with quantized data in wireless sensor networks,” IEEE Trans. Signal Process., vol. 57, no. 3, pp. 1190–1202, Mar. 2009. [27] D. Fudenberg and J. Tirole, Game Theory. Cambridge, MA, USA: MIT Press, 1991. [28] O. Ozdemir, R. Niu, and P. K. Varshney, “Tracking in wireless sensor networks using particle filtering: Physical layer considerations,” IEEE Trans. Signal Process., vol. 57, no. 5, pp. 1987–1999, May 2009.

Aditya Vempaty (S’12) was born in Hyderabad, India, on August 3, 1989. He received the B.Tech. degree in electrical engineering from the Indian Institute of Technology (IIT), Kanpur, in 2011, with academic excellence awards for consecutive years. Since 2011, he has been working towards the Ph.D. degree in electrical engineering at Syracuse University, Syracuse, NY. He is a Graduate Research Assistant with the Sensor Fusion Laboratory, Syracuse, where he was also an Undergraduate Research Intern during summer 2010. His research interests include statistical signal processing, detection and estimation theory, security in sensor networks, and data fusion.

Onur Ozdemir (S’06–M’10) was born in Ankara, Turkey, in 1980. He received the B.S. degree in electrical and electronics engineering from Bogazici University, Istanbul, Turkey, in 2003, and the M.S. and Ph.D. degrees in electrical engineering from Syracuse University, Syracuse, NY, in 2004 and 2009, respectively. He is a Research Scientist with ANDRO Computational Solutions, Rome, NY. While at Syracuse University, he was a Research Assistant with the Sensor Fusion Laboratory. He was an Intern at Mitsubishi Electric Research Laboratories, Cambridge, MA, in 2007 and 2009. His current research interests include statistical signal processing, data fusion, and wireless communications.

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Keshav Agrawal received the B.Tech. degree in electrical engineering in 2011 from the Indian Institute of Technology, Kanpur. He held a Student Researcher position at Syracuse University, Syracuse, NY, in summer 2010. He was a Research Assistant with the Hong Kong Polytechnic University during summer 2011. Since then, he has been pursuing the M.S.E.E. degree at the University of California, Los Angeles. His research interest lies in signal processing and communication including sensor array processing, cognitive radio, and distributed inference.

Hao Chen (M’05) received the B.S. and M.S. degrees from the University of Science and Technology of China (USTC), Hefei, in 1999 and 2002, respectively, and the Ph.D. degree from Syracuse University, Syracuse, NY, in 2007, all in electrical engineering. He is currently an Assistant Professor in Electrical and Computer Engineering, Boise State University, Boise, ID. Prior to joining Boise State in 2010, he was with Syracuse University as a Postdoctoral Research Associate and then a Research Assistant Professor. His research interests include statistical signal and image processing, and communications. Dr. Chen received the All University Doctoral Prize from Syracuse University for his Ph.D. dissertation.

Pramod K. Varshney (S’72–M’77–SM–82–F’97) was born in Allahabad, India, on July 1, 1952. He received the B.S. degree in electrical engineering and computer science (with highest honors), and the M.S. and Ph.D. degrees in electrical engineering from the University of Illinois at Urbana-Champaign in 1972, 1974, and 1976 respectively. From 1972 to 1976, he held teaching and research assistantships with the University of Illinois. Since 1976, he has been with Syracuse University, Syracuse, NY, where he is currently a Distinguished Professor of Electrical Engineering and Computer Science and the Director of CASE: Center for Advanced Systems and Engineering. He served as the Associate Chair of the department from 1993 to 1996. He is also an Adjunct Professor of Radiology at Upstate Medical University, Syracuse. His current research interests are in distributed sensor networks and data fusion, detection and estimation theory, wireless communications, image processing, radar signal processing, and remote sensing. He has published extensively. He is the author of Distributed Detection and Data Fusion (New York: Springer-Verlag, 1997). He has served as a consultant to several major companies. Dr. Varshney was a James Scholar, a Bronze Tablet Senior, and a Fellow while at the University of Illinois. He is a member of Tau Beta Pi and is the recipient of the 1981 ASEE Dow Outstanding Young Faculty Award. He was elected to the grade of Fellow of the IEEE in 1997 for his contributions in the area of distributed detection and data fusion. He was the Guest Editor of the Special Issue on Data Fusion of the IEEE PROCEEDINGS January 1997. In 2000, he received the Third Millennium Medal from the IEEE and Chancellor’s Citation for exceptional academic achievement at Syracuse University. He is the recipient of the IEEE 2012 Judith A. Resnik Award. He serves as a Distinguished Lecturer for the IEEE Aerospace and Electronic Systems (AES) Society. He is on the Editorial Board of the Journal on Advances in Information Fusion. He was the President of International Society of Information Fusion during 2001.