Location error estimation in wireless ad hoc networks

Ad Hoc Networks 13 (2014) 504–515

Contents lists available at ScienceDirect

Ad Hoc Networks journal homepage: www.elsevier.com/locate/adhoc

Location error estimation in wireless ad hoc networks Jeremy Gribben ⇑, Azzedine Boukerche School of Information Technology and Engineering, University of Ottawa, Ottawa, Ontario K1N 6N5, Canada

a r t i c l e

i n f o

Article history: Received 4 February 2013 Received in revised form 8 September 2013 Accepted 8 October 2013 Available online 18 October 2013 Keywords: Localization Location estimation CRLB Wireless Sensor network

a b s t r a c t Many ad hoc network applications rely on nodes having accurate knowledge of their geographic locations. However, inherent in all localization systems is a degree of error in computed positions, which can compromise the accuracy and efficiency of location dependent applications and protocols. We propose a scheme in which nodes estimate the amount of error present in their derived positions with a certain probability. Localization error variance is modeled with a function based on the calculated theoretical lower bound on estimator variance, given by the Cramér–Rao Lower Bound (CRLB). Probabilistic methods then use this variance model to estimate upper bounds on localization error, which are computed locally by wireless devices. Best fits between the model and the actual location error variance using both time of arrival (TOA) and received signal strength (RSS) distance measurements were determined by a least squares estimator over repeated localization simulations. The proposed method was used to accurately estimate location error at given probabilities in a multitude of randomly generated network topologies within ±10% of the actual localization error. Once known, estimates can be integrated into location dependent schemes to improve on their robustness to localization error. Ó 2013 Elsevier B.V. All rights reserved.

1. Introduction Wireless ad hoc networks have become increasingly important with the prevalence of wireless sensor networks (WSN) [1] and vehicular ad hoc networks (VANets) [2]. Many applications and protocols associated with these networks require precise location information as a precursor to their functioning, such as data mining in WSN, coverage, and routing. However, there is often a significant amount of positioning error associated with even the best localization systems [3], which can have a significant impact on the accuracy and efficacy of location-dependent applications. In this paper, we provide a means for wireless devices to probabilistically determine the amount of error present in their estimated positions for a given localization system, which can be incorporated into location sensitive

⇑ Corresponding author. Tel.: +1 6139838360. E-mail addresses: [email protected] (J. Gribben), [email protected] (A. Boukerche). 1570-8705/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.adhoc.2013.10.007

applications to improve on their robustness and overall effectiveness. A typical scenario for WSN consists of randomly deployed sensors collecting data and transmitting it to a base station for analysis [4]. If accurate location information is necessary for the proper interpretation of measured data, then inaccuracies of node positions can lead to false observations. By predicting the degree of localization error, one can assign a lower confidence or even reject sensed events associated with low position accuracy. Another fundamental problem in WSN is coverage, where we want to know if all points in a region are monitored by one or more sensors [5], so that additional sensors can be deployed to inadequately covered areas, or sensors can enter sleep mode to conserve energy in overly covered areas [6]. Most of these schemes assume that precise location information is available for calculation of coverage. However, in the presence of location errors, additional coverage holes or overly redundant sensor deployment can occur. With estimates on the amount of localization error, overly covered or under covered regions can be avoided. Location information

J. Gribben, A. Boukerche / Ad Hoc Networks 13 (2014) 504–515

is also useful for geographic routing [7], where data is routed based on geographic locations instead of network addresses. With location error estimation, nodes with larger position errors can be less used to avoid potentially inefficient paths. Location verification in secure localization schemes is another area of open research which aims to differentiate between errors due to malicious nodes, and error inherent to the localization system itself [8–10], the latter of which can be characterized by a suitable error estimation method. Finally, target tracking of mobile devices through an area using range and position information from other deployed nodes can involve very different levels of localization error depending on the available information in a given region [11]. Determining the amount of error in location estimates could thus help to guide decisions of mobile devices. For example, vehicles in a VANET would only have semi-automated driving and collision avoidance functionality available when highly accurate location information is available. Localization systems aim to determine the physical locations (coordinates) of all nodes in a network [3]. Most systems require a fraction of the nodes, called beacons or anchors, to know their positions a priori [12–15]. Other systems do not have such a requirement, but instead employ a relative coordinate system [16]. In the Global Position System (GPS) and Cricket location-support system [17] unlocalized nodes are a single communication hop away from beacons nodes, while in the Ad Hoc Positioning System (APS) and its variants [13–15,18] beacons can be multiple hops away. Computation of positions can either be distributed throughout the network, or computed centrally [19–23]. This paper focuses on multihop distributed localization systems such APS; however, regardless of the system used localization errors can be 10–20 m or more [3,13,24], necessitating the ability to detect poorly localized nodes. There are two key contributions which this paper makes to the localization problem in wireless ad hoc networks. First, we propose a model for location error variance in localization systems which wireless devices can use to estimate their true location error. The model is based on the fact that localization error variance behaves similarly to the theoretical lower bound on the variance of location estimators, given by the CRLB. The CRLB is easily computed locally, and is used in the location error variance model along with the number of available beacon nodes. The second contribution of this paper is a scheme for nodes to determine the amount of error in their position estimates with a given probability, p, where p is an input thresholding parameter to the system. The scheme uses the proposed model of error variance and the cumulative distribution function (cdf) of localization error to probabilistically determine the amount of error in nodes’ location estimates. Once known, nodes can compensate for this error in future applications which rely on location information. The remainder of this paper is organized as follows. Section 2 briefly describes the related work. Section 3 formally describes the problem under investigation. Section 4 discusses the proposed algorithm for error estimation. Section 5 presents simulation results for our scheme. Finally, the paper is concluded in Section 6.

505

2. Related work Localization in wireless ad hoc networks is a problem which has received a great deal of attention due to the importance of obtaining reliable position information. Open access services such as the Global Positioning System (GPS) are often unfeasible in these networks due to cost, energy usage, imprecision, and unavailability [25]. A number of shorter-range single-hop localization systems have been proposed to deal with some of these issues [12,17,26]. When reference nodes are not within radio range of unknown nodes, multi-hop localization techniques must be used. The Ad Hoc Positioning System (APS) [13] extends the concept of GPS in WSN by broadcasting beacon positions over multiple hops, where the number of hops and average hop size are calculated to allow estimation of the distances to beacon nodes without requiring direct communication. APS has been extended by numerous schemes to include an iterative refinement phase [14,15,18], where after obtaining initial position estimates from APS, nodes exchange position estimates with their one-hop neighbors, and treat these neighbors as intermediary reference devices. Nodes continually update their positions using the new positions of one’s neighbors, until each device eventually converges on a solution. For a complete review of wireless localization schemes we refer the reader to the many recent surveys available [3,27–29]. Much effort has been devoted to the theoretical analysis of localization error and its potential applications. First and foremost, analysis techniques are required to evaluate the performance of localization systems as compared to theoretical limits. The Geometric Dilution of Precision (GDOP) [30] is a widely used metric by the GPS community to quantify the difficulty of specific geometries for localization, by essentially relating position accuracy to measurement accuracy. The CRLB provides a lower bound on the variance of unbiased estimators [31], and was derived for single-hop RSS and TOA location estimators [32]. The CRLB was derived for DV-Hop based localization systems [33], and for general multi-hop localization systems using noisy range or angle measurements [34]. The position error bound (PEB) was derived by Jourdan et al. [35], which is based on the CRLB for ultra-wideband (UWB) systems and takes into account biases on range measurements found in cluttered environments. Furthermore, the concept of -localization accuracy outage was proposed which gives an indication of the PEB that can be expected with probability  as we move through an area [35]. A performance measure called the squared position error bound (SPEB) was derived by Shen and Win [36] which quantifies the limits of wideband localization in the presence of nonline-of-sight (NLOS) and multipath propagation, by analyzing the received waveforms themselves rather than the signal metrics such as TOA or RSS. A number of localization analysis techniques not based on information theory have been researched. Localizability testing aims to determine how many and which nodes in an arbitrary network can be successfully localized, and can be tested with triangulation [37], or more recently by nodes evaluating membership with ones neighbors in

506

J. Gribben, A. Boukerche / Ad Hoc Networks 13 (2014) 504–515

certain known localizable structures [38]. The probability of unlocalized nodes becoming localized is determined using a probabilistic method by Daneshgaran et al. [39]. Specifically, the authors determine the density requirements over a region for localization with high probability. The quality of trilateration (QoT) metric proposed by Yang and Liu [18] moves beyond the binary metric of localizability, and evaluates the probability that the estimated position of a given node is within a disk area centered at that point. In addition to providing a framework for evaluating localization performance, the analysis techniques provide for a real-time measure of the quality of service (QoS) of localization, which is exploited for several applications. The optimal selection of a subset of anchor nodes with the highest quality is beneficial in terms of accuracy, computational cost and energy efficiency, and are selected to minimize the GDOP [40,41] or the CRLB [42] metrics. Sleep scheduling of reference nodes is studied by Gribben et al. [43] to ensure the minimal number of active reference nodes while maintaining high localization QoS. The placement of anchor nodes in a region for optimal localization accuracy is evaluated using the CRLB [44] and the PEB [45] metrics. The QoT metric is used for iterative location refinement, where error propagation is limited by preferentially choosing references with a higher QoT [18]. In this paper we derive a method for estimating the amount of localization error present with a certain probability using a new model of localization error variance based on the CRLB, which can be incorporated into location-dependent applications. The proposed scheme differs from and expands upon other related work in a number of ways. The localization error metric can be computed locally by wireless nodes requiring very little information beyond their immediate neighborhoods making it fully distributed, whereas other methods such as the global CRLB [32,34], GDOP [30] and others are computed centrally and typically used only analytically. Furthermore, our method extends -localization accuracy [35] and related techniques by dealing with multi-hop localization scenarios with large numbers of beacon and unknown nodes. In addition, although TOA and RSS measurement models are considered, the proposed scheme requires that very few underlying assumptions about the localization protocol are made, since we provide a means to fit the error model to obtained simulation or experimental data for accurate results.

3. Problem statement In this work, we consider a wireless network composed of n randomly deployed nodes in set N , consisting of unknown nodes in U  N which do not know their positions, settled nodes in S  N which were originally in U but discovered their positions using a localization system, and beacon nodes in B  N which know their positions a priori. All devices have a communication range of r units, and are distributed in a two-dimensional squared sensor field Q = [0, s]  [0, s].

Each node i 2 N has Cartesian coordinates zi = (xi, yi) 2 R2, which represents the location of the node i in Q. For simplicity, we will only consider two dimensions in this work, but the methods here explained can be easily extended to three dimensions. The true distance between two nodes i and j is di,j =kzi  zjk. We denote the neighbors of node i by NðiÞ ¼ fj 2 N jdi;j 6 rg, which are the nodes within communication range of i. For simplicity, we consider symmetric communication links, i.e. if j 2 N(i), then i 2 N(j). Nodes are equipped with radio frequency (RF) transceivers for communication. Using the RSS or TOA of radio signals, i can estimate the distance to any j 2 N(i), denoted ~ . Accuracy of distance estimates are limited, as RSS and d i;j TOA measurements are highly prone to error. When RSS is used we assume log-normal shadowing, where distance measurements are a function of the received power at zi transmitted by j, Pi,j. Pi,j is Gaussian with mean power P i;j and variance r2dB in decibel milliwatts, given by

  Pi;j  N Pi;j ; r2dB ;

ð1Þ

Pi;j ¼ P 0  10np log 10 ðdi;j =d0 Þ where P0 is the received power at distance d0 as calculated by the free-space path loss formula, np is the path loss exponent and rdB is the standard deviation of the shadowing, which are measured from the environment. The estimated distance between nodes i and j is then given by

~ ¼ d0 P0 =P n1p d i;j i;j

ð2Þ

In the TOA case, the measured time of arrival between i and j is assumed to be Gaussian distributed with mean time di,j/c and variance r2T ,

  T i;j  N di;j =c; r2T ;

ð3Þ

where c is the speed of light and r2T is measured from the environment and is independent of di,j. The estimated dis~ ¼ c  T . This ranging tance between i and j is therefore d i;j i;j model is described in detail and verified experimentally by Patwari et al. [32]. With three or more distance measurements to nodes j 2 S [ B with known positions, a node is ^i Þ. The CRLB able to estimate its own position, ^ zi ¼ ð^ xi ; y places a lower bound on the variance of any unbiased estimator ^ h of a parameter h [31], and is given by inverse of the Fisher information matrix (FIM) I(h). That is, Cð^ hÞ P I1 ðhÞ, ^ ^ where CðhÞ is the covariance matrix of h. The ijth element of the FIM is given as

" # @ 2 ln pðx; hÞ ½IðhÞij ¼ E @hi @hj

ð4Þ

where p(x; h) is the pdf of the measurement data, and x is a random measurement taken at the true value of h. The CRLB was derived for position estimation [32], where the parameter vector h is the set of node locations, zi, and p(x; h) is given by the statistical model of distance measurements for RSS or TOA using log-normal shadowing or Gaussian noise, respectively. The minimum variance of

J. Gribben, A. Boukerche / Ad Hoc Networks 13 (2014) 504–515

the estimated position of a node i, with reference nodes R # fS \ NðiÞg, is given by Eqs. (5) and (6) for RSS and TOA, respectively [32],

r2i;RSS ¼



10np rdB log 10 "

r

2 i;TOA

¼c

2

2 T jRj

r

P

2 P

j2R

P

2 j2R di;j



k2R;k–j

di?j;k dj;k di;j di;k

#1 X X di?j;k dj;k 2 di;j di;k j2R k2R;k–j

2

ð5Þ

ð6Þ

where di\j,k is the shortest distance of node i to the line intersecting nodes j and k. For the remainder of this paper we will drop the RSS and TOA subscripts, and denote the CRLB simply by r2i . In practice, localization systems do not typically achieve the lower bounds in Eqs. (5) and (6), and have error slightly higher. Trilateration based methods represent the position and distance of a beacon node j to node i with the circle ~ . When three or more dis^i  yj Þ ¼ d equation ð^ xi  xj Þ þ ðy i;j tance and position measurements are available, these ^i Þ using a least squares equations can be solved for ð^ xi ; y method. This linearization simplifies computation and gives a good position estimate, but information is lost in the process and so these estimators do not achieve minimum variance. The nonlinear maximum-likelihood estimators (MLE) [32] give improved accuracy and are asymptotically optimal. The bias-reduced MLE used for RSS for a node i with reference nodes R is

^zi ¼ argmin fzi g

C ¼ exp

X j2R

ln

~ =C 2 d i;j 2

d ðzi ; zj Þ

!2 ;

ð7Þ

"  2 # 1 lnð10Þ rdB 2 10 np

while the MLE for the TOA case is

^zi ¼ argmin fzi g

X 2 cT i;j  dðzi ; zj Þ :

ð8Þ

j2R

In this paper, we assume that the position estimators in (7) and (8) are unbiased. In the case of TOA, the bias is assumed to be known for environments of interest and can be subtracted out from distance measurements, resulting in an unbiased estimator. One of the fundamental drawbacks of the RSS signal metric, however, is that there remains residual bias even with the bias-reduced estimator in (7). Therefore, we would expect greater location error in actual deployments, necessitating higher node densities and signal to noise. With this network model, the localization error estimation problem can be stated as follows. Definition 1 (Localization Error Estimation Problem (1)). For a given wireless node i 2 N , and probability p, 0 < p < 1, determine the minimum distance, d0i , such that zi j, of i is less than the amount of location error, jei j¼j zi  ^ or equal to d0i with probability greater than or equal to p. This is given as follows.

0

di ðpÞ ¼ argmin ½Prfjei j 6 zg P p

507

ð9Þ

z

Solving (9) allows applications to have a certain level of confidence in how much localization error to expect, which in turn enables one to design more robust, fault tolerant systems where localization error can be handled accordingly. Rearranging (9), we obtain an alternate form of the localization error bound prediction problem.

Definition 2 (Localization Error Estimation Problem (2)). For a given wireless node i 2 N , and distance d0i , determine the minimum probability, p, such that the location error, jeij, of i is less than or equal to dij with probability greater than or equal to p. This is given as follows. 0

0

pðdi Þ ¼ Prfjei j 6 di g

ð10Þ

This alternate form given by Eq. (10) allows applications to determine the probability at which the localization error is less than some specific value. For example, a sensing application may be interested in whether or not the localization error of a node is less than or equal to its sensing range to validate the accuracy of its sensed data.

4. Location error estimation In this section we present our solution to the localization error estimation problem. We first describe the main contributing factors to localization error in ad hoc wireless networks. Based on these error inducing parameters, a model of localization error is then derived which is designed to estimate the true variance of localization systems based only on information which is locally collected by wireless devices during the course of a multihop localization run. This model of location error variance is then used by probabilistic methods at each node to estimate the minimum amount of localization error with a given probability, or alternatively, the probability of localization error being less than a given amount. 4.1. Error inducing parameters in localization There are a number of potential sources for localization error in wireless networks, which can be categorized as extrinsic and intrinsic [34]. Extrinsic error pertains to physical effects on the propagation environment, including fading caused by obstacles and error due to movement. Intrinsic error is related to flaws within the hardware and software of wireless devices, preventing location estimators from achieving minimum variance. In this paper we propose a model which explicitly captures information from intrinsic error sources, while extrinsic error is dealt with more indirectly since it is much more unpredictable and difficult to handle. The system parameters which we are interested in which influence the error characteristics are the number of nodes, jN j, the number of beacons, jBj, the average node density, q, and the average number of hops to beacon nodes. As was found in our own simulations and in the work of others

508

J. Gribben, A. Boukerche / Ad Hoc Networks 13 (2014) 504–515

[46,24,34], the most important intrinsic factors for localization error are the number of beacons and node density; therefore, we adopt a model of localization error based primarily on these parameters. Remaining error sources not directly captured by the model are indirectly dealt with by scaling coefficients, which are determined by fitting the error model to experimentally obtained error statistics in realistic simulation scenarios.

each node i 2 N , where the jth realization of ^ zi is zi;j . denoted ^ 3. For each node i, compute r2i , and estimate the mean, d^ ^ Eðd zi Þ, and mean squared error, MSEð zi Þ, of zi, given by

^zi Þ ¼ Eðd

d^z Þ ¼ MSEð i

4.2. Localization error model From the asymptotic properties of the MLE, the estimators in Eqs. (7) and  (8) are asymptotically distributed according to ^ zi  N zi ; r2i for sufficiently large data records [31]. That is, with a sufficient number of RSS or zi has a Gaussian distriTOA measurements, the estimator ^ bution with mean zi, and variance equal to the CRLB, r2i , evaluated at the true position of zi. In practice, however, the CRLB is overly optimistic and is not achieved by localization systems, and so we introduce a model for localization variance which behaves closer to the actual variance of location estimates than the CRLB.





u2i r2i ; jBj ¼ ar2i þ bjBj þ c

Y 1X ^zi;j Y j¼1

ð11Þ

The first term in Eq. (11) takes the CRLB computed by node i; r2i , and scales it by a constant a. The value of r2i in this term gives a good approximation to the single-hop localization error of a node, and it is scaled by a to compensate for additional error due to multi-hop propagation and the fact that the positions of settled neighboring nodes are not exact. The second term incorporates the number of beacon nodes, jBj, since localization error decreases with an increasing number of beacons. The effect of the number of beacons is scaled by another constant b since the number cannot be used directly. Finally the third term is simply an additive constant c. This compensates for any remaining bias, which for the case of the TOA estimation becomes negligible since it is relatively unbiased, whereas for RSS it is important since RSS location estimation has been readily shown to be biased [32]. In heavily cluttered environments with significant non-line-of-sight (NLOS) conditions the accuracy of this model will be reduced; however with sufficiently high node density the model will on average give a reasonable indication of localization error for many practical applications. The values of a, b and c are determined with the Monte Carlo method, where extensive localization simulations are performed prior to physical deployment of devices in order to obtain statistical data on the performance of the localization system to be used. A least squares estimator is then used to choose a, b and c to minimize the difference between the error model, u2i , and the observed data from simulations. The steps for data generation for the Monte Carlo simulations are as follows: 1. Generate X independent network topologies, with nodes in N ¼ fN 1 . . . N X g, and varying numbers of beacon nodes. 2. Run the localization simulation Y times for each of the generated topologies to yield Y realizations of ^ zi for

ð12Þ

2 1 XY ^zi ÞÞ ð^z  Eðd j¼1 i;j Y

ð13Þ

Results from the simulation runs are then used as data for a least squares estimator of a, b and c which minimizes the squared error between the variance model, u2i , and the actual mean squared error of the location estimator, d^ MSEð zi Þ, given by

^h ¼ ½a b cT ¼ argmin a;b;c

X i2N

2 d^z Þ  ar2 þ b j B j þcÞ ð MSEð i i

ð14Þ

The solution to the least squares estimator in Eq. (14) is given by,

^h ¼ ðHT HÞ1 HT x

ð15Þ

where

2

r21

jBj1

r2jN j

jBj2 .. . jBjjN j

6 2 6 r2 6 H¼6 . 6 .. 4

1

3

7 17 7 ; .. 7 .7 5 1

3 d^z Þ MSEð 1 7 6 d^z Þ 7 6 MSEð 2 7 6 x¼6 7 .. 7 6 5 4 . d ^z Þ MSEð 2

ð16Þ

jN j

Here, the calculated CRLB, the number of available beacon nodes and the mean squared localization error of a given d^ node i 2 N are given by r2i ; jBji and MSEð zi Þ, respectively. The localization error variance of a particular node i is then estimated to be u2i , requiring only knowledge of the estimated locations of the neighbors of i, N(i), in order to compute r2i , the number of beacons nodes in the system, jBj, and values for the constants a, b and c, which are determined a priori to physical deployment of the network via localization simulation performed in the intended environment. 4.3. Location error estimation method In our network model we assume that position estimates are unbiased, meaning that Eð^ zi Þ ¼ zi . Therefore, the mean localization error ei is equal to zero, since

Eðei Þ ¼ Eðzi  ^zi Þ ¼ zi  zi ¼ 0

ð17Þ

For the localization error estimation problem we must determine the minimum probability, p, such that Pr(jeij 6 d) P p holds, for a given distance, d0i . As z^i is asymptoti  cally Gaussian distributed according to N zi ; u2i ; ei is also  Gaussian, with 0 mean and variance u2i , given by N 0; u2i . For the problem at hand we are only interested in the error distance, not direction. The magnitude (distance) of the

J. Gribben, A. Boukerche / Ad Hoc Networks 13 (2014) 504–515

error jeij then follows the half-normal distribution. Therefore, the probability of a node i being localized with error less than or equal to d is computed using the cdf of the half-normal distribution.

Prfjei j 6 dg ¼

1

rffiffiffiffi Z 2

ui

p

  u2 du exp  2u2i

d 0

ð18Þ

Substituting Eq. (18) into Eqs. (9) and (10), we get solutions for both forms of the localization error bound prediction problem in Eqs. (19) and (20) respectively.

"

1

rffiffiffiffi Z 2

ui

p

0

di ðpÞ ¼ argmin 06z6s

0

pðdi Þ ¼

1

rffiffiffiffi Z 2

ui

p

0

d0i

0

z

#   u2 du P p exp  2u2i

  u2 du exp  2u2i

ð19Þ

ð20Þ

The minimization problem in Eq. (19) can be solved trivially since we restrict the search to less than the size of the network area, s (otherwise position estimates would not be useful). These equations can be computed locally by wireless devices by computing u2i from Eq. (11), where a,b,c are known, and only position estimates of one’s single hop neighbors and the number of beacons are required. When run in conjunction with a localization scheme, this information can be obtained without requiring additional communication. As an example, the cdf from Eqs. (19) and (20) is shown in Fig. 1 with the value of ui set to 5.0 and 10.0. If we set p = 0.7, we see that with ui = 5.0 the minimum distance such that the error is less than that distance is d0i (p) = 5.2, whereas when ui = 10.0 the minimum distance increases to d0i (p) = 10.4. In general, the higher the values of u2i and p, the higher the value of d0i (p). 5. Simulation results

Probability

In this section we present simulation results which verify the correctness of the presented localization error estimation algorithm. Implementation is done using the

cdf, φ cdf, φ

Fig. 1. cdf of half-normal distribution with u = 5 and u = 10 and the system parameter p = 0.7.

509

network simulator ns-2 version 2.33. We use the same environmental parameters which were measured experimentally [32] to match the model in Eqs. (1) and (3). We have np = 2.30, rdB = 3.92 dB, and d0 = 1 m for RSS measurements, and rT = 6.1 ns for TOA measurements. An implementation of a localization scheme similar to that of Savarese et al. [14] was used, in which all unknown nodes initially estimate their locations using the positions and number of hops to available beacon nodes, followed by an iterative refinement phase where initial positions of neighboring nodes are used as intermediary reference devices to improve accuracy. It should be noted however that the methods derived in this paper do not depend on any specific localization scheme, but only on the limitations of the underlying measurement model, and so the selected localization implementation is of secondary importance. Nodes each have a radio range of 50 m [47] and are deployed randomly with a uniform distribution over a squared area of size [0, s]  [0, s], where node density is controlled by varying s. Differing percentages of beacon nodes, which know their positions at all times, are randomly selected from variable sized node populations. 5.1. Error variance model fitting The steps outlined in the previous section for data generation for Monte Carlo simulation are used to find values for the constants a, b and c which best fit the variance model given by Eq. (11). The total number of nodes in the network is varied at 200, 300, 400 and 500 nodes, the percentage of beacon nodes is set to 5%, 10%, 15%, 20% and 25% of the total nodes, average node density is set to 15, 30, 45, 70 and 85 nodes, and a random seed value which affects node deployment topology is varied from 1 to 10. This results in the generation of X independent network topologies with varying properties, where jXj = 4  5  5  10 = 1000. For each of the X independent topologies, Y = 32 runs of the implemented localization simulation are executed, and we store for each node i its estimated position, ^ zi , its calculated CRLB value, r2i , and its number of available beacon nodes, jBji . From the Y realizations of ^ zi , the MSE is calculated according to Eq. (13). Finally, all data are used by the least squares estimator given by Eq. (15), yielding values for a, b and c. Obtained results for the model fit are summarized in Table 1. We notice that the scaling parameters are significantly larger when RSS is used as compared with TOA, and that b and c are almost negligible in the TOA situation. This indicates that the error variance approaches the CRLB much more closely with TOA and that there is very little dependence on the number of available beacon nodes in this modality. The average MSE of nodes with varying node densities across the given X topologies is shown in Figs. 2 and 3 for the RSS and TOA cases, respectively. Alongside the MSE curves are the average computed values from the proposed error model, u2i , using the obtained values of a, b and c. These graphs clearly show that the error model closely matches the measured mean squared localization error across a range of average node densities. However, we

510

J. Gribben, A. Boukerche / Ad Hoc Networks 13 (2014) 504–515

c

0.8787 0.0016

85.1189 0.0014

notice for the TOA case that MSE increases by a much higher amount at lower node densities than does the error model, but the two follow each other extremely closely when the average node density is greater than 30. This is due to the presence of outliers at lower node densities in which unknown devices, which are typically located close to the extremities of the network area, are poorly connected to beacon devices resulting in degenerate configurations with high localization error, skewing the average MSE. These degenerate configurations are not present when node density is sufficient, and are not as noticeable when RSS is used since error is much higher, so that these effects are relatively negligible. The outlier detection problem, which aims to detect and reject the small number of outliers that can significantly degrade overall localization accuracy, is an area of ongoing research [48]. We test the closeness of fit of our error model by using the values of a, b and c obtained from the initial X topologies in Z newly generated topologies which differ from the initial set of X topologies by varying the deployment seed value from 11 to 20 (so that jZj = 1000). This simulates the scenario of generating an initial set of training data in the intended environment of interest in order to determine the fit parameters a, b, c, followed by the actual deployment which is completely independent, and makes use of the parameters found through the training set to estimate the error variance. Fig. 4 shows the average RMSE of localization error compared with the proposed error model for both the RSS and TOA measurement modes in the Z new topologies. With this we can see that the error model successfully estimates localization error deviation in an independent set of deployments, which shows the feasibility of estimating localization error variance in real-world environments, provided that the system model and deployment strategy of the training simulations describe the real world scenario with sufficient accuracy. 5.2. Localization error estimation The next set of experiments evaluate the effectiveness of the localization error estimation methods described by Eqs. (19) and (20). We simulate graphs with 300, 400 and 500 nodes, average node densities of 30, 45 and 70, and percentages of beacon nodes of 10% and 20%, with 10 random deployment seeds per configuration. For each of the 3  3  2  10 = 180 independent topologies we begin by running the localization scheme, followed by computing the minimum distance, d0i , such that the amount of location error, jeij, is less than or equal to d0i with probability greater than or equal to p using Eq. (19), for p = 0.1, 0.2, . . . , 0.9, 0.95,0.99. The average results of computing d0i over given node densities at the different values

2

b

4.7681 1.4595

Fig. 2. Localization error compared with estimated error from model – RSS.

)

a

2

RSS TOA

)

Table 1 Computed values of a, b and c.

Fig. 3. Localization error compared with estimated error from model – TOA.

for p are shown in Fig. 5 for the TOA case. We observe that at lower node densities the minimum distance at which localization error is bounded increases rapidly, especially when a higher probability of localization is desired. This means that we require higher node densities in order to obtain a high probability of localization within tight distance bounds. Similarly, when a high probability of localization is required, the distance at which localization error is bounded at that probability increases, and increases more rapidly as p approaches 1. The results with RSS show a similar trend, but with the computed distances being higher due to the higher error associated with RSS range measurements. Next, we run the localization simulation 1000 times on each of the generated topologies for statistical averaging. We store the amount of error in the estimated positions for each run, as well as the estimated variance given by the proposed error model. For each node i, the histogram of its localization error is generated, yielding its estimated pdf. The cdf for each node can then be estimated from the histogram by integrating all error values less than or equal to the desired distance. To test the effectiveness of the localization error estimation solution we then take the estimated cdf evaluated at the computed

J. Gribben, A. Boukerche / Ad Hoc Networks 13 (2014) 504–515

Fig. 4. Localization error compared with estimated error from model with new network topologies.

Fig. 5. Estimated localization error at given probabilities – TOA.

value of di(p)0 (i.e. the total number of location estimates 6 di(p)0 ) for a given probability p, where di(p)0 is computed from Eq. (19) (as was shown in Fig. 5), and compare the result with p. This gives the actual probability of the localization error being less than or equal to di(p)0 which is

511

obtained from the cdf of the 1000 localization runs, as compared to the selected probability p. Figs. 6 and 7 show the actual probability of localization error being less than or equal to di(p)0 versus the chosen probability, p, averaged over the given node densities for the RSS and TOA cases, respectively. With a perfect error estimator, the chosen probability would match exactly the actual probability of localization within that error. We notice that with RSS the error bound tends to be slightly over-estimated in that there is a higher probability than p of the error being less than di(p)0 , indicating that di(p)0 should have been chosen to be smaller. The opposite is the case when TOA is used, in that error bound is slightly under-estimated. In addition, there is a slight tendency of increasing probability of localization compared with the chosen probably with increasing node densities in the RSS, while the probability decreases with density with TOA. In spite of this however, we find good correlation between the actual and selected probabilities across the range of node densities, especially considering the dramatic variation of MSE across node densities as was seen previously in Figs. 2 and 3. The average over all node densities is shown in Fig. 8, which demonstrates that although there is some discrepancy between chosen and actual probabilities over the different node densities, on average we obtain a good fit. This is a limitation of the least squares fitting procedure used, in that the values found for a, b, c are an average best fit for all possible configurations, but do not work perfectly over the entire range. We also observe in the RSS case that when a higher probability of localization within di(p)0 is desired the chosen and actual probabilities do not match as well due to the inherent randomness of localization which prevents the actual probability from reaching unity. With TOA on the other hand, error estimation appears to be more effective at higher probabilities. Overall we observe that the estimated error at the chosen probabilities appear to match the actual probabilities on average within ±0.1, and slightly better when using TOA, which should be acceptable for use in location dependent applications. We next evaluate the effectiveness of the alternate form of the location error estimation problem which takes as

Fig. 6. Actual probability of localization error less than estimated localization error, d0i , for different node densities – RSS.

512

J. Gribben, A. Boukerche / Ad Hoc Networks 13 (2014) 504–515

Fig. 7. Actual probability of localization error less than estimated localization error, d0i , for different node densities – TOA.

input a given distance, d0i , and determines the minimum probability, p(d0i ), such that localization error is less than or equal to that distance, given by Eq. (20). We varied d0i from 2 m to 44 m at 2 m intervals in the RSS case, and from 0.2 m to 4 m at 0.2 m intervals with TOA, and computed the average value of p(d0i ) over the given node densities, shown in Fig. 9 for RSS (TOA shows similar behavior). We observe that at the same distance there is a higher probability of localization error being less than that distance the higher the node density is. For example, there is a 0.9 probability of being localized within 15 m when the node density is 30, while the probability is as low as 0.7 on average with only 10 neighbors. These estimated probabilities are then compared with the actual probabilities of error less than or equal to d0i as measured from the 1000 localization runs averaged over all node densities, shown in Figs. 10 and 11 for both RSS and TOA measurement modes, respectively. When TOA is used we achieve very accurate results, with the estimated and actual probabilities being almost identical. With RSS measurements results are not quite as accurate as we underestimate the probability of locali-

zation within shorter distances (d0i 6 15) and observe that the estimated probability increases at a rate greater than the actual probability, showing an imperfect fit with the proposed error model. This should be expected, however, due to the significantly larger error present in RSS based localization systems, and is therefore still acceptable for location dependent applications since errors in the location error estimation scale relative to the magnitude of overall location error. Also important to note with both measurement modes is the fact that initially when the desired error bound is set very small, the probability of localization within that bound is relatively low. The probability increases rapidly at first with increasing error distance, then reaches asymptotic behavior as p(d0i ) approaches 1. This may provide a good starting point for the selection of the system parameters p and d0i from Eqs. (19) and (20), respectively, for use in future applications. Specifically, based on the asymptotic conditions seen in Figs. 10 and 11, selecting p below 0.9, and likewise d0i below 15 m for RSS, or 1.25 m for TOA, would be good choices, since there is diminishing value in exceeding these ranges.

Fig. 8. Actual probability of localization error less than estimated localization error, d0i , averaged over all node densities.

Fig. 9. Estimated probability of localization error less than given distances – RSS.

J. Gribben, A. Boukerche / Ad Hoc Networks 13 (2014) 504–515

Fig. 10. Actual probability of localization error being less than distance given by localization error estimate, compared with estimated probability – RSS.

513

error with a given probability by comparing it with the actual probability of localization error being less than that upper bound. Results showed that the actual and given probabilities correlated within p = ±0.1. Similarly, we successfully estimated the probability of localization error being less than a given distance, with the estimated and actual probabilities of error less than that distance correlating well, especially when TOA measurement is used. In general, localization error can be better estimated when using TOA measurement as compared with RSS due to the reduced noise contribution in these measurements. However, although error estimates are not as accurate in RSS systems, they are likely even more useful since localization error is proportionally higher, further the necessitating the need to properly handle it. The methods in this paper are a promising tool for helping to quantify error in localization systems, which in future work can be integrated into existing applications such as coverage and routing protocols, localization quality of service for target tracking, and sensor network queries to increase their reliability and accuracy. Despite the promise shown by the proposed approach, future work is required to improve the localization error model to better include sources of extrinsic error such as obstacles in the environment, as well as by treating additional sources of intrinsic error such as multihop error propagation in greater detail. Finally, although the localization error estimation system should be applicable to a mobile setting, we would like to further validate the proposed techniques on mobile networks, as well as on a physical test bed of wireless devices.

References Fig. 11. Actual probability of localization error being less than distance given by localization error estimate, compared with estimated probability – TOA.

6. Conclusions In this paper we have developed a means to estimate position error from localization systems, which can be incorporated into location-dependant applications to improve their robustness and overall quality of service. We have put forth a model for localization error variance based on the CRLB, which has been successfully fit to the error variance of actual localization systems through a least squares estimator. This estimated variance was then integrated into the pdf of localization error, modeled as a Gaussian random variable, and its associated cdf in order to determine the minimum distance such that localization error is less than that distance with a given probability; or alternatively, the probability that localization error is less than a given distance. Simulation results have shown that the proposed error variance model closely matches the localization MSE, especially as node density is increased due to the asymptotic optimality of the MLE used. Through extensive Monte Carlo simulations, we determined that we can successfully estimate the upper bound on localization

[1] A. Boukerche, Algorithms and Protocols for Wireless Sensor Networks, vol. 62, Wiley-IEEE Press, 2008. [2] A. Boukerche, H. Oliveira, E. Nakamura, A. Loureiro, Vehicular ad hoc networks: a new challenge for localization-based systems, Computer Communications 31 (2008) 2838–2849. [3] A. Boukerche, H. Oliveira, E. Nakamura, A. Loureiro, Localization systems for wireless sensor networks, Wireless Communications, IEEE 14 (2007) 6–12. [4] A. Mainwaring, D. Culler, J. Polastre, R. Szewczyk, J. Anderson, Wireless sensor networks for habitat monitoring, in: Proc. 1st ACM Int. Workshop on Wireless Sensor Networks and Applications, ACM, pp. 88–97. [5] S. Meguerdichian, F. Koushanfar, M. Potkonjak, M. Srivastava, Coverage problems in wireless ad hoc sensor networks, in: IEEE INFOCOM, vol. 3, pp. 1380–1387. [6] C. Huang, Y. Tseng, H. Wu, Distributed protocols for ensuring both coverage and connectivity of a wireless sensor network, ACM Transactions on Sensor Networks (TOSN) 3 (2007). [7] M. Mauve, A. Widmer, H. Hartenstein, A survey on position-based routing in mobile ad hoc networks, IEEE Network 15 (2001) 30–39. [8] D. Al-Abri, J. McNair, On the interaction between localization and location verification for wireless sensor networks, Computer Networks 52 (2008) 2713–2727. [9] D. Liu, M.-C. Lee, D. Wu, A node-to-node location verification method, IEEE Transactions on Industrial Electronics 57 (2010) 1526–1537. [10] Y. Zeng, J. Cao, J. Hong, S. Zhang, L. Xie, Secure localization and location verification in wireless sensor networks: a survey, The Journal of Supercomputing (2010) 1–17. [11] A. Boukerche, Algorithms and Protocols for Wireless, Mobile Ad Hoc Networks, vol. 77, Wiley-IEEE Press, 2008. [12] N. Bulusu, J. Heidemann, D. Estrin, GPS-less low-cost outdoor localization for very small devices, Personal Communications, IEEE 7 (2000) 28–34.

514

J. Gribben, A. Boukerche / Ad Hoc Networks 13 (2014) 504–515

[13] D. Niculescu, B. Nath, Ad hoc positioning system (APS), in: Proceedings of GLOBECOM, San Antonio, 2001. [14] C. Savarese, K. Langendoen, J. Rabaey, Robust positioning algorithms for distributed ad-hoc wireless sensor networks, USENIX Technical Annual Conference (2002) 317–328. [15] A. Savvides, H. Park, M. Srivastava, The n-hop multilateration primitive for node localization problems, Mobile Networks and Applications 8 (2003) 443–451. [16] S. Capkun, M. Hamdi, J. Hubaux, GPS-free positioning in mobile ad hoc networks, Cluster Computing 5 (2002) 157–167. [17] N. Priyantha, A. Chakraborty, H. Balakrishnan, The Cricket locationsupport system, in: Conference on Mobile Computing and Networking (MOBICOM), ACM, pp. 32–43. [18] Z. Yang, Y. Liu, Quality of trilateration: confidence-based iterative localization, IEEE Transactions on Parallel and Distributed Systems 21 (2010) 631–640. [19] L. Doherty, K. Pister, L. Ghaoui, Convex position estimation in wireless sensor networks, IEEE Infocom 3 (2001) 1655–1663. [20] N. Patwari, R. Wang, Relative location in wireless networks, in: Vehicular Technology Conference (VTC 2001), vol. 2, 2001. [21] Y. Shang, W. Ruml, Y. Zhang, M. Fromherz, Localization from connectivity in sensor networks, IEEE Transactions on Parallel and Distributed Systems (2004) 961–974. [22] P. Biswas, Y. Ye, Semidefinite programming for ad hoc wireless sensor network localization, in: Proceedings of the 3rd International Symposium on Information Processing in Sensor Networks, IPSN ’04, ACM, New York, NY, USA, 2004, pp. 46–54. [23] R. Ouyang, A.-S. Wong, C.-T. Lea, Received signal strength-based wireless localization via semidefinite programming: noncooperative and cooperative schemes, IEEE Transactions on Vehicular Technology 59 (2010) 1307–1318. [24] G. Jordt, R. Baldwin, J. Raquet, B. Mullins, Energy cost and error performance of range-aware, anchor-free localization algorithms, Ad Hoc Networks 6 (2008) 539–559. [25] B. Parkinson, J. Spilker, Global Positioning System: Theory and Applications, Aiaa, 1996. [26] A. Paul, E. Wan, Rssi-based indoor localization and tracking using sigma-point kalman smoothers, IEEE Journal of Selected Topics in Signal Processing 3 (2009) 860–873. [27] G. Mao, B. Fidan, B.D. Anderson, Wireless sensor network localization techniques, Computer Networks 51 (2007) 2529–2553. [28] V. Lakafosis, M. Tentzeris, From single-to multihop: the status of wireless localization, Microwave Magazine, IEEE 10 (2009) 34–41. [29] J. Wang, R. Ghosh, S. Das, A survey on sensor localization, Journal of Control Theory and Applications 8 (2010) 2–11. [30] R. Yarlagadda, I. Ali, N. Al-Dhahir, J. Hershey, GPS GDOP metric, in: Radar, Sonar and Navigation, IEEE Proceedings, vol. 147, pp. 259– 264. [31] S. Kay, Fundamentals of Statistical Signal Processing: Estimation Theory, Prentice-Hall Signal Processing Series, 1993. [32] N. Patwari, A. Hero, M. Perkins, N. Correal, R. O’Dea, Relative location estimation in wireless sensor networks, IEEE Transactions on Signal Processing 51 (2003) 2137–2148. [33] D. Niculescu, B. Nath, Error characteristics of ad hoc positioning systems (APS), in: Proceedings of the 5th ACM International Symposium on Mobile Ad Hoc Networking and Computing, MobiHoc ’04, ACM, New York, NY, USA, 2004, pp. 20–30. [34] A. Savvides, W. Garber, R. Moses, M. Srivastava, An analysis of error inducing parameters in multihop sensor node localization, IEEE Transactions on Mobile Computing 4 (2005) 567–577. [35] D. Jourdan, D. Dardari, M. Win, Position error bound for UWB localization in dense cluttered environments, IEEE Transactions on Aerospace and Electronic Systems 44 (2008) 613–628. [36] Y. Shen, M. Win, Fundamental limits of wideband localization – Part I: A general framework, IEEE Transactions on Information Theory 56 (2010) 4956–4980. [37] X. Li, D. Hunter, Probabilistic model of triangulation, in: Proceedings of the 2008 ACM Symposium on Solid and Physical Modeling, ACM New York, NY, USA, pp. 301–306. [38] Z. Yang, Y. Liu, X.-Y. Li, Beyond trilateration: on the localizability of wireless ad hoc networks, IEEE/ACM Transactions on Networking 18 (2010) 1806–1814. [39] F. Daneshgaran, M. Laddomada, M. Mondin, Connection between system parameters and localization probability in network of randomly distributed nodes, IEEE Transactions on Wireless Communications 6 (2007) 4383–4389. [40] M. Phatak, S. Inc, C. San Jose, Recursive method for optimum GPS satellite selection, IEEE Transactions on Aerospace and Electronic Systems 37 (2001) 751–754.

[41] H. Maheshwari, A. Kemp, B. Peng, Localization performance comparison using optimal and sub-optimal lateration in wsns, in: 15th Asia-Pacific Conference on Communications, 2009, APCC 2009, pp. 842 –845. [42] D. Lieckfeldt, J. You, D. Timmermann, An algorithm for distributed beacon selection, in: Sixth Annual IEEE International Conference on Pervasive Computing and Communications, 2008, PerCom 2008, pp. 318 –323. [43] J. Gribben, A. Boukerche, R. Pazzi, Scheduling for scalable energyefficient localization in mobile ad hoc networks, in: 2010 7th Annual IEEE Communications Society Conference on Sensor Mesh and Ad Hoc Communications and Networks (SECON), pp. 1 –9. [44] J. Abel, Optimal sensor placement for passive source localization, in: International Conference on Acoustics, Speech, and Signal Processing, 1990, ICASSP-90, vol. 5, 1990, pp. 2927–2930. [45] D. Jourdan, N. Roy, Optimal sensor placement for agent localization, ACM Transactions on Sensor Networks (TOSN) 4 (2008) 13. [46] H.A.B.F. de Oliveira, A. Boukerche, E.F. Nakamura, A.A.F. Loureiro, An efficient directed localization recursion protocol for wireless sensor networks, IEEE Transactions on Computers 58 (2009) 677–691. [47] C. Technology, XBow IRIS XM2110CA Datasheet, September 11, 2008. November 30, 2009. , 2008. [48] L. Jian, Z. Yang, Y. Liu, Beyond triangle inequality: sifting noisy and outlier distance measurements for localization, in: INFOCOM, 2010 Proceedings IEEE, pp. 1 –9.

Jeremy Gribben received the B.Sc. degree in computer science from Carleton University, Ottawa, ON, Canada, and the M.Sc degree from the University of Ottawa, Ottawa, ON, Canada. He is currently working toward the Ph.D. degree with the PARADISE Research Laboratory, University of Ottawa. His current research interests include localization systems in wireless ad hoc networks.

Azzedine Boukerche held a faculty position with the University of North Texas, Denton, and was a Senior Scientist with the Simulation Sciences Division, Metron Corporation, San Diego, CA. He was also a faculty member with the School of Computer Science, McGill University, Montreal, QC, Canada, and taught at the Polytechnic of Montreal. He spent a year with the Jet Propulsion Laboratory (JPL)/ NASA-California Institute of Technology, Pasadena, where he contributed to a project centered on the specification and verification of the software used to control interplanetary spacecraft operated by JPL/ NASA Laboratory. He is a fellow of the Canadian Academy of Engineering and the founding Director of the PARADISE Research Laboratory, School of Information Technology and Engineering, University of Ottawa (uOttawa), Ottawa, ON, Canada. He is a Full Professor and holds a Canada Research Chair position with uOttawa. He has published several research papers. He served as Guest Editor for the Journal of Parallel and Distributed Computing (special issue for routing for mobile ad hoc, special issue for wireless communication and mobile computing, and special issue for mobile ad hoc networking and computing), ACM/Kluwer Wireless Networks, ACM/Kluwer Mobile Networks Applications, and the Journal of Wireless Communication and Mobile Computing. His current research interests include wireless ad hoc and sensor networks, wireless networks, mobile and pervasive computing, wireless multimedia, quality-of-service (QoS) service provisioning, performance evaluation and modeling of large-scale distributed systems, distributed computing, large-scale distributed interactive simulation, and parallel discrete-event simulation. Prof. Boukerche served as the General Chair for the Eighth Association for Computing Machinery (ACM)/IEEE Symposium on Modeling, Analysis, and Simulation of Wireless and Mobile Systems and the Ninth ACM/IEEE

J. Gribben, A. Boukerche / Ad Hoc Networks 13 (2014) 504–515 Symposium on Distributed Simulation and Real-Time Application (DSRT), the Program Chair for the ACM Workshop on QoS and Security for Wireless and Mobile Networks, the ACM/IFIPS Europar 2002 Conference, the IEEE/SCS Annual Simulation Symposium (ANNS 2002), ACM WWW 2002, IEEE MWCN 2002, IEEE/ACM MASCOTS 2002, IEEE Wireless Local Networks WLN 03-04; IEEE WMAN 04-05, and ACM MSWiM 98G99. He is a Technical Program Committee member of numerous IEEE and ACM sponsored conferences. He served as the Vice General Chair for the Third IEEE Distributed Computing for Sensor Networks Conference in 2007, as the Program Co-chair for the GLOBECOM 20072008 Symposium on Wireless Ad Hoc and Sensor Networks and the 14th IEEE ISCC 2009 Symposium on Computer and Communication Symposium, and as the Finance Chair for ACM Multimedia 2008. He also serves as a Steering Committee Chair for the ACM Modeling, Analysis, and Simulation for Wireless and Mobile Systems Conference; the ACM Symposium on Performance Evaluation of Wireless Ad Hoc, Sensor, and Ubiquitous Networks; and IEEE/ACM DS-RT. He serves as an Associate Editor of the IEEE T

515

RANSACTIONS ON PARALLEL AND D ISTRIBUTED S YSTEMS, the IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, Elsevier Ad Hoc Networks, the Wiley International Journal of Wireless Communication and Mobile Computing, Wileys Security and Communication Network Journal, the Elsevier Pervasive and Mobile Computing Journal, IEEE Wireless Communication Magazine, Elseviers Journal of Parallel and Distributed Computing, and SCS Transactions on Simulation. He received the Best Research Paper Award from IEEE/ACM PADS 1997, ACM MobiWac 2006, ICC 2008, ICC 2009, and IWCMC 2009. He also received the Third National Award for Telecommunication Software in 1999 for his work on distributed security systems on mobile phone operations. He was nominated for the Best Paper Award at IEEE/ACMPADS 1999 and ACMMSWiM 2001. He is the recipient of an Ontario Early Research Excellence Award (previously known as Premier of Ontario Research Excellence Award), Ontario Distinguished Researcher Award, and Glinski Research Excellence Award. He is a cofounder of the QShine International Conference on Quality of Service for Wireless/Wired Heterogeneous Networks (QShine 2004).