Chinese Journal of Aeronautics, (2015), xxx(xx): xxx-xxx

Chinese Society of Aeronautics and Astronautics & Beihang University

Chinese Journal of Aeronautics

JOURNAL OF

AERONAUTICS

cja@buaa.edu.cn www.sciencedirect.com

3 A novel particle filter approach for indoor

4 positioning by fusing WiFi and inertial sensors

5 Zhu Nan, Zhao Hongbo *, Feng Wenquan, Wang Zulin

6 School of Electronics and Information Engineering, Beihang University, Beijing 100191, China

7 Received 6 December 2014; revised 29 September 2015; accepted 29 September 2015

10 KEYWORDS

12 Fusion algorithm;

13 Indoor positioning;

14 Inertial sensor;

15 Rao Blackwellized particle

16 filter;

17 WiFi fingerprinting

Abstract WiFi fingerprinting is the method of recording WiFi signal strength from access points (AP) along with the positions at which they were recorded, and later matching those to new measurements for indoor positioning. Inertial positioning utilizes the accelerometer and gyroscopes for pedestrian positioning. However, both methods have their limitations, such as the WiFi fluctuations and the accumulative error of inertial sensors. Usually, the filtering method is used for integrating the two approaches to achieve better location accuracy. In the real environments, especially in the indoor field, the APs could be sparse and short range. To overcome the limitations, a novel particle filter approach based on Rao Blackwellized particle filter (RBPF) is presented in this paper. The indoor environment is divided into several local maps, which are assumed to be independent of each other. The local areas are estimated by the local particle filter, whereas the global areas are combined by the global particle filter. The algorithm has been investigated by real field trials using a WiFi tablet on hand with an inertial sensor on foot. It could be concluded that the proposed method reduces the complexity of the positioning algorithm obviously, as well as offers a significant improvement in position accuracy compared to other conventional algorithms, allowing indoor positioning error below 1.2 m.

© 2015 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

19 1. Introduction

20 Global navigation satellite system (GNSS) could provide accu-

21 rate positioning in the outdoor environment.1 However, the

22 limitation of signal propagation makes this technology difficult

* Corresponding author. Tel.: +86 10 82317210. E-mail address: bhzhb@buaa.edu.cn (H. Zhao). Peer review under responsibility of Editorial Committee of CJA.

for indoor positioning. Therefore, various systems offering 23

high performance for indoor localization have been proposed. 24

Due to the popularity and wide spread inside building, WiFi 25

positioning was recently introduced as a potential alternative 26

to GNSS in satellite signal denied areas. 27

In WiFi networks, the principal source of information is the 28

received signal strength (RSS). WiFi positioning requires the 29

use of a propagation model which describes the change in 30

RSS with distance. The log fading model is widely used for this 31

purpose. Recently, for indoor positioning, the prevalent tech- 32

nique is WiFi fingerprinting, which requires the database cre- 33

ation of RSS values from each access point (AP).2 When 34

positioning, user's device records its own value of RSS and 35

http://dx.doi.org/10.1016/j.cja.2015.09.009

1000-9361 © 2015 Production and hosting by Elsevier Ltd. on behalf of CSAA & BUAA.

This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

N. Zhu et al.

36 matches it against the pre-recorded database. Location is then

37 calculated based on good matches between new and stored val-

38 ues. The accuracy depends on the number of positions regis-

39 tered in the database. Besides, signal fluctuations over time

40 could induce errors and discontinuities in the user's trajectory.

41 In Ref. 3, an energy efficient WiFi indoor positioning algo-

42 rithm is proposed, using the probabilistic fingerprinting

43 method, to eliminate the fluctuations. Hybrid positioning sys-

44 tems were employed to enhance the performance of WiFi

45 indoor positioning in Ref. 4. Furthermore, the collaborative

46 RSS fingerprinting system was utilized to overcome the cost

47 and time-consuming problem of WiFi RSS positioning in

48 Ref. 5.

49 To minimize the fluctuation of RSS, other methods such as

50 the low-cost inertial sensors have been used. Due to their com-

51 plementary advantages, fusing both systems could increase the

52 positioning accuracy.6 Pedestrian step is detected by the iner-

53 tial sensors and the estimated walking direction and step

54 length are fed into the particle filter as a motion model to pre-

55 dict the new particles. The weight of the particle is updated by

56 computing the distance between the particle and the WiFi

57 localization result.7 Ref. 8 presents a sequential importance

58 resampling particle filter to fuse the accelerometer and WiFi

59 signals. Also, an augmented particle filter is proposed to simul-

60 taneously estimate location, step length and user heading. The

61 user heading could be estimated by the inertial sensor, then

62 updated by the user's trajectory in the measurement model

63 of the augmented particle filter.9 Inspired by our previous

64 study on inertial positioning, the pedestrian heading could be

65 obtained by the principle heading of building on map.10

66 Theoretically, for indoor positioning, PF can be employed

67 for any state model, but the major disadvantage of PF is that

68 sampling in high dimensional states can be inefficient.11-13 For

69 large area mapping, some approaches divide the whole envi-

70 ronment into several sub-areas which are estimated indepen-

71 dently, and then these local maps are joined through a

72 global optimization algorithms.14'15

73 This paper proposes a novel particle filter approach for

74 indoor positioning by fusing WiFi and inertial sensors. The

75 measurement model is developed using WiFi fingerprinting,

76 which accurately characterizes the RSS relation and could

77 measure the related noise. For the state model, the heading

78 information and the step length could be computed by fusing

79 the accelerometer and gyroscopes. In the proposed algorithm,

80 local areas are estimated independently by a local filter, and

81 then the trajectory of the local map origin is estimated by a

82 global filter. So the implementation of proposed Rao Black-

83 wellized particle filter (RBPF) for indoor positioning could

84 not only induce the complexity reduction, but also offer better

85 accuracy compared to other conventional algorithms.

86 The remaining sections of this paper are organized as fol-

87 lows: Section 2 presents the basic techniques of pedestrian iner-

88 tial sensor. The WiFi-based measurement method is described

89 in Sections 3 and 4 demonstrates the proposed RBPF algo-

90 rithm. Section 5 gives the trial setup and preliminary results.

91 Finally, the conclusion is drawn in Section 6.

2. Pedestrian inertial sensor method

and inertial sensors as input and outputs the user's location 95

upon each step. 96

The algorithm includes three major components: inertial 97

sensors, WiFi RSS and the RBPF. Inertial segment computes 98

the steps of the user and the length of each step. It also calcu- 99

lates the heading information aided by building layout, as 100

illustrated in our previous study.10 The pedestrian motion vec- 101

tor, [length, direction, time], would pass to RBPF as the state 102

model. 103

WiFi RSS records values periodically from all Aps as a RSS 104

vector of [rss1,rss2,rss3,...,time]. WiFi fluctuations could 105

cause notable variety in RSS vectors. The behavior of user 106

turning and entering room could mislead the inertial sensor, 107

due to the insufficient scanning of low-cost inertial sensor. 108

So the algorithm contains the turn distinguishing and entrance 109

discovering, as illustrated in Section 3. 110

PF method redistributes each particle according to the 111

pedestrian state at the particle propagation phase. At the cor- 112

recting phase, the algorithm corrects the weight of each parti- 113

cle according to the map and calculates the center of the 114

particles. Finally, in the resampling phase, the new center of 115

weighted particles is output as the current estimated position. 116

2.1. Zero velocity update 117

Zero velocity update (ZUPT) is one of the main improvements 118

available for pedestrian navigation and it is based on the phys- 119

ical property. During walking, the foot has to be briefly sta- 120

tionary while it is on the ground and at this time the foot 121

does not have any velocity.16 Therefore, the non-zero velocity 122

measurement from the inertial sensors during this period is 123

considered as an error and can be subsequently corrected. Fur- 124

thermore if this zero velocity measurement is used in Kalman 125

filter, as adopted in this paper, it could not only correct the 126

user's velocity, but also restrict the position error. ZUPT is 127

applied during each detected stance phase of the walking, so 128

the inertial errors are allowed to grow only between these 129

ZUPTs. Fig. 2 shows an example of detected ZUPT during a 130

walk and reveals that the algorithm is quite reliable. 131

However, there remains the unobservable heading error 132

that could cause the position drift. Because the heading of 133

the inertial sensor does not affect the velocity, ZUPT measure- 134

ments are unable to restrict the error. The relationship between 135

velocity errors and attitude errors in local level frame is shown 136

in Eqs. (1)-(3): 137

138 140

d vn = —/d «9 + /e«u

d ve — /d«/ — /n«u

d vd — —/e«/ + /n«9

141 143

(3) 146

93 Fig. 1 presents the architecture of the proposed fusion

94 approach. The proposed method takes the WiFi RSS sensors

where f is the force in the local frame and e/, eh, are the roll, 147

pitch and yaw errors respectively. During ZUPT, the horizon- 148

tal forces fE and fN in the local frame are basically zero and 149

specific force fD in the downward direction is approximately 150

close to the negative gravity constant. Therefore, the above 151

equations show that e/ and eh could result in the velocity errors 152

dvn, dVe and dvd, so e/ and eh are always observable. However, 153

the yaw error e9 is only observable by d ve and d vn , In order to 154

observe e9, the horizontal acceleration should not be zero, 155

A novel particle filter approach for indoor positioning by fusing WiFi and inertial sensors

Fig. 1 Architecture of the proposed fusion approach.

Time (

Fig. 2 ZUPT detection results.

which is impossible when using ZUPT. Therefore, the error becomes the crucial factor of heading drift.17

158 2.2. Building aiding measurements

159 Building aiding measurements are obtained by extracting the

160 principle heading of individual building on a map. After that,

161 the heading measurements will update the filter. This

162 algorithm will be shown as follows, to significantly reduce

163 the heading drift of the low-cost INS and make the initializa-

164 tion efficient.

165 The algorithm is based on two important assumptions.

166 Firstly, it is assumed that the pedestrians tend to be

167 constrained to a heading direction, which lies parallel to be

168 the outside of the building.18 Secondly, it is assumed that the

169 difference between the step and the outer orientation of the

170 building is the result of heading drift plus some uncertainty

171 resulting from the pedestrian not walking in a straight line.19

172 Due to the acceleration, the heading error is observable

173 through the position difference, as heading is used to deter-

174 mine the orientation of the accelerometer axes. This algorithm

175 will be entirely based on a simple illustration drawn in Fig. 3.

176 Step length d is computed based on the changes in horizon-

177 tal position (north and east):

Fig. 3 Sample of heading algorithm.

d = \J~dN + dE

The algorithm continues by making computation of a step

heading Ustep ■

Ustep = arctan —

The step heading is defined as the angle between two successive steps and it is calculated at each ZUPT epoch. ustep is the measured step heading; dE and dN are the changes in East and North.20

The measurement update is applied by forming the observation equation as follows:

u error ubuilding ustep

where uerror is the INS heading error, and ubuilding the current building orientation.

where nk is the measurement noise at kth epoch, and it repre- 200 sents the uncertainties when a pedestrian does not walk in 201 straight lines with respect to building orientations. 202

N. Zhu et al.

203 3. WiFi measurement

204 Inertial sensors could obtain relative displacement with high

205 accuracy in a short period. However, it suffers from accumula-

206 tive drift errors during walking. WiFi-based positioning system

207 could provide the absolute location estimation, while it sus-

208 tains the loss of accuracy when significant RSS fluctuations

209 happen. By fusing the two methods, it would exploit their com-

210 plementary advantages.21

211 Fingerprinting method consists of some signal power foot-

212 prints or signatures that define the position in the environ-

213 ment. This signature is made of the received signal powers

214 from different APs that cover the environment. WiFi finger-

215 printing method requires much more preparation time, how-

216 ever potentially gives more accurate positioning results.22

217 Also, even the AP redeployment in the same room could make

218 the fingerprint database different. Fig. 4 presents the measure-

219 ments recorded in RSS vectors during pedestrian walking from

220 A to B. It shows that the closer a pedestrian walks to the AP,

221 the higher RSS values are obtained. Also, there exist some fluc-

222 tuations in RSS values, which would be elaborated as follows.

223 3.1. Turn distinguishing

224 The WiFi method suffers from the fluctuation of RSS, mainly

225 due to the instable channel and human behavior. The fluctua-

226 tions could induce the algorithm to continuously choose a dif-

227 ferent position for the user even not moving or turning. So

228 reducing the unexpected jumps is necessary to improve the

229 rough positioning.

230 When the pedestrian walks, unconscious human behavior,

231 such as hand trembling, would mislead the WiFi sensors.23 If

232 such wrong estimation is not corrected, huge position errors

233 would appear when two methods fused.

234 Turn distinguishing algorithm is proposed to eliminate the

235 effect. When examining RSS vectors from each AP between

236 continuous steps, we choose the highest RSS values from the

237 unique AP. Then we use the chosen vector direction to confirm

238 whether the turn behavior occurs. If the angle of two consecu-

239 tive RSS vectors is higher than a threshold defined before, the

240 turn behavior would be affirmed. Otherwise, the heading direc-

241 tion would be replaced by previous step, as no turn exists in

242 motion. The algorithm is illustrated as follows in Table 1.

243 3.2. Room discovering

244 When a pedestrian enters a room, we could find a clear ten-

245 dency in the change of RSS vectors and the particles should

246 follow the motion. However, in real environments, the number

247 of particles is limited to typically 300, thus the distribution is of

248 radius 1 m, only covers half of the corridor. Therefore, there

249 could exist the situation that when people enter a room

250 through the door, particles keep dying with the position esti-

251 mated against the wall, as shown in Fig. 5(a) and (b). To alle-

252 viate that dilemma, the RSS vectors are utilized. If the RSS

253 values keep changing, the pedestrian should not be static and

254 move into the room. Then the algorithm queries the map to

255 locate the nearest door between the founded AP and current

256 position. The particle would be resampled with the weight 1,

257 while all other particles would be deleted. Thus pedestrian

motion estimated should be accurate after the resampling phase, as shown in Fig. 5(c).

4. RBPF algorithm

PF algorithm receives the motion vector [length, direction, time] from inertial sensors, and fuses with the WiFi RSS vector [rss1,rss2,rss3,...time], then outputs localization result. The particles are initialized as follows:

Pt = {<Pi. W)} , i = 1.2; •••, N

P = {x'v y'v h\)

(2) (9)

where p't is the estimated position with weight w\ of i particle at epoch t, N is the whole numbers of the particles, while fft denotes the heading information.

As the WiFi sensor could be sparse and short in range, the whole region is divided into several local areas as shown in Fig. 6.

The global map is divided into 4 local maps according to the pedestrian trajectory. The local map and global map are hierarchically estimated by RBPF. The algorithm is based on three assumptions as follows24:

(1) The local maps are independent of each other.

(2) The global estimates are independent of Raw data which is used for local maps.

(3) Indoor environments mainly consist of orthogonal line.

The third assumption is the same as the requirements of the building aiding measurements used in Section 2.2. Thus, we could define the map as follows:

! = {M, m1:s}

where M and m1:s represent global and local maps; s indicates the number of local maps.

The whole process of RBPF algorithm is shown in Fig. 7. Firstly, pedestrian walks in a local area, while processing by the local RBPF. Secondly, after closing loop for the local region, the local particles are merged into a single map and used in the global RBPF for measurement update. Thirdly, pedestrian walks into another local area and the localization particles are used as the sample distribution for updating the distribution in global RBPF. The whole process would iterate until the global map closure detected.

4.1. Local RBPF

Local RBPF is processed in the margin of local area. The particle pt is generated through three steps as follows:

4.1.1. Particle propagation The new location and head

fft — ut + e

x't — Xt_j + (lt + d) cos dt y\ — yt_1 + (lt + d) sin 6t

261 262

281 282

288 289

are 307

(11) 310

(12) 313

(13) 316

A novel particle filter approach for indoor positioning by fusing WiFi and inertial sensors

Fig. 4 Measurement of RSS while walking.

317 where ut is the step direction, and lt denotes the stride length; d

318 and e are zero-Gaussian noises for stride length and heading

319 respectively.

4.1.2. Particle correction

321 This step is to correct the weights of propagated particles. Due

322 to the boundary of local map, if the particle moves across the

323 wall, the weight would be given to zero. The weights are

324 updated as

Correction process will interact with WiFi component under particular conditions, such as the turn distinguishing and room discovering.

4.1.3. Resampling

The step is to delete the particles with weight 0 and regenerate new ones for the surviving particles. The weighted center of all

CJA 557 22 October 2015 ARTICLE IN PRESS No. of Pages 10

6 N. Zhu et al.

Table 1 Algorithm 1: turn distinguishing. Algorithm 1. turn distinguishing

Input: tc, tp1, tp2 // tc, tp1, tp2: current and last two epochs

Vc, Vp //Vc, Vp: current and last vector Output: Current heading direction / = arccos( Vc, Vp)/(|Vc|.|Vp|) If / e (p/4,3p/4) then return Current heading direction = Vc else

return Current heading direction = Vp End if

particles would be computed again and the current estimated position is output.

may result in a large position drift. The sampling frequency of inertial sensor was set at 50 Hz, while the sampling frequency of WiFi sensor was 5 Hz.

The trials were carried out in an indoor office area covering 362.6 m2, as shown in Fig. 6. There are four APs available and 30 reference points to be deployed. The distance between neighbor reference points is 1.2 m. During offline step, 8 training samples were collected per reference point to build the fingerprint database.

To show the convincing results, 6 pedestrian users were chosen to collect the data of 100 trajectories. The pedestrian moved at a regular walking speed of about 1 m/s, and the trajectory was designed, as shown in Fig. 6, including turn behavior and entering the room with AP3.

5.2. Performance of the proposed fusion method

4.2. Global RBPF

Global RBPF estimates the global area using the trajectory of local map. Every particle contains the unique global map estimation; however, it would increase the computation. So we alleviate the burden with all particles sharing local maps and the corresponding vectors. Thus the particles would include trajectories and weights only:

PS fU <)}

Ms = {(m1:„ V1:s)}

the particle weight

where n\ s the trajectory of local map, and V the vector in local map m.

Then we could process the global RBPF in Table 2. Firstly, the probability distribution in the local map is input as the localization particle pt; secondly, it combines them to generate new trajectory nS; finally, the algorithm outputs the global particle Ps .25

5. Field trial

5.1. Equipmental setup

The experiments were conducted to test the proposed approach. The pedestrian carried a foot mounted Microstrian inertial sensor, with Samsung Galaxy tablet on hand, as shown in Fig. 8. The low cost inertial sensor could induce errors that

To confirm the validity of the proposed fusion approach, positioning results with inertial senor and WiFi sensor separately are presented for comparison, as shown in Fig. 9(a). Results with the proposed method and the truth path are shown in Fig. 9(b).

In Fig. 9(a), the black dotted line indicates the path estimated with inertial sensor, while the red dotted line indicates the path estimated with WiFi sensor. There exist critical errors for the inertial sensor. The true trajectory is that the pedestrian entered the room with AP3, through the door, turned backwards and walked out. However, the black path computed by the inertial method, pass the wall into the room. Whereas the red path estimated by the WiFi method, presents accuracy results when entering the room. It is mainly because of the algorithm proposed in Sections 3.1 and 3.2.

Though WiFi localization obtains inaccurate tracking results along the whole path, it could provide useful information, especially along the orthogonal path, as shown in Fig. 9 (a). However we find that the WiFi method provides bad results severely, when pedestrian walked in the corner. The estimated location is unacceptably far from the truth.

Clearly, the proposed fusion performs best and provides the estimated trajectories matching the ground truth closest. Turn distinguishing is invoked in the corner, where the highest RSS values from the corresponding AP are found. Then we calculate the vector direction to confirm whether the turn behavior occurs.

After finding that the estimated position against the wall lasts for several epochs, we check whether RSS values keep

Fig. 5 Room discovering.

A novel particle filter approach for indoor positioning by fusing WiFi and inertial sensors

Fig. 6 Local areas and global areas.

Fig. 7 Flowchart of the proposed RBPF algorithm.

Table 2 Global RBPF.

Algorithm 2. Global RBPF

Input: p't // p't: local particle

P\_ 1 // P\_ 1 : previous global particle Output: P\ // P\: current global particle

For i = 1,2,..., N

n = ® n

End for

return P\ = {< n 1:s; >g

406 changing. The room discovering algorithm begins, and it finds

407 the nearest door between AP3 and current position. Then the

408 algorithm corrects the path estimated by resampling the

409 particle. From Fig. 9, it could be indicated that the estimated

position reaches the end point B only 0.8 m away from the 410

truth path. 411

We compare the positioning accuracy among various 412

approaches. As shown in Table 3, compared with inertial 413

sensor and WiFi sensor, the proposed approach performs 414

much better, while it could achieve mean position error by 415

1.2 m and standard deviation by 0.7 m. The corresponding 416

cumulative error distributions are also shown in Fig. 10. From 417

the figure, we could find that nearly 70% of the error 418

distance is below 1 m, which could achieve the need of indoor 419

positioning accuracy. 420

5.3. Computation burden 421

Positioning accuracy could be promoted by increasing particle 422

numbers; however, the computation and storage cost of PF is 423

proportional to the numbers. Due to the heavy computation 424

burden, large particle-based approach should be run on a ser- 425

ver and is unsuitable for real-time applications. Actually, there 426

is a tradeoff between position accuracy and computation 427

burden. 428

Fig. 8 Positioning equipment setup.

N. Zhu et al.

(b) Trajectory estimated with the proposed method and reference path Fig. 9 Trajectory estimated.

Table 3 Position errors.

Position method Mean error i(m) Standard deviation r(m)

Proposed fusion 1.2 0.7

Inertial sensor 2.1 1.6

WiFi sensor 2.8 2.1

429 This paper utilizes the local RBPF and global RBPF

430 algorithm to reduce the cost. According to the indoor area,

431 the size of each local area was set to 2.5 m x 3 m. For the local

432 RBPF, only 100 particles were used and reused each time when

433 entering new local area. The particles for global RBPF need

Error distance

Fig. 10 Accuracy comparison using different methods.

CJA 557 22 October 2015 ARTICLE IN PRESS No. of Pages 10

A novel particle filter approach for indoor positioning by fusing WiFi and inertial sensors 9

0 1 2 3 4 5 6

Error distance

Fig. 11 Accuracy comparison with different numbers.

relatively little cost because they do not possess their own areas, therefore 300 particles are used for the global RBPF. Thus, after the local RBPF, we approximate the particles as a Gaussian distribution, and sample 200 more particles to generate the 300 particles.

We compare the positioning accuracy between the proposed RBPF algorithm and the previous PF algorithm. Fig. 11 shows the cumulative error distributions using different particle numbers. We can find that the accuracy degrades severely when using PF algorithm with 300 particles, and only 47% of the error distance is below 1 m. If we enlarge the particle numbers, then the accuracy would increase. Thus, when the particle number is 500, the performance of PF algorithm would achieve comparable accuracy of the proposed RBPF. So it is more suitable for real-time indoor position by the proposed RBPF algorithm.

6. Conclusion

In this paper, a novel fusion algorithm for indoor positioning is proposed. The filter method is exploited to integrate inertial sensor, WiFi sensor and the map information. Also, local RBPF and global RBPF are introduced into the fusion algorithm. By dividing the indoor environments into several local areas, without computing the global areas, the computation could reduce greatly.

Preliminary trial results show that the proposed RBPF algorithm could achieve the positioning accuracy of 1.2 m and it meets the need of indoor positioning. Also, the calculation burden is nearly half of the conventional PF methods.

There remain some problems that should be addressed for practical use. We need to expand the proposed approach to the situation with non-orthogonal environments. Thus, these considerations would be developed in the future work.

Acknowledgments

The trial undertaken for this paper was partly conducted at Nottingham Geospatial Institute at the University of Nottingham, UK. The authors would like to express the sincere gratitude to Dr Meng for the infinite support and guidance throughout the trial.

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542 24. Lee T, Lee S, Oh S. A hierarchical RBPF SLAM for mobile robot

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549 Zhu Nan is a Ph.D. candidate at Beihang University. His current

550 research interests include satellite navigation and signal processing.

552 Zhao Hongbo received Ph.D. degree in communication and information

553 system from Beihang University in 2012. He has been teaching there

554 since 2012. His current research interests include signal processing,

555 satellite navigation and satellite communication.

Feng Wenquan received Ph.D. degree in communication and informa- 557

tion system from Beihang University, Beijing, China. He is a professor 558 and works in Beihang University. He has been teaching as the dean of 559

studies at Beihang University since 2011. His current research interests 560

include satellite navigation and satellite communication. 561

Zulin Wang received Ph.D. degree in communication and information 563 system from Beihang University, Beijing, China. He is a professor and 564 dean of School of Electronic and Information Engineering, Beihang 565 University. His current research interests include signal processing and 566

avionics electronic system. 567