Assessment of SFSDP Cooperative Localization Algorithm for WLAN Environment

Assess ment of SFSD P Cooperative Localization Algorithm fo r WLAN Environ ment Ebtesam Almazrouei, Naz ar Ali, and Saleh Al-Araji Khalifa Universit y, Abu Dha bi, UAE {Ebtesam.almaz rouei, ntali }@kustar.a c.ae Abstract —Cooperative localization for indoo r WiFi ne tworks have r eceived little at tention thus far. Many coopera tive loca tion algorithms exist for Wirel ess Sensor Network Applications but their s uitability f or WiFi based networks has not been studied. In this paper the perf ormance of the Sparse Fi nite Semi Def inite Program (SFSDP) has b een examined us ing real measurements data and under different indoor conditions. Effects of other network parameters such a s vary ing number of anchors and blind nodes are also included. Keywords—Cooperative localization, Indoor environment, SFSDP Localiza tion algorithm, Time of arrival, LOS/NLOS. I. I NTRODUCTION The main cha llenge f acin g Wi -Fi C ooperative Localizati on in indoor/urban en vironments is the multipath and non-line o f sight pr oblems that can degrade RSS and TOA ba sed distance estimation techni ques. The second major challe nge is t he design and developm ent of robust alg orithms to combine accurate ra nge/distance mea sureme nts to l ocalize APs in a network through centralized or distributed cooperative localization al gorithms. Cooperati ve localization f or wireless s ensor net works research has bee n vigorous over the la st decade[ 1]. In the literature, there a re ma ny c ooperative a lgorithm s de veloped to locate a number of blind nodes (unknown position) with a number of anchors ( known p osition) in wireless sensor networks (WS N). However , the suitabilit y of these WS N algorithms for cooperative localizations in Wi-Fi based networks and in p resence of multipath effect s has not r eceived similar attention. In [ 2, 3] it was c onclude d that ce ntralized algorithms such as the Se mi-Definite P r og ram ming (SDP ) provide more ac curate resul ts than th e distributed a lgorithm s with s imilar cost [ 4]. In [ 5] Doherty estimated node positions based on connectivity-induced constraints in a sensor network. He solve d the localizatio n problem as a co nvex optimi zation (linear) using SDP. Ouy ang, et al. [ 6] solved localization problem as a minimal optimization via SDP which obtained high accuracy with more complexity. Biswas and Ye [7] propos ed a F inite Semide finite Program (FSDP) a lgo rithm t o compute the approximate lo cation of senso r with an accurate solutio n. Kim [ 4] develo ped the S parse Finite Semidefin ite Program (SFSDP) to s olve large senso r network problem which can handle up to 6000 sensors in 2-dimensional problem. In this w ork, the pe rformance of existing c entralize d Cooperati ve Localiza tion al gorit hms suc h as SFSDP is studi ed in t he c ontext of T OA based WiFi netw orks i n i ndoor environments. The performanc e of the SFS DP algorithm developed by Kim [4] for sensor network is examined under realistic propagation channels that s uffer from multipath and NLOS impairment s. The e mpiric al model f or TOA r anging which was develope d b y the au thors [ 2] is used t o study the behavior of the SFSDP al gorithm. II. W IRELESS N ETWORK L OCALIZATION M ODEL For a specific network with b lind nodes s i and ancho rs a r , the Euclidean distances b etween the i th a nd j th blind no des d ij and between the i th blind node an d r th anc hor d ir s ho uld be determined. There will be a set of distance pairs N s which includes all the Euclide an distances between blind nodes such that d ij is not greater t han the radio range ρ , where N s ∈    . Th e radio r ange ρ is the signal ma ximum trave l d istance, i.e when the si gnal power equal s the n oise floor. Also, the Euclidean distance d ir such that d ir ∈ N a and N a is a subset o f    .                              (1)                                  (2) where s i = [ x i , y i ] T is the locatio n of the i th blind node, s i ∈ R l , i = 1,.., m in l di mensio nal space and m blind nodes. In this work l = 2 as on ly two dimensional networks are considered. Also, a r = [ x r , y r ] T is the known location of a nchor node r , a r ∈ R l , r = m +1, .., n . The estimated distances    and    a re computed as quadratic eq uation s to be appli ed in SD P:                           (3)                         (4) To solve the s ys tem of equations defined b y the network problem using SDP, the min imizatio n of the objectiv e function is giv en as [8]                                            (6 )                       (7) where ε is the erro r in distance estimatio n. T he error in position esti mation of blin d nodes is t he result of A WGN (with zer o mean)prese nce and t he propa gation condit ion. F or LOS c hannels, TOA e stimati on u sing W iFi Systems ( 20 MHz bandwidth) can be significa ntly corrupted b y the multipath while i n NLOS, both multi path and NLOS b ias are involv ed. Theref ore, the distance estima tion mode l can be ex pressed as,                   (8)      s   a  ‖  + 234,  + 56/8 56 (9) The authors in [ 2] m od elled the TOA estimation error for LOS and NLOS propagation f or stationary sce narios and i n presence of AWGN with a variance σ 2 as a normal distribu tion with a mean and varian ce. The models were d erived from real- time measurements carried out in a n indoo r environment [2, 9]. In this work, these models are incorporated in the S FSDP algorithm provided b y Kim [ 4] i n order to provide a realis tic and practical evaluatio n of t he algorithm’s performan ce. To t he best of the authors’ k nowledge, t his is the fir st work that invest igates the impact of realistic channel propagation condi tions on t he perf ormance of a cen tralized cooperativ e localizatio n algo rithm. In order to a naly ze t he performance of the algorithms, t he average po sition error P m is cal culated for all blind nod es, 9 :  ; 1  < ‖ s =   s  ‖ : > ? @   10 III. Simulation Setup a nd Anal ysis A 3 0 m x 30 m 2- Dimensional network is generated using the SFSDP s oftware with randoml y pla ced a nchors and blind nodes. T he s ize is chose n base d on the regular size of a t ypical WiFi network in indoor envi ronments with a radio range ρ = 15m. E xperimen tal data are used f or pr opagation errors for LOS a nd N LOS i n station ar y sce narios have means a nd variances of 6.98 m, 1. 87 m f or LOS and 16.06 m, 0.68 m for NLOS, respec tivel y [2] . Ge n erat e th e n et w o rk an d sav e t h e lo ca t io n o f unk n o w n A Ps Impl emen t SF SDP to lo ca t e u n kn o w n A Ps Co mp u te th e err o r an d pl o t th e f ig u res Start En d S et the Data parameters of the network Fig. 1. The structure of network simulation methodolo gy. Fig. 1 ill ustrates the main steps of the system methodol ogy. First, the networ k para meters are i dentifie d. Then, the soft ware gene rates a 2-Dimens ional netw ork with a specified number of anchors and bli nd nodes, and s ave their positions. S FSDP is then impl emented t o solve the blind nodes position using t he m odified S FSDP with t he noise model. After that, t he positi on er ror P m is compute d f or eac h b lind node a nd pl ots ar e genera ted o f t he t rue p osition a nd t he computed ones. A. AWGN Noise and Multi path Effects A 2-Dimensional network in a n i ndoor environment with 50 blind nodes an d 10 a nchors are placed. The radio range ρ is set to 15m. The nodes are placed ra ndoml y and three W iFi environment sce narios were considered; (1) with no ad ditive (a) (b) (c) Fig. 2. The p erfor mance of SFSDP wi th (a) Ideal channel, (b ) AWGN noise, an d (c) LOS/NLOS + noise effects. Green c ircles are the true position of blind nodes, red stars are the compu ted position, blue diamo nds are the anchor’s po sition, and blue lines are the position errors. noise and multipath effects (ideal channel), (2) with AWGN noise of a variance σ 2 = 0.3 m 2 , and (3) with AW GN (0.3 m 2 variance) an d LOS/ NLOS mult ipath effects. The percentage of NLOS blind nodes is 50% (2 5 nodes) of the total blind no des in the networ k. The performanc e of the S FSD P algorithm in locatin g b lind nodes within the 2-dimenti on ( 30 m x 30 m ) WiFi netw ork under the three scenari os is shown in Fig. 2. The bl ue diamonds are the p ositions of anch ors, the green circles ref er to the true location of blind nodes, and the red stars are the computed loc ations by t he S FSDP f or the bli nd nodes. The difference between the estimated an d the o riginal position o f the blind nodes is i ndicated by t he blue solid lines. From t he figure, it is clea r t hat the first scenari o, with no n oise or multipath ef fects, gives best results and t he comput ed locations by S FSDP are e xactl y the same as the true locations of blind nodes. Table 1summarise s s ome pos ition errors P m . The additi on of measure ment noise can cause a 2.4 8 m position e rror while the pos ition error i s increased dramatically to 23.2 3 m when realistic propaga tion err or are introduced. Table 1 . Performance of SFSDP with no noise, noise, a nd NLOS Eff ect. Scenarios Position error P m 1. Ideal Channel 9.5e-7m 2. Measurement noise 2.48m 3. Measurement noise and propagation error 23.23m B. Effect of Nu mber of Anchor s In t his section, the effec t of v arying the number of anchors in the ne twork on the SFSD P performance is expl ored. T he number of anchors is incre ased gradually fr om 3 until it reached 50% of the total number of blind nodes (2 5) a nchors while other parameters su ch as the radio r ange ρ , network dimensions and number of blind nodes ( m = 50), are kep t fixed. Fig. 3 sh ows the mea n p osition err or ( P µ ) defined in (11) for the thre e sce narios with L = 10 0 ran dom trial s while table 2 summari ses these resul ts. In e ach tria l the nodes were positioned rand oml y b y the program. 9 B  1 C < 9 : D ?   1 1 As expected, t he SFSDP estimates the posi tions of blind nodes precisel y for the i deal cha nnel, i.e. scenari o ( 1). Wh en measurement n oise ( σ 2 = 0.3 m 2 ) i s intr oduced, howe ver, the position err or P µ f ollows an i nverse relati onship wi th the number of anchors; P µ is 2 m, 1 m, a nd 0.9 m f or 5, 15, and 25 anchors, res pectivel y. A s light ly different be haviour was exhibited u nder sce nario (3) , with LOS/NLOS multipath effects an d n oise, as t he p osition err or P µ sh ows virtuall y no change w ith t he number of a nchors. This can be at tributed to the overwhelmin g effect of multipath component s on location estimation. Fig. 3. 100 t rial mean positon error vs number of anchors for the three scenarios. Table 2.Eff ect of number of anchors on position error P µ . Scenarios 1 2 3 5 Anchors 6e-5m 2m 6m 15 Anchors 3.5e-7m 1m 6m 25 Anchors 3e-7m 0.9m 6m C. Th e Effect of Density of t he Network. The effec t o f changing the number o f b lind nodes in a WiFi network is studi ed i n this section. The number of anchors is al wa ys 3 0% of the tot al number o f blind node s while a ll other parameters are kept t he sa me. Fig. 4 depic ts t he effec t o f increasing the d ensit y of the n etwor k (number of blind node s) on t he position er ror P m f o r 1 00 rand om trials for the three scenarios. Under scenari o 1, there is a perf ect match between the rea l and the esti mated l ocationsof the blind n odes. Nevertheless, for sce narios 2 a nd 3, the a lgrithm see ms undeciasi ve as there is fl uctuati ons in the m ean position er ror P µ . It conclu des tha t the SFSDP al gorithm fails to de termine the position of t he blind nodes w hen their number is var ied. Fig. 4. Effect of n etwork density on the mean positioning error f or the three scenarios . Table 3 als o shows t hat the r esults of SFS DP under scenario 3 has the highe st variance i n positi on estimation. Table 3. Performance of SF SDP with respect to network den sity. Scenarios Position mean P µ (m) Mean Variance Ideal Channel 8.1264e-7 1.2536e-12 Measurement Noise 3.2304 0.3502 Multipath and Measurement No ise 5.8446 1.2303 D. The Effec t of Radi o Range a nd NLOS Perce ntage The r adio ra nge ρ f or e ach bl ind node is i mportant because it identifie s its cover age area i n the netw ork. The position of blind nodes is estimated w hen i t fa lls in the covera ge ar ea of the anchor or blin d nodes. Also , the per centa g e of NLOS o r multipath severity in the ne twork im pacts the l ocalization accurac y of each blind n ode. In this section, the e ffect of multipaths is e xamined f or t hree radi o ran ges. The ra dio range is v aried from 15 m, 20 m, and 25 m, base d o n the size of the network bein g 30m x 30m. Th e number of anc hors i s kept at 3 while the percentage of NLOS range measurements is increased fr om 0 to 100%. Fig.5 il lustrates the position err or P m for 100 rand om trials as a functi on of NLOS perce ntage f or the three different radio ra nges. As e xpected, the position error P µ increases w ith increasing NLOS effects. The 0% NL OS means the er ror is solel y the result of noise. Fig.5.The effect of the NLOS percentage in the mean positioning err or for different radio ranges. IV. C ONCLUSION In this wor k, the performa nce of the SFSDP coope rative algorithm i nitially de veloped for Wire less Sensor Net works, has been e xamined f or indo or and Wi Fi suitabilit y. Empiric al TOA rangin g models, based on real time m easureme nts and data, were devel oped by the authors [2] and incorporate d in the SFSDP under different i ndoor conditi ons. This inclu ded, ideal channel, A WGN noise and a combination of noi se and (LOS/NLOS) m ultipath effe cts. The results s how that: 1) The performance of S FSDP in WiFi network under NLOS and propagati on c ondition degr ades, 2) C hangin g the W iFi network para meters s uch as number of blind nodes and number of anchors, ra dio range and N LOS perce ntages aff ect the accurac y of SFSDP in estimating the position of blind nodes. Thi s work c onfirmed t hat the performance of the SFSDP localization algorithm for w ireless sensor network has been drasticall y compr omised when used in WiFi-based networks with real TOA propa gation models. The ref ore, t here is a need to deve lop a more accurate c ooperative localizat ion algorithms for WLAN ind oor applicat ions. R EFERENCES [1] N. Patwari, “Location e stimation in sensor network s,” Thesis, 2005. [2] E. A lmazrouei, N. Alsindi, S. R. Al -Araji, N. Ali, Z. Chaloupka, and J. Aweya, “Measurements and c haracterizations of spatial a nd temporal TOA bas ed ranging f or in door W LAN channels,” (ICSPCS), December 2013, Gold Coast, Australia. [3] E. Almazrouei, “Cooperative Lo calization Techniques For WiFi (WLAN) Systems” MSc thesis, 2 015. [4] S. Kim, M. Kojima, H. Waki, and M. Yamashita, “Algorithm 920: Sfsdp: a sparse ver sion of f ull semidefinite programming relaxation for sensor network localization p robl ems,” ACM Transactions on Mathematical Sof tware (TOMS), vol. 38, no. 4, 2012. [5] L. Dohert y and L. El Ghaoui, “Convex p osition estimation in wirele ss sensor networks,” 20 th Annual J oint Conference of the IEEE Computer and Communications Societ ies. April 2001, Alaska, p p. 1655–1663. [6] R. W. Ouyang, A.-S. Wong, and C .-T. L ea, “Received signal st rength- based wireless localization via semidef inite progr amming: No n cooperative and cooperati ve schemes,” Vehicular Techn ology , IEEE Transactions on, vol. 59, no. 3, p p. 1307–1318, 2010. [7] P. Biswas, T.-C. Lian, T.-C. Wang, and Y. Ye, “Semidefinite programming b ased algorithms for sensor network localization,” ACM Transactions on Sensor Netwo rks (TOSN), vol . 2, no. 2, 2006. [8] H. Takekawa, T. Shimam ura, and S. A. Jimaa, “An E fficient and Effective Variable Step-Size NLMS Algorithm,” 42 nd ASILO MAR Conf. on Signals, System s and Computers, USA, October, 2008. [9] N. Al K hanbashi, N. Al Sin di, S. Al-Araji, N. Ali, Z. Chaloupka, V. Yenamandra, J. Aweya, “Real Time E valuation o f RF Fingerprints in Wireless LAN Localization Systems” 10th Workshop on Positioning, Navigation and Communication (WPNC), March 2013, Dresden, Germany.