Kalman Flter based Dead Reconng Algorthm for Mnmzng Networ Traffc between Moble Nodes n Wreless GRID Seong-Whan Km and K-Hong Ko Department of Computer Scence, Unv. of Seoul, Jeon-Nong-Dong, Seoul, Korea Tel: +8--10-5316, fax: +8--10-575 {swm7@uos.ac.r and jedgo@venus.uos.ac.r} Abstract. Conventonal GRID servce s statc (no moblty), and t has many drawbacs such as contnuous connecton, waste of bandwdth, and servce overloadng. Wreless GRID supports moblty, however t should consder geographc poston to support effcent resource sharng and routng. When the devces n the GRID are hghly moble, there wll be much traffc to exchange the geographc poston nformaton of each moble node, and ths maes adverse effect on effcent battery usage. To mnmze the networ traffc between moble users, we use dead reconng algorthm for each moble nodes, where each node uses the algorthm to estmates ts own movement (also other node s movement), and when the estmaton error s over threshold, the node sends the UPDATE (ncludng poston, velocty, etc) pacet to other devces. As the estmaton accuracy s ncreased, each node can mnmze the number of UPDATE pacet transmsson. To mprove the predcton accuracy of dead reconng algorthm, we propose Kalman flter based dead reconng approach. To experment our scheme, we mplement a popular networ game (BZFlag) wth our scheme added on each moble node, and the results show that we can acheve better predcton accuracy and reducton of networ traffc by 1 percents. Keywords: Dead reconng, Kalman flter, Wreless GRID 1 Introducton Conventonal GRID servce supports no moblty, and results n many drawbacs such as contnuous connecton, waste of bandwdth, and servce overloadng. Wreless GRID supports moblty and t should consder geographc poston to support effcent resource sharng and routng [1]. However, f the devce n the GRID s hghly moble, there wll be much traffc to manage the geographc poston of each moble node, and ths mae adverse effect on effcent battery usage. To mnmze the networ traffc between networng moble devces, dead reconng technque s used []. Each moble devce uses the algorthm to estmates ts movement and other devces movement, thereby, each devce can mnmze the transmsson of ts nformaton (poston, velocty, etc) to other enttes. R. Gossweler and R. J.
Laferrere ntroduced the dead reconng algorthm for the mult-user game [], and S. Aggarwal and H. Banavar proposed the use of globally synchronzed clocs among the partcpatng players and a tme-stamp augmented dead reconng vector that enables the recever to render the entty accurately [3]. In addton, W. Ca and F. B.S. Lee proposed a mult-level threshold scheme that adaptvely adjusted, based on the relatve dstance between enttes to reduce the rate of transmttng UPDATE pacets [4]. To mprove the predcton accuracy of dead reconng algorthm, we propose the Kalman flter based dead reconng approach. To smulate the moblty of moble devce scenaros n wreless GRID, we use a smple analogy, networ game (BZFlag). In secton, we revew the dead reconng and Kalman flter. In Secton 3, we propose a Kalman flter based dead reconng algorthm. In Secton 4, we apply our Kalman approach on BZFLAG game; show the expermental results wth mnmzed UPDATE pacets between game players. We conclude n secton 5. Related Wors The networng server technque can be mplemented usng three methods: (1) peer to peer, () clent server archtecture, and (3) dstrbuted server archtecture. In peer to peer, each entty transmts the occurred nformaton to each other. It s sutable for the small-scale networ. In clent server (CS) archtecture, the server collects all of the data from the clents, stores the changes n some data, and then sends the results to each partcpatng clent. For large-scale networs, we need dstrbuted server archtecture. To dstrbute server, we can use load dstrbuton method or map server method. Networng technques should mnmze (1) networ bandwdth and () networ delay..1 Locaton Awareness n Wreless Moble Networs In the wreless moble GRID, the GRID protocol s core concept parttons the geographc area nto several squares n GRIDs. Each GRID s elected the GRID s leader (so called gateway), and GRID leaders perform routng GRID by GRID. Ths protocol s locaton awared because t explots locaton nformaton n routng. Geographc locaton awareness can be GeoCast, GeoTora, and GeoGrd methods [10]. GeoCast: GeoCast sends a message to all moble devces wthn a desgnated geographc area (so called a geo-cast regon). Ths protocol dffers from tradtonal multcast, because the t uses two zones: forwardng zone and multcast regon. In the forwardng zone, the data pacet s sent by uncast to each other s devce, and n the multcast regon, the data pacet s sent by multcast to each other s devce. GeoTora: GeoTora derves from TORA (temporally ordered routng algorthm). TORA mantans a DAG (drected acyclc graph) wth the destnaton devce as sn; the data pacet s forwarded by the DAG s drecton to sn. GeoTora dvdes
nto TORA (DAG regon) and GeoCast regon. In GeoCast regons, moble devces perform the floodng, and n the DAG regon, moble devces perform an anycast from the source to any host. GeoGrd: GeoGrd s derved by the GRID protocol that have the GRID leader. GeoGrd uses two methods such as the floodng-based geo-castng and tcet-based geo-castng. The floodng-based geo-castng allows any grd leader n the forwardng zone to rebroadcast the messages, and the tcet-based geo-castng allows only tcet-holdng grd leaders to rebroadcast.. Revews on Dead Reconng Algorthms Snce each moble devce s physcally dstrbuted, updatng states (e.g. each moble devce s poston, etc) of the moble devces may generate a large amount of communcaton and thus saturate networ bandwdth. To reduce the number of state UPDATE pacets, the DR technque s used [4]. In addton to the hgh fdelty model that mantans the accurate poston about ts enttes, each moble devce also has a dead reconng model that estmates the poston of all enttes (both local and remote). Therefore, nstead of transmttng state UPDATE pacets, the estmated poston of a remote moble devce can be readly avalable through a smple and localzed computaton [4]. The moble devce compares real poston wth DR poston. If the dfference between real poston and DR poston s greater than a threshold, the moble devce nforms others remote enttes to update ther ghost object poston []. We can descrbe the smple dead reconng algorthm as follows. Algorthm : Dead Reconng for every receved pacet of remote entty do swtch receved pacet type { case UPDATE fx ghost poston of remote entty brea; case PLAYER_QUITING remove remote entty brea; } [Extrapolaton] Extrapolate all ghost poston based on the past state nformaton; f (local entty s true poston - local entty s extrapolated poston) > Threshold { Broadcast an UPDATE pacet to the group } Draw all ghost
3 Kalman flter based dead reconng algorthm In wreless GRID envronment, each moble devce s geographcally dstrbuted. A technque referred to as dead reconng (DR) s commonly used to exchange nformaton about movement among the moble devces [6, 7, 8]. Each moble devce sends nformaton about ts movement as well as the movement of the enttes t controls to the other moble devces usng a dead reconng vector (DRV). A DRV typcally contans nformaton about the current poston of the entty n terms of x, y and z coordnates (at the tme the DRV sent) as well as the trajectory of the entty n terms of the velocty component n each of the dmensons [3]. In ths paper, we use the moblty of networ game users to smulate the real geographcally dstrbuted moble devce envronments. For the networ game, we present a Kalman flter based dead reconng to optmze the networ traffc. A Kalman flter s a recursve procedure to estmate the states s of a dscrete-tme controlled process governed by the lnear stochastc dfference equaton, from a set of measured observatons t. The mathematcal model s shown n n Equaton (1) and Equaton (). s (1) = As 1 + w 1 t = Hs + r () The NxN matrx A represents an state transton matrx, w s an Nx1 process nose vector wth N(0, σ w ), t s Mx1 measurement vector, H s MxM measurement matrx, and r s Mx1 measurement nose vector wth N(0, ). To estmate the process, Kalman flter uses a form of feedbac control as shown n Fgure 1 [5]. We defne ŝ ŝ, p, p and as the pror state estmate, posteror state estmate, pror estmate error covarance, and posteror estmate error covarance, respectvely. s the Kalman gan. σ r K sˆ p Tme Update (Predct) = Asˆ 1 = Ap A T 1 +σ w Measurement Update (Correct) T p H K = T Hp H + σ sˆ = sˆ p = [ r ] + K [ t Hsˆ ] [ I K H ] p Fg. 1. Kalman flter cycle [5].
To evaluate our scheme, we used smple dead reconng scenaros (scheme 1) and optmzed dead reconng algorthm for game logc (scheme 3) for comparson. For scheme 1 and scheme 3, we use Kalman flter approach (scheme and scheme 4) to mprove the predcton performance of scheme 1 and scheme 3 as shown n Fgure. Scheme 1: Scheme : (x, y, z) (x, y, z) DR (vx, vy, vz) DR (vx, vy, vz) extrapolated (x, y, z) Kalman flter extrapolated (x, y, z) Scheme 3: Scheme 4: x, y, z x, y, z BZFlag DR vx, vy, vz, angle BZFlag DR vx, vy, vz angle extrapolated (angle) extrapolated (x, y, z) extraploated (vx, vy, vz) Kalman flter extrapolated (angle) extrapolated (x, y, z) extraploated (vx, vy, vz) Fg.. Kalman flter approach for dead reconng algorthm. Scheme 1 and scheme use DRV, whch ncludes only poston and velocty nformaton of each moble devce. In scheme 3 and scheme 4, we added the angle whch s a drecton of moble devce for predcton mprovements, and the DRV s (x, y, z, vx, vy, vz, angle, t). Scheme 3 s real dead reconng algorthm, whch s optmzed for BZFlag game logc. The detals of each schemes are as follows. Scheme 1: We compute the extrapolated poston usng last poston, last velocty, and tme step as follows. We performed the extrapolaton untl the dfference between the extrapolated poston and the true poston s under threshold. Extrapolated poston = last poston + last velocty * tme step;
Scheme : Scheme uses Kalman flter after computng the extrapolated poston as scheme 1. We performed the extrapolaton untl the dfference between the extrapolated poston and the true poston s under threshold. Extrapolated poston = Kalman Flter (last poston + last velocty * tme step); Scheme 3: To get a new extrapolated poston, the scheme uses two equatons dependng on the game entty s moton type as follows. We performed the extrapolaton untl the dfference between the extrapolated poston and the true poston s under threshold. f (lnear moton) { extrapolated poston = last poston + last velocty * tme step; } else { extrapolated poston = BZFlag functon(angle); } Scheme 4: Scheme 4 adds Kalman flter after computng the extrapolated (poston, velocty, and angle) as scheme 3. Our dead reconng algorthm (scheme 4) s descrbed as follows. float speed = (vx * cosf(angle)) + (vy * sn(angle)); // speed relatve to the tan's drecton radus = (speed / angular_velocty); float nputturncenter[]; // tan turn center float nputturnvector[]; // tan turn vector nputturnvector[0] = +sn(last_angle) * radus; nputturnvector[1] = -cos(last_angle) * radus; nputturncenter[0] = last_poston-nputturnvector[0]; nputturncenter[1] = last_poston-nputturnvector[1]; // compute new extrapolated angle usng Kalman flter float angle = Kalman (tme step * angular_velocty); float cos_val = cosf(angle); float sn_val = snf(angle); // compute new extrapolated poston const float* tc = nputturncenter; const float* tv = nputturnvector; new_x = tc[0]+((tv[0] * cos_val) - (tv[1] * sn_val)); new_y = tc[1]+((tv[1] * cos_val) + (tv[0] * sn_val)); new_z = last_poston + (vz * tme step); // compute new extrapolated velocty float vx = Kalman ((vx * cos_val) - (vy * sn_val)); float vy = Kalman ((vy * cos_val) + (vx * sn_val)); float vz = Kalman (vz);
4 Expermental Results In ths paper, we use a smple analogy: a popular on-lne game BZFlag to smulate geographcally dstrbuted moble devces. BZFlag (Battle Zone Flag) s a frst-person shooter game where the players n teams drve tans and move wthn a battlefeld. The am of the players s to navgate and capture flags belongng to the other team and brng them bac to ther own area. The players shoot each other s tans usng shootng bullets The movements of the tans (players) as well as that of the shots (enttes) exchanged among the players usng DR vectors [3, 9]. The expermental data are the poston value and the velocty value gotten n BZFlag game. We used the expermental data of 8301 numbers, and the threshold to 0.09. We compared the number of DRV pacet transmsson and the average predcton error E as shown n (3). (x, y, z) represent the true poston, (newx, newy, newz) represent the extrapolated poston, and (n) represent the number of data. E = n= 8301 = 1 ( x newx ) + ( y newy ) n + ( z newz ) (3) Table 1 shows the expermental result. Table 1 shows that the number of DRV transmsson of scheme and scheme 4 s smaller than that of scheme 1 and scheme 3, respectvely. Table 1. Font szes of headngs. Table captons should always be postoned above the tables. Scheme 1 Scheme Scheme 3 Scheme 4 # of DRV transmsson 4657 3965 703 611 E 4.511.563 0.4745 0.4048 In BZFlag game, t uses the game optmzed dead reconng algorthm, whch means that t consders the two more vectors (orentaton and angle) to predct the poston more accurately. Scheme 3 mproves the smple dead reconng approaches: scheme 1 and scheme. In scheme 4, we used Kalman flter predcton on velocty and angle, and Fgure 3 compares the scheme 3 and scheme 4 over 8000 tme steps. For better comparson, we computed movng average for each 0 samples. The dotted lne and the sold lne show the result of scheme 3 and scheme 4, respectvely.
Error 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 0.1 0 Average error 1 41 81 11 161 01 41 81 31 361 401 Tme steps scheme 3 scheme 4 Fg. 3. Comparson of predcton accuracy for 8301 tme step duraton. Fgure 4 shows the predcton errors n X and Y drecton, respectvely. Scheme 3, whch uses BZFlag game optmzed logc, shows fluctuatons, and when the predcton error s over than 0.9, the BZFlag clents should send dead reconng pacets. Mnmzng dead reconng pacets also mnmzed networ latency and the game responses tme. Even n the detaled vew, the predcton errors of scheme 4 are smaller than the predcton errors of scheme 3. 5 Conclusons In ths paper, we propose the Kalman flter approach to mprove the dead reconng algorthm for geographcally orented networng between moble nodes n wreless GRID envronments. Our scheme mproves the accuracy of dead reconng predcton, and mnmzes the networ traffc among the moble devces. Instead of expermentng geographcally dstrbuted moble devces, we use a popular on-lne game BZFlag, and compare our scheme wth the state-of-the-art dead reconng algorthm optmzed for game logc. Our Kalman flter based dead reconng scheme reduces more than 10% of networ traffc over game optmzed dead reconng algorthms. Reduced networ traffc can mae effcent battery usage.
(a) (b) Fg. 4. Error n X and Y predcton: (a) errors n X drecton, (b) errors n Y drecton
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