TOWARDS APPLICATIONS OF PARTICLE FILTERS IN WILDFIRE SPREAD SIMULATION

Transcription

1 Proceedings of he 008 Winer Simulaion Conference S. J. ason R. Hill L. oench and O. Rose eds. TOWARDS APPLICATIONS OF PARTICLE FILTERS IN WILDFIRE SPREAD SIULATION Feng Gu Xiaolin Hu Deparmen of Compuer Science Deparmen of Compuer Science Georgia Sae Universiy Georgia Sae Universiy 34 Peachree Sree Suie 450 Alana GA USA 34 Peachree Sree Suie 450 Alana GA USA ABSTRACT Wildfire propagaion is a complex process influenced by many facors. Simulaion models of wildfire spread such as DEVS-FIRE are imporan ools for sudying fire behavior. This paper presens how he sequenial one Carlo mehods i.e. paricle filers can work ogeher wih DEVS-FIRE for beer simulaion and predicion of wildfire. We define an applicaion framework of paricle filers for he problem of wildfire spread using he DEVS-FIRE model and discuss several applicaions. A case sudy example is provided and preliminary resuls are presened. INTRODUCTION Wildfire propagaion is a complex process influenced by many facors such as spaial fuel weaher condiions and landscape. In pas years several models were developed o sudy and predic he fores fire spread. Examples include FARSITE (Finney 998) BehavePlus (Andrews e al. 005) and DEVS-FIRE (Naimo e al. 008). In all hese models he saes of he sysem such as fire fron rae of spread speed perimeer and burned area a differen ime seps are compued based on informaion including spaial fuel daa weaher daa and landscape daa. In a dynamic daa-driven environmen where imely sensor daa (e.g. fire frons and burned areas of a wildfire from saellie images) are available i is desirable o updae a simulaion model wih he curren sysem sae for beer simulaion and predicion of wildfire. The problem arises abou sae esimaion of dynamic sysems. Sequenial one Carlo mehods ofen referred o as paricle filers are a se of saisical mehods o sudy dynamic sysems by recursively esimaing he probabiliy densiy funcion ha can be used o compue differen esimaed saes (Douce e al. 00; Schön 006). In pracical applicaions he probabiliy densiy funcion is represened by a se of samples also called paricles and heir corresponding weighs. any approaches of generaing samples are proposed o solve he problem ha we canno obain he samples from he arge densiy. These include perfec sampling sampling imporance resampling accepance-rejecion sampling eropolis-hasings independence sampling. Each of hese echniques has is own advanages and disadvanages so hey can be adoped in various occasions (Simandl e al. 007). In his paper we formalize he applicaion of paricle filers based on he wildfire spread model of DEVS-FIRE (Naimo e al. 008). Wihin his framework we define several applicaions of paricle filers ha could be developed using he wildfire spread simulaion model. These applicaions include dynamic sae esimaion saic parameer calibraion and reconsrucion of hisorical imely parameers. As a case sudy example we show how he dynamically changing wind speed and wind direcion in a fire spreading scenario can be esimaed based on observed fire frons and burned areas using he DEVS-FIRE model. We noe ha alhough he case sudy example deals wih wind daa he formalized paricle filers-based framework can be adaped and exended o oher applicaions for wildfire spread. The res of his paper is organized as follows. Secion briefly discusses relaed applicaions of paricle filers. Secion 3 describes he basic mehods and algorihms of paricle filers. Secion 4 formalizes he applicaions of paricle filers in DEVS-FIRE. Secion 5 provides a case sudy example. Secion 6 presens he experimen resuls and analysis. Secion 7 draws some conclusions. RELATED WORK Paricle filers have been used in many applicaions such as image processing communicaions chemisry biology and social sciences. (Wang e al. 00) used paricle filers o solve he problem of muliuser deecion in signal processing. (Gusafsson e al. 00) designed a framework for he problems of posiioning navigaion and racking based on paricle filers and some general algorihms were described. Based on a one Carlo mehod (Fox e al. 00) discussed robo localizaion one of he key problems of mobile robos in which he iniial posiion of he robo was unknown. Therefore sensor daa were uilized o esimae he robo s posiions. (Zhang e al. 003) provided anoher applicaion of paricle filers in biology. In his paper

2 populaions of compac long chain off-laice polymers were generaed based on a sequenial one Carlo mehod o explore he relaionship beween packing densiy and chain lengh. In he fores fire lieraure (Bradley 007) presened an approach o esimae and rack fores fires based on paricle filers in video processing in which images informaion obained from miniaure air vehicles was used. Anoher research direcion of paricle filers in fores fire spread sysem is daa assimilaion. (andel e al. 007; Douglas e al. 006; Coen e al. 007) used paricle filers o sudy fire behaviors of wildfire models. Their work was based on wo kinds of fire models reacion-diffusionconvecion parial differenial equaions-based model and he level se mehod model. By esimaing he emperaure and fuel supply of each cell of he area he oupus of he fire could be calculaed by he funcion of he fire model based on level se mehod. This oupu was reaed as he measuremen o updae he emperaure and fuel supply by comparing esimaed oupus and observed daa. ore deails can be found in hese papers. 3 THE NON-LINEAR DYNAIC SYSTE ITS STATE ESTIATION AND PARTICLE FILTERS 3. The Non-linear Sae Space odel A ypical non-linear sae space model can be denoed by formula (Jazwinski 970) s+ = f ( s ) + v () m = g( s ) + w where s and m are he sae variable and he measuremen variable respecively; he funcions of f and g define he evoluion of he sae variable and he measuremen variable; v and w are wo independen random variables o generae he sae noise and he measuremen noise; is a se of saic parameers. According o arkov propery a sysem can be describe as s + ~ p ( s+ s s... s ) = p ( s+ s ) () where p (s) describes a se of probabiliy densiy funcions and p ( s + s ) represens he evoluion of he sysem over ime +. According o he model we can calculae he nex sae using he curren informaion a ime. Using he arkov propery and hidden arkov model (Douce e al. 000) () can be changed in he form of s+ ~ p ( s+ s ) = pv ( s+ f ( s )) (3) m ~ p ( m s ) = pw ( m g( s )) where we use muual independence of he measuremen noise w o denoe ha of observaion over and he process noise v is also muually independen over ime. 3. Sae Esimaion and Filer Densiy Afer formalizing he dynamic sysem as a sae space model we can esimae he fuure sae according o he hisory informaion conained in he curren sae. This also comes from probabiliy densiy funcion p ( y xs ). For he esimaion problem is he nex or he las sep of s. Similarly i is he filering densiy problem when s equals. Considering (3) according o Bayes heorem we obain he Chapman-Kolmogorov equaion (Jazwinski 970) p ( s+ ) = p ( s+ s ) p ( s ) ds (4) p ( s+ s ) p ( s+ T ) p ( s T ) = p ( s ) ds+ (5) p ( s ) and + p ( m s ) p ( s ) p ( s ) =. (6) p ( m ) From he above equaions we can see here are no effecive mehods o recursively esimae he saes of nonlinear dynamic sysems. This resuls in many approximaion algorihms o solve he problem. These algorihms eiher linearize he model o solve or find an opimal soluion by numerical mehods. The widely used Kalman filer (see e.g. (Kailah e al. 000)) belongs o he firs caegory. Sequenial eno Carlo mehods or paricle filers are in a differen caegory in which probabiliy densiy funcions are approximaed by a series of paricles. 3.3 Paricle Filers Generally speaking a paricle filers algorihm is a numerical mehod o approximae condiional filering disribuion. Considering filer densiy in (6) we can obain p ( s ) p ( m s ) p ( s ). (7) ( Le he arge densiy s ) = p ( s ) he imporance weigh q s ) = p ( m s ) and he sample densiy ( ( = ( s ) q( s ) sd( s sd s ) p ( s ) hen we can generae he formula ). Therefore we need o obain samples from he arge densiy. There are various algo-

3 rihms designed for his goal including perfec sampling imporance sampling accepance-rejecion sampling and eropolis-hasings independence sampling which were discussed in (Liu e al. 998; Bølviken e al. 00; Chib e al. 995). Among all hese sampling algorihms SIR (Sampling Imporance Resampling) is widely used in many applicaions o generae samples from he arge densiy. We can consruc he approximaion of he arge densiy ~ ] N [ i] [ i] ˆ ( x) = q~ ( x ) δ ( x x ) N i= [i where q ( x ) is he normalized imporance weigh of he sample and δ is he Dela funcion. The imporance weigh of a sample specifies he possibiliy of is being generaed. However his approach has he limiaion ha he whole process relies on hese iniially generaed samples. To improve he algorihm a resampling sep is added according o ( ~ [ i] [ j] ) ~ ( [ j] P x = x = q x ) i= N. ore deails abou he algorihm can be found in (Gordon e al. 993). In summary he major seps of paricle filers based on sampling imporance resampling is described below. Sep : iniialize N paricles. Sep : calculae imporance weighs. Sep 3: normalize imporance weighs. Sep 4: resampling. Sep 5: predic new paricles for fuure use. Sep 6: go o Sep o execue he nex ime sep. 4 APPLICATIONS OF PARTICLE FILTERS USING THE DEVS-FIRE SIULATION ODEL 4. Overview of The DEVS-FIRE odel DEVS-FIRE is an inegraed simulaion environmen for surface wildfire spread and conainmen based on Discree Even Sysem Specificaion (DEVS) (Zeigler e al. 000). I uses a cellular space o model a fores and each cell corresponds o a sub-area of he fores. Fire spreading is a propagaion process ha burning cells ignie heir unburned neighbor cells. The speed of fire spreading is calculaed based on condiions including spaial fuel daa landscape daa and weaher daa of he area. Besides fire spread simulaion DEVS-FIRE also suppors fire suppression simulaion and opimizaion of firefighing resource deploymen for conaining a fire. ore deails abou DEVS-FIRE can be found in (Naimo e al. 008). In he paper we only consider he aspec of fire spread simulaion. Ignoring he implemenaion deails he DEVS-FIRE fire spread model can be describe as x = DF( fuel aspec slope weaher x ) + x x + where and are he sysem saes ha represen he fire spreading siuaion (i.e. which cells are ignied and which cells are no) a ime sep and + respecively each of which can be denoed by a wo-dimensional marix wih elemens or 0 represening wheher he cell is ignied or no. fuel is a saic inpu parameer o define he fuel models of each cell in he cell space. slope and aspec refer o he saic inpu parameers o specify landscape of each cell in he cell space. weaher means an inpu parameer o define he wind speeds and wind direcions a differen ime. DF sands for he model of he dynamic fire spread sysem. According o we can compue oupus of he model such as fire frons fire perimeers and burned areas. 4. Towards A Framework of Applicaions of Paricle Filers Using DEVS-FIRE Given ha DEVS-FIRE is a simulaion model for dynamical wildfire spread in a fores his secion discusses several applicaions of paricle filers ha could be developed based on DEVS-FIRE. These discussions inend o define a framework of he applicaions of paricle filers o he problem of wildfire spread using he DEVS-FIRE model. The firs applicaion corresponds o sae esimaion of wildfire spread using DEVS-FIRE. When we have observed real daa a some ime seps from sensors or saellie images we can esimae he saes e.g. fire frons of he sysem based on he observed daa using paricle filers. A every ime sep we generae paricles e.g. differen fire fron shapes and hen updae he weigh of each paricle based on he sensor daa from he real fores. According o he paricles and heir corresponding weighs he nex fire shape can be obained. In his way he informaion from real daa is incorporaed ino he DEVS-FIRE model o beer predic he fire propagaion in pracical applicaions. Anoher applicaion of paricle filers is o calibrae he saic parameers of DEVS-FIRE. In his case he saic parameers should be exended wih saes hus ransforming he problem ino an opimal filer problem (Douce e al. 003). For example an imporan parameer in DEVS- FIRE is he fireline inensiy hreshold ha is used o decide wheher an ignied cell is burnable or no. Given he real fire spreading observaion daa e.g. burned areas for some ime period he hreshold can be approximaed by paricle filers. To do ha we randomly assign N paricles wih values in a pre-defined range. Using hese paricles as inpus we run DEVS-FIRE model N imes for his ime period o obain heir corresponding burned areas. Then comparing hese areas wih he real burned areas we can compue he weigh of each paricle and choose he paricles x

4 having larger weighs for use of he nex sep. Recursively execuing his process he hreshold will converge o a small range so we can use his as he esimaed hreshold. Anoher applicaion is o reconsruc imely parameers (i.e. esimae wha happened before) for a given se of observaion daa. For example in DEVS-FIRE wind daa always change wih ime advances. If knowing he fire frons and burned areas from ime 0 o + we can esimae he pas wind daa condiions using paricle filers. This problem is similar o ha of smoohing all pas saes using measuremen daa (see (Gibson 003) for more deails). Each of he above applicaions deals wih a differen aspec. Thus he specific deails of paricle filers will also be differen. Despie ha hey all share a similar implemenaion srucure ha corresponds o he general srucure of paricle filers and uses he simulaion model of DEVS-FIRE. Figure illusraes a srucure of paricle filers based on DEVS-FIRE for he sae esimaion applicaion described above. Every ime sep we use he paricle filers componen o generae paricles run simulaions based on he paricles and obain measuremens. Comparing he measuremens wih he observed daa OBD we can calculae he weighs of he paricles and normalize hem. Using he paricles and heir weighs we can ge he value of sae variable SV a ime and he esimaion of he nex sae SV a ime + according o he + DEVS-FIRE simulaion model. Saic parameers SV DEVS-FIRE 5 A CASE STUDY EXAPLE 5. The Case Sudy Example SV + OBD Paricle filers Figure : Sae esimaion using DEVS-FIRE As a case sudy example his secion shows how paricle filers can be applied o wind speed and wind direcion esimaion using he DEVS-FIRE model. I is known ha wind speed and direcion can significanly affec he spreading of a wildfire. Being able o esimae he dynamic changing wind speed and direcion hus is helpful and can complemen he weaher daa colleced from weaher saions for beer predicion of wildfire spread. In his example we use hree erms o differeniae hree ypes of wind daa: ) real daa he real wind speeds/direcions ha need o be esimaed. In he example hese daa are arificially generaed by a compuer program every 0 minues. A fire spread simulaion using he real daa is referred o as he real fire spread ; ) weaher daa he wind speeds/direcions ha are obained from a local weaher sae. These daa are only available every hour (assuming no measuremen errors); 3) esimaed daa he wind speeds/direcions esimaed from he paricle filers. This example esimaes he wind speeds/direcions every 0 minues. Our goal is o show ha he esimaed daa will follow he same rend of he real daa and fire spread simulaion using he esimaed daa gives beer predicion resul han using he weaher daa. To apply paricle filers we define he wind daa as he sae variable and esimae hem according o he observaion daa. The observaion daa used in his example are he fire frons and burned areas ha are colleced every 0 minues from he real fire spread (fire spread simulaion using he real daa). Based on he above discussion he dynamic sysem under sudy is defined as follows. wind + = f ( wind ) + v B = cala( DF( fuel aspec slope wind )) + w B = A + A where wind = wsp wdir ] is he sae variable he [ wind daa (wind speed wsp and wind direcion wdir ) a ime ; B is he measuremen variable he new burned area of he fire from ime o + ; A and A + are observed burned areas of he fire a ime and + respecively. v and w are he noises of wind and B respecively. cala is used o calculae he burned areas from ime o + based on he observed fire frons a ime. DF is he DEVS-FIRE simulaor and fuel aspec and slope are reaed as he saic inpu parameers. Here he key idea is o esimae he wind daa a ime based on he new burned area afer one ime sep for a given fire fron a ime. In he process of sae esimaion he noises of he sae variable and he measuremen variable are used. The noises are muually independen variables generaed by normal disribuions as follows. v ~ N(0 σ ) and w ~ N(0 σ ). v w

5 5. Implemenaions of Paricle Filers Based on he dynamic sysem formalized above we implemen he paricle filer algorihm as shown below.. Iniialize N paricles for i = 0 o N Randomly generae vwsp (0) and vwdir(0) according o normal disribuions N(0 σ vwdir ) respecively; wsp ( 0) = wsp0 + vwsp( 0); N(0 σ vwsp wdir ( 0) = wdir0 + vwdir( 0); ) and. Compue weighs for i = 0 o N Randomly generae vwsp ( and vwdir( according o normal disribuions N(0 σ vwsp ) and N(0 σ vwdir ) respecively; wsp( = f wsp ( wsp( k )) + vwsp( ; wdir( = f wdir ( wdir( k )) + vwdir( ; wind ( = [ wsp( wdir( ]; Randomly generae w( according o normal disribuion N(0 σ w ) ; B ( = cala( PF( wind( )) + w( ; weighs( = oba( k + ) oba( B( ; weighs( k ) σ w ( ) weighs i k = e ; σ w π 3. Normalize weighs s _ ws = 0; for i = 0 o N s _ ws = s _ ws + weighs( ; for i = 0 o N n _ ws( = weighs( / s _ ws; 4. Resampling q ( 0) = n _ ws(0 ; for i = o N q ( i) = q( i ) + n _ ws( ; Uniformly generae N numbers beween 0 and and sor hem as array u ; coun = ; for j = 0 o N while ( q ( coun) < u( j)) coun = coun +; emp ( j) = wind( coun ; for l = 0 o N wind ( l = emp( l); 5. Oupu saes (he esimaed wind daa) os ( = 0; for i = 0 o N os ( = os( + wind( * n _ ws( ; In his algorihm sep iniializes N paricles. Wih ime advances sep o sep 5 are execued as shown in Figure. Sar Paricles iniializaion N Observed daa? Weighs compuaion N Weighs normalizaion Resampling Saes oupu Figure : Flow of paricle filers algorihms of case sudy There are several proposed sampling algorihms for example sysemaic sampling (Kiagawa 996) and residual sampling (Liu e al. 998). Among hem he sysemaic sampling is widely used (Hol 004). We use sysemaic sampling in our implemenaions oo. Y N End

6 6 EXPERIENTS AND RESULTS 6. Experimens Design Based on he example described above we design wo experimens as follows. The firs one uses a uniform fuel model (fuel model 7) wih simple wind flow and zero slope and aspec. The wind is generaed as follows. The iniial wind speed is miles/hour. In he firs half of he enire process ha lass for 5 hours he wind speed increases 0.5 mile/hour every ime sep (0 minues) and hen decreases 0.5 mile/hour every ime sep. The wind direcion keeps a fixed value of 80 degrees. In he second experimen we use non-uniform GIS daa where cells have differen fuel models aspecs and slopes. The iniial wind speed and wind direcion are 5 miles/hour and 80 degrees. Then every ime sep he wind speed increases or decreases a number beween 0~ miles/hour based on ha of he las sep and he wind direcion is 80±0 degrees. Table and Table show he real wind daa (column and column 3) generaed based on he wind flow model described above. Noe ha hese are he daa ha need o be esimaed by he paricle filers. Based on he real wind daa we use DEVS-FIRE o run he simulaions o obain he fire frons and heir corresponding burned areas every 0 minues (hese are he observaion daa). Table and Table also show he weaher daa (column 4 and 5). We assume he weaher daa are known only a every hour. Our goal is o esimae he wind daa every 0 minues for he ime when he weaher daa are no available. This is achieved using paricle filers based on he observaion daa of fire frons and burned areas. The paricle filers algorihm uses 50 paricles. The simulaions are run for 5 hours and he wind flow model used in he paricle filers for boh experimens is as follows. wsp( ) = wsp( ) + N(04) =... wdir( ) = 80 + N(040) =... Table : Wind daa of experimen Time Real Real Weaher Weaher wsp wdir wsp wdir 0: : : : : : : : : : : : : : : : : : : : : : : : : : : : : : Table : Wind daa of experimen Time Real Real Weaher Weaher wsp wdir wsp wdir 0: : : : : : : : : : : : : : : : : : : : : : : : : : : : : :

7 6. Experimens Resuls 6.. Case : Uniform Fuel wih Simple Wind Condiion Figure 3 displays he saes of wind speed every 0 minues for case. Figure 4 shows he saes of wind direcion of each ime sep of case. In he figures real daa mean wind daa used o obain observed areas in paricle filers and weaher daa esimaed daa sand for he wind daa every hour and esimaed wind daa by paricle filers respecively. From Figure 3 and Figure 4 we can see ha 0 Wind speed (miles/hour) Wind direcion (degrees) Real daa Weaher daa Esimaed daa Time sep (every 0 minues) Figure 3: Wind speeds of case Real daa Weaher daa Esimaed daa Time sep (every 0 minues) Figure 4: Wind direcions of case he esimaed wind speeds and wind direcions have he same rend as hose of he real wind condiions. Therefore in he pracical applicaions if we only know he wind condiion every ime period (e.g. hour) we can esimae he wind daa each ime slo beween his ime according o observed daa by paricle filers. Figure 5 displays he burned areas wih hree wind condiions form ime sep o 0. From he figure we can conclude ha compared o using weaher daa he burned areas compued by using esimaed wind daa are closer o he ones calculaed by real wind daa. This means ha he esimaed daa can be used o produce more accurae predicions. Burned area (ha) Real daa Weaher daa Esimaed daa Time sep (every 0 minues) Figure 5: Burned areas of case 6.. Case : GIS Daa wih Complex Wind Condiion Figure 6 and Figure 7 show he wind speeds and wind direcions of case. From he picures we can draw similar conclusions as before. Figure 8 displays he burned areas wih he hree ypes of wind daa from ime sep o 4. From he picure we can see ha he esimaed areas fall beween he areas obained by using real daa and by using weaher daa. Wind speed (miles/hour) Real daa Weaher daa Esimaed daa Time sep (every 0 minues) Figure 6: Wind speeds of case

8 Wind direcion (degrees) Burned area (ha) Real daa Weaher daa Esimaed daa Time sep (every 0 minues) Real daa Weaher daa Esimaed daa 7 CONCLUSIONS Figure 7: Wind direcions of case 3 4 Time sep (every 0 minues) Figure 8: Burned areas of case In his paper we discussed he basic knowledge of paricle filers mehod and hen consruced he non-linear dynamic sysem model of DEVS-FIRE fire spread model according o he specificaion of sequenial one Carlo mehods. Alhough here are many possible applicaions of paricle filers using DEVS-FIRE we focus on he wind esimaion as a case sudy in he paper. Preliminary resuls show ha paricle filers are powerful ools ha can be used in he problem of wildfire spread simulaion. Fuure work will proceed along he following direcions: ) precisely esimae he fire shapes by using observaion daa from saellie images; ) apply paricle filers o esimae he saic parameers from he observaion daa and smooh parameers o sudy pas saes according o observaion daa; 3) develop advanced mehods o reduce he compuaion cos of paricle filers ha use large number of paricles. REFERENCES Andrews P. L. C. D. Bevins R. C. Seli BehavePlus fire modeling sysem version 3.0: User's Guide Gen. Tech. Rep. RRS-GTR-06WWW Revised. Ogden UT: Deparmen of Agriculure Fores Service Rocky ounain Research Saion 3 p. Bølviken E. P. J. Acklam N. Chrisophersen and J. -. Sørdal. 00. one Carlo Filers for Non-linear Sae Esimaion. Auomaica 37(): Bradley Jusin Paricle Filer Based osaicking for Fores Fire Tracking. aser hesis Brigham Young Universiy. Chib S. and E. Greenberg Undersanding The eropolis Hasings Algorihm. The American Saisician 49(4): Coen J. L. J. andel e al A Wildland Fire Dynamic Daa-driven Applicaion Sysem. h Symposium on Inegraed Observing and Assimilaion Sysems for he Amosphere Oceans and Land Surface (IOAS-AOLS). Douce A. S. J. Godsill and C. Andrieu On Sequenial one Carlo Sampling ehods for Bayesian Filering. Saisics and Compuing 0(3): Douce A. N. D. Freias N. Gordon (eds.). 00. Sequenial one Carlo mehods in pracice. New York: Springer-Verlag. Douce A.V. Tadic Parameer Esimaion in General Sae-space odels Using Paricle ehods Ann. Ins. Sais. ah. 55(): Douglas C. C. D. B. Jonahan e al DDDAS Approaches o Wildland Fire odeling and Conaminan Tracking. Proceedings of he 006 Winer Simulaion Conference 7-4. Finney ark A FARSITE: Fire Area Simulaor odel Developmen and Evaluaion Unied Saes Deparmen of Agriculure Fores Service Rocky ounain Research Saion Research Paper RRS- RP-4 Revised arch 998 revised February 004. Fox D. Thrun S. Burgard W. & Dellaer F. 00. Paricle Filers for obile Robo Localizaion. In Sequenial one Carlo ehods in Pracice (eds A. Douce J. F. G. de Freias and N. J. Gordon). New York: Springer- Verlag. Gibson S. H aximum Likelihood Esimaion of ulivariable Dynamic Sysems via he E Algorihm. PhD hesis The Universiy of Newcasle Newcasle NSW Ausralia. Gordon N. J. D. J. Salmond and A. F.. Smih Novel Approach o Nonlinear/Non-Gaussian Bayesian

9 Sae Esimaion. In IEE Proceedings on Radar and Signal Processing Gusafsson F. F. Gunnarsson N. Bergman U. Forssell J. Jansson R. Karlsson and R. -J. Nordlund. 00. Paricle Filers for Posiioning Navigaion and Tracking. IEEE Transacions on Signal Processing 50(): Hol J Resampling in Paricle Filers. aser Thesis Deparmen of Elecrical Engineering Linköping Universiy Sweden. Jazwinsk A. H Sochasic Processes and Filering Theory. ahemaics in science and engineering. Academic Press New York USA. Kailah T. A. H. Sayed and B. Hassibi Linear Esimaion. Informaion and Sysem Sciences Series. Prenice Hall Upper Saddle River NJ USA. Kiagawa G one Carlo Filer and Smooher for Non-Gaussian Nonlinear Sae Space odels. Journal of Compuaional and Graphical Saisics 5(): 5. Liu J. S. and E. Chen Sequenial one Carlo ehods for Dynamics Sysems. Journal of American Saisical Associaion 93: andel J. D. Jonahan e al A Wildland Fire odel wih Daa Assimilaion. CC Repor 33 ahemaics and Compuers in Simulaion. Naimo L. X. Hu and Y. Sun DEVS-FIRE: Towards an Inegraed Simulaion Environmen for Surface Wildfire Spread and Conainmen SIULATION: Transacions of The Sociey for odeling and Simulaion Inernaional Vol. 84 Issue 4 April 008 pp Schön Thomas B Esimaion of Nonlinear Dynamic Sysems Theory and Applicaions. Ph.D. Disseraion Linköpings Universiy Sweden. Simandl. Sraka O Sampling Densiies of Paricle Filer: A Survey and Comparison. American Conrol Conference Wang X. D. Rong Chen Jun. S. Liu. 00. one Carlo Bayesian Signal Processing for Wireless Communicaions Journal of VLSI Signal Processing Sysems 30(00) Zhang J. Rong Chen C. Tang J. Liang Origin of Scaling Behavior of Proein Packing Densiy: A Sequenial one Carlo Sudy of Compac Long Chain Polymers. JOURNAL OF CHEICAL PHYSICS 8(3) Zeigler B. P. H. Praehofer and T. G. Kim Theory of modeling and simulaion nd Ediion Academic Press. FENG GU is a Ph.D. candidae in he Compuer Science Deparmen a Georgia Sae Universiy. His research ineress include modeling and simulaion and sysem validaion and calibraion. XIAOLIN HU is an assisan professor in he Compuer Science Deparmen a Georgia Sae Universiy. His research ineress include modeling and simulaion auonomous agen and muli-agen sysems and simulaion-based developmen. AUTHOR BIOGRAPHIES

10 Proceedings of he 008 Winer Simulaion Conference S. J. ason R. Hill L. oench and O. Rose eds.