Realtime Particle Filters


 Dina Sutton
 1 years ago
 Views:
Transcription
1 Realime Paricle Filers Cody Kwok Dieer Fox Marina Meilă Dep. of Compuer Science & Engineering, Dep. of Saisics Universiy of Washingon Seale, WA 9895 Absrac Paricle filers esimae he sae of dynamical sysems from sensor informaion. In many real ime applicaions of paricle filers, however, sensor informaion arrives a a significanly higher rae han he updae rae of he filer. The prevalen approach o dealing wih such siuaions is o updae he paricle filer as ofen as possible and o discard sensor informaion ha canno be processed in ime. In his paper we presen realime paricle filers, which make use of all sensor informaion even when he filer updae rae is below he updae rae of he sensors. This is achieved by represening poseriors as mixures of sample ses, where each mixure componen inegraes one observaion arriving during a filer updae. The weighs of he mixure componens are se so as o minimize he approximaion error inroduced by he mixure represenaion. Thereby, our approach focuses compuaional resources (samples) on valuable sensor informaion. Experimens using daa colleced wih a mobile robo show ha our approach yields srong improvemens over oher approaches. Inroducion Due o heir samplebased represenaion, paricle filers are well suied o esimae he sae of nonlinear dynamic sysems. Over he las years, paricle filers have been applied wih grea success o a variey of sae esimaion problems including visual racking, speech recogniion, and mobile roboics []. The increased represenaional power of paricle filers, however, comes a he cos of higher compuaional complexiy. The applicaion of paricle filers o online, realime esimaion raises new research quesions. The key quesion in his conex is: How can we deal wih siuaions in which he rae of incoming sensor daa is higher han he updae rae of he paricle filer? To he bes of our knowledge, his problem has no been addressed in he lieraure so far. The prevalen approach in real ime applicaions is o updae he filer as ofen as possible and o discard sensor informaion ha arrives during he updae process. Obviously, his approach is prone o losing valuable sensor informaion. A firs sigh, he sample based represenaion of paricle filers suggess an alernaive approach similar o an anyime implemenaion: Whenever a new observaion arrives, sampling is inerruped and he nex observaion is processed. Unforunaely, such an approach can resul in oo small sample ses, causing he filer o diverge [, 2]. In his paper we inroduce realime paricle filers (RTPF) o deal wih consrains imposed by limied compuaional resources. Insead of discarding sensor readings, we disribue he
2 (a) (b) z z z z z + z + 2 z (c) z 2 z z z z 2 + S u u S + S S S u u S 2 u S S Figure : Differen sraegies for dealing wih limied compuaional power. All approaches process he same number of samples per esimaion inerval (window sizeq hree). (a) Skip observaions, i.e. inegrae only every hird observaion. (b) Aggregae observaions wihin a window and inegrae hem in one sep. (c) Reduce sample se size so ha each observaion can be considered. samples among he differen observaions arriving during a filer updae. Hence RTPF represens densiies over he sae space by mixures of sample ses, hereby avoiding he problem of filer divergence due o an insufficien number of independen samples. The weighs of he mixure componens are compued so as o minimize he approximaion error inroduced by he mixure represenaion. The resuling approach naurally focuses compuaional resources (samples) on valuable sensor informaion. The remainder of his paper is organized as follows: In he nex secion we ouline he basics of paricle filers in he conex of realime consrains. Then, in Secion, we inroduce our novel echnique o realime paricle filers. Finally, we presen experimenal resuls followed by a discussion of he properies of RTPF. 2 Paricle filers Paricle filers are a samplebased varian of Bayes filers, which recursively esimae poserior densiies, or beliefs, over he sae of a dynamical sysem (see [, ] for deails):!#" $ () Here % is a sensor measuremen and is conrol informaion measuring he dynamics of he sysem. Paricle filers represen beliefs by ses & of weighed samples ' )(++,  0/ (+.,. Each (.+, is a sae, and he  (+., are nonnegaive numerical facors called imporance weighs, which sum up o one. The basic form of he paricle filer realizes he recursive Bayes filer according o a sampling procedure, ofen referred o as sequenial imporance sampling wih resampling (SISR):. Resampling: Draw wih replacemen a random sae from he se & according o he (discree) disribuion defined hrough he imporance weighs (.+,. 2. Sampling: Use and he conrol informaion o sample 2 according o he disribuion 2!, which describes he dynamics of he sysem.. Imporance sampling: Weigh he sample 2 by he observaion likelihood Each ieraion of hese hree seps generaes a sample ' 22 / represening he poserior. Afer 4 ieraions, he imporance weighs of he samples are normalized so ha hey sum up o one. Paricle filers can be shown o converge o he rue poserior even in nongaussian, nonlinear dynamic sysems [4]. A ypical assumpion underlying paricle filers is ha all samples can be updaed whenever new sensor informaion arrives. Under realime condiions, however, i is possible ha he updae canno be compleed before he nex sensor measuremen arrives. This can be he case for compuaionally complex sensor models or whenever he underlying poserior requires large sample ses [2]. The majoriy of filering approaches deals wih his problem by skipping sensor informaion ha arrives during he updae of he filer. While his approach works reasonably well in many siuaions, i is prone o miss valuable sensor informaion.
3 z z z z z 2 S S S S 2 + S S +2 + α α 2 α α α 2 α Esmaion window z + Esimaion window + Figure 2: Real ime paricle filers. The samples are disribued among he observaions wihin one esimaion inerval (window size hree in his example). The belief is a mixure of he individual sample ses. Each arrow addiionally represens he sysem dynamics. Before we discuss ways of dealing wih such siuaions, le us inroduce some noaion. We assume ha observaions arrive a ime inervals, which we will call observaion inervals. Le 4 be he number of samples required by he paricle filer. Assume ha he resuling updae cycle of he paricle filer akes and is called he esimaion inerval or esimaion window. Accordingly, observaions arrive during one esimaion inerval. We call his number he window size of he filer, i.e. he number of observaions obained during a filer updae. The h observaion and sae wihin window are denoed and, respecively. Fig. illusraes differen approaches o dealing wih window sizes larger han one. The simples and mos common aproach is shown in Fig. (a). Here, observaions arriving during he updae of he sample se are discarded, which has he obvious disadvanage ha valuable sensor informaion migh ge los. The approach in Fig. (b) overcomes his problem by aggregaing muliple observaions ino one. While his echnique avoids he loss of informaion, i is no applicable o arbirary dynamical sysems. For example, i assumes ha observaions can be aggregaed opimally, and ha he inegraion of an aggregaed observaion can be performed as efficienly as he inegraion of individual observaions, which is ofen no he case. The hird approach, shown in Fig. (c), simply sops generaing new samples whenever an observaion is made (hence each sample se conains only 4 samples). While his approach akes advanage of he anyime capabiliies of paricle filers, i is suscepible o filer divergence due o an insufficen number of samples [2, ]. Real ime paricle filers In his paper we propose real ime paricle filers (RTPFs), a novel approach o dealing wih limied compuaional resources. The key idea of RTPFs is o consider all sensor measuremens by disribuing he samples among he observaions wihin an updae window. Addiionally, by weighing he differen sample ses wihin a window, our approach focuses he compuaional resources (samples) on he mos valuable observaions. Fig. 2 illusraes he approach. As can be seen, insead of one sample se a ime, we mainain smaller sample ses a $$ $!. We rea such a virual sample se, or belief, as a mixure of he disribuions represened in i. The mixure componens represen he sae of he sysem a differen poins in ime. If needed, however, he complee belief can be generaed by considering he dynamics beween he individual mixure componens. Compared o he firs approach discussed in he previous secion, his mehod has he advanage of no skipping any observaions. In conras o he approach shown in Fig. (b), RTPFs do no make any assumpions abou he naure of he sensor daa, i.e. wheher i can be aggregaed or no. The difference o he hird approach (Fig. (c)) is more suble. In boh approaches, each of he sample ses can only conain 4 samples. The belief sae ha is propagaed by RTPF o he nex esimaion inerval is a mixure disribuion where each mixure componen is represened by one of he sample ses, all generaed independenly from he previous window. Thus, he belief sae propagaion is simulaed by "$# sample rajecories, ha for compuaional convenience are represened a he poins in ime where he observaions are inegraed. In he approach (c) however, he belief propagaion is simulaed wih only 4 independen samples.
4 We will now show how RTPF deermines he weighs of he mixure belief. The key idea is o choose he weighs ha minimize he KLdivergence beween he mixure belief and he opimal belief. The opimal belief is he belief we would ge if here was enough ime o compue he full poserior wihin he updae window.. Mixure represenaion Le us resric our aenion o one esimaion inerval consising of observaions. The opimal belief%! a he end of an esimaion window resuls from ieraive applicaion of he Bayes filer updae on each obseraion []: %! $$ $ " #$ $$ " $ (2) Here denoes he belief generaed in he previous esimaion window. In essence, (2) compues he belief by inegraing over all rajecories hrough he esimaion inerval, where he sar posiion of he rajecories is drawn from he previous belief. The probabiliy of each rajecory is deermined using he conrol informaion $$ $, and he likelihoods of he observaions %$ $$ along he rajecory. Now le denoe he belief resuling from inegraing only he observaion wihin he esimaion window. RTPF compues a mixure of such beliefs, one for each observaion. The mixure, denoed, is he weighed sum of he mixure componens, where denoes he mixure weighs: where and % $$ $ % %! " $.$.$ " $ (). Here, oo, we inegrae over all rajecories. In conras o (2), however, each rajecory selecively inegraes only one of he observaions wihin he esimaion inerval..2 Opimizing he mixure weighs We will now urn o he problem of finding he weighs of he mixure. These weighs reflec he imporance of he respecive observaions for describing he opimal belief. The idea is o se hem so as o minimize he approximaion error inroduced by he mixure disribuion. More formally, we deermine he mixing weighs "! by minimizing he KLdivergence [5] beween and #.! $&%(')+#, /.0 2 #!" 4.%! (4) $&%(')+#, / # 4! " $ (5) In he above 8 :9 # ; <. Opimizing he weighs of mixure approximaions can be done using EM [6] or (consrained) =?> gradien descen [7]. Here, we perform a small number of gradien descen seps o find he mixure weighs. Denoe by Noe ha ypically he individual predicions $ can be concaenaed so ha only wo predicions for each rajecory have o be performed, one before and one afer he corresponding observaion.
5 he crierion o be minimized in (5). The gradien of is given by ' # '! ' # " $ $$ $ (6) The sar poin for he gradien descen is chosen o be he cener of he weigh domain8, ha is $ $$.. Mone Carlo gradien esimaion The exac compuaion of he gradiens in (6) requires he compuaion of he differen beliefs, each in urn requiring several paricle filer updaes (see (2), ()), and inegreaion over all saes. This is clearly no feasible in our case. We solve his problem by Mone Carlo approximaion. The approach is based on he observaion ha he beliefs in (6) share he same rajecories hrough space and differ only in he observaions hey inegrae. Therefore, we firs generae sample rajecories hrough he esimaion window wihou considering he observaions, and hen use imporance sampling o generae he beliefs needed for he gradien esimaion. Trajecory generaion is done as follows: we draw a sample from a sample se of he previous mixure belief, where he probabiliy of chosing a se &) is given by he mixure weighs. This sample is hen moved forward in ime by consecuively drawing samples from he disribuions! a each ime sep $$ $. The resuling rajecories are drawn from he following proposal disribuion : $$ $ #" #$$ $ " (7) Using imporance sampling, we obain samplebased esimaes of weighing each rajecory wih or and! by simply %, respecively (compare (2) and ()). is generaed wih minimal compuaional overhead by averaging he weighs compued for # he individual disribuions. The use of he same rajecories for all disribuions has he advanage ha i is highly efficien and ha i reduces he variance of he gradien esimae. This variance reducion is due o using he same random bis in evaluaing he diverse scenarios of incorporaing one or anoher of he observaions [8]. Furher variance reducion is achieved by using sraified sampling on rajecories. The rajecories are grouped by deermining conneced regions in a grid over he sae space (a ime ). Neighboring cells are considered conneced if boh conain samples. To compue he gradiens by formula (6), we hen perform summaion and normalizaion over he grouped rajecories. Empirical evaluaions showed ha his grouping grealy reduces he number of rajecories needed o ge smooh gradien esimaes. An addiional, very imporan benefi of grouping is he reducion of he bias due o differen dynamics applied o he differen sample ses in he esimaion window. In our experimens he number of rajecories is less han of he oal number of samples, resuling in a compuaional overhead of abou % of he oal esimaion ime. To summarize, he RTPF algorihm works as follows. The number 4 of independen samples needed o represen he belief, he updae rae of incoming sensor daa, and he available processing power deermine he size of he esimaion window and hence he number of mixure componens. RTPF compues he opimal weighs of he mixure disribuion a he end of each esimaion window. This is done by gradien descen using he Mone Carlo esimaes of he gradiens. The resuling weighs are used o generae samples for he individual sample ses of he nex esimaion window. To do so, we keep rack of he conrol informaion (dynamics) beween he differen sample ses of wo consecuive windows.
6 8m 54m Fig. : Map of he environmen used for he experimen. The robo was moved around he symmeric loop on he lef. The ask of he robo was o deermine is posiion using daa colleced by wo disance measuring devices, one poining o is lef, he oher poining o is righ. 4 Experimens In his secion we evaluae he effeciveness of RTPF agains he alernaives, using daa colleced from a mobile robo in a realworld environmen. Figure shows he seup of he experimen: The robo was placed in he office floor and moved around he loop on he lef. The ask of he robo was o deermine is posiion wihin he map, using daa colleced by wo laserbeams, one poining o is lef, he oher poining o is righ. The wo laser beams were exraced from a planar laser rangefinder, allowing he robo only o deermine he disance o he walls on is lef and righ. Beween each observaion he robo moved approximaely 50cm (see [] for deails on robo localizaion and sensor models). Noe ha he loop in he environmen is symmeric excep for a few landmarks along he walls of he corridor. Localizaion performance was measured by he average disance beween he samples and he reference robo posiions, which were compued offline. In he experimens, our realime algorihm, RTPF, is compared o paricle filers wih skipping observaions, called Skip daa (Figure a), and paricle filers wih insufficien samples, called Naive (Figure c). Furhermore, o gauge he efficiency of our mixure weighing, we also obained resuls for our realime algorihm wihou weighing, i.e. we used mixure disribuions and fixed he weighs o. We denoe his varian Uniform. Finally, we also include as reference he Baseline approach, which is allowed o generae 4 samples for each observaion, hereby no considering realime consrains. The experimen is se up as follows. Firs, we fix he sample se size 4 which is sufficien for he robo o localize iself. In our experimen 4 is se empirically o 20,000 (he paricle filers may fail a lower 4, see also [2]). We hen vary he compuaional resources, resuling in differen window sizes. Larger window size means lower compuaional power, and he number of samples ha can be generaed for each observaion decreases o (4 ). Figure 4 shows he evoluions of average localizaion errors over ime, using differen window sizes. Each graph is obained by averaging over 0 runs wih differen random seeds and sar posiions. The error bars indicae 95% confidence inervals. As he figures show, Naive gives he wors resuls, which is due o insufficien numbers of samples, resuling in divergence of he filer. While Uniform performs slighly beer han Skip daa, RTPF is he mos effecive of all algorihms, localizing he robo in he leas amoun of ime. Furhermore, RTPF shows he leas degradaion wih limied compuaional power (larger window sizes). The key advanage of RTPF over Uniform lies in he mixure weighing, which allows our approach o focus compuaional resources on valuable sensor informaion, for example when he robo passes an informaive feaure in one of he hallways. For shor window sizes (Fig. 4(a)), his advanage is no very srong since in his environmen, mos feaures can be deeced in several consecuive sensor measuremens. Noe ha because he Baseline approach was allowed o inegrae all observaions wih all of he 20,000 samples, i converges o a lower error level han all he oher approaches.
7 Average Localizaion error [cm] Baseline Skip daa RTPF Naive Uniform Average Localizaion error [cm] Baseline Skip daa RTPF Naive Uniform Time [sec] (a) Time [sec] (b) Average Localizaion error [cm] Baseline Skip daa RTPF Naive Uniform Time [sec] (c) Localizaion speedup Window size Fig. 4(a)(c): Performance of he differen algorihms for window sizes of 4, 8, and 2 respecively. The axis represens ime elapsed since he beginning of he localizaion experimen. The axis plos he localizaion error measured in average disance from he reference posiion. Each figure includes he performance achieved wih unlimied compuaional power as he Baseline graph. Each poin is averaged over 0 runs, and error bars indicae 95% confidence inervals. Fig. 4(d) represens he localizaion speedup of RTPF over Skip daa for various window sizes. The advanage of RTPF increases wih he difficuly of he ask, i.e. wih increasing window size. Beween window size 6 and 2, RTPF localizes a leas wice as fas as Skip daa. Wihou mixure weighing of RTPF, we did no expec Uniform o ouperform Skip daa significanly. To see his, consider one esimaion window of lengh. Suppose only one of he observaions deecs a landmark, or very informaive feaure in he hallway. In such a siuaion, Uniform considers his landmark every ime he robo passes i. However, i only assigns 4 samples o his landmark deecion. Skip daa on he oher hand, deecs he landmark only every h ime, bu assigns all 4 samples o i. Therefore, averaged over many differen runs, he mean performance of Uniform and Skip daa is very similar. However, he variance of he error is significanly lower for Uniform since i considers he deecion in every run. In conras o boh approaches, RTPF deecs all landmarks and generaes more samples for he landmark deecions, hereby gaining he bes of boh worlds, and Figures 4(a) (c) show his is indeed he case. In Figure 4(d) we summarize he performance gain of RTPF over Skip daa for differen window sizes in erms of localizaion ime. We considered he robo o be localized if he average localizaion error remains below 200 cm over a period of 0 seconds. If he run never reaches his level, he localizaion ime is se o he lengh of he enire run, which is 574 seconds. The axis represens he window size and he axis he localizaion speedup. For each window size speedups were deermined using ess on he localizaion imes for he 0 pairs of daa runs. All resuls are significan a he 95% level. The graph shows ha wih increasing window size (i.e. decreasing processing power), he localizaion speedup increases. A small window sizes he speedup is 2050%, bu i goes up o 2.7 imes for larger windows, demonsraing he benefis of he RTPF approach over radiional paricle filers. Ulimaely, for very large window sizes, he speedup decreases again, which is due o he fac ha none of he approaches is able o reduce he error below 200cm wihin he run ime of an experimen. (d)
8 5 Conclusions In his paper we ackled he problem of paricle filering under he consrain of limied compuing resources. Our approach makes nearopimal use of sensor informaion by dividing sample ses beween all available observaions and hen represening he sae as a mixure of sample ses. Nex we opimize he mixing weighs in order o be as close o he rue poserior disribuion as possible. Opimizaion is performed efficienly by gradien descen using a Mone Carlo approximaion of he gradiens. We showed ha RTPF produces significan performance improvemens in a robo localizaion ask. The resuls indicae ha our approach ouperforms all alernaive mehods for dealing wih limied compuaion. Furhermore, RTPF localized he robo more han 2.7 imes faser han he original paricle filer approach, which skips sensor daa. Based on hese resuls, we expec our mehod o be highly valuable in a wide range of realime applicaions of paricle filers. RTPF yields maximal performance gain for daa sreams conaining highly valuable sensor daa occuring a unpredicable ime poins. The idea of approximaing belief saes by mixures has also been used in he conex of dynamic Bayesian neworks [9]. However, Boyen and Koller use mixures o represen belief saes a a specific poin in ime, no over muliple ime seps. Our work is moivaed by realime consrains ha are no presen in [9]. So far RTPF uses fixed sample sizes and fixed window sizes. The nex naural sep is o adap hese wo srucural parameers o furher speed up he compuaion. For example, by he mehod of [2] we can change he sample size onhefly, which in urn allows us o change he window size. Ongoing experimens sugges ha his combinaion yields furher performance improvemens: When he sae uncerainy is high, many samples are used and hese samples are spread ou over muliple observaions. On he oher hand, when he uncerainy is low, he number of samples is very small and RTPF becomes idenical o he vanilla paricle filer wih one updae (sample se) per observaion. 6 Acknowledgemens This research is sponsored in par by he Naional Science Foundaion (CAREER gran number ) and by DARPA (MICA program). References [] A. Douce, N. de Freias, and N. Gordon, ediors. Sequenial Mone Carlo in Pracice. Springer Verlag, New York, 200. [2] D. Fox. KLDsampling: Adapive paricle filers and mobile robo localizaion. In Advances in Neural Informaion Processing Sysems (NIPS), 200. [] D. Fox, S. Thrun, F. Dellaer, and W. Burgard. Paricle filers for mobile robo localizaion. In Douce e al. []. [4] P. Del Moral and L. Miclo. Branching and ineracing paricle sysems approximaions of feynamkac formulae wih applicaions o non linear filering. In Seminaire de Probabilies XXXIV, number 729 in Lecure Noes in Mahemaics. SpringerVerlag, [5] T. M. Cover and J. A. Thomas. Elemens of Informaion Theory. Wiley Series in Telecommunicaions. Wiley, New York, 99. [6] W. Poland and R. Shacher. Mixures of Gaussians and minimum relaive enropy echniques for modeling coninuous uncerainies. In Proc. of he Conference on Uncerainy in Arificial Inelligence (UAI), 99. [7] T. Jaakkola and M. Jordan. Improving he mean field approximaion via he use of mixure disribuions. In Learning in Graphical Models. Kluwer, 997. [8] P. R. Cohen. Empirical mehods for arificial inelligence. MIT Press, 995. [9] X. Boyen and D. Koller. Tracable inference for complex sochasic processes. In Proc. of he Conference on Uncerainy in Arificial Inelligence (UAI), 998.
SELFEVALUATION FOR VIDEO TRACKING SYSTEMS
SELFEVALUATION FOR VIDEO TRACKING SYSTEMS Hao Wu and Qinfen Zheng Cenre for Auomaion Research Dep. of Elecrical and Compuer Engineering Universiy of Maryland, College Park, MD20742 {wh2003, qinfen}@cfar.umd.edu
More informationBayesian Filtering with Online Gaussian Process Latent Variable Models
Bayesian Filering wih Online Gaussian Process Laen Variable Models Yali Wang Laval Universiy yali.wang.1@ulaval.ca Marcus A. Brubaker TTI Chicago mbrubake@cs.orono.edu Brahim Chaibdraa Laval Universiy
More informationMaintaining MultiModality through Mixture Tracking
Mainaining MuliModaliy hrough Mixure Tracking Jaco Vermaak, Arnaud Douce Cambridge Universiy Engineering Deparmen Cambridge, CB2 1PZ, UK Parick Pérez Microsof Research Cambridge, CB3 0FB, UK Absrac In
More information4. The Poisson Distribution
Virual Laboraories > 13. The Poisson Process > 1 2 3 4 5 6 7 4. The Poisson Disribuion The Probabiliy Densiy Funcion We have shown ha he k h arrival ime in he Poisson process has he gamma probabiliy densiy
More informationMarkov Models and Hidden Markov Models (HMMs)
Markov Models and Hidden Markov Models (HMMs (Following slides are modified from Prof. Claire Cardie s slides and Prof. Raymond Mooney s slides. Some of he graphs are aken from he exbook. Markov Model
More informationImproved Techniques for Grid Mapping with RaoBlackwellized Particle Filters
1 Improved Techniques for Grid Mapping wih RaoBlackwellized Paricle Filers Giorgio Grisei Cyrill Sachniss Wolfram Burgard Universiy of Freiburg, Dep. of Compuer Science, GeorgesKöhlerAllee 79, D79110
More informationA dynamic probabilistic modeling of railway switches operating states
A dynamic probabilisic modeling of railway swiches operaing saes Faicel Chamroukhi 1, Allou Samé 1, Parice Aknin 1, Marc Anoni 2 1 IFSTTAR, 2 rue de la Bue Vere, 93166 NoisyleGrand Cedex, France {chamroukhi,same,aknin}@ifsar.fr
More informationChapter 8: Regression with Lagged Explanatory Variables
Chaper 8: Regression wih Lagged Explanaory Variables Time series daa: Y for =1,..,T End goal: Regression model relaing a dependen variable o explanaory variables. Wih ime series new issues arise: 1. One
More informationSinglemachine Scheduling with Periodic Maintenance and both Preemptive and. Nonpreemptive jobs in Remanufacturing System 1
Absrac number: 050407 Singlemachine Scheduling wih Periodic Mainenance and boh Preempive and Nonpreempive jobs in Remanufacuring Sysem Liu Biyu hen Weida (School of Economics and Managemen Souheas Universiy
More informationTask is a schedulable entity, i.e., a thread
RealTime Scheduling Sysem Model Task is a schedulable eniy, i.e., a hread Time consrains of periodic ask T:  s: saring poin  e: processing ime of T  d: deadline of T  p: period of T Periodic ask T
More informationA Distributed MultipleTarget Identity Management Algorithm in Sensor Networks
A Disribued MulipleTarge Ideniy Managemen Algorihm in Sensor Neworks Inseok Hwang, Kaushik Roy, Hamsa Balakrishnan, and Claire Tomlin Dep. of Aeronauics and Asronauics, Sanford Universiy, CA 94305 Elecrical
More informationA Bayesian framework with auxiliary particle filter for GMTI based ground vehicle tracking aided by domain knowledge
A Bayesian framework wih auxiliary paricle filer for GMTI based ground vehicle racking aided by domain knowledge Miao Yu a, Cunjia Liu a, Wenhua Chen a and Jonahon Chambers b a Deparmen of Aeronauical
More informationThe Application of Multi Shifts and Break Windows in Employees Scheduling
The Applicaion of Muli Shifs and Brea Windows in Employees Scheduling Evy Herowai Indusrial Engineering Deparmen, Universiy of Surabaya, Indonesia Absrac. One mehod for increasing company s performance
More informationMaking a Faster Cryptanalytic TimeMemory TradeOff
Making a Faser Crypanalyic TimeMemory TradeOff Philippe Oechslin Laboraoire de Securié e de Crypographie (LASEC) Ecole Polyechnique Fédérale de Lausanne Faculé I&C, 1015 Lausanne, Swizerland philippe.oechslin@epfl.ch
More informationMultiprocessor SystemsonChips
Par of: Muliprocessor SysemsonChips Edied by: Ahmed Amine Jerraya and Wayne Wolf Morgan Kaufmann Publishers, 2005 2 Modeling Shared Resources Conex swiching implies overhead. On a processing elemen,
More informationLoad Prediction Using Hybrid Model for Computational Grid
Load Predicion Using Hybrid Model for Compuaional Grid Yongwei Wu, Yulai Yuan, Guangwen Yang 3, Weimin Zheng 4 Deparmen of Compuer Science and Technology, Tsinghua Universiy, Beijing 00084, China, 3, 4
More informationMarket Liquidity and the Impacts of the Computerized Trading System: Evidence from the Stock Exchange of Thailand
36 Invesmen Managemen and Financial Innovaions, 4/4 Marke Liquidiy and he Impacs of he Compuerized Trading Sysem: Evidence from he Sock Exchange of Thailand Sorasar Sukcharoensin 1, Pariyada Srisopisawa,
More informationStatistical Analysis with Little s Law. Supplementary Material: More on the Call Center Data. by SongHee Kim and Ward Whitt
Saisical Analysis wih Lile s Law Supplemenary Maerial: More on he Call Cener Daa by SongHee Kim and Ward Whi Deparmen of Indusrial Engineering and Operaions Research Columbia Universiy, New York, NY 1799
More informationUSE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES
USE OF EDUCATION TECHNOLOGY IN ENGLISH CLASSES Mehme Nuri GÖMLEKSİZ Absrac Using educaion echnology in classes helps eachers realize a beer and more effecive learning. In his sudy 150 English eachers were
More informationJournal Of Business & Economics Research September 2005 Volume 3, Number 9
Opion Pricing And Mone Carlo Simulaions George M. Jabbour, (Email: jabbour@gwu.edu), George Washingon Universiy YiKang Liu, (yikang@gwu.edu), George Washingon Universiy ABSTRACT The advanage of Mone Carlo
More informationAn Online Learningbased Framework for Tracking
An Online Learningbased Framework for Tracking Kamalika Chaudhuri Compuer Science and Engineering Universiy of California, San Diego La Jolla, CA 9293 Yoav Freund Compuer Science and Engineering Universiy
More informationTEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS
TEMPORAL PATTERN IDENTIFICATION OF TIME SERIES DATA USING PATTERN WAVELETS AND GENETIC ALGORITHMS RICHARD J. POVINELLI AND XIN FENG Deparmen of Elecrical and Compuer Engineering Marquee Universiy, P.O.
More informationImproving Unreliable Mobile GIS with Swarmbased Particle Filters
Improving Unreliable Mobile GIS wih Swarmbased Paricle Filers Fama Hrizi, Jérôme Härri, Chrisian Bonne EURECOM, Mobile Communicaions Deparmen Campus SophiaTech, 450 Roue des Chappes Bio, France {hrizi,
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE
Profi Tes Modelling in Life Assurance Using Spreadshees PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART ONE Erik Alm Peer Millingon 2004 Profi Tes Modelling in Life Assurance Using Spreadshees
More informationParticle Filtering for Geometric Active Contours with Application to Tracking Moving and Deforming Objects
Paricle Filering for Geomeric Acive Conours wih Applicaion o Tracking Moving and Deforming Objecs Yogesh Rahi Namraa Vaswani Allen Tannenbaum Anhony Yezzi Georgia Insiue of Technology School of Elecrical
More informationPrincipal components of stock market dynamics. Methodology and applications in brief (to be updated ) Andrei Bouzaev, bouzaev@ya.
Principal componens of sock marke dynamics Mehodology and applicaions in brief o be updaed Andrei Bouzaev, bouzaev@ya.ru Why principal componens are needed Objecives undersand he evidence of more han one
More informationTime variant processes in failure probability calculations
Time varian processes in failure probabiliy calculaions A. Vrouwenvelder (TUDelf/TNO, The Neherlands) 1. Inroducion Acions on srucures as well as srucural properies are usually no consan, bu will vary
More informationEvolutionary building of stock trading experts in realtime systems
Evoluionary building of sock rading expers in realime sysems Jerzy J. Korczak Universié Louis Paseur Srasbourg, France Email: jjk@dpinfo.usrasbg.fr Absrac: This paper addresses he problem of consrucing
More informationRepresenting Periodic Functions by Fourier Series. (a n cos nt + b n sin nt) n=1
Represening Periodic Funcions by Fourier Series 3. Inroducion In his Secion we show how a periodic funcion can be expressed as a series of sines and cosines. We begin by obaining some sandard inegrals
More informationThe naive method discussed in Lecture 1 uses the most recent observations to forecast future values. That is, Y ˆ t + 1
Business Condiions & Forecasing Exponenial Smoohing LECTURE 2 MOVING AVERAGES AND EXPONENTIAL SMOOTHING OVERVIEW This lecure inroduces imeseries smoohing forecasing mehods. Various models are discussed,
More informationMeasuring macroeconomic volatility Applications to export revenue data, 19702005
FONDATION POUR LES ETUDES ET RERS LE DEVELOPPEMENT INTERNATIONAL Measuring macroeconomic volailiy Applicaions o expor revenue daa, 1970005 by Joël Cariolle Policy brief no. 47 March 01 The FERDI is a
More informationCombination of UWB and GPS for indooroutdoor vehicle localization
ombinaion of UW and for indooroudoor vehicle localizaion González J., lanco J.L., Galindo., OrizdeGaliseo., FernándezMadrigal J.., Moreno F.., and Marínez J.L. {jgonzalez, jlblanco,cipriano,jafma}@cima.uma.es,
More informationMorningstar Investor Return
Morningsar Invesor Reurn Morningsar Mehodology Paper Augus 31, 2010 2010 Morningsar, Inc. All righs reserved. The informaion in his documen is he propery of Morningsar, Inc. Reproducion or ranscripion
More informationInformation Theoretic Evaluation of Change Prediction Models for LargeScale Software
Informaion Theoreic Evaluaion of Change Predicion Models for LargeScale Sofware Mina Askari School of Compuer Science Universiy of Waerloo Waerloo, Canada maskari@uwaerloo.ca Ric Hol School of Compuer
More informationGraphing the Von Bertalanffy Growth Equation
file: d:\b1732013\von_beralanffy.wpd dae: Sepember 23, 2013 Inroducion Graphing he Von Beralanffy Growh Equaion Previously, we calculaed regressions of TL on SL for fish size daa and ploed he daa and
More informationDistributed Online Localization in Sensor Networks Using a Moving Target
Disribued Online Localizaion in Sensor Neworks Using a Moving Targe Aram Galsyan 1, Bhaskar Krishnamachari 2, Krisina Lerman 1, and Sundeep Paem 2 1 Informaion Sciences Insiue 2 Deparmen of Elecrical EngineeringSysems
More informationMathematics in Pharmacokinetics What and Why (A second attempt to make it clearer)
Mahemaics in Pharmacokineics Wha and Why (A second aemp o make i clearer) We have used equaions for concenraion () as a funcion of ime (). We will coninue o use hese equaions since he plasma concenraions
More informationInformation Theoretic Approaches for Predictive Models: Results and Analysis
Informaion Theoreic Approaches for Predicive Models: Resuls and Analysis Monica Dinculescu Supervised by Doina Precup Absrac Learning he inernal represenaion of parially observable environmens has proven
More informationThe Transport Equation
The Transpor Equaion Consider a fluid, flowing wih velociy, V, in a hin sraigh ube whose cross secion will be denoed by A. Suppose he fluid conains a conaminan whose concenraion a posiion a ime will be
More informationUnderstanding Sequential Circuit Timing
ENGIN112: Inroducion o Elecrical and Compuer Engineering Fall 2003 Prof. Russell Tessier Undersanding Sequenial Circui Timing Perhaps he wo mos disinguishing characerisics of a compuer are is processor
More informationNetwork Discovery: An Estimation Based Approach
Nework Discovery: An Esimaion Based Approach Girish Chowdhary, Magnus Egersed, and Eric N. Johnson Absrac We consider he unaddressed problem of nework discovery, in which, an agen aemps o formulae an esimae
More informationEconomics 140A Hypothesis Testing in Regression Models
Economics 140A Hypohesis Tesing in Regression Models While i is algebraically simple o work wih a populaion model wih a single varying regressor, mos populaion models have muliple varying regressors 1
More informationMachine Learning in Pairs Trading Strategies
Machine Learning in Pairs Trading Sraegies Yuxing Chen (Joseph) Deparmen of Saisics Sanford Universiy Email: osephc5@sanford.edu Weiluo Ren (David) Deparmen of Mahemaics Sanford Universiy Email: weiluo@sanford.edu
More informationDistributing Human Resources among Software Development Projects 1
Disribuing Human Resources among Sofware Developmen Proecs Macario Polo, María Dolores Maeos, Mario Piaini and rancisco Ruiz Summary This paper presens a mehod for esimaing he disribuion of human resources
More informationRelative velocity in one dimension
Connexions module: m13618 1 Relaive velociy in one dimension Sunil Kumar Singh This work is produced by The Connexions Projec and licensed under he Creaive Commons Aribuion License Absrac All quaniies
More informationModule 4. Singlephase AC circuits. Version 2 EE IIT, Kharagpur
Module 4 Singlephase A circuis ersion EE T, Kharagpur esson 5 Soluion of urren in A Series and Parallel ircuis ersion EE T, Kharagpur n he las lesson, wo poins were described:. How o solve for he impedance,
More informationTerm Structure of Prices of Asian Options
Term Srucure of Prices of Asian Opions Jirô Akahori, Tsuomu Mikami, Kenji Yasuomi and Teruo Yokoa Dep. of Mahemaical Sciences, Risumeikan Universiy 111 Nojihigashi, Kusasu, Shiga 5258577, Japan Email:
More informationAP Calculus BC 2010 Scoring Guidelines
AP Calculus BC Scoring Guidelines The College Board The College Board is a noforprofi membership associaion whose mission is o connec sudens o college success and opporuniy. Founded in, he College Board
More informationConstant Data Length Retrieval for Video Servers with Variable Bit Rate Streams
IEEE Inernaional Conference on Mulimedia Compuing & Sysems, June 173, 1996, in Hiroshima, Japan, p. 151155 Consan Lengh Rerieval for Video Servers wih Variable Bi Rae Sreams Erns Biersack, Frédéric Thiesse,
More informationA Note on Using the Svensson procedure to estimate the risk free rate in corporate valuation
A Noe on Using he Svensson procedure o esimae he risk free rae in corporae valuaion By Sven Arnold, Alexander Lahmann and Bernhard Schwezler Ocober 2011 1. The risk free ineres rae in corporae valuaion
More informationSPEC model selection algorithm for ARCH models: an options pricing evaluation framework
Applied Financial Economics Leers, 2008, 4, 419 423 SEC model selecion algorihm for ARCH models: an opions pricing evaluaion framework Savros Degiannakis a, * and Evdokia Xekalaki a,b a Deparmen of Saisics,
More informationGLAS Team Member Quarterly Report. June , Golden, Colorado (Colorado School of Mines)
GLAS Team ember Quarerly Repor An Nguyen, Thomas A Herring assachuses Insiue of Technology Period: 04/01/2004 o 06/30//2004 eeings aended Tom Herring aended he eam meeing near GSFC a he end of June, 2004.
More informationFourier Series Solution of the Heat Equation
Fourier Series Soluion of he Hea Equaion Physical Applicaion; he Hea Equaion In he early nineeenh cenury Joseph Fourier, a French scienis and mahemaician who had accompanied Napoleon on his Egypian campaign,
More informationLarge Scale Online Learning.
Large Scale Online Learning. Léon Boou NEC Labs America Princeon NJ 08540 leon@boou.org Yann Le Cun NEC Labs America Princeon NJ 08540 yann@lecun.com Absrac We consider siuaions where raining daa is abundan
More information1. The graph shows the variation with time t of the velocity v of an object.
1. he graph shows he variaion wih ime of he velociy v of an objec. v Which one of he following graphs bes represens he variaion wih ime of he acceleraion a of he objec? A. a B. a C. a D. a 2. A ball, iniially
More informationMACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR
MACROECONOMIC FORECASTS AT THE MOF A LOOK INTO THE REAR VIEW MIRROR The firs experimenal publicaion, which summarised pas and expeced fuure developmen of basic economic indicaors, was published by he Minisry
More informationINVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS
INVESTIGATION OF THE INFLUENCE OF UNEMPLOYMENT ON ECONOMIC INDICATORS Ilona Tregub, Olga Filina, Irina Kondakova Financial Universiy under he Governmen of he Russian Federaion 1. Phillips curve In economics,
More informationCHARGE AND DISCHARGE OF A CAPACITOR
REFERENCES RC Circuis: Elecrical Insrumens: Mos Inroducory Physics exs (e.g. A. Halliday and Resnick, Physics ; M. Sernheim and J. Kane, General Physics.) This Laboraory Manual: Commonly Used Insrumens:
More informationRandom Walk in 1D. 3 possible paths x vs n. 5 For our random walk, we assume the probabilities p,q do not depend on time (n)  stationary
Random Walk in D Random walks appear in many cones: diffusion is a random walk process undersanding buffering, waiing imes, queuing more generally he heory of sochasic processes gambling choosing he bes
More informationOn Tracking The Partition Function
On Tracking The Pariion Funcion Guillaume Desjardins, Aaron Courville, Yoshua Bengio {desjagui,courvila,bengioy}@iro.umonreal.ca Déparemen d informaique e de recherche opéraionnelle Universié de Monréal
More informationState Machines: Brief Introduction to Sequencers Prof. Andrew J. Mason, Michigan State University
Inroducion ae Machines: Brief Inroducion o equencers Prof. Andrew J. Mason, Michigan ae Universiy A sae machine models behavior defined by a finie number of saes (unique configuraions), ransiions beween
More informationRandom Scanning Algorithm for Tracking Curves in Binary Image Sequences
Vol., No., Page 101 of 110 Copyrigh 008, TSI Press Prined in he USA. All righs reserved Random Scanning Algorihm for Tracking Curves in Binary Image Sequences Kazuhiko Kawamoo *1 and Kaoru Hiroa 1 Kyushu
More information1.2 Goals for Animation Control
A Direc Manipulaion Inerface for 3D Compuer Animaion Sco Sona Snibbe y Brown Universiy Deparmen of Compuer Science Providence, RI 02912, USA Absrac We presen a new se of inerface echniques for visualizing
More informationStochastic Recruitment: A LimitedFeedback Control Policy for Large Ensemble Systems
Sochasic Recruimen: A LimiedFeedback Conrol Policy for Large Ensemble Sysems Lael Odhner and Harry Asada Absrac This paper is abou sochasic recruimen, a conrol archiecure for cenrally conrolling he ensemble
More informationA Robust Exponentially Weighted Moving Average Control Chart for the Process Mean
Journal of Modern Applied Saisical Mehods Volume 5 Issue Aricle 005 A Robus Exponenially Weighed Moving Average Conrol Char for he Process Mean Michael B. C. Khoo Universii Sains, Malaysia, mkbc@usm.my
More informationAutomatic measurement and detection of GSM interferences
Auomaic measuremen and deecion of GSM inerferences Poor speech qualiy and dropped calls in GSM neworks may be caused by inerferences as a resul of high raffic load. The radio nework analyzers from Rohde
More informationAppendix A: Area. 1 Find the radius of a circle that has circumference 12 inches.
Appendi A: Area workedou s o OddNumbered Eercises Do no read hese workedou s before aemping o do he eercises ourself. Oherwise ou ma mimic he echniques shown here wihou undersanding he ideas. Bes wa
More informationChapter 2 Problems. 3600s = 25m / s d = s t = 25m / s 0.5s = 12.5m. Δx = x(4) x(0) =12m 0m =12m
Chaper 2 Problems 2.1 During a hard sneeze, your eyes migh shu for 0.5s. If you are driving a car a 90km/h during such a sneeze, how far does he car move during ha ime s = 90km 1000m h 1km 1h 3600s = 25m
More informationChapter 4. Properties of the Least Squares Estimators. Assumptions of the Simple Linear Regression Model. SR3. var(e t ) = σ 2 = var(y t )
Chaper 4 Properies of he Leas Squares Esimaors Assumpions of he Simple Linear Regression Model SR1. SR. y = β 1 + β x + e E(e ) = 0 E[y ] = β 1 + β x SR3. var(e ) = σ = var(y ) SR4. cov(e i, e j ) = cov(y
More informationSampling TimeBased Sliding Windows in Bounded Space
Sampling TimeBased Sliding Windows in Bounded Space Rainer Gemulla Technische Universiä Dresden 01062 Dresden, Germany gemulla@inf.udresden.de Wolfgang Lehner Technische Universiä Dresden 01062 Dresden,
More informationPrice Controls and Banking in Emissions Trading: An Experimental Evaluation
This version: March 2014 Price Conrols and Banking in Emissions Trading: An Experimenal Evaluaion John K. Sranlund Deparmen of Resource Economics Universiy of MassachusesAmhers James J. Murphy Deparmen
More information1. BACKGROUND 11 Traffic Flow Surveillance
AuoRecogniion of Vehicle Maneuvers Based on SpaioTemporal Clusering. BACKGROUND  Traffic Flow Surveillance Conduced wih kinds of beacons mouned a limied roadside poins wih Images from High Aliude Plaforms
More informationA New Adaptive Ensemble Boosting Classifier for Concept Drifting Stream Data
A New Adapive Ensemble Boosing Classifier for Concep Drifing Sream Daa Kapil K. Wankhade and Snehlaa S. Dongre, Members, IACSIT Absrac Wih he emergence of largevolume and high speed sreaming daa, mining
More informationEfficient Onetime Signature Schemes for Stream Authentication *
JOURNAL OF INFORMATION SCIENCE AND ENGINEERING, 61164 (006) Efficien Oneime Signaure Schemes for Sream Auhenicaion * YONGSU PARK AND YOOKUN CHO + College of Informaion and Communicaions Hanyang Universiy
More informationIntrinsic Localization and Mapping with 2 Applications: Diffusion Mapping and Marco Polo Localization
Inrinsic Localizaion and Mapping wih Applicaions: Diffusion Mapping and Marco Polo Localizaion Frank Dellaer, Fernando Alegre, and Eric Beowulf Marinson College of Compuing, Georgia Insiue of Technology
More informationPrice elasticity of demand for crude oil: estimates for 23 countries
Price elasiciy of demand for crude oil: esimaes for 23 counries John C.B. Cooper Absrac This paper uses a muliple regression model derived from an adapaion of Nerlove s parial adjusmen model o esimae boh
More informationTimeExpanded Sampling (TES) For Ensemblebased Data Assimilation Applied To Conventional And Satellite Observations
27 h WAF/23 rd NWP, 29 June 3 July 2015, Chicago IL. 1 TimeExpanded Sampling (TES) For Ensemblebased Daa Assimilaion Applied To Convenional And Saellie Observaions Allen Zhao 1, Qin Xu 2, Yi Jin 1, Jusin
More informationIndividual Health Insurance April 30, 2008 Pages 167170
Individual Healh Insurance April 30, 2008 Pages 167170 We have received feedback ha his secion of he e is confusing because some of he defined noaion is inconsisen wih comparable life insurance reserve
More informationANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS
ANALYSIS AND COMPARISONS OF SOME SOLUTION CONCEPTS FOR STOCHASTIC PROGRAMMING PROBLEMS R. Caballero, E. Cerdá, M. M. Muñoz and L. Rey () Deparmen of Applied Economics (Mahemaics), Universiy of Málaga,
More informationBayesian model comparison with unnormalised likelihoods
Saisics and Compuing manuscrip No. (will be insered by he edior) Bayesian model comparison wih unnormalised likelihoods Richard G. Everi Adam M. Johansen Ellen Rowing Melina EvdemonHogan Each of hese
More informationResearch Question Is the average body temperature of healthy adults 98.6 F? Introduction to Hypothesis Testing. Statistical Hypothesis
Inroducion o Hypohesis Tesing Research Quesion Is he average body emperaure of healhy aduls 98.6 F? HT  1 HT  2 Scienific Mehod 1. Sae research hypoheses or quesions. µ = 98.6? 2. Gaher daa or evidence
More informationHouse Price Index (HPI)
House Price Index (HPI) The price index of second hand houses in Colombia (HPI), regisers annually and quarerly he evoluion of prices of his ype of dwelling. The calculaion is based on he repeaed sales
More informationA Brief Introduction to the Consumption Based Asset Pricing Model (CCAPM)
A Brief Inroducion o he Consumpion Based Asse Pricing Model (CCAPM We have seen ha CAPM idenifies he risk of any securiy as he covariance beween he securiy's rae of reurn and he rae of reurn on he marke
More informationMonte Carlo Observer for a Stochastic Model of Bioreactors
Mone Carlo Observer for a Sochasic Model of Bioreacors Marc Joannides, Irène Larramendy Valverde, and Vivien Rossi 2 Insiu de Mahémaiques e Modélisaion de Monpellier (I3M UMR 549 CNRS Place Eugène Baaillon
More informationNewton's second law in action
Newon's second law in acion In many cases, he naure of he force acing on a body is known I migh depend on ime, posiion, velociy, or some combinaion of hese, bu is dependence is known from experimen In
More informationUsing Monte Carlo Method to Compare CUSUM and. EWMA Statistics
Using Mone Carlo Mehod o Compare CUSUM and EWMA Saisics Xiaoyu Shen Zhen Zhang Absrac: Since ordinary daases usually conain change poins of variance, CUSUM and EWMA saisics can be used o deec hese change
More informationAcceleration Lab Teacher s Guide
Acceleraion Lab Teacher s Guide Objecives:. Use graphs of disance vs. ime and velociy vs. ime o find acceleraion of a oy car.. Observe he relaionship beween he angle of an inclined plane and he acceleraion
More informationPROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART TWO
Profi Tes Modelling in Life Assurance Using Spreadshees, par wo PROFIT TEST MODELLING IN LIFE ASSURANCE USING SPREADSHEETS PART TWO Erik Alm Peer Millingon Profi Tes Modelling in Life Assurance Using Spreadshees,
More informationModelBased Monitoring in LargeScale Distributed Systems
ModelBased Monioring in LargeScale Disribued Sysems Diploma Thesis Carsen Reimann Chemniz Universiy of Technology Faculy of Compuer Science Operaing Sysem Group Advisors: Prof. Dr. Winfried Kalfa Dr.
More informationRotational Inertia of a Point Mass
Roaional Ineria of a Poin Mass Saddleback College Physics Deparmen, adaped from PASCO Scienific PURPOSE The purpose of his experimen is o find he roaional ineria of a poin experimenally and o verify ha
More informationAnalogue and Digital Signal Processing. First Term Third Year CS Engineering By Dr Mukhtiar Ali Unar
Analogue and Digial Signal Processing Firs Term Third Year CS Engineering By Dr Mukhiar Ali Unar Recommended Books Haykin S. and Van Veen B.; Signals and Sysems, John Wiley& Sons Inc. ISBN: 073807 Ifeachor
More informationLecture 18. Serial correlation: testing and estimation. Testing for serial correlation
Lecure 8. Serial correlaion: esing and esimaion Tesing for serial correlaion In lecure 6 we used graphical mehods o look for serial/auocorrelaion in he random error erm u. Because we canno observe he u
More informationExponentially Weighted Moving Average Control Charts with TimeVarying Control Limits and Fast Initial Response
Exponenially Weighed Moving Average Conrol Chars wih TimeVarying Conrol Limis and Fas Iniial Response Sefan H. Seiner Dep. of Saisics and Acuarial Sciences Universiy of Waerloo Waerloo, Onario N2L 3G1
More informationChapter 8 Student Lecture Notes 81
Chaper Suden Lecure Noes  Chaper Goals QM: Business Saisics Chaper Analyzing and Forecasing Series Daa Afer compleing his chaper, you should be able o: Idenify he componens presen in a ime series Develop
More informationWhy Did the Demand for Cash Decrease Recently in Korea?
Why Did he Demand for Cash Decrease Recenly in Korea? Byoung Hark Yoo Bank of Korea 26. 5 Absrac We explores why cash demand have decreased recenly in Korea. The raio of cash o consumpion fell o 4.7% in
More informationChapter 7. Response of FirstOrder RL and RC Circuits
Chaper 7. esponse of FirsOrder L and C Circuis 7.1. The Naural esponse of an L Circui 7.2. The Naural esponse of an C Circui 7.3. The ep esponse of L and C Circuis 7.4. A General oluion for ep and Naural
More informationTracking of Multiple Moving Sources Using Recursive EM Algorithm
EURASIP Journal on Applied Signal Processing 24:18, 1 11 c 24 Hindawi Publishing Corporaion Tracking of Muliple Moving Sources Using Recursive EM Algorihm PeiJung Chung Deparmen of Elecrical Engineering
More informationDigital Data Acquisition
ME231 Measuremens Laboraory Spring 1999 Digial Daa Acquisiion Edmundo Corona c The laer par of he 20h cenury winessed he birh of he compuer revoluion. The developmen of digial compuer echnology has had
More informationNikkei Stock Average Volatility Index Realtime Version Index Guidebook
Nikkei Sock Average Volailiy Index Realime Version Index Guidebook Nikkei Inc. Wih he modificaion of he mehodology of he Nikkei Sock Average Volailiy Index as Nikkei Inc. (Nikkei) sars calculaing and
More informationDuration and Convexity ( ) 20 = Bond B has a maturity of 5 years and also has a required rate of return of 10%. Its price is $613.
Graduae School of Business Adminisraion Universiy of Virginia UVAF38 Duraion and Convexiy he price of a bond is a funcion of he promised paymens and he marke required rae of reurn. Since he promised
More information