World Appled Scences Journal 7 (Specal Issue of Computer & IT): 98-6, 9 ISSN 88.495 IDOSI Publcatons, 9 Integraton of Global Postonng System and Inertal Navgaton System wth Dfferent Samplng Rate Usng Adaptve Neuro Fuzzy Inference System Ahmed M. Hasan, Kharulmzam Samsudn, Abdul Rahman Raml, Raja Syamsul Azmr and Salam A. Ismaeel Computer Systems Research Group, Department of Computer and Communcaton Systems Unverst Putra Malaysa, 434 UPM-Serdang, Malaysa Abstract: Integraton of the Global Postonng System (GPS) and Inertal Navgaton System (INS) has become ncreasngly common n the last two decades, because the characterstcs of GPS and INS are complementary and the ntegraton between both systems wll maxmze ther advantages and mnmze ther weakness. Over tme, nertal navgators drft from ther preset algnments. Or, the ntal algnment may have been corrupted by vehcle moton, wth mperfect transfer of algnment and veloctes to the navgator. Also, there may not have been enough tme to perfect algnment. In such case, navgators can be beneft from adng such as GPS. The ntegraton between the GPS and INS leads to accurate navgaton soluton by overcomng each of ther respectve shortcomngs. And to make ths ntegraton possble the dfference between the GPS and INS systems n samplng rate must be solved before any ntegraton can be work properly. In ths paper, the GPS low rate problem s solved by predctng or extrapolatng the mslad readng data of the GPS to be attuned wth those of INS data usng Adaptve Neuro Fuzzy Inference System (ANFIS). Hence, the gap between the two systems readng data s solved to provde synchronzaton between the INS and GPS systems. So, t s possble to compare the readng data of both systems. Three strateges have been proposed and the results shows superor performance n predctng mssed GPS data wth lowest mean error. Key words : Global Postonng System (GPS) Inertal Navgaton System (INS) Adaptve Neuro fuzzy Inference System (ANFIS) navgaton systems samplng data rate INTRODUCTION GPS s a constellaton of satelltes developed by the Unted States Department of Defense mltary as a navgaton utlty. Frst launched n 98 and fully operatonal snce 99, GPS satelltes have become ncreasngly mportant to both mltary and cvlan navgaton. They use one-way rangng as ther fundamental navgaton technque []. GPS s capable of provdng precse postonng nformaton to an unlmted number of users anywhere on the planet. However, GPS can provde ths type of nformaton only when there s a drect lne of sght to four or more satelltes. Regrettably, ths requrement s not constantly possble snce a GPS sgnal may be lost when movng around obstacles (n canopy, urban areas, nsde tunnels, between large buldng and tree lned streets, etc), or sgnal jammng by an adversary forces or bad weather condtons. Therefore overall GPS accuracy degrades regardng the above reasons. In other words, the system does not work properly n urban areas due to sgnal blockage and attenuaton that may deterorate the overall postonng accuracy [-4]. On the other hand, navgaton systems, n partcular nertal navgaton systems (INSs), have become mportant components n dfferent mltary and cvl applcatons. INS s a self-contaned system that conssts of two set of sensors three orthogonal accelerometers and three orthogonal gyroscopes, whch measure three lnear accelerometers and three angular rates, respectvely. These measurements need to be processed to get poston and velocty nformaton [5]. Regrettably, the INS cannot substtute the GPS or operate as a standalone system. Durng the mechanzaton of processng the IMU output, the accuracy of INS soluton deterorate wth tme due to the nherent sensors errors that reveal consderable long-term error growth n poston and velocty [6, 7]. These long-term errors ncludng whte nose correlated random nose, bas nstablty and angle random walk. Also, It must be mentoned that there errors are stochastc n nature and can cause a sgnfcant Correspondng Author: Ahmed M. Hasan, Computer Systems Research Group, Department of Computer and Communcaton Systems, Unverst Putra Malaysa, 434 UPM-Serdang, Malaysa 98
World Appl. Sc. J., 7 (Specal Issue of Computer & IT): 98-6, 9 degradaton n the INS performance over a long perod of operaton. Therefore INS and GPS are often pared together n order to provde a navgaton system that has superor performance n comparson wth ether a GPS or an INS standalone system. There are many GPS applcatons, ncludng ar, land, and marne navgaton, precson agrculture, surveyngand precse tmngand there are dfferent recevers specfc to each applcaton [8]. BACKGROUND The last two decades have shown an ncreasng trend n the use of navgaton technologes n several applcatons ncludng land vehcles and automated car navgaton. Navgaton systems ncorporate the Global Postonng System (GPS) and the Inertal Navgaton System (INS) both can be used for wde range of navgaton functons. Each has ts strength and weaknesses. Ths work ams to provde a hgh superorty method to aggregate dfferent data rate GPS wth INS data wthout sacrfcng performance even f usng low cost nertal sensors. The INS and GPS are dfferent n the samplng rate because the INS s very fast system, whch produces data at a hgh data rate, compared to the GPS recever whch s slower than the INS. Hence, there s gab between the two systems readng data. Some researchers overcomes ths problem by choosng the GPS and INS systems wth the same samplng rate as n [9], or usng kalman flter to predct the samplng between nstants as n []. Furthermore, There are several sgnfcant drawbacks related to kalman flter such as the requrement for a pror nformaton of the system and measurement covarance matrces for each new sensor, that could be tough to accurately verfed, another typcal problem related to kalman flterng s the observablty of dfferent states, therefore weak observablty of some of the error states that may lead to unstable estmates of another error states [7, -4]. Whle the proposed ntellgent predctor s general and not depend on the type of the sensor, from the lterature t s obvous that there s a lack of research that focus on consderng or solvng ths problem whle solvng t wll open a wde range of flexblty to ntegrate dfferent rate systems such as GPS and INS of any type wth dfferent samplng rate. In ths paper we wll use Adaptve Neuro fuzzy Inference System (ANFIS) to predct the samplng of GPS data between nstants. Most of the researchers provoked to nvestgate an alternatve approach to the KF due to the nadequacy of the KF, n ths paper artfcal ntellgence chosen to be the hard core of the ntellgent predctor. Mult-layer Perceptron (MLP) neural networks have been used by many researchers n dfferent felds [3, 5, 6]. However, MLP neural networks have some problems, such as ther black-box nature, the lack of knowledge representaton powerand the selecton of the proper structure and sze to perform the requred real tme mplementaton. ANFIS were chosen as the core for the new predctor ntegraton technque for several reasons: () rapd ablty of nput and output mappng, therefore, well-matched for mappng the GPS data as nput to extrapolated mssng data as outputs; () the proposed modeless system requres no pror knowledge of the GPS sensor nformaton and hence ncrease the ablty for learnng process; (3) ANFIS s a fxed smple structure wth reduced computaton resources leadng to real tme mplementaton. Hence, ANFIS s more smplest compared to MLPNNs that need to determne the optmal number of hdden layer and number of neuron s n each layer [7, 8]. layer layer layer3 layer4 layer5 X A II w w N A w f Y B II w N w w f B Fg. : Schematc of the Neuro-fuzzy model [9] 99
World Appl. Sc. J., 7 (Specal Issue of Computer & IT): 98-6, 9 ADAPTIVE NEURO FUZZY INFERENCE SYSTEM (ANFIS) ANFIS s an adaptve network based on fuzzy nference systems. It combnes fuzzy logc and neural networks to facltate the hybrd learnng procedure. ANFIS archtecture conssts of fve consecutve layers as llustrated n Fg. [9]. Each layer conssts of a number of nodes () that perform dfferent operaton accordng to the nternal node functon. The frst layer contans a number of Membershp Functons (MFs) assocated wth each nput varable to project the nput parameters nto the fuzzy doman. Each membershp functon s defned by a set of non-lnear parameters. Known as the antecedent parameters{a, b,c }. Each node n the second layer operates a multplcaton between the sgnals comng from the frst layer and provdes the product (w ) for the followng layer. The thrd layer normalzes the output of each nodes of the pervous layer wth respect to the total output of all nodes (w). Nodes n the fourth layer contan functons wth a set of lnear parameters known as consequent parameters {p, q, r }. These parameters are estmated durng the forward propagaton usng least square method. The last layer sums all ncomng sgnals and provdes the overall outputs. ANFIS utlzes a hybrd learnng technque, n whch there are two man algorthms nvolved. Frst s the feed forward propagaton, whch based on least square adjustments to estmate the consequent parameters, defned n layer 4. The second algorthm s the feed backward propagaton that s based on the gradent descent optmzaton technque to adjust (update) the antecedent membershp functon parameters. The forward propagaton represents the fuzzy reasonng, whle the backward propagaton represents the neural computatons. In the followng subsectons s a detaled descrpton of the ANFIS process starts wth the clusterng data set at the nput layer and descrbng both the feed forward and backward propagaton procedures. Input data clusterng: Input data sets are clustered nto a number of parttons such that the lkeness wthn each partton s larger than the lkeness among the parttons. Ths clusterng s used manly to determne the locaton of membershp functon, thus, t provdes fast and accurate generaton of the fuzzy relatonshp between the nput and output data sets. Generally, ncreasng the number of MFs guarantees hgh resoluton of mappng the nput varables. Such hgh resoluton s necessary to capture the hgh dynamc that mght exst n the nput data. In ths work, the subtractve clusterng method s used. Subtractve Membershp functon Input sequence Fg. : Generalzed bell membershp functon clusterng requres no pror knowledge of the number of the clusters. It only requres the cluster radus, whch ndcates the range of the nfluence of a cluster and hence determnes the number of the antecedent membershp functons []. For n nput data ponts {x,., x n }, each one s assumed as a canddate for cluster centers. The densty measure at each data pont x s, then, computed as follow []: D () n x x j = exp j= (r/) a where r a s a cluster radus and t s the only external parameter requred for ths process. Data pont of a hghest densty measure D c ndcates many near data ponts n the neghborhood, and hence s selected as the center of the frst cluster x c. The second cluster center, then, s derved by computng the densty measure agan, but wth the followng revsed expresson []: D D D exp x xc = c (r/) b where r b s selected equal to.5 r a to prevent closely spaced cluster centers. In Equaton, data ponts near to the center of the frst cluster have less densty measure and thus unlkely to be selected as a center of the next cluster. As wth the frst cluster center, the hghest densty measure s computed by Equaton and s selected as the second cluster center. Ths step s repeated untl a number of cluster centers are derved to adequately group the nput data set. ()
World Appl. Sc. J., 7 (Specal Issue of Computer & IT): 98-6, 9 Clusterng the nput data set s the frst process to accurately determne the number of fuzzy membershp functons and the ntal parameter of each membershp functon. These parameters are updated usng the gradent descent optmzaton technque through the backpropagaton algorthm [9]. The followng step to the clusterng the nput data set s the fuzzfcaton of ths data set. Mappng nput data set nto fuzzy doman: The number of the membershp functons derved by the subtractve clusterng method s based on ntal antecedent parameters for each membershp functon as presented n Fg.. These antecedent parameters hghly affect the output of each functon and hence they shall be updated n order to provde the desred nput-output relatonshp. In ths step, the nput varables (crsp nputs) are mapped nto the fuzzy doman usng the membershp functons (MFs). Bell shape MF was used here. Functon parameters {a, b, c} of the bell shape MFs determne the wdth, spread and center of the MF respectvely as n the followng expresson. w (x) = + b x c Where x s the nput varable and w (x) s the membershp (weght) of the nput varable x to the fuzzy set. Least square adjustments n feed forward propagatons: The normalzed weghts are the output of layer 3 and are used to determne the desred output y of layer 4. a w (3) (4) y= wf = w(p x+ q y+ r) Where are {p, q, r } the lnear unknown consequent parameters estmated usng the method of the least squares []. Gradent descent n feed backward propagatons: The antecedent parameters of the membershp functons are updated durng the feed backward propagaton. Ths backward propagaton s based on the gradent descent optmzaton algorthm []. Ths method s the most frequently used n nonlnear optmzaton technque due to ts smplcty. The steepest descent formula s presented as follow: θ k+ = θk η g (5) where s the antecedent parameters {a, b, c}, k s the epoch number, η s the step sze parameter, g s the gradent of the network error wth respect to the antecedent parameters. The network error s defned as a square sum of dfference between the network output and the desred output. Therefore, usng an nput-output data set allows the backpropagaton algorthm to update the antecedent membershp functon parameters. The step sze parameter η affects the convergence tme of the nput-output mappng process. If η s chosen too small, the convergence tme wll be slower and f chosen too hgh, the algorthm mght not be stable. The ANFIS algorthm s mplemented usng MATLAB envronment by wrtng a specfc program for ths purpose. The algorthm allows changng the ntal step sze durng tranng based on the error measure of the ANFIS predcton. In summary, the paramount advantage of ANFIS s usng the hybrd learnng algorthm to tran the network parameters. Durng the forward pass, the functonal sgnal feed tll layer 4, and then the lnear consequent parameters are estmated usng least squares estmates. In the backward pass, backpropagaton algorthm s used to determne the antecedent parameters whle the consequent parameters are kept fxed. THE PROPOSED ANFIS FOR GPS DATA PREDICTION For GPS/INS system ntegraton, synchronzaton must be provded between GPS and INS systems, to make t possble to compare the readng data of both systems. Predctng or extrapolatng the mssng readng data of the GPS to be compatble wth those of the INS data can accomplsh to solve the dfference n samplng rate problem between the two systems. Dfferent strateges are used to predct the GPS data (data at ntermedate tmes). The thrd strategy was more accurate from the frst and second strateges but they are the key for the thrd accurate strategy. So, they wll be llustrated n next subsectons to show the effect of usng dfferent strateges on the extrapolaton for more nvestgaton and research. Fgure 3 shows the flowchart for the general extrapolaton process of GPS data predcton. The adaptve neuro fuzzy nference system s proposed as a core to solve the dfference n data rate between GPS and INS (.e to predct the GPS data at ntermedate tmes). The tranng phase was carred out after ntalzng all poston and velocty networks wth learnng rate =.6, number of rules = 6, learnng parameters (c =[-,],b =[-4,4],a =[.,3]), number of epochs =. Utlzng the learned
World Appl. Sc. J., 7 (Specal Issue of Computer & IT): 98-6, 9 Start Read data from GPS recever estmate the readng data at tme. second was completed, then we use the data at tme, and. second to estmate the data at tme ". second" and so on (notce that the data at tme " second" wll be used wth the data obtaned from the estmaton process at tme ". second"). Fgure 5 shows the second extrapolaton strategy of GPS data. Calculate the number of samples between tme ntervals whch depend on the data rate dfference between INS and GPS Use one of the three strateges to extrapolate the GPS data Use the extrapolated GPS data n the proposed INS/GPS system End Fg. 3: General extrapolaton process of GPS data predcton parameters (c, b, a), the followng three strateges were used to extrapolate the GPS data as follows: Frst strategy: The frst strategy supposes that the GPS and INS provde readng data each and. second respectvely. It assume that we have the frst two readng data at tme and second of the GPS and the ntellgent predctor wll be used to extrapolate the GPS data at tme {.,.,.,.9} seconds then the readng data at tme 3 second wll be already avalable and we do not need to process t to be extrapolated further more t can be assgned from INS data. So, the readng data at tme, and 3 seconds was avalable and the ANFIS wll be extrapolate the GPS data at tme {3., 3.,., 3.9} seconds and contnue ths processng untl reach the end of the number of samples. It must be notced that we extrapolate the readng from tme (. to.9) seconds dependng on readng data at tme (and ) seconds whch are avalable. Fgure 4 shows the frst extrapolaton strategy of GPS data. Second strategy: Snce the INS readng data s delvered every. second then after readng of INS data was receved the estmaton process was accomplshed to estmate the readng data at tme. second dependng on two prevous readng data at tmes (.9 and ) seconds and after the processes to Thrd strategy: The man dea s the same as second strategy but to acheve more accurate result some readng data from the INS system wll be assgned n the estmaton process to reduce the oscllaton, whch obtaned from the estmaton process. So, the readng data n nteger tmes such as (, 3, 4,, etc) seconds, wll be assgned nstead of estmated them whch produce more accurate estmated trajectory. Table shows the performance of the results obtaned from the three strateges. Fgure 6 compares between the true trajectory and the extrapolated trajectores resulted from mplementng the three strateges for poston and velocty components. Fgure 7 shows a comparson between the errors of the three strateges for all components. The mean square error can be calculated usng, Where n MSE = E (6) = model E model =E real -E predcted (7) Also the standard devaton can be calculated usng, / n (8) Standard devaton = (x x) n = where n x= x (9) n = and n s the number of elements n the sample. RESULTS AND CONCLUSION Ths paper ntroduced a new method for solvng the dfference n data rate between GPS and INS system based on ANFIS. From the results obtaned n ths paper we can conclude that the ANFIS gves a better soluton to the problem of dfference n samplng rates n a short tme nterval. In general, thrd strategy produces better results, n terms of the standard devaton and means values, than the other two strateges snce t uses the true trajectory data of the nearest samples to the extrapolated one. The three strateges gve better
World Appl. Sc. J., 7 (Specal Issue of Computer & IT): 98-6, 9 Table : Performance of the ntellgent predctor based ANFIS Poston (m) Velocty (m/sec) ------------------------------------------------------------------------------------------------------------------------------------ X-Axs Y-Axs Z-Axs North East Down Frst strategy MSE 8.5543e-6.4583e-5.3569e-5.888.43.55 STD 8.4..495 5.5438 4.5569 5.6643 Mean.866.3 6.443-4.559 6.55-7.988 Elapsed tme (s).54.54.54.337.338.53 Predcton tme (s) 8.3359e-4 6.5539e-4 6.5559e-4 6.5665e-4 6.5547e-4 6.554e-4 Second strategy MSE 5.334e-7 4.8876e-5 8.37e-6.663.55. STD 4.556.6679 8.444 4.5334 3.4556 5.887 Mean -.4456-3.6634-8.5573-8.586.9-6.9 Elapsed tme (s).677.445.497.557.556.559 Predcton tme (s).998e-4 8.8e-4.9e-4 8.7765e-4 8.66e-4 9.99e-4 Thrd strategy MSE 3.957e-6.9963e-6 4.8899e-7.8.67.77 STD 3. 3.53 5.9.47.8 3.3 Mean 8.39-4.6 5.98 -.9635 3.976 -.9966 Elapsed tme (s).443.533.534.533.533.533 Predcton tme (s) 6.99e-4 8.9875e-4 8.9985e-4 8.5e-4 8.5e-4 8.5e-4 Must be avalable 3 Assgned data not estmated...3...9 Last no. of sample Data to be estmated Fg. 4: Frst strategy for GPS data extrapolaton Used to estmate next readng data at tme. 3.9. Must be avalable Last no. of sample Fg. 5: Second strategy for GPS data extrapolaton 3
World Appl. Sc. J., 7 (Specal Issue of Computer & IT): 98-6, 9 3.854 x 6 3.85 3.7 x 6 3.79 3.78 3.85 3.77 3.848 3.76 X-Axs 3.846 (m) 3.75 Y-Axs (m) 3.74 3.844 3.73 3.84 3.7 3.84 3.7 3.456 x 6 3.454 3.45-3.45 - Z-Axs (m) 3.448-3 North Drecton (m/sec) -4 3.446-5 3.444-6 8 7 7 6 6 5 5 4 4 3 East Drecton (m/sec) 3 Down Drecton (m/sec) - - Fg. 6: Comparson between the true and predcted trajectores usng three strateges for poston and velocty n all drectons results n extrapolatng the velocty components than the poston components. It can be sad that ANFIS requre pror knowledge of the trajectory. To solve ths problem a database must be bult for the selected trajectores to be used (.e. roads n the cty for the movng vehcle). On the other hand, the ANFIS has an advantage over other algorthms such as Neural Network n terms of the capacty requred n memory to mplement the 4 predcton algorthms regardng to the programs that wll be used. However, the thrd strategy provde acceptable postons and velocty accuraces compared to the other strateges t s also possble to enhance ts accuraces by optmzng the nternal system parameters usng evolutonary technques such as Genetc Algorthm (GA) or Partcle Swarm Optmzaton (PSO) and other optmzaton technques as a future development.
World Appl. Sc. J., 7 (Specal Issue of Computer & IT): 98-6, 9 5 4 5 3-5 Error n X-Axs (m) Err - - - -5-3 5 5 5-5 - Error n Zxs (m) -5 Error n North Drecton (m/sec) -5 - - -5-5 5 4 8 3 6 4 Err Error n Down Drecton (m/sec) - - -4 - -6 Fg. 7: Resulted Error evaluated usng three strateges for poston and velocty n all drectons REFEENCES. Wellenhof, B.H., H. Lchteneggerand J. Collns,. GPS Theory and Practce, by Sprnger- Verlag/Wen.. Mohnder, S., R. Lawerence and P. Angus, 7. Global Postonng Systems, Inertal Navgaton and Integraton, nd Edn. A John Wley & Sons. Inc. Publcaton. 3. Noureldn, A., A. Osmanand N. El-Shemy, 4. A Neuro -wavelet Method for Mult-Sensor System Integraton for Vehcular Navgaton. Meas. Sc. Technol., 5: 44-4. 4. Panah, S., M.R. Delavar, 8. A GIS-based Dynamc shortest path Determnaton n Emergency Vehcles. World Appled Scences Journal, 3 (): 88-94. 5
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