GPS Receiver Autonomous Integrity Monitoring Algorithm Based on Improved Particle Filter

Transcription

1 2066 JOURL OF COMPUTERS, VOL. 9, O. 9, SEPTEMBER 204 GPS Recever utonoous Integrt Montorng lgorth Based on Iproved Partcle Flter Ershen Wang School of Electronc and Inforaton Engneerng, Shenang erospace Unverst, Shenang, Chna Eal: Tao Pang, Zhan Zhang and Pngpng Qu School of Electronc and Inforaton Engneerng, Shenang erospace Unverst, Shenang, Chna bstract Relablt of a navgaton sste s one of great portance for navgaton purposes. Therefore, an ntegrt ontorng sste s an nseparable part of avaton navgaton sste. Falures or faults due to alfunctons n the sstes should be detected and repared to eep the ntegrt of the sste ntact. ccordng to the characterstc of GPS (Global Postonng Sste recever nose dstrbuton and partcle degenerac and saple povershent proble n partcle flter, an proved partcle flter algorth based on genetc algorth for detectng satellte falures s proposed. The cobnaton of the re-saplng ethod based on genetc algorth and basc partcle flter s used for GPS recever autonoous ntegrt ontorng (RIM. Dealng wth the low weght partcles on the bass of the genetc operaton, genetc algorth s used to classf the partcles. It brngs the selecton, crossover and utaton operaton n genetc algorth nto the bass partcle flter.the ethod for detectng satellte falures whch affect onl subsets of sste easureent. In addton to a an partcle flter, whch processes all the easureents to gve the optal state estate, a ban of aular partcle flters s also used, whch process subsets of the easureents to provde the state estates whch serve as falure detecton references. The consstenc of test statstcs for detecton and solaton of satellte fault s establshed. The falure detecton s undertaen b checng the sste state logarthc lelhood rato (LLR. The RIM algorth cobned the genetc partcle flter and the lelhood ethod s llustrated n detal. Eperental results based on GPS real raw data deonstrate that the algorth under the condton of non- Gaussan easureent nose can prove the accurac of state estaton, effectvel detect and solate fault satellte, prove the perforance of the fault detecton. Eperental results deonstrate that the proposed approach s avalable and effectve for GPS RIM. Inde Ters global postonng sste(gps; recever autonoous ntegrt ontorng(rim;genetc algorth (G;partcle flter; fault detecton I. ITRODUCTIO Wth the developent of the global navgaton satellte sste (GSS and the ncrease of user perforance reureents for GSS servce, for safet-crtcal applcatons of global navgaton satellte sste (GSS, such as arcraft and ssle navgaton sstes, t s portant to be able to detect and eclude faults that could cause rss to the accurac and ntegrt, so that the navgaton sste can operate contnuousl wthout an degradaton n perforance[-3]. Because t needs a long te for satellte fault ontorng to alar through controllng the satellte navgaton sste tself, usuall wthn 5 nutes to a few hours, that can't eet the deand of ar navgaton[4]. s a result, to ontor the satellte fault rapdl n the clent part, nael the Recever utonoous Integrt Montorng (RIM has been researched a lot. Currentl, RIM algorth ncludes two categores: one s to the snapshots algorth usng the current aount of pseudorange observaton, the other s the RIM algorth based on alan flter. The snapshots algorth does not need eternal support eupent, and t has the advantage of fast speed and pleent easl, and t has been wdel used at present. Ths nd of algorth anl has Part space (Part ethod, the su of least Suares of the Error (SSE ethod, and the largest nterval ethod, etc. Kalan flterng algorth s b usng hstorcal easure to prove the perforance, and t has a strong dependence to the a pror error characterstc, but the actual error characterstcs s dffcult to accuratel forecast. Moreover, ths algorth reures easureent nose obe Gaussan dstrbuton, and the nose s ver dffcult to strctl obe Gaussan dstrbuton n the actual easureent, at ths pont, the perforance of the algorth wll downgrade uch [5-7]. Varous flterng ethods have been studed for reducng the easureent nose level or ntegratng a GSS wth other sensors so that the navgaton sste can estate ts poston ore accuratel and relabl. Because flters reduce the nose level of easureents usng prevous nforaton, the can provde a better ntegrt ontorng perforance than snapshot algorths can. However, snce ost flters, such as Kalan flters, presue that the easureent error and dsturbance follow a Gaussan dstrbuton, ther perforance can degrade f ths assupton s not correct. Because GSS easureent error does not follow a Gaussan dstrbuton perfectl[8], the alan flter approach has to use an naccurate error odel that a cause perforance degradaton. 204 CDEMY PUBLISHER do:0.4304/cp

2 JOURL OF COMPUTERS, VOL. 9, O. 9, SEPTEMBER To address ths proble, a new ntegrt ontorng algorth usng partcle flters (PF s proposed. Partcle flters can deal wth nonlnear/non-gaussan dnac sstes as well as lnear/gaussan sstes[9-0]. The basc partcle flterng ethods, such as Seuental Iportance Saplng (Seuental Iportance Saplng ethod has a proble of partcle degradaton, as a result, solvng ths proble anl reles on two e factors: choosng the portance denst functon and resaplng strateg. lthough the resaplng strateg can solve the proble of partcle degradaton, but at the sae te wll brng the saple depleton proble, that s the power value of partcle s selected for an tes, and t wll contan an repeated saplng results, thus dverst of partcles wll be lost. The cobnaton of the re-saplng ethod based on genetc algorth and basc partcle flter s used n GPS recever autonoous ntegrt ontorng (RIM.The proposed algorth estates a dstrbuton of a easureent resdual fro the posteror denst and detects eceedngl large resduals to satsf a false alar rate. Ths algorth can detect faults based on an accurate estaton of the posteror dstrbuton, and t can detect and eclude faults alost sultaneousl, so that the sste can eclude a fault easureent easl. Wth a non-gaussan easureent error, a genetc partcle flter can estate the dstrbuton of the state ore accuratel than a basc partcle flter can, and therefore t has a better ntegrt ontorng perforance. In addton, f the sste s also hghl nonlnear, then the perforance wll also be better. The paper s organzed as follows. Frst, a theor of a partcle flter s brefl revewed. Then the genetc algorth s descrbed n detal. nd the genetc algorth s cobned wth the partcle flter. The general schee of the approach followed b a genetc partcle flterng based on log lelhood rato (LLR approach to FDI s presented. The net secton s a descrpton of the sste and easureent euaton of GPS sste. Fnall, based on the real GPS raw data, the GPS autonoous ntegrt ontorng sste and ts usefulness are presented wth the nuercal sulatons. II. FULT DETECTIO BSED O PRTICLE FILTER Fault detecton refers to detect the estence of the ontored sste fault, fault solaton refers to dentf the source of fault or falure of the sste when a falure occurs. Partcle flter algorth s a nd of algorth based on seuental onte carlo and the seuental portance saplng (SIS flter. PF s a odern Baesan ethods based on nuercall approatng posteror dstrbutons of nterest. Partcle flters are suted for nonlnear state-space odels and non-gaussan nose. Through the probablt denst dstrbuton functon fro the sste, the saples s generated, and through the sste state euaton and easureent euaton, forecast the saplng set and update to approate rando Baesan estaton of nonlnear sste. Snce Gordon proposed seuental portance resaplng partcle flter algorth based on onte carlo ethod, the partcle flterng has becoe one of the hot research topcs n the state estaton proble of nonlnear sste and non-gaussan nose. nd now t s wdel used n navgaton, autoatc control, target tracng, and so on, and successfull appled to the dnac sste falure detecton probles[-4]. The prncple of detectng the fault based on partcle flter algorth s applcable to an nonlnear and nongaussan sste. It has no an ltaton wth the sste process nose and easureent nose, and t s eas to get the optal state estaton. The error of the partcle flter s closel related to odel satch, and wth the ncrease of odel satch, the partcle flter error wll ncrease rapdl[5]. Based on ths concluson, the partcle flter s appled n fault detecton. Meanwhle, RIM algorth tself evaluates the consstenc of the state of the sste.. Basc Partcle Flter lgorth Partcle flters can deal wth nonlnear/non-gaussan dnac sstes as well as lnear/gaussan sstes. The seuental portance saplng (SIS algorth s a Monte Carlo (MC ethod that fors the bass for ost seuental MC flters developed over the past decades[6]. Ths seuental MC (SMC approach s nown varousl as bootstrap flterng[7], the condensaton algorth, partcle flterng, nteractng partcle approatons[8]. It s a technue for pleentng a recursve Baesan flter b MC sulatons. The e dea s to represent the reured posteror denst functon b a set of rando saples wth assocated weghts and to copute estates based on these saples and weghts. s the nuber of saples becoes ver large, ths MC characterzaton becoes an euvalent representaton to the usual functonal descrpton of the posteror probablt denst functon (PDF, and the SIS flter approaches the optal Baesan estate. Ths secton brefl ntroduces the basc SIR algorth to provde a bacground to our proposed ntegrt ontorng algorth. In order to develop the detals of the partcle flter algorth, frst, let s consder the dnac state space odel below: X = f( X -,v- Z = h( X,n Where s a state vector, z s an output easureent vector, f(.,. and h(.,. are state transton functon and easureent functon respectvel. v s a process nose vector ndependent of current state, and n s a easureent nose vector ndependent of states and the sste nose. The epectaton and the varance of the states are obtaned fro the posteror probablt denst functon (PDF, whch s epressed usng a ass functon of rando saples and assocated weghts, as shown n euaton (. The rando saples are nown as partcles. ( ( p( z = ω δ( ( : s = 204 CDEMY PUBLISHER

3 2068 JOURL OF COMPUTERS, VOL. 9, O. 9, SEPTEMBER 204 { Where = = } z: z,,...,. The partcles are derved fro the pror dstrbuton, and the assocated weghts are calculated usng euatons (2 and (3. ( ( ( ω = ω / s ω (2 = p( z p( ω ω ( ( ( ( ( = ( ( (, z ( ( The condtonal probabltes ( ( (3 p( and p z whch are nown as the transton pror denst and lelhood denst, respectvel, are deterned b the sste defnton. The portance ( ( denst (, z whch s not defned b the proble, s a desgn paraeter chosen b the desgner. popular choce of the portance denst n the SIS algorths s the transton pror denst. ( ( ( ( (, = ( z p (4 Ths ethod s ver sple and eas to pleent. However, t has a degenerac proble whch can be tgated b usng a resaplng (or selecton procedure. Ths algorth s called the SIR flter. The SIS algorth thus conssts of recursve propagaton of the weghts and support ponts as each easureent s receved seuentall. The basc prncple of partcle flter algorth s that: Frst, based on the pror condtonal dstrbuton of sste state vector, the state space generates a group of rando saples, these saples called partcles. Then based on the easureent value adust constantl the partcle weght and poston of the partcle dstrbuton, odfed ntal pror condtonal dstrbuton. The algorth s a recursve flterng algorth, coonl used to handle non-gaussan and nonlnear sstes state and paraeter estaton. The huge coputatonal burden s the bottlenec of partcle flter algorth. Basc partcle flter algorth can be descrbed b the followng steps: (Intalzed ccordng to the pror probablt p, the ntal partcles { } s ( 0 0 = are obtaned, the weght value of the partcles s / S. (2 For =,2, perforng the followng steps; State predcton Pror partcles etracted based on the state euaton of sste at te. 2 { X (:=,2,,}~p( X X Update Update partcle weghts at te : w w p z = w p ( z h ( = ( where,=,2,3... noralzed: s.the weght values are e S S = = w = w w, w = (3Resaplng Fro the set of partcles ( X,w, accordng to the values of the portance resaplng, gettng a new set of partcles ( X ˆ,,, =. (4 Estate. State estaton Calculatng the sste state estaton value at s current te: ˆ w X = Then, =+, go to steps (2. B. Degenerac Proble of Basc Partcle Flter coon proble wth the SIS partcle flter s the degenerac phenoenon. It s thus possble to avod a degenerac phenoenon. Practcall, after a few teratons of the algorth, all but one of the noralzed portance weghts are ver close to zero, and a large coputatonal burden s devoted to updatng traectores whose contrbuton to the fnal estate s alost zero. fter a few teratons, all but one partcle wll have neglgble weght. It has been shown that the varance of the portance weghts can onl ncrease over te, and thus, t s possble to avod the degenerac phenoenon. Ths degenerac ples that a large coputatonal effort s devoted to updatng partcles whose contrbuton to the approaton s alost zero. sutable easure of degenerac of the algorth s the effectve saple sze eff. s eff = s 2 ( w = Where w = p(, z: / (, z s referred to as the true weght. Ths can not be evaluated eactl, but an estate eff of eff can be obtaned b the followng euaton. eff = s 2 ( w = Where w s the noralzed weght. otce that eff, and sall s eff ndcates severe degenerac. Clearl, the degenerac proble s an undesrable effect n partcle flters. The brute force approach to reducng ts effect s to use ver large partcles. Ths s often practcal, therefore, there are two ethods for the degenerac phenoenon: good choce of portance denst and usng of resaplng. The latter s descrbed as follows. Resaplng partcle flter can suppress weght degradaton, but t ntroduces other practcal probles, 204 CDEMY PUBLISHER

4 JOURL OF COMPUTERS, VOL. 9, O. 9, SEPTEMBER for eaple, the resaplng partcle no longer ndependent. Moreover, t lts the opportunt to parallelze snce all the partcles ust be cobned. nd the partcles that have hgh weghts are statstcall selected an tes. Ths leads to a loss of dverst aong the partcles as the resultant saple wll contan an repeated ponts. Ths proble, whch s nown as saple povershent, s severe n the case of sall process nose. s a theoretcal bass of evolutonar thought, the genetc echans to solve the proble of partcle degradaton probles provdes an portant gudng deolog, and t has obvous advantages of nhertance choce. s a result, usng genetc algorth operaton such as crossover, utaton and reproducton to produce new saples, t can abandon the resaplng sple tradeoff shortcongs, and at the sae te, t eets the deand of satsfng the reureents of saple dverst [9-20]. generc partcle flter s then as descrbed as follows. C.Partcle Flter Based on Genetc lgorth Resaplng Genetc algorth s search optzaton algorth of sulatng bologcal evoluton on the coputer based on natural selecton and genetc echans. Because the genetc algorth reflects a nd of evolutonar thought, t has the certan reference value to solve the proble of degradaton of partcle flter[2]. Copared wth genetc algorth, the partcle flter algorth has an ntal saple collecton, and a collecton of each ndvdual represents a possble soluton of the sste, these ndvduals change wth the state transton euaton and has the hgh ftness ndvduals to reproduce. The Partcle Flter GPF (Genetc lgorth based Partcle Flterof Genetc lgorth and resaple are to ntroduce the selecton, crossover and utaton operaton n Genetc lgorth nto the basc Partcle Flter lgorth nstead of the tradtonal resaplng ethod. In ths paper, the partcle evoluton operaton does not need for encodng and decodng operaton, but drectl operate wthn the scope of the real nuber. Genetc resaplng process s the genetc echans of eecuton, whch s for each partcle status wth weghts, the crossover and utaton operaton s done as followng: ( Crossover operaton Two partcles are randol selected fro the partcle n s concentraton (,, n=, ccordng to the followng euatons for crossover operaton. ~ n = α + ( α + η ~ n n = α + ( α + η Where, η ~ (0, Σ, α ~ U (0,.The crossover prncple s: ~ n If ( z a{ p( z, p( z } p >, then tae the partcles ~ ~, or tae the partcles wth the n probablt s p ( z a{ p( z, p( z }. It s the sae wa to tae or abandon partcles ~ n wth ~. (2 Mutaton operaton One partcle ( s = fro partcles sets s randol selected and the varaton operaton s done accordng to ~ = +η, η ~ (0, Σ. The utaton prncple s: If p( z > p( z,select the partcles, or select the partcles wth the probablt p( z / p( z.ccordng to the crossover and utaton operaton above, the new partcles sets s {, w } = wll be got, and then get state estaton b the followng epresson. ˆ = s ~ ω = The advantage of ntroducng the genetc algorth s to prove the effcenc of the use of the partcle and to ae the nuber of partcles decreased, whch s needed b posteror probablt dstrbuton when approatng to the sste state varables. On the other hand, due to the genetc algorth can effectvel ncrease the dverst of the partcle, restran effectvel the saple povershent. III RIM BSED O GEETIC LGORITHM PRTICLE FILTER D LIKELIHOOD RTIO GSS-based navgaton sstes ust have an ntegrt ontorng sste that contans two an functons: detecton and ecluson of satellte faults and 2 estaton of the uncertant of the poston solutons. The sste calculates decson varables and copares these to thresholds that have been set to satsf the ntegrt reureents for the desred operaton. If an decson varable eceeds the threshold, then the sste concludes that the correspondng easureent has a fault, and ecludes the detected fault. RIM nclude two functons: detecton of satellte whether there s a fault, dentf a fault satellte, and the navgaton calculatng process wll be reoved[22]. Through the establshent of lelhood rato test statstc consstenc nspecton, and test statstcs calculated usng the easured values, t can approatel descrbe the fault as uch as possble. Detecton threshold s the threshold of the fault test statstcs of the udgent sste, the threshold could be obtaned accordng to the reureents of the false alar rate detecton.. GPS Observaton Euaton The GPS dnac sste odel s as follows: X = F X + w Where, X = [ r, r, r, Δδ ] T s three densonal z 204 CDEMY PUBLISHER

5 2070 JOURL OF COMPUTERS, VOL. 9, O. 9, SEPTEMBER 204 poston and GPS-recever cloc offset, and F s a transton atr whch s an dentt atr n the statc case[23]. The GPS sgnal conssts of a cloc sgnal and a navgaton essage that s apltude odulated. Each satellte sends the cloc sgnal n two dfferent bands, L and L2. The GPS recever receves the sgnal corrupted b nose and other sources of error. The raw easureents of the code and carrer phase pseudoranges are presented as follows[24]. ρ ( = R ( + c Δδ + T ( + E ( + ε ( where: ρ : code pseudoranges ( : satellte nuber R : dstance between the recever and satellte poston( c : speed of lght ( s Δ δ : cobned cloc offsets of the recever and satellte cloc wth respect to GPS te (s E : effect of epheers error ( I : onospherc dela ( T : trophospherc dela ( ε : code observaton nose ( The data of satellte coordnates ( s, s, s, z pseudo-range ρ and te error Δ δ s got fro the GPS recever. The proble of fault detecton conssts of ang the decson on the presence or absence of faults n the ontored sste. n FDI sste for GPS ntegrt ontorng s desgned. The an falures to be detected affect onl a subset of the sste easureents. reference sste unaffected b falures s reured for the FD whch ontors the state estate of a PF[25]. ssung the nuber of the satelltes used for calculatng s = 6, and a satellte s falure, so tae 5 (that s - fro all of the observatons, whch fors a new observaton subsets C ( C. 5 6 M ˆ,p M ( ˆ,p ( B ˆ,p B ( F ˆ,p F ( S( S( B S( F Fgure. Falure detecton prncple dagra based on genetc partcle flter algorth where,2,3,4,5,6 are the current easureent values, ncludng the pseudorange between the satellte and recever obtaned b coputng and the vsble satellte coordnates got fro satellte navgaton essage. Partcle flter GPF J( J = B,C,D,E,F,G s the nput for subsets of the easurng values. J J { ˆ, p (, J = B, C, D, E, F, G } s b easurng a subset gven after the correspondng partcle flter state estaton and the lelhood probablt denst M 3 B ( = ( = 4 ( = C D E ( = 4 ( = 3 ( = F ( = Fro each nput easured value of PFs we can now, when a postonng satellte fals, one of s aular PFs wll not contan the easured values send fro the fault satelltes, and then we can detect fault satellte through consstenc test. B. Logarthc Lelhood Rato Test Statstc The log-lelhood rato s defned as a functon of a rando varable as follows. pα ( s ( = ln (5 p α 0( The LLR test s defned as the probablt denst functon of the aular GPF and an GPF rato, the LLR can be coputed as follows: p ( ( s ( ln p = (6 The cuulatve LLR of easureent ( ( Y ( = to can be epressed as: p S = ln (7 p Y 204 CDEMY PUBLISHER

6 JOURL OF COMPUTERS, VOL. 9, O. 9, SEPTEMBER Because the sste state estaton of the lelhood functon can be epressed as noralzed PF partcle approated weghts, the above forula p ( Y and p ( Y can be epressed as follows: p Y w = p Y w = ( ( (8 ( ( (9 fter calculatng the cuulatve LLR functon S of ever oent, accordng the feature of cuulatve LLR functon S, that s under the noral crcustance, wth the te s ncreasng, the functon curve s stable, and when data s changng, that wll engage to a postve drft. Reflectng on the functon curve s a dfferent fro other te. Usng ths feature the sste falure can be detected. C. RIM Based on Genetc Partcle Flter Based on partcle flter algorth and the logarthc lelhood rato (LLR ethod, ths paper s to pleent satellte fault detecton and solaton. It s usng partcle flter on the sste b processng the easured values of calculated each oent corresponds to the logarthc lelhood rato (LLR. Then ae the LLR accuulated of wndow functon each te, the test statstc s obtaned for accuulatve LLR at ths oent. fter that, accordng to the fault caused b the changng n consstenc to detect falure oent, the fault detecton and solaton of satellte s realzed. Based on genetc partcle flter and logarthc lelhood rato RIM algorth can be detaled as follows: ccordng to the coordnates ( r,r, rz of the recever, generate the ntal set of partcles o ( : =,2, for an PF partcle fro the { } pror probablt denst functon(pdf p ( 0 aular PFs partcles { ( : =,2,, } 0,,and the 0 ( = 0 ( for =,2,...,. The an PF processes all easureents ( s total nuber of easureents, whle the aulares, process subset of easureents (- easureents. Repeatng the followng steps for each te : State predcton. The partcles of { o ( : =,2, } and { 0 ( : =,2,, } are ntroduced nto the sste state euaton, usng the forula ( to obtan partcles predcted values ( and (. 2 Calculate the partcles weght, Tae the predcted values of the partcles ( ( and the -th satellte poston coordnates ( s,s, sz and the te error Δ δ, and so on nto the sste easureent euaton to obtan the predcted -th ρ ρ satellte pseudo-range value.tae the and pseudo-range easureent value ρ nto the weght calculaton forula and noralze the to obtan the noralzed partcle weghts ( and (. ω ω 3 Lelhood evaluaton On recept of the easureent, the lelhood of the predctve state saples fro the an PF are evaluated as ( ( ( ω = p z whle the lelhood of the predctve state saples fro the aular PFs can be epressed as follows. ( ( ( ω = p z 4 LLR calculaton LLR S ( s coputed b euaton as follows. w ~ r ( = S ( = ln r= w ~ r ( = 4 Decson functon Decson functon for FD defned as the followng euaton: ( β = a a S U + Q 5 Fault detecton If β > τ (the decson threshold value s τ, the fault alar te s set to β <τ, then no fault, go to step (7. 6 Fault solaton In > t t a = t and up to step (6; f a, reove the accuulated LLR Q satelltes largest subset of the satellte, nael d D ( g = arg a S > t forula. g as faled satellte ta a nuber, deternng a falure satellte nuber of the satellte, the satellte n turn, can be solated fro the easured value. 7 Status update The portance weght ( of the predctve state ω saples { ( :,2,..., } fro the an PF = and ω ( of the predctve state saples { ( : =,2,..., } fro the aular PFs are calculated as follows: 204 CDEMY PUBLISHER

7 2072 JOURL OF COMPUTERS, VOL. 9, O. 9, SEPTEMBER 204 ω ( = ω ( and ω ( = ω ( = ω ( = ω ( Then,the fltered saples { ( : =,2,..., } for the an PF and { ( : =,2,..., } for the aulares are obtaned b resaplng { ( :,2,..., = } and { ( : =,2,..., } respectvel. Therefore, the resaplng partcles of partcle flter are updated. IV. EXPERIMETS uercal sulatons on GPS postonng llustrate the FDI perforance of the proposed approach for GPS ntegrt ontorng.. Eperents Condtons In ost GSS applcatons, the pseudorange easureent error s assued to follow a Gaussan dstrbuton. However, ths s not true. In general, the core part of the error dstrbuton can be characterzed well usng a Gaussan dstrbuton, but the tal part of the dstrbuton s heaver than that of a Gaussan dstrbuton. The heaver tal s due to ground-reflected ultpaths or to ssteatc recever/antenna errors. Our sulaton used a Gaussan core-laplacan (GL tal probablt denst functon (PDF as the recever true error dstrbuton to sulate a heav-taled odel, whch wll be appled to our partcle flter ethod. The eperental raw observaton data are obtaned b GPS recever 220, the observaton data ncludng the satellte recever poston locaton nforaton and pseudorange values, the statc easureent data s 48 s. at ths te, there are 6 satelltes used for PVT resoluton, the uber of the satellte s 3,5,8,9,2,22 respectvel, and the correspondng pseudorange value Y = (,,,,, can be epressed as t the sae te, the RCB-4H recever bloc ontors that the satellte s worng norall, and poston stead. In order to sulate when a satellte s falure, whether the algorth could detecton effectvel, we add soe devaton. Here, we add 50 devaton to O.9 satellte at te20~48(=20~48. In the eperent, the partcle =00, the calculated decson functon of wndow length s selected as 30, the eperental data observaton nose obes gaussan ernel Laplace dstrbuton. B. Eperents Results and nalss In order to contrast wth GPF algorth and PF algorth for perforance RIM, two ontorng algorths are pleented respectvel n ths wor. Fgure 2. Decson functon for fault detecton under nonal condton Fgure 3. Cuulatve LLR for fault solaton under nonal condton It can be seen fro fgure 2 that the decson functon has reaned stead under fve, n fgure 3, each aular PF and GPF accuulatve LLR functon curve s fluctuate, but ts value s not ore than 5. Fgure 4. Decson functon for fault detecton under fault condton 204 CDEMY PUBLISHER

8 JOURL OF COMPUTERS, VOL. 9, O. 9, SEPTEMBER Fgure 5. Cuulatve LLR for fault solaton under fault condton Fgure 4 and fgure 5 are gven after a satellte falure, genetc partcle flter algorth and basc partcle flter algorth used n GPS recever autonoous ntegrt ontorng of the eperental results. s seen fro the fgure 4, the decson functon appeared a sgnfcant up n = 202 te, over the detecton threshold, and n oents = 205, RIM algorth adopts the genetc gves warnng of partcle flter algorth, whle the basc partcle flter ethod s used n the RIM algorth at = 20 te alar s gven. t the sae te, accordng to the above descrbed n secton 3.2 of the prncple of fault detecton, t can udge that the o.9 satelltes s faled, so the satellte data of o.9 satellte durng ths perod of te (Poston Veloct and Te when PTV calculatng should be abandoned, that wll guarantees relablt for locatng. It can be seen fro the fgure 4 and fgure 5, a genetc partcle flter algorth and basc partcle flter algorth n the RIM algorth can successfull detect and solate fault satellte, ts detecton perforance s superor to the basc partcle flter and the logarthc lelhood rato (LLR cobnng the RIM algorth. Genetc algorth s ntroduced to prove the estated accurac of partcle flter. The paraeters n two nds of algorths are shown n table. TBLE PRMETER COMPRISO BETWEE PRTICLE FILTER D G PRTICLE FILTER LGORITHM lgorth PF GPF Partcle nuber Effectve partcle nuber RMSE Where, the average nuber of effectve partcles and RMSE can be calculated b: eff s = ( ω (0 = ( 2 RMSE = s 2 ( ˆ ( s = s the talbe shows, the RMSE of GPF s saller than that of PF, that sas the estaton accurac of GPF s hgher than PF flter. When the partcles =00, the effectve saple of PF s , f we ncrease the partcle nuber to =300, and the effectve saple nuber s ; correspondngl, when partcle nuber of GPF =00, the effectve saple s , whle partcles nuber =300, the effectve saple s Seen fro the table, to PF and GPF algorth, rsng the partcle nuber can ncrease the effectve partcle, at the sae te, t can decrease RMSE, whch prove the accurac perforance; under the condton of the partcle nuber s the sae, copared wth the PR algorth, the GPF algorth can ncrease the effectve saple nuber, and prove the state estaton accurac. V. COCLUSIOS new approach of fault detecton and solaton (FDI for GPS ntegrt ontorng b cobnng partcle flters wth genetc algorth s proposed. The algorth can prove the state estated accurac of partcle flter. The approach sets up a ban of aular genetc partcle flters and an genetc partcle flter. The logarthc lelhood rato (LLR test statstc s used to chec the consstenc between the state estate of the an partcle flter and those of the aulares. Through GPS recever eperent platfor saples the observaton data, nuercal sulatons verf that the algorth cobned the genetc partcle flter (GPF algorth wth logarthc lelhood rato (LLR s feasble and effectve for GPS recever autonoous ntegrt ontorng (RIM n the non-gaussan easureent nose envronent. The paraeters coparsons of RMSE and effectve partcle nuber are gven. The results deonstrate that the detecton perforance s superor to that of the basc partcle flter. CKOWLEDGMET The wor are supported n part b a grant fro the atonal atural Scence Foundaton of Chna(o.606, the eronautcal Scence Foundaton of Chna(o. 20ZC5400, the Jont Funds of the atural Scence Foundaton of Laonng Provnce(o REFERECES [] YU Y, KIM D. Integrt ontorng algorths usng flterng approaches for hgher navgaton perforance: consderaton of the non-gaussan gnss easureents[c].proceedngs of IO GSS 20th Internatonal Techncal Meetng of the Satellte Dvson, Fort Worth, TX, 2007: [2] Isha Mohaad; Mohd. lauddn Mohd. l and Mahaod Isal, valablt, Relablt and ccurac of GPS Sgnal n Bandar Baru Bang for the Deternaton of Vehcle Poston and Speed[C]. Proceedng of the 2009 Internatonal Conference on Space Scence and Councaton, Port Dcson, eger Seblan, Malasa,pp [3] Yoch Morales and Taash Tsubouch, GPS Movng Perforance on Open S and Forested Paths, Proceedngs 204 CDEMY PUBLISHER

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