Performance Analysis of MEMS based Pedestrian Navigation Systems

Transcription

1 Pefomance Analysis of MEMS based Pedestian Navigation Systems Damien Kuba, Ecole Nationale de l Aviation Civile / TéSA, Fance Chistophe Macabiau, Ecole Nationale de l Aviation Civile, Fance Michel Monneat, Alcatel Space, Fance BIOGRAPHY Damien Kuba is a Ph.D. student in the field of pesonal positioning in the signal pocessing lab of the Ecole Nationale de l Aviation Civile (ENAC) in Toulouse, Fance. He gaduated in 22 as an electonics enginee fom the ENAC, and eceived the same yea his Maste degee in signal pocessing. Chistophe Macabiau gaduated as an electonics enginee in 1992 fom the Ecole Nationale de l Aviation Civile (ENAC) in Toulouse, Fance. Since 1994, he has been woing on the application of satellite navigation techniques to civil aviation. He eceived his Ph.D. in 1997 and has been in chage of the signal pocessing lab of the ENAC since 2. Michel Monneat gaduated fom the ENSICA (Ecole Nationale Supéieue d Ingénieu de Constuctions Aéonautiques) engineeing school. Afte being involved within Alcatel Space in many ada pogams, in chage of the onboad pocessing of the ARGOS / SARSAT payload, he has been involved in the Galileo pogam since 1998, fo the signal design and pefomance aspects. He is cuently involved in Alcatel Space LBS pogams. ABSTRACT Fist diven by the egulation on emegency call, seveal methods ae studied to enable the location of one use whethe he is outdoos o indoos. Moeove, location based sevices tae moe and moe impotance, and as a consequence, the ability of poviding such a location becomes a geat challenge. Assisted satellite navigation solutions ae investigated, but they encounte big issues in indoo envionment. The main eason is the wea powe of the signals to acquie and pocess. Theefoe, complementay techniques shall be developed to supply o enhance GPS based positioning solutions when GPS eception is disupted. MEMS based techniques ae pomising ones. In this pape, the pefomance of a MEMS based Pedestian Navigation System (PNS) is studied. As the PNS is assumed to be used duing GPS outages, only the navigation using exclusively MEMS sensos is addessed. The Pedestian Navigation Module (PNM) elies on fou components: a thee axes acceleomete, a thee axes gyo and a thee axes magnetomete, as well as a pessue senso. The fou sensos ae low-cost ones. Two diffeent MEMS based positioning methods ae investigated, as well as two cases of use. In a fist time, the taditional inetial navigation is discussed and its pefomance analysed. The distinction is made between the constained navigation, meaning that the sensos ae igidly attached to the use body, and the non-constained one, whee the sensos ae fee of movement with espect to the use. In a second time, the navigation based on senso output signatue is discussed. In this second positioning technique, the tavelled distance and the heading estimation ae done sepaately. The tavelled distance is computed based on step length o velocity estimation, wheeas the heading computation is based on gyo and magnetomete measuements. As fo the inetial navigation, two cases of use ae consideed, whethe the sensos ae igidly attached to the use body o not. Results point out the fact that the unconstained navigation leads to wose esults than the constained one, whateve the navigation method. The second method based on signal signatue is the best one, and is well adapted fo constained navigation. It povides a good estimation of the tavelled distance and also a eliable heading, even if low cost sensos ae used. Moeove, the second method is moe obust on senso motion with espect to the use body. In the unconstained navigation mode, the tavelled distance as well as the heading can be estimated with accuacy depending on the type and numbe of PNM movements occuing duing the wal. The availability is then all the moe educed as the numbe of PNM movements incease. INTRODUCTION The expanding demand of Location-Based Sevices Pesented at ION GNSS 25, San Diego 1

2 (LBS) is cuently boosting pesonal positioning technologies. Among them, Assisted GPS (AGPS) and High Sensitive GPS (HSGPS) ae vey adapted to povide the location of the use in many use cases. Howeve, even if the afoementioned techniques ae vey efficient, they do not cove all aeas the LBS ae liely to be povided. Especially in deep indoo envionments, they suffe fom a lac of availability. To povide a continuous location solution, such GPSbased systems have to be augmented. In this pape, the augmentation using low-cost MEMS sensos fo pesonal positioning is addessed. The focus is put on the pefomance of the senso assembly as an altenative positioning system duing GPS signals outages, in tems of accuacy and availability. Two navigation methods ae investigated, one based on taditional stap-down Inetial Navigation System (INS) algoithm, the othe based on acceleomete signal signatue algoithm. Fo both methods, the Pedestian Navigation Module (PNM) used in the study is supposed to have its own dynamic. This dynamic would be those of the use o not. The two use cases ae investigated, so that the MEMS-based PNM is tested as a typical handled positioning system. The pape is oganized as follows. In the fist section, the senso assembly is descibed, and acceleometes as well as gyometes ae oughly chaacteized. In the next two sections, navigation methods dedicated to the positioning of pedestians ae pesented, as well as thei specific algoithm. Section IV deals with typical issues encounteed in pedestian navigation that ae taen into account in the afoementioned algoithms. Finally, section V pesents the esults of actual tests conducted with the PNM. I MEASUREMENT UNIT The PNM is composed of fou diffeent types of sensos. They ae acceleometes, gyometes, magnetometes and a pessue senso. The pessue senso is an Intesema MS5534 [1]. It is a stable and tempeatue compensated senso capable of,1 mba esolution (appoximately 1 mete) with an accuacy within /-,5 mba once calibated. The senso is used in a elative mode. Infomation about the height and vetical speed of the pedestian is obtained using the following pessue-to-altitude elation : T z( P) = γ P P R a γ g 1 whee: z is the altitude of the senso. P is the pessue at altitude z. P is equal to 113,25 hpa. T is equal to 288,15 K. γ is equal to -6,5 C/m fo z < 11m. R a is equal to 287,1 J/g/K fo dy ai. g is equal to 9,8665 m/s². The acceleomete tiad is composed of Analog Device ADXL22E acceleometes [2]. They ae capable of,1 m/s² RMS noise fo a bandwidth of 3 Hz. To chaacteize the tun-on bias (o static bias), 1 data sets wee collected while one idling acceleomete was sensing the gavity vecto upwads and downwads. Then, the mean value of the measuements was compaed to zeo to find the tun-on bias. The pocess was epeated fo each of the thee axes. Results ae given in Figue 1 and summed up in Table 1. Bias (m/s 2 ) S.F. (%) Acceleometes tun-on bias X axis Y axis Z axis Run Acceleometes tun-on Scale Facto X axis Y axis Z axis Run Figue 1 Acceleomete tun-on bias and S.F. Bias (m/s²) X axis Y axis Z axis S.F. (%) Bias (m/s²) S.F. (%) Bias (m/s²) S.F. (%) Mean -,61 -,96 -,5 -,76,182 -,58 Std,3,28,1,4,4,8 Table 1 Acceleometes tun-on bias. The gyos of the PNM ae Analog Device ADXRS3 [3]. They ae affected by a,7 deg/s RMS noise fo a bandwidth of 5 Hz. The tun-on bias of the thee sensos is chaacteized using the above 3 measuements. The tun on-bias is consideed equal to the mean of gyos output while the PNM is idling. Results ae plotted in Figue 2 and summed up in Table 2. Pesented at ION GNSS 25, San Diego 2

3 Bias (deg/s) Gyometes tun-on bias X axis Y axis Z axis whee : Supescipt between bacets stands fo the coodinate system in which vectos ae expessed. m stands fo mobile, o PNM. (e) stands fo the ECEF efeence fame. (I) stands fo the Inetial efeence fame. Ω is the otation vecto of (e) elative to (I). e/ I v is the velocity of the mobile elative to (e). m / e Run Figue 2 Gyos tun-on bias. X axis (deg/s) Y axis (deg/s) Z axis (deg/s) Mean -,114 -,215 -,41 Std,298,28,357 Table 2 Gyos tun-on bias. The magnetic sensos ae Philips KMZ52 [3], [4]. They ae vey sensitive (16 mv/v / A/m) but consequently measuements ae easily affected by had and soft magnetic petubations. This low-cost senso assembly (about $15) is then used in the following fo pesonal navigation. Two common navigation methods ae implemented. They ae discussed in the next two sections. II INERTIAL NAVIGATION a) Pinciple The fist method studied fo pedestian navigation is based on the taditional INS algoithm. In the classical inetial navigation, acceleomete measuements ae basically compensated fo gavity and inetial foces. They ae then integated twice in the navigation fame to get the position of the unit. M (I ) Let be the position vecto of the PNM in the inetial fame (I). Its time deivative with espect to (I) and expessed in (I) is given by : The acceleomete tiad senses the tue acceleation of the PNM biased by the gavitational field. The fundamental pinciple of the dynamic applied to the PNM in the inetial fame (I) yields to : f = a m / I G Equation 2 ( M ) whee : (m) stands fo the mobile efeence fame. (m) f is the specific foce measued by the acceleometes. a m / I is the tue PNM acceleation elative to (I). ( ) G m ( M ) is the gavitational field expessed in (m), at point M of the PNM. Equation 2 combined with the time deivative of Equation 1 yields to the following elation : d dt whee : ( g v = m / e f g ( M ) I Equation 3 Ω e / I v m / e =. I ) ( M ) G ( M ) Ω ( Ω M ) g is the local gavity vecto. e / I e / I Quantities of inteest ae those expessed in the navigation fame (n) (Noth, East, Down). Using the otation matix R I2n fom (I) to (n), Equation 3 can be e-witten as : d dt v m / e = f g ( M ) n / e 2 n Equation 4 ( n) ( Ω Ω ) v e / I m / e d dt M = v Ω M m / e e / I I Equation 1 whee : ( Ω n) n / e is the otation vecto of (n) elative to (e). Pesented at ION GNSS 25, San Diego 3

4 Equation 4 is the diffeential equation of inetial navigation. Based on this equation, the usual INS mechanization is implemented as shown in Figue 3. The otation matix R m2n that otates measuements fom the mobile fame (m) into the navigation fame (n) is computed using the otation quatenion q. Position and velocity ae computed evey sampling peiod T s. mechanization. They ae twofold. Indeed, fist ode Taylo expansion models ae used to compute some paametes, as fo example quatenion. On the othe hand, some quantities estimated at epoch ae used in the computation pocess at epoch 1. Nevetheless, in the following this type of eo is consideed negligible with espect to the pevious one. In ode to analyse the pefomance of the navigation algoithm, a popagation eo method is used. Based on a dynamic eo model of the INS as those pesented in [6], the position, velocity and attitude eo δp, δv and δρ ae popagated using the state tansition matix F. The popagation model is those of Equation 5, whee all submatices ae developed in [6] : Figue 3 INS mechanization. The accuacy of such navigation algoithm is addessed in the next sub-section. b) Accuacy The accuacy of the navigation system pesented in Figue 3 mainly depends on two issues. The most impotant one is the quality of the sensos used in the PNM. Because of manufactue pocess and senso technology, the output of the senso is usually diffeent fom the actual input, so that the geneal senso measuement model is as follows : a [ 1 S( t) ] a ( t) b( t) n( ) ( t) = t output tue δp& Fpp δv& Fvp δρ& = Fρp δε& a δε & g Fpv Fvv Fρv F pρ Fvρ Fρρ F F vε a ε aε a F F ρε g ε gε g δp δv δρ δε a δε g Equation 5 INS eo model n n v ρ n n n The state vecto is augmented by acceleometes eos δε a including bias and scale facto models, and gyometes eos δε g including bias model. The pefomance of the senso assembly is then analyzed using the popagation model of Equation 5. Fo the simulation, the PNM is assumed to be at est, and biases and scale facto values ae those computed in section I. The esulting pedicted hoizontal RMS position eo is plotted in Figue 4 as the blue dashed cuve. Given the low-cost sensos used in the assembly, the hoizontal RMS eo is pedicted to be nealy 57 metes afte 6 seconds. n ε a n p ε g ε a ε g whee : a is the actual quantity to measue. tue a is the value povided by the senso. output S is the scale facto affecting the tue measuement. b is the bias affecting the tue measuement. n is the senso noise. Eo (m) Pedicted eo INS Eo Hoizontal RMS Eo Both acceleomete and gyomete measuements ae affected. As a consequence, bias and scale facto intoduce dift in the computation of the otation matix R m2n, as well as in the integation of acceleation and velocity. They both contibute to a decease of the oveall accuacy. The second facto esponsible fo position, velocity and attitude eo comes fom appoximations made in the Time (s) Figue 4 Hoizontal position eo. Pesented at ION GNSS 25, San Diego 4

5 To assess the simulation esult, eal data wee collected fom the idling PNM ove 6 seconds and pocessed though the navigation algoithm depicted in Figue 3. The esulting hoizontal RMS eo is plotted as the ed solid cuve in Figue 4. Both hoizontal eos ae close fom each othe. Thee is only a slight diffeence mainly due to stochastic models chosen fo biases and scale facto, which pobably do not match pefectly the eality. Nevetheless, the eo popagation model matches quite well the INS static behaviou so that it can be used to find ways fo impoving the navigation solution. As discussed above, eos in the navigation algoithm ae basically those intoduced by biases and scale facto. To analyze the effect of each facto, thee independent eo popagation simulations ae conducted. They all involve only one eo paamete among acceleomete bias, acceleomete scale facto and gyomete bias to avoid intefeence between these factos. Values used in the eo model ae again these of section I. Pedicted hoizontal RMS eos ae plotted in Figue 5. Fom the thee eo factos, the bias affecting the gyomete measuements is the one that degades significantly the accuacy of the navigation algoithm. Opposite, the acceleomete scale facto has vey little effect on the oveall accuacy. 7 6 Only gyo bias Only acc. bias Only acc. S.F. Hoizontal RMS Eo c) Enhanced Inetial Navigation (EIN) Algoithm To compensate fo acceleomete and gyomete biases and enhance the inetial navigation algoithm, it is necessay to go beyond classical compensation methods based on stochastic eo models. Indeed, these models ae only appoximations of the actual behaviou of biases affecting the measuements. Thus, thee ae still esidual eos that degade the oveall pefomance. One eliable way to impove bias estimation is to use extenal data. Given ou senso assembly, additive extenal measuements can indeed be used to povide edundant infomation fo bias estimation. The gyomete biases ae liely to be estimated using acceleometes fo inclination dift and magnetometes fo heading dift. The combination of the thee sensos povides a dift-fee attitude, which can be fit in the inetial navigation algoithm to compensate fo gyo biases effect. Acceleometes biases ae moe difficult to estimate using ou PNM assembly. Nevetheless, some assumptions can be made about the spectum of the measuements to limit the esidual eo. Moeove, once otated into the navigation fame (n), acceleomete vetical channel can also be checed with pessue senso measuements to limit vetical velocity and vetical position dift. With all these impovements, the classical inetial navigation algoithm is modified, such as the EIN System mechanization is as follows : 5 4 Eo (m) Time (s) Figue 5 Biases and Scale Facto impact. Consequently, the impovement of the navigation algoithm elies fist on the eduction of the effect of gyomete bias and then acceleomete bias. Scale facto effect is fom this sub-section neglected. The next sub-section deals then with the impovement of the classical inetial navigation algoithm. Figue 6 EIN System Mechanization. III SIGNAL SIGNATURE-BASED NAVIGATION a) Pinciples The second pedestian navigation method studied in this pape is based on the signatue of the PNM acceleomete signal. To cope with the issue of acceleomete bias, a model lining the velocity o step length of the pedestian and chaacteistics of the sensed acceleation is established as descibed in [7] and [8] : Pesented at ION GNSS 25, San Diego 5

6 s p = f1( individual paametes) v p = f2( individual paametes) whee : s is the step length of the waling pedestian. p 1 v p is the velocity of the waling pedestian. f and f 2 ae the model function. They can be linea o non linea. The individual paametes used to model the actual pedestian velocity ae computed based on the acceleation signal. To get id of the oientation of the PNM containing the acceleometes, the acceleation signal is consideed to be the total acceleation magnitude defined as : 2 2 ( a ) ( a ) ( a ) 2 a = x, y, z, Equation 6 Global acceleation whee : a is the global acceleation magnitude sensed by the PNM at epoch. This global acceleation is biased by the gavity vecto. a is the acceleation along the x axis of the x, PNM, expessed in the mobile fame (m) at epoch. a is the acceleation along the y axis of the y, PNM, expessed in the mobile fame (m) at epoch. a is the acceleation along the z axis of the z, PNM, expessed in the mobile fame (m) at epoch. Based on the signal of Equation 6, paametes ae computed to model the velocity o step length of the waling pedestian. These paametes ae chosen in such a way they eflect the behaviou of the wal. To fit the mathematical model with the actual velocity model, a egession algoithm is then applied on the computed paametes using extenal velocity measuements when they ae available. The pedestian velocity model can then be expessed as follows : v p β1 β2 = α PARAM α PARAM L 1 1 whee : α i and β i ae the egession coefficients. PARAM ae the paametes computed based on the total acceleation i a. 2 2 Once the velocity model is found, the cuvilinea distance that is tavelled is estimated by integation. In a second time, the azimuth of displacement is estimated. Then the tajectoy can be econstucted though a classical Dead Reconing algoithm : N E 1 = N d 1 = E d [, 1] cos( ψ ) [, 1] sin( ψ ) whee : ψ is the azimuth of displacement at epoch. N is the noth position of the pedestian at epoch. E is the east position of the pedestian at epoch. d [, 1] is the cuvilinea distance tavelled between epoch and 1. b) Signal Signatue-Based Navigation Mechanization As it has been pesented in the pevious sub-section, both distance and heading estimation ae done sepaately. In this study, the tavelled cuvilinea distance computation is pefomed though the estimation of the pedestian velocity. Depending on the navigation mode (constained o unconstained), the model is established using an association of paametes chosen among vetical velocity, fequency, mean, Root Mean Squae and thid-ode moment. The vetical velocity is povided by the pessue senso, wheeas the othes ae computed fom the global acceleation of Equation 6. The heading infomation is usually obtained though the integation of gyomete measuements. In this pape, the heading infomation is computed using the attitude filte descibed in section II. The Signal Signatue-Based Navigation (SSBN) System is then mechanized as depicted in Figue 7. Pedestian velocity estimation Pessue senso Thee axes acceleomete Position Dead Reconing Algoithm Azimuth of displacement Attitude Filte Thee axes gyomete Thee axes magnetomete Figue 7 SSBN System Mechanization. Pesented at ION GNSS 25, San Diego 6

7 IV NAVIGATION ISSUES Befoe testing the algoithms descibed in the two pevious sections, two typical issues affecting both navigation methods and occuing while waling ae investigated. They ae Eule s angles singulaity and displacement diection detection. a) Eule Singulaities Eule s angles ae used to define the attitude of the PNM in the navigation fame. The definition used in this pape is the one pesented in Figue 8. φ is the oll angle, θ the pitch angle and ψ the yaw angle. φ Noth Obviously, when the pitch angle eaches /-9, the oll and yaw angles ae mathematically not defined; and thus can not be ecoveed fom the otation matix R m2n. Since the PNM will be put in a pocet in any diection, this use case may happen. To avoid the singulaity, the pitch angle is continuously checed. If it goes highe than a detemined theshold, then the PNM is vitually otated along the pitch angle, so that no singulaity should appea. As an illustation, Figue 9 gives an example of the Eule s Angles Singulaity Resolution (EASR) algoithm developed in this study. The bold pat of each plot is the coected angle. Thee ae no singulaities left afte pocessing. Roll and yaw angles ae pefectly obsevable, even fo pitch angle values of /-9. Eule's Angles Singulaity θ East φ (deg) -5 Uncoected φ Coected φ ψ Down θ (deg) 5 EASR algoithm engaged Figue 8 Eule s angles definition. Usually, these angles ae computed fom the otation matix R m2n defined in section II and III. Thee ae diffeent ways of computing this otation matix, whethe using diect cosine method o quatenion integation. The quatenion method is used in this pape. The diect cosine expession of R m2n is as follows : R m2n cθ cψ = cθ sψ sθ whee : c stands fo cosine. s stands fo sine. sϕ sθ cψ cϕ sψ sϕ sθ sψ cϕ cψ sϕ cθ cϕ sθ cψ sϕ sψ cϕ sθ sψ sϕ cψ cϕ cθ Fom these expessions, it is clea that the Eule s angles can be computed accoding to the thee elations below : R m2n (3,2) ϕ = actan Rm2n (3,3) θ = acsin (3,1) 2n ( ) R m R ψ = actan R m2n m2n (2,1) (1,1) ψ (deg) Uncoected ψ Coected ψ Samples Figue 9 Eule s angles singulaity esolution. b) Displacement Diection Detection Fo both navigation methods, thee ae two typical cases of use in which the azimuth of displacement has to be estimated. It depends on the motion of the PNM elative to the use, whethe it follows the movement of the pedestian o not. In the fist case called constained navigation, the PNM is fixed anywhee onto the use, o simply put in a pocet of the use. The heading computed by the PNM is thus the displacement azimuth, biased by an additive constant because of the non alignment of the PNM heading axis and the body diection of wal. In the second case called unconstained navigation, the tue azimuth of displacement is not the heading povided by the PNM, since the PNM has got its own movement elative to the pedestian. Figue 1 illustates the issue. The oientation of the heading axis of the PNM is liely to change, as well as the diection of wal, but both ae not coelated. Thus, tacing the heading of the PNM is Pesented at ION GNSS 25, San Diego 7

8 no moe elevant. Noth Displacement diection Expeiments ae conducted in thee phases. Fist, the static behaviou of the algoithms is tested. Second, the pefomance of the constained navigation algoithm is analysed. Finally, the unconstained navigation is addessed. PNM Heading axis v N α PNM v E East a) Static algoithm pefomance In this test, the PNM is laying at est in a pocet of the use fo 6 seconds, in a andom attitude. Thee algoithms ae compaed : the Classical and Enhanced Inetial Navigation algoithms (espectively CIN and EIN), and the Signal Signatue-Based Navigation (SSBN) algoithm. Results ae plotted in Figue Hoizontal RMS Eo 55 5 CIN algo. EIN algo. SSBN algo. 45 Figue 1 Unconstained navigation issue. The solution investigated in this pape is based on velocity estimation in the navigation fame (n). Whateve the technique used fo navigation, the velocity accessible fom the PNM measuements is the velocity of the PNM elative to the gound. It can be decomposed as follows : Eo (m) v = v v PNM / g whee : u stands fo use. g stands fo gound. PNM / u u / g Assuming the velocity of the PNM elative to the use v negligible compaed to those of the use elative PNM / u to the gound v u / g, east and noth velocities of both navigation algoithms can then be used fo the computation of the tue displacement azimuth. As shown in Figue 1, it is given by : v α = actan v Equation 7 Tue Displacement Azimuth. V TESTS RESULTS In this section, the two methods pesented in Figue 6 and in Figue 7 ae tested as pedestian navigation systems. In the tests conducted, GPS data ae only used to ecove the initial heading infomation. These data also give the diffeent efeence tajectoies. E N Time (s) Figue 11 Static Eo. As it could be expected, The SSBN algoithm outpefoms the two othe algoithms. Indeed, the eo is mete at the end of the un, since it is based on motion detection. Although it still emains some esidual eo, the EIN algoithm gives good esults compaed to the CIN one. Afte 6 seconds of navigation, the eo is indeed educed by 95% (fom 57 metes fo the CIN algoithm to 25 metes fo the EIN algoithm). The impovement povided by the attitude filte is thus vey effective. b) Constained Navigation Dynamic tests ae conducted to analyse the behaviou of the diffeent navigation algoithms. In this sub-section, only constained pedestian navigation is addessed. This means that the PNM is put on a pocet of the use with a andom attitude, and is no moe moved until the end of the un. Figue 12 shows the tajectoies of the fist constained navigation test. This test lasts 1min and 1s, and the tue DGPS tajectoy is epesented as the blue solid cuve. Pesented at ION GNSS 25, San Diego 8

9 The offset between the displacement diection and the PNM heading axis was found manually. The SSBN solution is the moe accuate one, with a final hoizontal RMS eo of about 5m. No majo dift whethe in attitude o in position is noticeable on this shot duation un. plotted in Figue 13. The navigation solution is accuate within 2 metes ove the whole test peiod, with a final hoizontal RMS eo of 16 metes Refeence SSBN Solution Noth (m) EIN algo. Refeence SSBN algo. CIN algo. East (m) 1 5 Finish Stat Noth (m) Figue 13 SSBN Solution 1% GPS data used. Stat East (m) Figue 12 Navigation Solutions. The geen dotted plot stands fo the EIN position solution. Its final hoizontal eo is about 9 metes. Although the pedestian is waiting fo 3 seconds and no dift is emaable at the beginning, this is not the case at the end of the un. Indeed the blac asteis is located at the actual end of the wal, so that the position dift while the pedestian is stopped fo anothe 3 seconds is clealy obsevable. On the othe hand, the attitude of the pedestian matches quite well those of the efeence, with no appaent heading dift. Consequently, it can be stated that the attitude povided by the attitude filte is eliable. The filte is efficient in emoving gyo difts. Howeve, it fails to estimate accuately the acceleation biases affecting the measuements, leading to a difting position solution. Nevetheless, it clealy outpefoms the CIN algoithm, whose position solution is epesented by the blac dash-dotted plot. The impovement is of about 9% since the coesponding final hoizontal eo is 95 metes (The whole tajectoy is not plotted hee fo visual convenience). As seen above, the attitude filte is dift-fee but does not emove all the bias contained in the acceleomete measuements. On the othe hand, the SSBN algoithm is moe obust on such bias. Theefoe, to assess the complementay of the attitude filte and the SSBN algoithm, anothe test is conducted ove a longe peiod. In this un, the pedestian wals 1 m in 13 min with the PNM put in a pocet with a andom attitude. The PNM is still not moved duing the un. The esulting tajectoy using 1% of GPS data fo velocity model calibation is The same tajectoy is plotted using only 1% of GPS data fo velocity model calibation. Those 1% of data ae collected between the beginning of the wal and the geen asteis, as shown in Figue 14 (appoximately 1 minute). The accuacy of the SSBN solution stays within 25 metes ove the whole path. This coesponds to 12 minutes of navigation without GPS data. The final hoizontal RMS eo is 18 metes. East (m) Refeence SSBN Solution Finish Stat Noth (m) Figue 14 SSBN Solution 1% GPS data used. Even with a little pat of data fo calibation, the velocity model povides good estimates of the cuvilinea tavelled distance. Accuacy stays within acceptable limits that ae suitable fo LBS applications duing GPS outages. Moeove, tajectoies fom Figue 12 and Figue 13 ae not affected by Eule s angles singulaities, since both econstucted and efeence path match. A position solution can then be povided egadless of any Pesented at ION GNSS 25, San Diego 9

10 oientation of the PNM. c) Unconstained Navigation Howeve, the position solution may be affected by the movement of the PNM, if the latte is contained in a handheld device such as a cell phone o a PDA. To assess the capability of the SSBN algoithm to povide a eliable position solution while the PNM is moved duing the wal, anothe dynamic test is pefomed. In this test, a pedestian follows an athletic tac of 25 metes fo 4 minutes. At the beginning of the test, the PNM is in the pocet of the pedestian, with a andom attitude. While waling, he pulls andomly the PNM out and moves it as if he would loo at a cell phone. Then he eplaces it inside his pocet. The movements of the PNM ae done accoding to the assumption made in section IV b). The PNM is moved 13 times duing the un. The esulting tajectoies ae given in Figue 15. Moeove, as shown is Figue 16, the MSSBN heading shape is appoximately those of the GPS, which is taen as efeence. Consequently, this tends to pove the efficiency of the displacement diection detection algoithm discussed above. Heading (deg) Refeence heading Modified SSBN heading SSBN heading 8 6 Refeence SSBN Solution Modified SSBN Solution Steps Figue 16 Displacement diection detection esult. 4 East (m) Stat Noth (m) Figue 15 Unconstained navigation solutions. The blac squaes ae fo epochs at which the PNM is moved (except the fist one). The uncoected tajectoy computed with the SSBN algoithm is clealy not elevant of the actual path followed by the pedestian. Howeve, the coected tajectoy computed with the Modified SSBN (MSSBN) algoithm matches quite well the tue tajectoy. Both tavelled distance and displacement diection ae coheent with the actual ones. Indeed, thee is no noticeable dift in the cuvilinea tavelled distance. The velocity model once calibated is thus obust to such PNM movements duing the wal. Fo visual convenience, the tajectoy computed with the Modified EIN algoithm, (i.e. the EIN algoithm modified to estimate both Noth and East velocities) is not plotted hee fo compaison. The acceleation biases yield to a difting position that goes quicly out of the figue. CONCLUSION The aim of this pape was to analyse the pefomance of two MEMS-based navigation algoithms used in an altenative positioning system duing GPS outages. The algoithms ely on fou common low-cost sensos. They have been tested unde two diffeent use cases: fist, the constained navigation, and second, the unconstained navigation. Since in both cases the PNM is placed in a pocet of the pedestian with a andom attitude, an Eule s angles contol algoithm has been successfully implemented to avoid singulaities that would degade the heading infomation. Eos souces have been identified and classified with espect to thei impact on the oveall accuacy. It has been shown that the gyo biases ae esponsible fo most of the eos, moe than acceleomete biases. Consequently, a filte has been designed to cope with these issues and povide a dift-fee attitude. Its integation with the CIN algoithm has led to the implementation of an EIN algoithm. The pefomance of the EIN algoithm is moe than 9% bette than the CIN algoithm using the same sensos. Howeve, even if the navigation solution dift is well educed because of the attitude filte, this is not enough to be used as an altenative positioning system fo pedestian. Indeed, acceleomete biases ae badly estimated and consequently ae esponsible fo the esidual eos. The position is difting so that this algoithm can only be used fo shot tem positioning fo both constained and unconstained navigation. Pesented at ION GNSS 25, San Diego 1

11 To cope with this issue, a SSBN algoithm has been implemented. Coupled with the attitude filte, this algoithm povides eliable position solutions ove time, with a hoizontal RMS eo within 25 metes fo 12 minutes of constained navigation without GPS assistance fo velocity model calibation. The unconstained navigation mode has also been studied and tested with the MSSBN algoithm. In this mode, the PNM has got its own motion elative to those of the pedestian. Assuming a low PNM dynamic with espect to pedestian motion, it has been shown that the tue displacement diection could be estimated with an acceptable accuacy (25 metes fo 4 minutes of navigation). Even if the hoizontal RMS eo is highe than in the constained navigation mode, the modified algoithm maes the system obust to medium motion of the PNM. Consequently, the SSBN and MSSBN algoithms ae the moe suitable fo pedestian navigation duing GPS outages. ACKNOWLEDGMENTS The autho would lie to than Ph.D. student Benjamin Chibout and D. Chistophe Macabiau fo thei help duing the collect of the data used in this pape. REFERENCES [1] Intesema MS5534 data sheet. [2] Analog Devices ADXL22E data sheet. [3] Analog Devices ADXRS3 data sheet. [4] Philips KMZ52 data sheet. [5] Philips Application Note AN22. [6] Faell J. A., Bath M. The Global Positioning System & Inetial Navigation. [7] Ladetto Q. (23). Ph.D. thesis epot. [8] Gabaglio V. (23). Ph.D. thesis epot. Pesented at ION GNSS 25, San Diego 11