Use of High Sensitivity GNSS Receiver Doppler Measurements for Indoor Pedestrian Dead Reckoning

Transcription

1 Sensors 3, 3, ; do:.339/s34433 Artcle OPEN ACCESS sensors ISSN Use of Hgh Senstvty GNSS Recever Doppler Measurements for Indoor Pedestran Dead Reckonng Zhe He, Valére Renaudn, Mark G. Petovello and Gérard Lachapelle * PLAN Group, Schulch School of Engneerng, he Unversty of Calgary, 5 Unversty Drve NW, Calgary, AB N N4, Canada; E-Mals: zhehe@ucalgary.ca (Z.H.); valere.renaudn@fsttar.fr (V.R.); mark.petovello@ucalgary.ca (M.G.P.) * Author to whom correspondence should be addressed; E-Mal: Gerard.Lachapelle@ucalgary.ca; el.: ; Fax: Receved: 6 February 3; n revsed form: 6 March 3 / Accepted: 6 March 3 / Publshed: 8 March 3 Abstract: Dead-reckonng (DR) algorthms, whch use self-contaned nertal sensors combned wth gat analyss, have proven to be effectve for pedestran navgaton purposes. In such DR systems, the prmary error s often due to accumulated headng drfts. By tghtly ntegratng global navgaton satellte system (GNSS) Doppler measurements wth DR, such accumulated headng errors can usually be accurately compensated. Under weak sgnal condtons, hgh senstvty GNSS (HSGNSS) recevers wth block processng technques are often used, however, the Doppler qualty of such recevers s relatvely poor due to multpath, fadng and sgnal attenuaton. hs often lmts the benefts of ntegratng HSGNSS Doppler wth DR. hs paper nvestgates the benefts of usng Doppler measurements from a novel drect vector HSGNSS recever wth pedestran dead-reckonng (PDR) for ndoor navgaton. An ndoor sgnal and multpath model s ntroduced whch explans how conventonal HSGNSS Doppler measurements are affected by ndoor multpath. Velocty and Doppler estmated by usng drect vector recevers are ntroduced and dscussed. Real expermental data s processed and analyzed to assess the veracty of proposed method. It s shown when ntegratng HSGNSS Doppler wth PDR algorthm, the proposed drect vector method are more helpful than conventonal block processng method for the ndoor envronments consdered heren. Keywords: hgh senstvty GNSS; ndoor multpath; pedestran dead reckonng; tght ntegraton; Doppler measurements; drect vector processng

2 Sensors 3, Introducton A wde range of commercal applcatons such as emergency servces and cell phone locaton-based servces (LBS) have drven the development of pedestran navgaton technology over the past several years. Wth a demand for low cost and hgh relablty, attenton has been gven to usng addtonal sensors or devces such as W-F, nertal sensors and ZgBee rados to ntegrate wth GNSS recevers. In partcular, nertal sensors that can provde DR nformaton have proven to be of great potental [ 4]. For pedestran navgaton, the PDR algorthm s often utlzed because t makes best use of the fact that users are most lkely to move on foot, and the costs of the requred nertal sensors are relatvely low. Much research has thus been drected towards mprovng PDR algorthms, ether on relable step length detecton or mproved headng estmaton, such as [5 8]. On the other hand, GNSS recevers are often used together wth PDR algorthms due to the fact that ther errors are not accumulated. Many researchers have nvestgated ntegratng PDR algorthms wth global postonng system (GPS) recevers. he feasblty and performance of usng a low-cost moton sensor ntegrated wth GPS and dfferental GPS (DGPS) was assessed n [9]. he performance of usng pedestran dead-reckonng wth a mcro-electro-mechancal system (MEMS) nertal measurement unt (IMU) to ad hgh senstvty GPS n harsh envronment was reported n []. Generally speakng, the absolute accuracy of the ntegrated system s governed by the accuracy of the GNSS recevers. In order to enhance the performance of the GNSS recever, a typcal method s to ncrease the coherent ntegraton, as shown n [3]. However, extremely long coherent ntegraton requres that strngent requrements be met, such as to compensate for user moton, whch s not the focus of ths paper. Instead, the spatal gans obtaned by non-coherent ntegraton among satelltes are explored. As sgnal degradaton s nherent for ndoor GNSS sgnals, even f hgh senstvty recevers are stll able to generate measurements n such challenged envronments, ther qualty s usually poor. For example, pseudorange observatons n shoppng malls or tower block buldngs are largely based and can result n to 6 m horzontal root mean squared errors, even wth commercal HSGNSS [], and n these ndoor envronments, the benefts of ntegratng PDR wth HSGPS are often lmted due to multpath and fadng. he performance of PDR ntegrated wth conventonal HSGPS usng Doppler measurements n varous ndoor scenaros was assessed n []. Results showed that the performance mprovement of ntegratng conventonal HSGPS s Doppler measurements wth PDR was bottlenecked by the qualty of Doppler measurement. It also ndcated that HSGPS Doppler whch uses block processng technques [3,4] n some ndoor envronments cannot provde benefcal Doppler measurements. Wth ths n mnd, the major objectve of ths paper s to nvestgate a new method of generatng HSGNSS Doppler measurements wth the goal of mprovng PDR mplementaton n certan degraded sgnal scenaros. A drect vector processng method s thus proposed and developed. Frst, the velocty maxmum lkelhood estmate (MLE) s obtaned. hen, Doppler measurements are generated based on such velocty MLE. he advantage of ths approach s ts relablty n harsh ndoor envronments where lne of sght (LOS) and/or non-los (NLOS) sgnals are present. Subsequently, the beneft of these measurements for mprovng PDR algorthms ndoors s nvestgated. he methodology proposed here s analyzed based on the ndoor sgnal and multpath models, whch are ntrnscally related wth the dstrbuton of multpath statstcs. Real expermental data s then presented to further verfy the effectveness of the proposed methodology.

3 Sensors 3, he contrbutons of the paper are two-fold. Frst, a new drect vector processng recever archtecture s ntroduced and developed, whch s shown to provde a more relable velocty soluton as well as Doppler measurements. Second, by usng the new Doppler measurements ntegrated wth PDR, the results are shown to mprove the horzontal velocty accuraces by factors of more than 9% over the tradton mplementaton. hus the effectveness and benefts of the proposed Doppler estmaton method are demonstrated and valdated. he paper s organzed as follows: n Secton, the sgnal and multpath models are ntroduced. After revewng the archtecture of conventonal HSGNSS recevers, the proposed drect vector recever s ntroduced. hen the velocty and Doppler estmaton wth drect vector processng n ndoors are dscussed n detal. In Secton 3, the HSGNSS/PDR tght ntegraton algorthm used n ths paper s ntroduced. In Secton 4, real ndoor data s processed and analyzed. PDR-only soluton, HSGPS/PDR tght ntegraton wth conventonal Doppler and proposed Doppler measurements solutons are shown, compared, and dscussed. Fnally, conclusons are drawn n Secton 5.. Drect Vector Processng n Indoor Multpath Envronments In ths secton, an ndoor sgnal and multpath model s frst ntroduced. he model s used to analyze how ndoor multpath sgnals affect conventonal HSGNSS Doppler estmaton. After that, the proposed drect vector recever archtecture s ntroduced and dscussed wth comparson to the conventonal HSGNSS recever... Sgnal and Multpath Model he envronment consdered heren s ndoors wth dense multpath, where the multpath delay spread s usually smaller than one chp duraton, or equvalently, the coherence bandwdth s much larger than the sgnal bandwdth (spreadng code bandwdth n GNSS case). Under ths scenaro, a non-frequency selectve channel or flat-fadng channel s usually assumed whch mples the multpath tme-delay s non-resolvable [5]. Once the rado frequency sgnal s receved by the antenna, the recever down-converts t to near baseband. At ths pont, the general complex sgnal envelope can be expressed as: N sat r ( t) a x ( t ) h ( t) w( t), N () l sat In Equaton (), N sat s the number of satelltes n vew, a s the sgnal ampltude, τ s the lne-of-sght (LOS) sgnal tme delay, h (t) s the channel gan seres. x (t) = d (t)p (t) s defned as the product of the spreadng code or pseudo random nose (PRN) code, p (t) and the navgaton data bts, d (t). w(t) s nput addtve whte Gaussan nose. Here the nose w(t) s assumed ndependent of the sgnal and has a flat power spectrum over the pre-correlaton bandwdth. In the ndoor case, the channel gan seres can be further broken down as follows [6]: K h( t) e A ( t) e K K M M ' j( D, max cos cos t ) jd, Max cosm cos m t j m m m h ( t) h ( t) LOS, NLOS, ()

4 Sensors 3, From Equaton (), he NLOS channel gan has M multpath components, Am,, m are the m weghtng factor, azmuth and elevaton angles for m th multpath component. K s the Rcean factor for th satelltes, whch s the rato between LOS and NLOS sgnal powers. he subscrpt represents LOS component, whle subscrpt m represents one NLOS path. It s noted that the channel gan seres s decomposed nto two components; one for the LOS sgnals and one for all NLOS sgnals. he frst term on the rght hand sde n the above equaton s the LOS channel gan seres. he term nvolvng the summaton s the channel gan due to NLOS sgnals. For convenence, the total channel gan seres s defned to have unty power. Havng presented the basc sgnal model wth dense multpath, attenton s now gven to how ths sgnal s handled wthn a GNSS recever, and how t affects the conventonal HSGNSS Doppler estmaton. he conventonal block processng technque for Doppler measurement s dscussed n [4] and s based on the Doppler frequency MLE. Wth the notaton ntroduced above, the correlator output for th satellte wth code delay and Doppler frequency, j, fd,, k can be expressed as: j fd,, kns [ ](,,,, ) [ ] (, ) j fd k s j y n r n x n e (3) j fd,, kns where x ( n ) e represents the local code multpled wth the local carrer replca, whch s, j has a code delay of τ,j and a Doppler frequency shft of f D,,k where k,,..., K represents the ndces of the searchng range for Doppler frequency. If the coherent ntegraton nterval uses N samples, the Doppler MLE of a sngle satellte can be obtaned from Equaton (3) as follows: N ˆ f arg max y [ n] D, (,,,, ) : j f k K D k N n k: K n n j fd,, kns, j, N arg max r[ n] x ( ns, j ) e k: K N N a arg max h [ n] e k: K N j fd,, k ns arg max a I ( f ) arg max a P( f D,, k D,, k k: K ), j (4) In Equaton (4), t s apparent that the sngle Doppler frequency estmaton wll be drectly affected by the channel gan seres statstcs. More precsely, ths test statstc s I (f), whch denotes perodogram of the channel gan seres. hs statstc s an asymptotcally unbased spectral estmator [7] of the true power spectral densty (PSD) of channel gan seres.e., P (f). Due to the fact that all estmators are based on tme-lmted sequences, the actual spectrum s the PSD of channel gan seres convolved wth spectrum of the tme wndow. However, the perodogram s a reasonable approxmaton of actual PSD. So throughout the paper, the deal PSD of channel gan seres (P (f) for th satellte) s nvestgated nstead of I (f). In the vector form, the Doppler MLEs for all avalable satelltes wll be: Nsat Nsat D a I fd,, k a P fd,, k k : K k : K f ˆ arg max ( ) arg max ( ) (5)

5 Sensors 3, From Equaton (4) and (5), t s also observed that for ndvdual Doppler MLE, each channel or satellte s processed ndependently. When a channel s tme varyng, the so called Doppler spread s sometmes ntroduced [8]. hs term s defned as frequency spread n the sgnal spectrum due to dfferent sgnal propagaton paths contrbutng to a sngle fadng channel. Consequently, n some non-symmetrc rng scatterng envronments (.e., where multpath from certan drectons s much stronger than other drecton), the NLOS components domnate the sgnal. hen the PSD of the channel gan seres wll be sgnfcantly dstorted by certan channel parameters, and Doppler MLE can be based. he most mportant channel parameters n ths regard are the multpath angle-of-arrvals (AOAs). As such, once the dstrbuton of the multpath AOA s specfed, the deal PSD of the channel gan can be derved [6]. In a more compact form, f the NLOS carrer power spectrum s expressed as a functon of multpath AOAs, then the overall carrer power spectrum has the followng form: K P( f ) P ( f ) P ( f ) NLOS, LOS, K K K g ( f,,,, ) ( f f ) K NLOS, avg,, avg,, D, K In Equaton (6), K s the Rcean factor, f D, s the LOS Doppler, avg,, avg,,,,, respectvely represent averaged multpath azmuth, elevaton angle and beamwdth for azmuth and elevaton angles. Functon g NLOS, descrbes the major power dstrbuton of all multpath components for the th satellte. Its shape and centre are determned by the above mentoned multpath AOA parameters. In Equaton (6), when the Rcean factor K s extremely small, multpath wll domnate the sgnal and the Doppler MLE for ths satellte may be based. It s noted that as coherent ntegraton tme s extended, the LOS sgnal power mght be accumulated to the pont where t s usable, and the multpath power mght decrease due to exceedng the coherence tme of fadng channel. However t s not practcal to unlmtedly ncrease the coherent ntegraton tme, whch usually calls for strngent requrements for both oscllator and nertal systems. In real scenaros, t s more common to have combned LOS and NLOS sgnals or NLOS-only sgnals present n the correlator outputs, whch are the focus of the paper... Conventonal and Drect Vector GNSS Software Recever Archtectures he archtecture of a conventonal hgh senstvty GNSS software recever that uses block processng technque s llustrated n Fgure. he receved ntermedate frequency (IF) data s frst fed to a Doppler removal and correlaton (DRC) block. After the ntegraton module, whch mght have coherent or non-coherent form, the despread and demodulated sgnals are then processed by a block processng technque. he pseudorange and Doppler measurements are estmated by selectng the maxmum power n the correlator outputs (code phase and Doppler doman). Wth such measurements, the user poston and velocty can be estmated by ether least squares or Kalman flterng. When t comes to weak sgnal condtons, these measurements are often themselves based and lead to very large resduals. An effectve way to deal wth such measurements s to weght them accordng to ther accuraces. Due to the fact that the Doppler estmaton accuracy s nversely proportonal to the receved sgnal power, once accurate sgnal power can be estmated, such weghtng can be appled. (6)

6 Sensors 3, However, the C/N estmaton wll get worse under weak sgnal condtons, whch lmts the benefts of usng conventonal HSGNSS Doppler measurements. Fgure. Conventonal hgh senstvty GNSS recever archtecture. Recever rackng Channels Integraton Correlaton Map Receved IF Data Bt Adng Reference NavSoluton I jq DRC ( I Q ) NCO Channel #K Dopplers I jq DRC ( I Q ) NCO Channel # NavSoluton Navgaton Flter Fgure. Drect vector GNSS recever archtecture. Recever rackng Channels Receved IF Data Integraton Correlaton Map Velocty Doman I jq DRC ( I Q ) NCO Channel #K Projecton NavSoluton Nav-Doman MLE Sum up Power Bt Adng DRC NCO I jq ( I Q ) Channel # Projecton Velocty Uncertantes Reference NavSoluton Drect vector recever archtecture s thus proposed n Fgure. Wth scrutny of the fgure, one can observe that n drect vector recever, the sgnal power n the Doppler doman for all satelltes s projected onto the velocty domans. In ths way, the estmated velocty solutons are based on all the nformaton contaned n all correlator outputs across all satelltes whch s essentally the velocty MLE. As for conventonal hgh senstvty GNSS recevers, the velocty estmaton s only based on the Doppler MLEs, whch dscards some nformaton before fnal soluton s made. Another major beneft of the drect vector recever s that weghtng s automatcally performed accordng to the receved sgnal strength [9]. In such drect vector processng, all the power n correlator doman s preserved

7 Sensors 3, untl a navgaton soluton s obtaned. For example n ths paper, once a vald velocty soluton s obtaned, the Doppler measurement for each satellte can be generated accordngly. Detals of how the velocty MLE n the presence of multpath sgnals s obtaned are dscussed n the followng secton..3. Drect Vector Processng n Indoor Multpath It s known that the measured Doppler frequency from GNSS recevers has the followng relatonshp wth the user velocty: fd, ( v) ( u, x( vu,x - vsat,, x) u, y ( vu,y - vsat,, y ) u ( v - v )) cdt,,..., N, z u,z sat,, z sat where λ s the wavelength of transmtted RF sgnal, vu,x, vu,y, v u,z are the user ECEF user veloctes, s the ndex of current satellte, vsat,, x, vsat,, y, v sat,, z are the ECEF satellte veloctes, u [ u. x, u, y, u, z ] s the drecton unt vector from the satellte to the recever, cdt s the recever clock drft. As such, the user velocty vector s assumed to also nclude the clock drft term,.e., v u, xyz [ vu, x, vu, y, vu, z, cdt]. Due to the nvarance property of maxmum lkelhood estmates [], the velocty MLE can then be easly obtaned by: Nsat Nsat vˆ ML arg max a I ( v) arg max a P ( v ). (8) v v From Equaton (8), one can see that the fnal velocty soluton s obtaned by weghtng avalable carrer power spectrums for all satelltes. he weghtng factors are automatcally chosen as the actual sgnal powers (a ). he physcal nterpretaton of velocty MLE can be consdered as follows. Frst, the LOS sgnal power whch s an mpulse n the Doppler doman can be projected to the velocty doman on a satellte by satellte bass. Analogously, the NLOS sgnal power can also be projected nto the velocty doman. he pont n the velocty doman that has the greatest power wll represent the fnal estmate. In the followng, how the velocty MLE s obtaned n the presence of ndoor multpath sgnals wll be shown n detal. In order to project the sgnal power from the Doppler doman to the velocty doman, the relatonshp between the Doppler to the velocty can be used. For example, a small offset n the Doppler wll cause a small offset n the velocty, these two terms are lnearly related as shown n Equaton (9): e fd, u, x, u, y, u, z, u, xyz u, xyz Cn u, enu u, enu v a v a v e v (9) In Equaton (9), e s the projecton vector from velocty to the Doppler for th satellte. C e n s the rotaton matrx from navgaton frame to the earth frame. v u, enu s the user velocty offset vector wth respect to the velocty searchng centre n navgaton frame whch also ncludes the clock drft term. f D, s the Doppler frequency offset for ths satellte relatve to Doppler searchng centre. In order to vsualze the effect of multpath on velocty estmaton, t s convenent to frst consder the two dmensonal case. Assumng vertcal velocty and clock drft are already known or constraned, (7)

8 Sensors 3, 3 43 the Doppler offset s then only related wth two horzontal velocty offsets ( and vn ). he carrer PSD over the Doppler doman s shown n the upper part of Fgure 3. hs s based on Equaton (6). ak he sold green lne s the LOS sgnal power gven by and s located at the LOS Doppler offset, K. On the other hand, the major NLOS sgnal power s dstrbuted over a small regon, and has a f D, maxmum power of a g( fdmp, ) K wth a frequency offset of f DMP,. In the velocty doman, the LOS sgnal s equally dstrbuted over the lne or plane e v u f. Smlarly, for the NLOS power, the D, peak power s along the lne or plane e v u f, and powers of ts adjacent regon can be DMP, evaluated wth dfferent offsets accordng to Equaton (6). Fgure 3. Power projecton from Doppler doman to velocty doman (D case). ve Peak power PSD Adjacent regon a g ( f) K ak ( f fd, ) K Doppler Doman f f DMP, f D, e v f DMP, e v f v N D, Velocty Doman Power v E As more satelltes are consdered, the stuaton tends to that shown n Fgure 4. In ths case, there are three satelltes consdered. All three LOS powers ntersect at the pont A, so the power of pont A denotes the total power for LOS sgnals. It s also shown that there are other ntersecton ponts, such as pont B (two NLOS power together wth one LOS), pont C (two NLOS power only), and pont C (one NLOS power and one LOS power). he more ntersectons located at a partcular pont, the more power wll be observed, and the more probable t wll be the fnal velocty estmate. In the velocty doman, the pont that contans the maxmum power wll be consdered as the fnal estmate of the velocty. he velocty estmaton procedure shown n Fgure 4 reles on many factors. Under dfferent scenaros, t may have totally dfferent performance. Frstly, f all LOS components are domnatng the sgnal, or equvalently, the Rcean factors for all three satelltes are very large, then pont A wll

9 Sensors 3, 3 43 naturally be the fnal estmate and should be smlar to the least squares velocty estmaton that processes Doppler MLEs ndependently. Secondly, f only one LOS component has a large Rcean factor, say the yellow curve, and the other two satellte sgnals have domnant NLOS components, then the power of pont A may have less power than that of pont B thus potentally makng pont B the fnal estmate. In ths case, the result s not based on LOS sgnals only, but wth partal LOS nformaton and partal NLOS nformaton. In other scenaros, t s equally possble that pont C or pont D mght have the maxmum power, whch should be avoded. Consequently an admssble regon s defned n order to dscard such outlers, and the sze of the regans vares accordng to dfferent user actvtes. For example, the horzontal acceleraton durng walkng n ths paper s assumed wthn the range ± m/s. Fgure 4. Velocty MLE wth channel dstorton (D case). e v f DMP 3,3 e v f D 3,3 v N e v f DMP, e v f D, A Admssble Range e v f D, C B Power D e v f DMP, v E On the other hand, as the number of satelltes tracked ncreases, the LOS sgnal power n the velocty doman s accumulated wthout loss, whle the NLOS sgnal power n velocty doman s usually dspersed. he reason s that the projecton matrx E [ e ; e ; e 3 ] from user velocty to LOS Doppler offset array ( f D ) s calculated for LOS sgnal propagaton. In other words, f D s n the column space of the projecton matrx. For the NLOS Doppler offset array, ths s generally not true. he other reason s that the multpath statstcs for each satellte are generally dfferent and tme varyng, whereas the LOS sgnal s predctable and determnstc. If by accumulatng power between satelltes, the total power of LOS components contnues to ncrease and f t surpasses all the dspersed NLOS power, a relatvely good velocty estmate wll occur. Another acceptable scenaro s smlar to pont B n the Fgure 4, where the power s hghest wth a combnaton of LOS and NLOS components. If more than two LOS powers ntersect at pont B along wth other NLOS power, the fnal estmate then takes advantages of both LOS and NLOS sgnal components.

10 Sensors 3, 3 43 he above secton dscusses the power projecton n two dmensonal spaces. In the followng, the same prncples are extended to the real scenaro where four velocty states need to be estmated. Assumng there are N sat avalable satelltes, the four-dmensonal hyper-planes of LOS powers for all satelltes are gven by: e v f e en v f sat u, enu D, vu, enu fd, u, enu D, Nsat or Ev u, enu f Each hyper-plane s assocated wth the LOS sgnal power of D a K a K a N K sat,,..., K K K Analogously, the NLOS sgnal power s dstrbuted over the hyper-planes and has a certan amount of power accordng to g, ( f ) n Equaton (6) wth dfferent frequency offsets: NLOS N N () sat sat. e v f e en v f sat u, enu DMP, vu, enu fdmp, u, enu DMP, Nsat or Ev u, enu f DMP () For example, the peak powers assocated wth each hyper-plane of NLOS sgnal are a a a Nsat g ( fdmp,), g ( fdmp,),..., gm ( fdmp, N ). All hyper-planes descrbed n sat K K K Nsat Equatons () and () fnally form the velocty doman. he pont n velocty doman assocated wth the maxmum power wll be consdered as the velocty MLE. he velocty MLE can be obtaned by usng the Equatons (8), (9), (), and (). he offset assocated wth maxmum power n the velocty doman s consdered as fnal estmate of velocty. Once the velocty MLE s obtaned, the Doppler measurements for each satellte can then be computed accordng to Equaton (9). In ths drect vector processng method, the Doppler measurements are based on maxmum use of LOS/NLOS sgnal power and maxmum use of mutual nformaton between each satellte. In ths way, a certan amount of nformaton shared among satelltes (see Fgure 4) s fully utlzed before arrvng at a result. In contrast, conventonal block processng methods only use Doppler MLE, whose resdual can be qute large n ndoor envronments, potentally causng the soluton not to converge. In the followng sectons, the Doppler estmated from block processng and drect vector processng methods wll be evaluated and compared by ntegratng wth PDR algorthms wth real expermental data. 3. HSGPS/PDR ght Integraton In ths secton, the system model for the HSGNSS/PDR tght ntegraton s frst ntroduced. he measurement or observaton models are then presented. Followng ths, the ntegraton performance of usng conventonal and the proposed Doppler measurements wth a PDR algorthm wll be assessed n the next secton.

11 Sensors 3, System Model he system state vector for the PDR flter s shown n Equaton () and ncludes (n order) the user s 3D coordnates n the local level frame, the horzontal and vertcal speeds, the walkng headng drecton and the GNSS recever s clock drft n unts of range rate (.e., multpled by the speed of lght, c): x E, N, U, vh,, vv, cdt () he GNSS recever clock bas s not present, snce n ths paper only the Doppler measurements are used to update the ntegraton flter. In turn, ths s because the paper focuses on assessng the beneft of the proposed Doppler measurements for PDR. he system dynamc model of the pedestran s poston follows the equatons of a classcal PDR mechanzaton and s gven by: E v h N v U v h v sn( ) cos( ) (3) he veloctes and the headng are further modeled as random walk processes: v v h v vh vv (4) Smlarly, the clock drft state s modeled as: v h v u cdt cdt (5) In Equatons (4) and (5),,, and cdt are the whte Gaussan drvng nose of the correspondng state elements. he spectral densty of the clock drft error nose s computed usng a standard clock stablty model, as found n []. It s noted that dscrepances between PDR-derved velocty and GNSS-derved velocty are expected. In partcular, due to the repettve nature of the human gat, Doppler measurements typcally exhbt oscllatons over the course of a full gat cycle. In contrast, by ts very nature, PDR veloctes are effectvely averaged over the course of a step and do not contan these oscllatons, thus ntroducng an oscllatory dscrepancy between the PDR- and GNSS-derved values. Correspondngly, these oscllatons should be modeled to properly ntegrate the velocty nformaton based on Doppler measurements. For copng wth these oscllatons over a step, the classcal PDR has been modfed n ths work. Normally, the flter state s only propagated when a step s detected. In the proposed approach, however, Doppler measurements are used at each GNSS measurement epoch, typcally at a hgher rate than the step frequency. As such, the PDR flter s propagated at ths hgher rate as well. However, PDR observatons are stll only used when a step s detected. It s expected that ths approach wll average the oscllatng effects sensed by Doppler measurements over one step. he advantage of ths asynchronous measurement update s that the ntegrated system could track the rapd changes of the headng sensed by the IMU or other headng sensors.

12 Sensors 3, On the other hand, there are also some dsadvantages wth ths new ntegraton method. Frst, the computatonal load s ncreased because the flter s propagated more frequently. In ths paper, a coherent ntegraton tme of 5 ms s used, such that the measurement update tme for Doppler s Hz, so computatonal load s not a major concern. Second, as the coherent ntegraton tme ncreases, the Doppler measurement actually conveys nformaton about the average velocty (and thus atttude) durng the ntegraton nterval. However, ths type of averaged Doppler measurement s stll usable snce t can help to allevate the long term headng drft of the PDR system. 3.. Measurement Model Havng ntroduced the system model of the ntegraton flter, the followng dscusses the measurement models. here are two types of measurement updates for the proposed tght ntegraton; from the PDR and from the GNSS Doppler. he PDR sensor update s composed of step length updated and headng update. he measured step length and walkng drectons are related to the user s poston and velocty through the followng equatons: where s s the user s step length, s v t obs h step SL (6) tstep s the step duraton and step s the averaged headng over the last step. he measured GNSS Doppler s related to the pedestran s velocty va Equatons (7) and (9). In order to be consstent wth other observaton models, t s lsted agan here: fd, ( v) ( u, x( vu,x - vsat,, x) u, y ( vu,y - vsat,, y ) u, z ( vu,z - vsat,, z )) cdt f where η f s the nose nduced by the recever. After lnearzaton of Equaton (7), then the observaton equaton s: fˆ D, fd, f, D ˆ ve f fd, D, fd, fd, M 3 v H n M cdt v u fˆ f DN, DN, sat Rx fd, N sat sat In Equaton (8), Flter H, Nsat 3 33 Nsat fˆ fˆ fˆ D, D, D, M Flter vh vv cdt η f are the flter predctons and f, f, f, D D D M Rx (7) (8) are the measurements from the recever. he subscrpt N sat before N sat was used denotes the number of satelltes. H, 3 cos( )sn( ), cos( )cos( ), sn( ) s the desgn matrx from veloctes to

13 Sensors 3, pseudorange rates, ε and α are the elevaton angles and azmuth angles for each satellte. λ s the wavelength of the transmtted GNSS sgnal, and matrx 3 3 s defned as: 33 sn( ) vh cos( ) cos( ) vh sn( ) It s noted that PDR only provdes nformaton n the horzontal plane renderng the vertcal velocty unobservable except wth Doppler observatons. o further constran the vertcal component of the pedestran s poston, barometer records could be used, although ths was not done here. Smlarly, ndoors, pedestrans are manly walkng on flat surfaces and only change ther elevaton when clmbng/descendng stars or when takng an elevator. 4. Data Processng and Analyss hs secton deals wth real expermental data processng and analyss n order to assess the benefts of ntegratng conventonal and proposed HSGNSS Doppler measurements wth PDR sensors. Frst, the data collecton s descrbed brefly. hen the analyss and results are descrbed. For smplcty, only GPS satelltes are used, but t s expected that results would lkely mprove f a multple GNSS constellaton were used. 4.. Data Collecton Descrpton he expermental data was collected on the campus of the Unversty of Calgary. he prmary peces of equpment were an NI front-end, a Novatel SPAN recever and a LCI IMU [], all of whch are shown n Fgure 5, mounted on a backpack. Fgure 5. Prmary equpments used n data collecton. SPAN M LCI IMU, CP, and SPAN M recevers are shown on the left; NI front-end s shown on the rght. (9)

14 Sensors 3, he raw IF data was collected wth the NI front-end at a rate of 5 Msps (complex). he reference trajectory s shown n Fgure 6. hs trajectory s generated usng Novatel Inertal Explorer M wth a Novatel SPAN M system. he SPAN M system used here ncludes a tactcal grade IMU (LCI) and a hgh precson GNSS recever,.e., SPAN M recever. he Inertal Explorer M uses dfferental GNSS measurements to tghtly ntegrate wth IMU. However, the hgh precson SPAN M recever cannot provde GNSS measurements ndoors due to the fact that the sgnal C/N s too weak for standard trackng loops. In such cases, the soluton s computed only usng IMU measurements. In order to get better results, both forward/backward smoothng and coordnate updates are used. By usng ths approach, the estmated poston standard devaton was better than 3 m at all tmes, and the estmated velocty standard devaton was better than. m/s. he trajectory contans several dfferent ndoor envronments, and two spots are chosen to emphasze how Doppler from drect vector HSGPS outperforms that from conventonal HSGPS (scenaro A and scenaro B). he pedestran carres a backpack contanng an antenna, the NovAtel SPAN system and LCI IMU. he cable from the backpack s connected to the NI front-end. One of the benefts of the proposed drect vector processng s ts autonomous weghtng by power (equvalent to C/N ). Ideally, f t s possble to get accurate enough C/N estmates n the conventonal HSGPS, the results can be very close to the proposed approach. However, there are some dffcultes for C/N estmaton n weak sgnal and multpath condtons. As shown n Fgure 6, C/N values are fluctuatng durng the ndoor perods. hs s caused by the user-satellte dynamc and multpath (or fadng) phenomenon. he other fact s that, as the sgnal s weak along wth multpath, the C/N estmator wll tself exhbt a larger varance or even be based. By usng these erroneous C/N weghts, the conventonal HSGPS may perform even worse. he sky plot of all avalable GPS satelltes s shown n Fgure 7. o begn the test, the pedestran walks n a crcular path outsde the buldng n order to algn the nertal system. hen, the user walks through the nsde of the buldng wth perodc returns outsde n order to mantan an accurate reference soluton (detals below). Fnally, crcular moton s repeated agan at the end of the test n open sky scenaro n order to facltate backward processng of the data. he raw IF data was processed usng the GNSRx-ss software recever [3] n order to get the raw correlator values over a pre-defned Doppler search range from whch Doppler MLE can be easly obtaned. In the GSNRx-ss recever, assstance nformaton such as raw data bts, nomnal trajectory and broadcast ephemerdes are also provded as nput. At each measurement epoch, the reference trajectory s used to compute nomnal pseudorange and Doppler values for each satellte n vew, whch are then passed to the sgnal processng channels. Each channel then computes a grd of correlators around the nomnal code phase and Doppler values. Fnally, the maxmum correlator outputs are used to generate pseudorange and Doppler measurements. In practce, a reference soluton would not be avalable to control the center of the search range. he major mpact of ths s that the search range n the Doppler doman would lkely have to ncrease n order to accommodate the resultng velocty errors and resultng n an ncreased computaton load. As long as the searchng space ncreases, the same estmaton performance has been demonstrated.

15 Sensors 3, Fgure 6. Data collecton actual trajectory, ndoor scenaros, and correspondng C/N plots (one epoch s.5 s) scenaro A pcture taken facng east, scenaro B pcture taken facng south. Fgure 7. Sky plots of all avalable GPS satelltes GPS 5 6 GPS 6 GPS 6 7 9GPS GPS 5 9 GPS 3 GPS GPS 9 5 GSNRx-ss wth a coherent ntegraton of 5 ms s used. Wth ths coherent ntegraton tme, t s expected that a desrable pre-detecton SNR can be obtaned. After projectng the correlator outputs onto the velocty doman, the velocty powers are computed usng Equatons (8) and (9).

16 Velocty Offset [m/s] Velocty Offset [m/s] Velocty Offset [m/s] Sensors 3, In Fgure 6, the C/N profles of abovementoned two ndoor scenaros are also shown. In scenaro A, one can see that the power of three satelltes s relatvely stronger than the others, beng n the range of to 37 db-hz. he other fve satelltes have very weak sgnals n the range of to 5 db-hz. Gven the sky plot shown n Fgure 7 and the pcture of scenaro A n Fgure 6, one can assume that the satellte n the south part of the sky can penetrate the south-facng wndows, resultng n larger C/N values, such as PRN 5, 8 and 9. In scenaro B, one can see that C/N values of sx satelltes ncrease to between 5 and 35 db-hz durng epoch 4 to. Referrng to the sky plot n Fgure 7 and the pcture n Fgure 6 one can see that the sgnals transmtted by the satelltes from the south and east portons of the sky penetrate the wndows more easly, such as PRN 9 PRN Velocty MLE Once correlator outputs from the recevers are avalable, the MLE veloctes are computed frst. he resultng velocty doman power dstrbutons n the two ndoor envronments are depcted n Fgures 8 and 9. Vertcal axes are the velocty offsets wth respect to the reference soluton computed by usng the NovAtel SPAN M system. Horzontal axes are the tme axes. he whte crcles represent the maxmum powers at a gven epoch. And the color of any one pxel n the mage represents nstantaneous receved sgnal power across all satelltes n that canddate velocty soluton. Due to the fact that the centre of the bns s algned wth the user s true velocty, f the LOS sgnals are domnant, the largest power should be located at the centre. Fgure 8. Power dstrbutons n east, north and up velocty domans (top left, top rght and bottom) Scenaro A. -. x x me [s] me [s] x me [s]

17 Velocty Offset [m/s] Velocty Offset [m/s] Velocty Offset [m/s] Sensors 3, Fgure 9. Power dstrbutons n east, north and up velocty domans (top left, top rght and bottom) Scenaro B. -. x x me [s] me [s] x me [s] In scenaro A, t can be observed that around epoch 5 s, the total receved power s the greatest and the domnant power s located very near the reference soluton; the LOS sgnal appears to domnate the sgnal. However n the succeedng epochs, NLOS sgnals seem to domnate the receved sgnal. he error statstcs of the proposed drect vector and conventonal HSGPS velocty solutons for ths scenaro are summarzed n able. One can see that the proposed algorthm outperforms the conventonal one by 75%, 75%, and 89% n the east, north and up velocty axs, respectvely. able. Velocty RMS errors ndoor scenaro A. Velocty RMS Errors Drect Conventonal Improvement East (m/s) % North (m/s) % Up (m/s) % Snce the multpath statstcs are envronment-dependent, t s useful to show that the proposed algorthm works n varous ndoor envronments. In Fgure 9, the dstrbuton of the total receved sgnal power over velocty domans s plotted. It can be observed that the power s concentrated and consstent from tme to 4 s. Along wth C/N plots, t s lkely that the subject s approachng the wndows durng ths perod. he RMS velocty errors of the proposed drect vector and conventonal HSGPS are summarzed n able. One can see the proposed algorthm outperforms the conventonal one by 4%, 7%, and 83% n the east, north and up velocty axs, respectvely.

18 Sensors 3, 3 43 able. Velocty RMS errors ndoor scenaro B. Velocty RMS Errors Drect Conventonal Improvement East (m/s).9.5 4% North (m/s).3.6 7% Up (m/s) % Comparng results of the above two scenaros, two major phenomena are observed. Frst, the accumulated power fluctuates more from epoch to epoch whle ndoors. Second, the locaton of the peak power n the velocty doman largely depends on the multpath statstcs or envronments HSGPS/PDR Integraton Performance In drect vector processng, the velocty MLE s frst obtaned, and then the correspondng Doppler measurements are computed. It s then convenent to assess the performance of the HSGPS/PDR tght ntegraton usng varous types of observaton. In the followng paragraphs, the performance of the PDR only navgaton soluton and HSGPS/PDR tght ntegraton wth conventonal and proposed Doppler measurements s assessed. Here tght ntegraton uses only Doppler measurements to update the user velocty and headng. No pseudorange measurements are used. In ths way, the accumulatng errors caused by naccurate Doppler measurements wll become more apparent. he other reason to choose HSGPS/PDR ntegraton wth conventonal and proposed Doppler measurements s to make the results comparable. If the velocty MLE s drectly ntegrated wth PDR, t s then a loose ntegraton scheme. hs mght obscure the benefts of the measurements and ntegraton schemes. By usng the same ntegraton scheme, the benefts of better Doppler measurements wll become evdent. For the DR algorthms, the step event s frst detected by usng pattern recognton technques wth a MEMS accelerometer [4] and the step length s calculated by usng an averaged reference velocty. In ths way, the step length estmaton error wll be very small. he methods of step length estmaton have reached a good and consstent level of accuracy, especally wth foot and belt mounted sensors, thus t s not a concern n ths paper. Only the long term headng accuracy s the focus of the paper. Regardng the PDR headng nformaton, only one tactcal grade vertcal gyroscope rgdly attached to the backpack s used to provde headng angles wth accumulated errors. And such headng angles are fed drectly to the PDR flter. he trajectores of PDR only and HSGPS/PDR tght ntegraton wth conventonal and proposed Doppler measurements are shown n Fgure. It can be seen that the PDR only soluton s much smoother, whch shows better short-term accuracy. However, as tme evolves, the PDR only soluton s rotated due to the large headng drft and s based by hundreds of metres. When ntegratng PDR wth conventonal HSGPS, the shape of the trajectory s severely dstorted. On the other hand, ntegratng PDR wth the proposed approach gves a soluton whch allevates the headng drft and better preserves the shape of the trajectory as compared to the other two cases.

19 Up[m] North[m] East[m] Sensors 3, 3 43 Fgure. rajectores of varous navgaton solutons. Reference PDR Only HSGPS(conv)+PDR HSGPS(dr)+PDR Among all three navgaton solutons, t can be seen that the navgaton soluton wth the proposed Doppler measurements ntegrated wth PDR s the nearest to the reference trajectory, whch valdates the effectveness of the proposed method. In order to further show the error characterstcs, the poston and velocty errors are plotted as a functon of tme n Fgures and. Fgure. Poston errors of varous navgaton solutons me [s] PDR only PDR+HSGPS(conv) PDR+HSGPS(dr)

20 Percentle Percentle Vu Error Vn Error Ve Error Sensors 3, 3 43 Fgure. Velocty errors of varous navgaton solutons me [s] PDR only PDR+HSGNSS(conv) PDR+HSGNSS(dr) o further analyze the results, the cumulatve hstograms of the horzontal and vertcal poston errors are gven n Fgure 3. wo key thngs are worth notng. Frst, the errors are clearly non-gaussan, whch s not surprsng gven the operatng envronment and the hgh probablty of hghly-varyng NLOS errors. Second, t can be observed that the proposed method has consderably better horzontal postonng performance compared to the conventonal HSGPS/PDR soluton. For the vertcal poston error, both solutons are smlar untl about 7 m, at whch pont the proposed method begns to outperform the conventonal HSGPS/PDR soluton. Fgure 3. Cumulatve hstograms of horzontal and vertcal poston errors. Horzontal Error Vertcal Error Conventonal Drect 5 5 Poston error [m] Conventonal Drect Poston error [m] he correspondng RMS error statstcs are summarzed n able 3. As shown, the east poston errors of conventonal HSGPS/PDR soluton are nearly twce that of the PDR-only soluton. Regardng the north poston RMS errors, t can be seen that the mprovement of the proposed soluton over conventonal approach s not as apparent as east drecton. hs s very lkely due to the fact that the

21 Sensors 3, user dsplacements along the east-west axs are much larger than the dsplacements along north-south drecton for the whole trajectory. hus the poston errors n north drecton are not as easly observed as east drecton. Smlarly, for the east velocty errors, t s observed that the conventonal HSGPS/PDR ntegrated soluton also degrades performance. hs s because the Doppler MLEs n the ndoors are not as relable and may even bas the results. However, the drect vector HSGPS/PDR ntegrated navgaton soluton shows that both the poston and the velocty RMS errors have notceable mprovements as compared to PDR-only soluton. For example, the east, north and RMS poston errors of the proposed algorthm have mprovements of 4% and 6% as compared to PDR-only soluton. Smlarly, the north velocty accuracy has an mprovement of 3% as compared to PDR-only soluton. One can also observe that there s.3 m/s degradaton n the east velocty when ntegratng drect vector HSGPS wth PDR. However, the drect vector HSGPS/PDR velocty stll outperforms conventonal HSGPS/PDR velocty by 6%, and 9% n the east and north axes, respectvely. able 3. Poston and velocty RMS errors. Poston RMS Errors (m) Velocty RMS Errors (m/s) East North Up East North Up PDR-only PDR+HSGPS (conv.) PDR+HSGPS (dr.) hese results suggest that drect vector HSGPS Doppler actually reduces such errors on average, whch, as dscussed below, mproves headng determnaton. For ths data set, the beneft from drect vector HSGPS Doppler s more sgnfcant n the north drecton. o further llustrate the mprovement, the mean velocty errors are shown n able 4. It can be seen that the proposed method generally outperforms the PDR only soluton n both the east and north axs, and the basness of east velocty has a slght mprovement wth respect to conventonal approach. able 4. Mean velocty errors. Velocty Mean errors (m/s) East North Up PDR-only..6. PDR+HSGPS (conventonal)... PDR+HSGPS (drect)... In Fgure 4, the estmated headngs are plotted. It can be seen that the error of the proposed method s generally smaller than wth conventonal HSGPS/PDR and does not exhbt the long-term drft seen n the PDR-only headng.

22 Headng Error [deg] Sensors 3, Fgure 4. Interpolated headng errors. PDR only PDR+HSGPS(conv) PDR+HSGPS(dr) Conclusons In ths paper, the combned ndoor sgnal and multpath model s frst ntroduced. How multpath affects conventonal HSGNSS Doppler measurements s then dscussed. After that drect vector recever archtecture s proposed and compared to conventonal hgh senstvty GNSS recevers. he conventonal method performs well n most good scenaros, and the proposed method s the maxmum lkelhood extenson to the conventonal method, whch wll asymptotcally approach the performance bound. How velocty and Doppler measurements are obtaned wth drect vector processng performng n ndoor multpath envronments s also nvestgated. In order to evaluate the benefts of Doppler estmated wth the proposed drect vector processng method over conventonal block processng method, Doppler estmated wth both approaches are tghtly ntegrated n a detaled navgaton flter, whch follows a PDR strategy. Comparsons are made between PDR only soluton and ntegrated solutons. From the expermental results, the followng conclusons can be drawn: In ndoor envronments, the drect vector processng makes the best use of LOS and NLOS sgnal power for each satellte. Addtonally, the mutual nformaton between satelltes s further used before arrvng at a soluton. Velocty estmaton by usng drect vector HSPGS outperforms the conventonal HSGPS for two ndoor scenaros consdered heren. he HSGPS Doppler measurements obtaned by usng drect vector processng are thus more relable and helpful than conventonal HSGPS Doppler measurements for headng estmaton. In weak sgnal and multpath condtons, the beneft of usng conventonal HSGPS Doppler measurements s very lmted due to the fact that proper weghtng cannot be correctly set. However, the proposed drect vector processng method autonomously weghs the navgaton soluton accordng to power (equvalent to C/N ), whch s actually the maxmum lkelhood estmate of the navgaton soluton, and performs no worse or better than the conventonal approach.

23 Sensors 3, By ntegratng the Doppler measurements from the proposed drect vector processng wth PDR, the solutons show mprovements n east and north velocty estmaton of 6% and 9% for the ndoor scenaros consdered heren as compared to the conventonal approach. Currently only the GPS system n L band s used. In an on-gong project, the GLONASS sgnals n L and L bands wll also be ncluded. It can be expected that wth ncreased number of satelltes, the proposed Doppler wll have a tendency to be closer to the true value under certan crcumstances. Varous ndoor envronments wll be assessed n order to show the strength and weakness of the methods proposed n ths paper. Regardng the ntegraton, other headng sensors, such as magnetometers, and low-cost MEMS gyroscopes wll also be ncluded, and the benefts of usng HSGNSS Doppler measurements n varous ndoor envronments wll be further assessed and analyzed. Acknowledgments Fnancal support from Research In Moton (RIM), the Natural Scence and Engneerng Research Councl of Canada, Alberta Advanced Educaton and echnology and the Western Economc Dversfcaton Canada s acknowledged. References. Foxln, E. Inertal head-tracker sensor fuson by a complementary separate-bas Kalman flter. IEEE Comput. Graph. Appl. 5, 5, Babu, R.; Wang, J. Ultra-ght Integraton of Pseudoltes wth INS. In Proceedngs of the 6 IEEE/ION Poston, Locaton, and Navgaton Symposum, San Dego, CA, USA, 5 7 Aprl 6; pp Pany,.; Wnkel, J.; Redl, B.; Restle, M.; Wörz,.; Schwekert, R.; Nedermeer, H.; Ameres, G.; Essfeller, B.; Lagrasta, S.; et al. Performance of a Partally Coherent Ultra-ghtly Coupled GNSS/INS Pedestran Navgaton System Enablng Coherent Integraton mes of Several Seconds to rack GNSS Sgnals Down to.5 db-hz. In Proceedngs of the nd Internatonal echncal Meetng of he Satellte Dvson of the Insttute of Navgaton (ION GNSS 9), Savannah, GA, USA, 5 September L,.; Petovello, M.; Lachapelle, G.; Basnayake, C. Real-me Ultra-ght Integraton of GPS L/LC and Vehcle Sensors. In Proceedngs of the Internatonal echncal Meetng of the Insttute of Navgaton, San Dego, CA, USA, 4 6 January. 5. Ladetto, Q.; Gabaglo, V.; Mermnod, B. wo Dfferent Approaches for Augmented GPS Pedestran Navgaton. In Proceedngs of the Internatonal Symposum on Locaton Based Servces for Cellular Users (LOCELLUS ), Munch, Germany, 5 7 February. 6. Randell, C.; Djalls, C.; Muller, H. Personal Poston Measurement Usng Dead Reckonng. In Proceedngs of the Seventh Internatonal Symposum on Wearable Computers, Whte Plans, NY, USA, 8 October 3; pp Afzal, H.; Renaudn, V.; Lachapelle, G. Mult-magnetometer based perturbaton mtgaton for ndoor orentaton estmaton. Navgaton, 58, Renaudn, V.; Sus, M.; Lachapelle, G. Step length estmaton usng handheld nertal sensors. Sensors,,