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A novel peer to peer aided acquisition strategy tailored to Galileo E1 receivers

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Aim of this paper is to investigate the benefits of different P2P aiding information related to the satellites in view on an acquisition strategy tailored to Galileo E1 receivers. The basic idea is to perform an aided acquisition, suitable to a
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  See discussions, stats, and author profiles for this publication at: https://www.researchgate.net/publication/224183959 A novel peer to peer aided acquisition strategy tailored to Galileo E1 receivers CONFERENCE PAPER  · OCTOBER 2010 Source: IEEE Xplore CITATIONS 2 READS 12 3 AUTHORS: Letizia Lo PrestiPolitecnico di Torino 177   PUBLICATIONS   828   CITATIONS   SEE PROFILE Davide MargariaIstituto Superiore Mario Boella (ISMB) 45   PUBLICATIONS   168   CITATIONS   SEE PROFILE Jaron SamsonEuropean Space Agency 38   PUBLICATIONS   103   CITATIONS   SEE PROFILE Available from: Jaron SamsonRetrieved on: 04 February 2016  52 nd  International Symposium ELMAR-2010, 15-17 September 2010, Zadar, Croatia A Novel Peer to Peer Aided Acquisition StrategyTailored to Galileo E1 Receivers Letizia Lo Presti ∗ , Davide Margaria ∗ , Jaron Samson §∗ Electronics Department, Politecnico di Torino, 10129 Torino, Italy § ESA (ESTEC / TEC-ETN), Noordwijk, The NetherlandsEmails:  letizia.lopresti@polito.it, davide.margaria@polito.it, jaron.samson@esa.int   Abstract —Aim of this paper is to investigate the benefits of different P2P aiding information related to the satellites in viewon an acquisition strategy tailored to Galileo E1 receivers. Thebasic idea is to perform an aided acquisition, suitable to a mass-market receiver, based on a secondary code wipe-off on thereceived signal and exploiting the periodicity of the primarycode in order to reduce the computational complexity. Thisstrategy is presented in the paper from the theoretical pointof view, discussing the benefits of different aiding informationand providing also some preliminary simulation results. In detailthe analysis has been focused on the performance degradation inpresence of an imperfect wipe-off due to time assistance errors.  Index Terms —Peer-to-peer, acquisition, Galileo, E1. I. I NTRODUCTION The paradigm of peer-to-peer (P2P) cooperative localizationrelies on the possibility to exploit the existence of directcommunication links among nodes of a network, generallyequipped with  Global Navigation Satellite System  (GNSS)receivers, to transmit collaboration data thus enabling deter-mination of nodes location anytime and anywhere. It is wellknown that GNSS systems provide highly reliable positioningwhen at least four satellites are visible at the node receiverantenna [1]. This is generally guaranteed in open sky out-door environments. On the contrary, in urban canyons, underdense foliage and indoors the line-of-sight (LOS) betweensatellites and receiver’s antenna is often obstructed and GNSS-based localization heavily degrades or completely fails. Underthese circumstances other localization techniques based on theconcept of collaboration can be considered. These alternativemethods can be classified in two categories:1) Methods based on GNSS-data only,2) Methods based on both GNSS data and other positioningmeasurements taken by other sensors (e.g. terrestrialranging, inertial sensors, odometers, etc...).The purpose of the work described in this paper is toinvestigate the possibility of using the exchange of GNSS dataonly to improve the peer capability to locate itself. In particularthe case of a peer located in a light indoor environment andaided by other peers located in  Open Sky  (OS) is considered. This work is partially supported by the European Space Agency in theframework of the P2P Positioning Project and some concepts presented hereare patent pending. Any opinions, findings and conclusions or recommen-dations expressed in this material are those of the author(s) and do notnecessarily reflect the views of our sponsor. We intend for  Light Indoor   (LI) the reception of the  Signal In Space  (SIS) with a moderately low Carrier-to-noise ratio( C/N  0  <  40  dB-Hz), as for example under a canopy or insideof a building, near to a window [2]. A possible scenario of thiskind is a cluster of vehicles or pedestrians (the so-called peers),some of them in open sky, and others in an LI environment.The concept of P2P positioning based only on GNSS datais that a GNSS receiver (hereafter called  target receiver  , or target peer  ), in an LI status, can fix its position by usingboth some internal measurements of GNSS type and GNSSdata provided by the other peers, called  aiding peers . Theyare typically OS peers, but we included in this group alsopeers in LI status which have been able, in some way, tofix their positions. In fact both of them are able to provideassistance to the target peer. In detail in this paper we wantto analyze the feasibility of P2P methods for mass-marketapplications, based on receivers which are normally focusedon obtaining sufficiently accurate localization with minimumcost, striking at the same time for low power consumption,low cost, and low hardware complexity. Thus, the introductionof P2P networking in mass market receivers shall lead tomore efficient and robust positioning without any significantcomplexity increase in the terminal. In this paper the case of a Galileo single frequency receiver working in the E1 bandand exploiting only the E1 pilot channel for the acquisition isconsidered [3].Several methods can be envisaged to enable the conceptof P2P positioning based on exchange of GNSS data only.The work described in this paper is a part of a bigger activityaimed to investigate if this kind of assistance, only based onGNSS data, can be realized. A first class of P2P methodsto be considered includes all the techniques working at thephysical layer (acquisition and tracking); in this class themethods can be derived starting from the Assisted GNSS (A-GNSS) methodology [4], but taking into account the specificcharacteristics of the P2P aiding data. Other techniques work at the range layer and are based on the idea of using someposition data of the aiding peers in the neighborhood of thetarget peer to evaluate the Position, Velocity and Time (PVT)of the LI peer. Finally the OS peers can behave as pseudo-satellites, which can be used by the target peer to fix itsposition. Only methods working at the physical layer andbased on aided acquisition are considered in this paper. In 417  52 nd  International Symposium ELMAR-2010, 15-17 September 2010, Zadar, Croatia detail, for each Space Vehicle (SV) in view, the aiding peersare assumed to estimate and share to the target peer thefollowing data: the Carrier to Noise density ratio ( C/N  0 ), theDoppler frequency shift and the secondary code delay for theGalileo E1 pilot channel.After this introduction, the paper is then organized as fol-lows: next Section discusses the time synchronization problemof a network of peers, providing an overview of possible syn-chronization protocols and achievable performance in terms of timing errors, impairing also the accuracy of assistance infor-mation. After that, the proposed aided acquisition approach ispresented from the theoretical point of view, discussing alsothe advantages of each available assistance data. After that,a simple empirical metric is defined and then used in orderto obtain preliminary simulation results on the acquisitionperformance in presence of time assistance errors. At the end,some conclusions are drawn on the obtained results.II. S YNCHRONIZED NETWORK OF PEERS Time synchronization between the peers is the basic require-ments in order to allow them to cooperate, sharing assistanceinformation on the received signals. In fact the availabilityof an accurate time reference is an important element of assistance. In the case of A-GPS, [4] mentions two cases: •  fine time assistance : when a priori time is known with anaccuracy better than the Pseudo-Random Noise (PRN)code length period (accuracy usually better than 1 msand worse than 10 µ s); •  coarse time assistance : when a priori time is known withworse accuracy.In general, the synchronization problem is an importantissue in several applications based on distributed systems,including multiple computing nodes that need to exchangeinformation. Time synchronization in a computer network aims to provide a common timescale for local clocks of nodesin the network. Since all hardware clocks are imperfect, localclocks of nodes may drift away from each other in time, soobserved time or durations of time intervals may differ foreach node in the network. However, for many applications ornetworking protocols, it is required that a common view of time exist and be available to all or some of the nodes in thenetwork at any particular instant [5].As an example, in a Wireless Sensor Network (WSN),the sensor nodes (usually tiny low power devices) need tobe synchronized in order to coordinate their sensing andcommunication tasks. In general, clock synchronization isviewed as a critical factor in maintaining the good functioningof WSNs due mainly to their decentralized organization andtiming uncertainties caused by the imperfections in hardwareoscillators and message delays at the physical and mediumAccess Control (MAC) layer. In addition, synchronization of WSN nodes is crucial for implementing fundamental opera-tions such as transmission scheduling, power management (inorder to increase the network efficiency and lifetime), datafusion (data collected at different nodes are aggregated into ameaningful result), localization, target tracking, and securityprotocols to name only few applications [6].It must also be noticed that the localization in WSN isa topic that has been already investigated, assuming alsohybrid GNSS + WSN systems. Typically, GNSS is consideredneeded to localize specific, so-called ”anchor”, nodes fromwhich range measurements are performed and position of blind (eventually mobile) nodes estimated [7]. However, fewstudies have been carried out where WSN is used to aid GNSSreceivers, sharing assistance information.Many synchronization protocols tailored to WSN applica-tions based on inexpensive hardware (low cost oscillators)have been recently proposed in literature (e.g. see [5], [6]).These protocols, due to their simplicity and flexibility, canbe considered as good candidates and can be easily adaptedfor synchronizing low-cost mass-market devices in a P2Ppositioning scenario.For these reasons the WSN synchronization protocols willbe considered in the following as the reference technologyin order to investigate the possible synchronization errors andtheir impact on the assistance.  A. WSN synchronization protocols The synchronization protocols for WSNs can be categorizedin different classes, depending on various criteria and require-ment used in their design. A possible simple categorization,based on the  synchronization approach , can be useful inorder to understand the message exchange and the operationsperformed in each protocol [6]: •  sender-receiver  : one of two nodes, which are synchro-nizing with each other, sends a timestamp message whilethe other one receives it; •  receiver-receiver  : a reference node transmits synchroniza-tion signals and two synchronizing nodes receive thesesignals and record the reception time; •  receiver-only : a group of nodes can be simultaneouslysynchronized by listening the message exchanges of apair of nodes.A prominent example of the first class is the Timing-Synchronization Protocol for Sensor Networks (TPSN) [8]. Itincludes a level discovery phase, after which each node is as-signed a level corresponding to the hop-number distance fromthe root (master) node, thus building a hierarchical structure.Afterwards, the synchronization phase starts, where couplesof nodes perform a two-way message exchange in order tocalculate their clocks relative phase and the propagation delay.On the other hand the Reference Broadcast Synchroniza-tion (RBS) method [9] is based on the concept of receiver-to-receiver synchronization. A reference node broadcasts abeacon message to its neighbors, then the receiving nodesexchange the arrival time of the beacon as a reference tocompare the phase between their clocks.Finally, two examples of the third class (receiver-onlysynchronization) are the Flooding Time Synchronization Pro-tocol (FTSP) [10] and the Accuracy-Driven SynchronizationProtocol (ADSP) [11], [12]. Both are based on a similar 418  52 nd  International Symposium ELMAR-2010, 15-17 September 2010, Zadar, Croatia TABLE IS OURCES OF DELAYS IN  WSN  MESSAGE TRANSMISSIONS  [10] Delay component Magnitude Send and Receive 0 - 100 msAccess 10 - 500 msTransmission / Reception 10 - 20 msPropagation  <  1  µ s for distances up to 300 metersInterrupt Handling  <  5  µ s in most casesEncoding plus Decoding 100 - 200  µ sByte Alignment 0 - 400  µ s idea: a reference node frequently broadcasts timestamps tosynchronize multiple recipients. The main difference is in thecomputational complexity of the two protocols: in FTSP eachnode performs a linear regression on data from the referenceand itself to estimate its clock offset and drift, whereas thesynchronization in ADSP is based on simpler formulas but itis able to achieve synchronization error similar to the one inFTSP.  B. Synchronization errors and accuracy It is important to point out that the achievable synchroniza-tion accuracy in network of peers depends on several factors,like the quality of available hardware platforms (clocks andwireless communication blocks), the number of peers to besynchronized, the size and topology of the cluster, the ap-proach used by the synchronization protocol and other designconstraints (e.g. a limited number of message exchanges inorder to reduce the energy consumption).In general the synchronization accuracy is mainly limited bythe sources of delays and latencies in message exchanges thatcan not be easily predicted or compensated by the synchro-nization procedure. Table I summarizes the main deterministicand non-deterministic components of the time delays in WSNmessage transmissions and their magnitudes. For a detailedanalysis of each source, please refer to [10].Network delay modeling has been an active research topicsince the 1980s. As noticed in [6], the most commonlyproposed distributions for non-deterministic network delaysare the Gaussian, Exponential, Gamma, and Weibull pdfs.In general, it is difficult, if not impossible to assess whichdistribution model may be fit to capture the network delaydistribution in a given WSN. This is due to the fact thatvarious factors may impact the distribution of network delaysdifferently. For the sake of simplicity, the Gaussian distributionwill be considered in the following in order to model bothtransmission delays and synchronization errors. The correct-ness of this assumption is also enforced by the experimentalresults obtained both in [8] and [9].Most of the delay sources in Table I are effectively avoidedor compensated by the synchronization protocols previouslylisted in Section II-A, exploiting precise time-stamping tech-niques (at the MAC layer or at the radio level) and usingother interesting solutions in order that only non-deterministicdifferences between the sender and the receiver times mayimpact on the final synchronization error. A comparison be- TABLE IIC OMPARISON OF TIME - SYNCHRONIZATION APPROACHES  [12] Synchronization protocol Average error Maximum error RBS 29.13  µ s 93  µ sTPSN 16.9  µ s 44  µ sFTSP 1.48  µ s 6.48  µ sADSP 1.51  µ s 6  µ s tween the performance achievable by the different protocolsin terms of synchronization accuracy is then provided in [12]and summarized in Table II, showing that a synchronizationaccuracy of a few  µ s is feasible with low-cost WSN hardwareand state-of-the-art synchronization approaches.It must be noticed that the performances in Table IIare referred to the same hardware/software platforms(MICA/MICA2 motes using TinyOS 1.x) and considering asingle-hop setup (only two nodes are synchronized). On theother hand, if a large number of peers need to be synchronized(multi-hop scenario), the synchronization errors tend to growslowly across many hops, as noticed in several papers (e.g.see [8] and [9]). In fact, assuming independent Gaussiandistributed synchronization errors for each couple of peerswith standard deviation  σ , it can be demonstrated that thestandard deviation of the resulting synchronization error incase of two peers connected by an  n -hop path is bounded to σ √  n  [9].As a final remark, assuming a P2P positioning system basedon WSN technology, the synchronization between the clocksand then the accuracy of the time assistance can be assumedto be affected by errors with magnitude less than 500  µ s (0.5ms). This bounding value will be assumed in the followingas a reasonable working hypothesis in order to investigatethe impact of time assistance errors on an aided acquisitionstrategy.III. S IGNAL MODEL AND AIDED ACQUISITION STRATEGY Considering a GNSS receiver able to receive and processonly the pilot channel transmitted by a Galileo satellite inthe E1 band [3], the received signal after the typical down-conversion from the RF carrier frequency to an IntermediateFrequency (IF) can be modeled as r IF  ( t ) =   2 P  R c  p ( t − τ   p ) c s ( t − τ   p )cos α IF   (1)where  α IF   = 2 π ( f  IF   +  f  d ) t  +  ϕ IF  ,  P  R  is the power of the received SIS,  τ   p  is the propagation delay,  f  IF   is the IFcarrier frequency,  f  d  is the Doppler shift,  ϕ IF   is the carrierphase,  c  p ( t )  is the Galileo E1 primary code, and  c s ( t )  is thesecondary code. The primary code is a periodic sequenceof 4092 chips, with a repetition period  T   p  = 4  ms. Thesecondary code is a sequence of 25 chips, and the chipduration is  T  c,s  =  T   p  = 4 ms. The signal  r IF   is generallysampled at the sampling frequency  f  s  = 1 /T  s , where  T  s  isthe sampling interval. In a real-life receiver the discrete-timesignal  r IF  [ n ] =  r IF  ( nT  s )  is buried in the thermal noise  W  [ n ] ,therefore the signal processed in the digital part of the receiver 419  52 nd  International Symposium ELMAR-2010, 15-17 September 2010, Zadar, Croatia can be written as y IF  [ n ] =  r IF  [ n ] + W  [ n ]  (2)where  W  [ n ]  is a white Gaussian random sequence with zeromean and a variance 1 σ 2 W   =  N  0 f  s / 2 .The first operation performed by the digital section of thereceiver is the  acquisition , which detects the presence or not of a specific satellite, and performs also a rough estimation of theDoppler frequency  f  d , and of the delay  τ   of the incoming codewith respect to a local code  c l ( t ) =  c  p ( t ) c s ( t ) , generating anestimated parameter vector p ( A ) = [ˆ τ  ( A ) ,  ˆ f  ( A ) d  ] . It is importantto highlight that  τ   is not the propagation delay  τ   p , but a delaywith respect to a code locally generated at the receiver end.The acquisition system can be considered the bottle neck of the receiver. In fact it requires a considerable computationaleffort, contributing to increase the  Time To First Fix  (TTFF).Therefore we believe that the main goal of the P2P positioningtechniques (working at the physical layer) should be to lightenthe acquisition operations of the assisted peers. This criterionhas driven our work on how to devise physical layer P2Ppositioning algorithms.The most time consuming operation performed by theacquisition block is the evaluation of the so called AmbiguityFunction (AF), [13], also called Cross Ambiguity Function(CAF), [14], defined as R y,r (¯ τ,  ¯ f  d ) = 1 N  N  − 1  n =0 y IF  [ n ] c l ( nT  s − ¯ τ  ) e j 2 π ( f  IF  + ¯ f  d ) nT  s (3)where  N   is the number of samples contained in the coherentintegration period  T  int  =  NT  s ,  c l ( t )  is the local code, and thetwo variables  ¯ τ   and  ¯ f  d  are test variables, which are discretizedin order to evaluate the CAF in a grid of points, called  searchspace . In this space the detector of the acquisition systemselects the vector  p ( A ) = [ˆ τ  ( A ) ,  ˆ f  ( A ) d  ] , searching the locationof the CAF peak. We address here the problem of reducingthe dimension of the search space by exploiting the assistanceprovided by the aiding peers.Considering the acquisition of the Galileo E1 pilot signal,a classical way to evaluate the CAF in (3) is to process asnapshot of the signal  y IF  [ n ]  taken in a time window of  T  int  =  MT   p  length (multiple of the primary code period),where  M   is an integer. The snapshot is first multiplied bya local signal of the type  s [ n ] = exp[  j 2 π ( f  IF   + ¯ f  d ) nT  s ] and then a circular correlation is performed with a local code c l [ n ] . This last operation is generally performed by using theDiscrete Fourier Transform (DFT) properties [15]. In theorythe local code  c l [ n ]  should be obtained by sampling the code c  p ( t ) c s ( t )  of the satellite we are looking for. The presenceof the secondary code makes this operation quite complexespecially when  M   ≫  1 . Then the idea is to try to wipe-off the secondary code using the information coming fromthe aiding peers. In fact, if an estimate of the secondary code 1 This value refers to the variance of the thermal noise with powerspectrum density  G W  ( f  ) =  N  0 / 2  filtered at IF level in the bandwidth ( − f  s / 2 , + f  s / 2) delay is available to the target peer with enough accuracy, itis possible to multiply the received signal samples by a localreplica of the secondary code samples, in order to simplifythe acquisition removing the secondary code transitions. Thisapproach leads to a remarkable reduction on the computationalburden with respect to conventional approaches based on a fullcode search, which usually require long FFT operations andzero-padding on the local code in order to avoid secondarycode transitions. Obviously the presence of time assistanceerrors, due to synchronization inaccuracies, implies a wrongsecondary code wipe-off and then a degradation on the CAFpeak, reducing the acquisition performance. These aspects willbe discussed in next Section.IV. C IRCULAR CORRELATION WITH CODE WIPE - OFF In case of ideal secondary code wipe-off (without synchro-nization errors), let us consider an IF signal of the type y ′ IF  ( t ) =   2 P  R c  p ( t − τ  )cos α IF   + W  [ n ]  (4)obtained from (1) and (2) just dropping the secondary code.Assuming the sum in (3) as an approximation of an integralin continuous time domain, it is possible to rewrite the CAFas the sum of smaller integrals, as R ′ y,r (¯ τ,  ¯ f  d ) ∼ = 1 T  intM  − 1  k =0 T  p   0 c  p ( t − ¯ τ  ) φ IF  ( t + kT   p ) dt  (5)where  T  int  =  MT   p  and φ IF  ( t ) =  y ′ IF  ( t ) e j 2 π ( f  IF  + ¯ f  d ) t (6)This means that the local code now becomes simpler since,exploiting the secondary code wipe-off and the periodicityof the primary code, only a local replica of the primarycode  c  p ( t )  has to be generated and circularly shifted in theinterval  (0 ,T   p ) . This corresponds to a circular correlation andcan be implemented exploiting the well-known approach forFFT parallel acquisition in the time domain, based on DFTproperties [15]. In this way the delay  ¯ τ   spans only the rangeof interest  (0 ,T   p ) , avoiding useless computations outside thisrange. At the same time the advantages of a long coherentintegration time ( T  int ) on the noise term still remain, thanksto the coherent summation of   M   integrals.If the secondary-code wipe-off is not perfect the method canbe still used, but the local code does not completely match theresidual code of the incoming signal, which can be written as c wo ( t ) =  c  p ( t − τ  ) c s ( t − τ  ) c s ( t − τ   + ∆ t S  )  (7)where  ∆ t S   is due to the synchronization errors. If   ∆ t S   issmall enough, the product  c s ( t − τ  ) c s ( t − τ   + ∆ t S  )  gives aquite perfect sequence of ones, except at the border of thesecondary chips, when there is a sign transition. In this casewe can say that c wo ( t ) ∼ =  c  p ( t − τ  )  (8) 420
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