May 29, 2009 - 1/12. Performance Evaluation of a GPS L5 Software. Receiver Using a Hardware ... L5 signal (likely a block IIR-M satellite with an additional ...
Performance Evaluation of a GPS L5 Software Receiver Using a Hardware Simulator Cécile Mongrédien, M. Elizabeth Cannon, Gérard Lachapelle PLAN Group Department of Geomatics Engineering Schulich School of Engineering University of Calgary CANADA
BIOGRAPHY Cécile Mongrédien is a PhD candidate in the Department of Geomatics Engineering at the University of Calgary, Canada, where she is a member of the Position, Location and Navigation (PLAN) research group. In 2004 she graduated from ENAC (French University for Civil Aviation), Toulouse, France, as an electrical engineer majoring in digital communications. Her research focuses on GPS modernization as well as GNSS receiver design. Dr. Gérard Lachapelle holds a CRC/iCORE chair in Wireless Location in the Department of Geomatics Engineering. He has been involved with GPS developments and applications since 1980 and has authored/co-authored numerous publications and software. More information is available on the following website: http://plan.geomatics.ucalgary.ca. Dr. Elizabeth Cannon is Dean of the Schulich School of Engineering at the University of Calgary. She has been involved with GPS research since 1984 and has published numerous papers on static and kinematic positioning. She is a Past President of the ION and the recipient of numerous awards for her work. ABSTRACT The GPS L5 signal, part of the U.S. effort to modernize its Global Positioning System (GPS), was designed to support safety-of-life applications such as civil aviation navigation. Its structure was therefore designed to provide higher performance in terms of measurement accuracy, tracking robustness and tracking sensitivity. However, in order to effectively improve upon the GPS L1 C/A signal performance, new receiver architectures have to be designed for the acquisition, tracking and navigation data demodulation processes. This paper aims at implementing such architectures in a full GPS L5 software receiver and validating them using a GPS L5 hardware simulator. First, a cascaded acquisition scheme is proposed. The first step, very similar to GPS L1 C/A acquisition is used to estimate the Doppler frequency and PRN code delay of the satellites in view. The second step is then used to estimate the NH code delay (and perform data bit synchronization) and refine the frequency estimate. A pilot-only tracking is then introduced. The navigation message decoding is performed in parallel on the data channel; the in-phase prompt correlator outputs used are calculated on the data channel using the tracking information derived from the pilot-only tracking loops. To recover the actual navigation data bit, the symbols previously obtained are fed into a Viterbi decoder. Following this operation, the subframe synchronization, and ephemeris parameters extraction can be initiated. A navigation solution using eight satellites is then used to validate the overall implementation of the software. Other figures of merits, such as the tracking loop lock detectors or pseudoranges measurement accuracy, are also shown to illustrate the software capacities. INTRODUCTION The US government plans to augment the only fully operational GPS civil signal (GPS C/A) by implementing two new civil signals on the GPS satellites to be launched in the coming years. Three block IIR-M satellites, transmitting the GPS L2C signal, have already been successfully launched and brought online. The first satellite transmitting the GPS L5 signal (likely a block IIR-M satellite with an additional demonstration payload) is expected to be launched in early 2008.
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The GPS L5 signal is the focus of this paper. It was designed to provide improved inherent multipath and narrow-band interference mitigation capacities, as well as improved tracking and data demodulation sensitivity. As described in the following section, GPS L5 has a data (I5) and a pilot (Q5) channel that are synchronized and orthogonal. The pilot component is implemented to enable more robust carrier tracking and facilitate re-acquisition in degraded environments. To compensate for the 3 dB loss entailed by the data/pilot implementation and provide more reliable data demodulation, Forward Error Correction (FEC) is applied to the navigation message on the I5 channel. NH codes are modulated on top of the PRN on each channel. Introduced to improve narrow-band interference mitigation capacities, they also improve cross-correlation amongst spreading codes and facilitate data bit synchronization. In order to demonstrate and quantify (beyond theoretical derivations) the accuracy gain that can be expected from this signal, a full GPS L5 software receiver is developed. Validation of a cascaded acquisition algorithm and a coherent data-pilot combined tracking was already presented in Mongrédien et al. (2006). In light of the above, this paper focuses on the implementation and validation of the navigation message decoding and positioning algorithms. Following a brief review of the GPS L5 signal structure and data collection system used, the acquisition and tracking algorithms used are described. The implementation of a Viterbi decoder and subframe synchronization algorithms is then discussed. Finally, the 8-satellites navigation solution is presented. Each individual algorithm is tested and validated using GPS L5 RF samples obtained from a Spirent GSS 7700 hardware simulator and down-converted to IF using a NovAtel Euro-L5 Card, which served as a front-end. GPS L5 SIGNAL STRUCTURE The full GPS L5 signal structure can be found in the GPS L5 Interface Control Document (IS-GPS-705 2005). However, a summary of its main characteristic is presented herein. The L5 Signal will be transmitted at 1176.45 MHz with a minimum specified power of -154.9 dBW, equally shared between its two quadrature components. The exact structure of the signal is given by:
d (t )c XI (t )NH 10 (t ) cos(2πf L 5 t + φ ) s(t ) = 2 P + c XQ (t )NH 20 (t )sin (2πf L 5 t + φ )
(1)
Where P is the total power of the received L5 signal, d is the FEC encoded navigation message, c XI and c XQ are the data and pilot PRN code respectively, NH10 and NH 20 are the data and pilot NH code respectively, f L 5 is the L5 carrier frequency and φ is the time-varying carrier phase delay. As illustrated in Equation 1, each of the two quadrature components is bi-phase modulated with a different PRN of length 10230 chips. On the data channel, the PRN codes are further modulated by the navigation message and a 10-bit NH sequence; on the pilot channel, the PRN codes are further modulated by a 20-bit NH sequence. Due to the FEC encoding, the data channel will be transmitting the encoded navigation message at a 100 Hz rate in order to maintain an effective navigation message rate of 50 Hz. In turns, the 10 ms data symbols and the 20 ms data bits are perfectly synchronized with the NH10 and NH20 sequence respectively. The pilot channel allows significant phase tracking sensitivity gain since the absence of data enables the use of a pure PLL and of longer coherent integration time. The NH codes help to further spread the power across the spectrum by narrowing the code spectral line separation from 1 kHz to 100 Hz and 50 Hz in the data and pilot channel respectively, enhancing the GPS L5 signal mitigation capacities against narrow-band interferences. Additionally, they make data bit synchronization more robust. The use of longer PRN sequences improves the cross-correlation and auto-correlation side peak protection to 26.4 and 29 dB respectively, while the use of a faster chipping rate enhances the signal inherent mitigation capacities against multipath. In addition to the FEC encoding used, the GPS L5 navigation message format (C-NAV) significantly differs from the one used on L1 C/A (NAV). In order to improve the accuracy of the satellite position obtained from the broadcast ephemeris, new parameters were introduced to compute the orbit semi-major axis, mean motion and rate of right ascension. Also, the rather rigid NAV format used on GPS C/A is replaced by a highly flexible sequence of 63 subframes. Each subframe is 300 bit long and the control segment can modify the broadcasting order of these subframes as it sees fit. HARDWARE SIMULATOR AND TEST SET-UP To fully evaluate the GPS L5 signal performance, the accuracy of the Single Point Positions (SPP) derived from this signal will be studied herein. However, in the absence of any operational GPS satellite that transmits on the L5
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frequency, it is necessary to use a simulated signal. The relevance of this approach, however, is conditioned by the fidelity with which the simulator can replicate a typical GNSS environment. To this end, the use of a hardware simulator provides the best opportunity so far. Its ability to individually simulate any component of the GNSS error source budget provides the levels of flexibility, controllability, and reproducibility necessary to validate software receiver algorithms. The Spirent GSS 7700 hardware simulator is used herein to simulate the GPS L5 RF signal. To convert this signal to IF samples (input taken by the GPS L5 software receiver), a NovAtel Euro-L5 card is used as an RF front-end to output the digital I and Q samples at 28 MHz. These IF samples are then buffered using an Altera UP-2 FPGA development board and stored using a National Instrument Data Acquisition (NI-DAQ) card in a PC. This set-up is illustrated in Figure 1. An OCXO clock is used to provide the time reference.
Figure 1: Test Set-Up Even though the use of a hardware simulator enables the simulation of all GNSS error sources, only noise was considered herein. The reason for that is the necessity to first develop and validate the full software receiver, prior to any further performance analysis. At each step, algorithm validation can be performed using the truth data provided by the hardware simulator.
ACQUISITION GPS L5 acquisition is defined as the estimation of the incoming signals’ local carrier and local code. The local codes considered herein as the NH-modulated PRN codes. Several acquisition strategies have been investigated in the past (Tran & Hegarty 2002, Hegarty et al 2003, Macabiau et al 2003, Yang et al 2004, Mongrédien et al. 2006). The cascaded approach, described in the three latter publications, is used herein. The reason for that is two-fold. First it reduces the computational requirements compared to a direct approach (where coherent integration over a minimum of 20 ms would be needed). Second, it limits the risk of false NH code acquisition that can occur when the frequency resolution is too low. The cascaded scheme implemented herein can be broken down in three steps. The first one, referred to as coarse acquisition, aims at estimating the Doppler frequency and PRN code delay. The second step, referred to as coarse tracking, is a frequency refinement step where basic tracking loops are implemented to insure convergence of the PRN code and Doppler frequency estimates. Finally, the last step, referred to as fine acquisition, is used to estimate the NH code delay. Coarse Acquisition The GPS L5 coarse acquisition is a two-dimensional search in time (code delay) and frequency over a given uncertainty region. The signal detection is based on a hypothesis testing scenario that is similar to the one used for GPS C/A. The two hypotheses H1 the signal is present and H0 the signal is absent, are tested against a particular threshold to determine whether a particular satellite is in view or not. The threshold is computed based on the desired probability of false alarm (10-4 here), and on the observed noise level under hypothesis H0. The coarse acquisition is performed in the frequency domain using a zero-padded FFT. The use of a zero-padding strategy, introduced in Yang et al. (2004), helps alleviate the unknown NH bit transitions that could potentially deteriorate the correlation peak and compromise the reliability of the acquisition. The use of the FFT, on the other hand, provides interesting computational savings. In the frequency domain, it is possible: 1) to search all the PRN code delays in a single operation and 2) to perform Doppler removal simultaneously for all the satellite by a simple circular shift on the incoming signal FFT. On a final note, it is important to mention that, in order to improve the detection performance, it is possible to combine the power available in the data and pilot channels, and/or in several consecutive correlations. Coarse Tracking and Fine Acquisition As mentioned previously, the coarse tracking step is introduced to refine the Doppler frequency estimate and limit the risk of false NH code delay acquisition. To this end, an one-ms FLL based tracking is implemented. Mongrédien et al. (2006) demonstrated that, in this case, the FLL (and DLL) pull-in range and sensitivity are compatible with those of the coarse acquisition step described previously. In order to improve noise mitigation, a simple data/pilot combining scheme is proposed. At this stage, the pilot channel does not exhibit the property of a dataless channel and both
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channels still have similar tracking performance. The average of the data and pilot discriminator output is then used to update the NCOs and drive the code and carrier tracking loop. To confirm convergence of the carrier tracking loop, the following lock detector is used: cross 2 − dot 2 (2) C2 f = cross 2 + dot 2 Where
cross = IPk −1QPk − IPk QPk −1 = Dk Dk −1 sin (2πε f ,k TP ) , dot = IPk −1 IPk + IPk −1QP = Dk Dk −1 cos(2πε f ,k TP ) ,
IP , QP are the one ms in-phase and in-quadrature correlator outputs at the subscripted epoch, ε f ,k is the frequency error at epoch k, and TP is the coherent integration time.
Assuming, no external disturbance, this can be simplified as: C2 f ≈ cos(4πε f ,k TP )
(3)
Ideally, an FLL detector locked around 0.95 would guarantee a frequency error less than 25 Hz. However, as illustrated in Figure 2, this detector remains very noisy, even after smoothing. Despite this behaviour, it has been considered that this detector, if not a good frequency error estimator, could still be used as a reliable frequency lock indicator.
Figure 2: FLL Smoothed Lock Detector for All Satellites in View Upon convergence of the lock detector on the data and pilot channel, of the one-ms pilot correlator outputs are correlated with the NH20 code. Even though possible, no attempts to recombine the data and pilot channel were made. The reason for this is three-fold. Firstly, the presence of unknown data bit transitions on the data channel combined with the use of two different NH sequences would make this combining very tedious. Secondly, the resulting power loss is expected to remain minimal as the NH20 correlation properties are superior to that of the NH10. Finally, this implementation enables direct and simultaneous acquisition of the NH20, NH10 and data bit boundary; whereas a combined scheme would not give the NH20 bit boundary, requiring an additional step if coherent integration longer than 10 ms were envisioned. As illustrated in Figure 3, the correlation peaks obtained after convergence of the coarse tracking are clear and unambiguous for all the satellites in view.
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Figure 3: Normalized Fine Correlation for All satellites in View TRACKING Once the NH codes have been acquired, a more accurate and reliable tracking can be envisioned. To this end, the use of longer coherent integration time and/or pure PLL tracking is of major interest. Their use is, however, restricted to the pilot channel, as unknown data bit transitions (that is, 180o phase shifts) still occur on the data channel. Data/Pilot Combining As mentioned earlier, it is possible to improve the overall tracking performance of the receiver by implementing a data/pilot combined tracking. This was done, for coarse tracking, by averaging the data and pilot discriminators’ output. After NH alignment, however, the pilot channel exhibits far better phase tracking performance due to the absence of unknown data bit transitions. This makes the data/pilot combining more tedious, as one must endeavours to jointly benefit from the reliability of pure pilot tracking, and the improved noise resistance of combined tracking. Mongrédien et al. (2006) introduced a correlator level combining that was shown to improve carrier tracking reliability, sensitivity and accuracy. However beneficial this strategy, it is not implemented here in order to lessen the computational requirements. Instead of six correlators per channel, the pilot-only tracking strategy implemented here only uses a single correlator (the in-phase prompt) on the data channel. This is sufficient to recover the navigation message symbol bits and decode the navigation message parameters. This approach was already recommended by Ries et al (2002) and Bastide (2004) for similar reasons. Carrier Tracking The Pilot-only carrier tracking is initialized here as an FLL, which, after convergence, transits into a PLL. The coherent integration time is set to 10 ms. The use of longer integration, even thought technically possible is avoided at this stage to widen the FLL pull-in range and limit the risk of loss of lock. Julien (2005) underlined the potential drawbacks entailed by self normalization when using the atan2 discriminator. For this reason, a coherent PLL discriminator is chosen here. Code Tracking It is not possible to implement a Narrow-Correlator on the GPS L5 code tracking loop. As discussed in Betz and Kolodzieski (2000), for a given front-end filter bandwidth, a point of diminishing return will be reached when decreasing the Early-Late spacing. Indeed, as can be seen in Figure 4, front-end filtering tends to round-off the correlation function, deteriorating the separation between the Early and Late value around the peak. To avoid this problem a one-chip Early-Late spacing is implemented herein.
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Figure 4: Impact of Front-End Filtering on the GPS L5 PRN codes correlation function To optimize the code tracking performance, several discriminators and normalization were investigated herein. Following the analysis proposed in Julien (2005), it was decided to implement a dot-product discriminator with an Early-plus-Late normalization, as given by: (2 − δ ) . (I E − I L )I P + (QE − QL )QP (4) VDLL ,DP 2 = 2 (I E + I L )I P + (QE + QL )QP Where δ is the Early-Late spacing, in chip. Even though the use of an Early-plus-Late type of discrimination necessitates the use of an additional correlator, this choice was motivated by: 1) the reduction of the squaring losses for both the discriminator and normalization, and 2) the cancellation of the quadratic term in ε τ . As shown in Figure 5, the linear tracking covers the [-0.5; +0.5] chip range. Outside this region, this discriminator offers a less favourable behaviour as it tends to always underestimate the code tracking error. This can make tracking perilous as it implies that the receiver will be unable to correct a growing error. However, the use of a wide Early-Late spacing and of a very precise carrier aiding should help reduce the impact of dynamics on code tracking, and limit the occurrence of such problem.
Figure 5: Normalized Dot-Product Discriminator Output using a 1 chip Early-Late Spacing Results The tracking performances for all the satellites in view are illustrated in Figure 6 and Figure 7. The former shows the Doppler tracked by two different satellites over a period of 75 s. The level of noise observed for both the high and low elevation satellite is fairly low. This is a consequence of the high signal power used in the simulation. However, it also demonstrate proper implementation and convergence of the code and carrier tracking loops, which is confirmed in Figure 7 were excellent CN0 and PLL Lock detector values are shown for all satellites in view.
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Figure 6: Tracked Doppler [Hz] for a High (left) and Low (right) elevation Satellite
Figure 7: CNo [dB-Hz] (left) and PLL smoothed Lock Detector (right) for All the Satellites in View NAVIGATION MESSAGE DECODING The GPS L5navigation message decoding is a three-step process. First, the symbol bit sign must be recovered using the data channel in-phase prompt correlator outputs. Second, the symbol stream must be transformed in the corresponding data stream using a Viterbi Decoder. And finally, subframe synchronization must be performed Symbol bit recovery To validate the symbol bit recovery algorithm used herein, the probability distribution function obtained using more than 50,000 data correlator outputs is shown in Figure 8. This figure confirms that the hard decision algorithm used herein will produce a BER close to zero.
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Figure 8: Symbol Bit Probability Distribution Function FEC Encoding and Viterbi Decoder The use of the FEC encoding scheme shown in Figure 9 makes the implementation of the GPS L5 navigation message decoding slightly more complex than that of GPS L1 C/A as the symbol stream obtained in the previous step needs to be converted to the actual navigation message data stream before any subframe synchronization can be attempted or any ephemeris parameter can be read. The actual implementation of the Viterbi decoder, however tedious, remains fairly simple and is well documented. It is however important to remember two particular aspect of this implementation. Firstly, in the case of GPS L5, The alignment of the data and symbol bit is determined by the NH10 and NH20 sequence respectively. Also, the use of a Viterbi decoder introduces a delay that is function of this decoder’s constrain length. A constrain 5 is used herein, introducing a delay of 6,956,400 chip (or 68 data symbols).
Figure 9: GPS L5 Convolution Encoder Subframe Synchronization As previously mentioned, the GPS L5 CNAV format significantly differs from that of GPS L1 C/A. This fosters the need for a new subframe synchronization algorithm. To this end, the subframe structure is highlighted in Figure 10. The features of interest for the synchronization are: 1) the preamble, 2) the PRN number, 3) the Z-count, and 4) the cyclic redundancy check. The preamble used on L5 and L1 C/A are similar. Once it is detected in the data stream, the synchronization algorithm checks that PRN number corresponds to the PRN of the satellite being tracked, that the Zcount is increasing by one from one subframe to the next, and that the parity of the subframe is correct. If any of these checks failed, the algorithm is reset to preamble detection. Once synchronization is confirmed, the navigation parameters can be read. In terms of ephemeris and clock parameters, the subframes of interest are 10 and 11, and 30 to 36 respectively.
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Figure 10: 300-bit Subframe Format Once the satellite ephemeris and clock parameters have been read, it is possible to compute the satellite position and clock error at transmit time, and to use them in the navigation solution described in the next section NAVIGATION SOLUTION Iterative Least-Squares Solution Using Pseudoranges The navigation solution implemented herein is a simple iterative Least-Squares algorithm that uses pseudoranges measurements only. The only significant difference with the L1 C/A navigation algorithms lies in the computation of the pseudoranges. The computation of the pseudoranges involves the precise determination of the propagation delay through differentiation of the receive and transmit time. However, the use of a Viterbi Decoder introduces a delay of 68 symbol bits that need to be accounted for. The approach taken herein is summarized in the following equations:
TR = TT + TP + TD
(5)
Where TR , TT , TP and TD are the receive, transmit, propagation and decoding time respectively. The actual pseudorange corresponds to the propagation time, which is function of the satellite Doppler. Typically the receive time is common to all the satellite in views, whereas the transmit time is different for all satellites and is determined as a byproduct of the subframe synchronization algorithm. Following similar logic, the receive time, is kept common for all satellites, and the transmit time is modified to account for the decoding time. Finally, the pseudoranges can be calculated as follows:
PR = c(TR − TT ,new ) Where PR is the pseudorange,
(6)
c the speed of light, TT ,new = TT + TD is the modified transmit time.
It is important to note that the navigation solution implemented herein is a rather basic one. More advanced implementation should definitively consider 1) the addition of some carrier smoothing algorithm to mitigate the effect of noise and multipath, and 2) the use of Doppler measurement to produce a receiver velocity and clock drift estimates in addition to the position and clock offset estimates already available from pseudoranges measurement. TEST RESULTS The results presented herein are intended to demonstrate the GPS L5 tracking accuracy and resulting positioning accuracy. For this reason, the constant components are removed from the pseudoranges and position solution. The magnitude of these biases is limited to less than a few meters in both the measurement and position domains.
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Pseudorange Accuracy To illustrate the pseudorange measurement accuracy, the software compares its own measurements with the true geometric ranges. The latter is derived using the known receiver position and the computed satellite positions. This Estimated Pseudorange Error (EPE) calculation can only be considered valid if one assumes that the computation of the satellite positions is not erroneous in the first place. In order to verify that this was indeed the case, the satellite position computations using the L5 ephemeris parameters was cross-checked using the L1 C/A parameters in C3NAV2TM (independent software developed earlier in the PLAN group). Both approaches yielded identical results, thus validating the EPE calculations. The EPE obtained are illustrated both in Figure 11 and Table 2.
Figure 11: Estimated Pseudorange Errors In the absence of all error sources but noise, the accuracy of the pseudoranges measurements depends solely on the implementation of the code (and carrier) tracking loops. In the case at hand, the use a carrier-aided code tracking loop provides a level of accuracy close to theoretical expectations. Further investigations should help determine the best code tracking parameters (including coherent integration time, loop filter order and bandwidth, discriminator and normalization). Table 1: Pseudoranges Error Statistic PRN 6 7 16 18 21 24 26 29
EPE Std. Dev. [cm] 26.3 18.0 19.3 23.1 21.0 18.6 22.0 20.3
Position Accuracy To quantify the position accuracy, the east, north and up errors relative to the known receiver position are computed. These results are illustrated in both Figure 12 and Table 2.
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Figure 12: Scatter Plot of North and East Errors [m] The position accuracy observed is again in line with L5 SPP theoretical expectations. Further investigations will help quantify the benefits of carrier smoothing and velocity estimation. Table 2: Position Error Statistics Parameter Error STD [cm]
East 7.0
North 15.0
Up 25.1
CONCLUSION AND FUTURE WORK A full GPS L5 software receiver was implemented and tested herein using a hardware simulator. The acquisition of the signal is greatly affected by the introduction of NH codes on both the data and pilot channel. To alleviate the problems related to unknown data bit transitions, the acquisition process is broken down in three steps and the actual NH code delay acquisition is only performed after successful convergence of the coarse tracking loops. Despite the existence of more accurate data/pilot combined tracking algorithms, a pilot-only tracking algorithm was used herein to lessen the computational burden. This algorithm was shown to provide excellent tracking accuracy as well as highly reliable symbol bit recovery. This in turns enabled accurate decoding of the ephemeris and clock parameters. The pseudoranges measurements and navigation solution accuracy analysis proved to be very satisfying. The results shown here validate the overall implementation of this GPS L5 software receiver and open the way to further investigations. Specifically, the implementation of a more advanced navigation solution is in progress. A Kalman Filter and a carrier smoothing algorithm will be used to provide high accuracy position, velocity and clock parameters estimate. Also, the impact of various error sources on code and carrier tracking will be thoroughly investigated to optimize both tracking loops implementation. ACKNOWLEDGEMENTS The authors would like to thank Florence Macchi and Cyrille Gernot for the help and useful insights they provided during the preparation of this paper. The Informatics Circle Of Research Excellence and the GEOIDE Networks of Centres of Excellence are acknowledged for financial support. REFERENCES Bastide, F. (2004), Analysis of the Feasibility and Interest of Galileo E5a/E5b and GPS L5 Signals for Use with Civil Aviation, Ph.D. Thesis, Institut National Polytechnique de Toulouse, No 2137. Betz, J. and R. Kolodziejski (2000), Extended Theory of Early-Late Code Tracking for a Bandlimited GPS Receiver, Navigation: Journal of The Institute of Navigation, Vol.47, No.3, Fall 2000. Hegarty, C., M. Tran, and A.J. Van Dierendonck (2003), Acquisition Algorithms for the GPS L5 Signal, Proceedings of the US Institute of Navigation GNSS (Portland, OR, USA, Sept. 9-12)
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IS-GPS-705 (2005), Interface Specification – Navstar GPS Space Segment / Navigation L5 User Interfaces, ARINC Incorporated, September 2005 Julien, O. (2005), Design of Galileo L1F Tracking Loops, Ph.D. Thesis, Department of Geomatics Engineering, University of Calgary, UGCE Report 20227. Macabiau, C., L. Ries, F. Bastide, J-L. Issler (2003), GPS L5 Receiver Implementation Issues, Proceedings of the US Institute of Navigation GNSS (Portland, OR, USA, Sept. 9-12). Mongrédien C., G. Lachapelle, M.E. Cannon (2006), Testing GPS L5 Acquisition and Tracking Algorithms Using a Hardware Simulator, Proceedings of the US Institute of Navigation GNSS (Fort Worth, TE, USA, Sept. 26-29). Ries, L., C. Macabiau, O.Nouvel, Q. Jeandel, W. Vigneau, V. Calmettes and J-L. Issler (2002), A Software Receiver for GPS-IIF L5 Signal, Proceedings of the US Institute of Navigation GNSS (Portland, OR, USA, Sept. 24-27). Tran, M. (2004), Performance Evaluation of the New GPS L5 and L2 Civil (L2C) Signals, Navigation: Journal of the Institute of Navigation, Vol.51, No.3, Fall 2004. Tran, M. and C. Hegarty (2002), Receiver Algorithms for the New Civil GPS Signals, Proceedings of the US Institute of Navigation NTM (San Diego, CA, USA, Jan 28-30) Van Dierendonck, A.J. (1997) GPS Receivers in Global Positioning System: Theory and Applications Volume I, Progress in Astronautics and Aeronautics Volume 164, AIAA. Yang, C. (2000), GPS Code Correlation with FFT under Pseudo-Quadrature Sampling, Proceedings of the US Institute of Navigation NTM (Anaheim, CA, USA, Jan. 26-28) Yang, C., C. Hegarty, and M. Tran (2004), Acquisition of the GPS L5 Signal Using Coherent Combining of I5 and Q5, Proceedings of the US Institute of Navigation GNSS (Long Beach, CA, USA, Sept. 21-24).
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