Performance Evaluation of a GPS L5 Software Receiver Using a

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					              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

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:

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.

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.

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

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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.

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.

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.

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
         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

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.

   ENC 07, Geneva, Switzerland, 29May-June 1, 2007                                                                 5/12
              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:
        VDLL ,DP 2 =
                     (2 − δ ) . (I E − I L )I P + (QE − QL )QP                                                 (4)
                        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

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

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 Z-
count 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

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 by-
product 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 )                                                                                            (6)

Where PR is the pseudorange,       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.

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

                                           Table 1: Pseudoranges Error Statistic
                                                 PRN             EPE Std. Dev. [cm]
                                                   6                   26.3
                                                   7                   18.0
                                                  16                   19.3
                                                  18                   23.1
                                                  21                   21.0
                                                  24                   18.6
                                                  26                   22.0
                                                  29                   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                 East         North            Up
                            Error STD [cm]                  7.0      15.0               25.1

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.

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.

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   ENC 07, Geneva, Switzerland, 29May-June 1, 2007                                                          12/12

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