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Sep 28, 2007 - and 3 years at Telecom INT and eventually ended up with .... stages. The first stage includes a coarse acquisition of frequency offset alongside estimation of the CM .... (VTEC) and the elevation angle E of the satellite through.
A Novel L1 and L2C Combined Detection Scheme for Enhanced GPS Acquisition Cyrille Gernot, Surendran Konavattam Shanmugam, Kyle O’Keefe and Gerard Lachapelle Position Location Navigation (PLAN) Group, Department of Geomatics Engineering, University of Calgary, Alberta, Canada.

BIOGRAPHY Cyrille Gernot is a PhD. student in the Department of Geomatics Engineering at the University Of Calgary Schulich School of Engineering. He arrived in Calgary in early 2006 to perform a six month internship in the PLAN Group under the supervision of Dr. Gerard Lachapelle. This training period concluded 5 years of general engineering education with 2 years of preparation school and 3 years at Telecom INT and eventually ended up with a proposition to stay in Calgary as a MSc. student. After a few months in the PLAN Group, he finally transferred from MSc. to PhD. at the beginning of May 2007. He expects to complete his PhD. in September 2009. Surendran K. Shanmugam is a PhD candidate in the Department of Geomatics Engineering at the University of Calgary. He received his MSc in Electrical Engineering at the same university in 2004 following the bachelor’s in Electronics and Communication Engineering, at the Anna University (India) in 2001. His research interests include high-sensitivity GPS, ground based wireless location and generally in the areas of communications theory and statistical signal processing. Kyle O’Keefe is an Assistant Professor of Geomatics Engineering at the University of Calgary. He completed PhD and BSc. degrees in the same department in 2004 and 2000. He has worked in positioning and navigation research since 1996 and in satellite navigation since 1998. His major research interests have been in GNSS system simulation and assessment, space applications of GNSS, carrier phase positioning, and local and indoor positioning with ground based ranging systems. Dr. Gérard Lachapelle is a professor in the Geomatics Engineering at the University of Calgary. He holds a CRC/iCORE chair in wireless location. He has been involved with GNSS research, developments and applications for the past 25 years and has authored/coauthored numerous related publications, software and licenses. His primary research interests are in the areas of positioning, location and navigation. More ION GNNS 2007, Fort Worth TX, 25-28 September 2007

information is available on the PLAN Group website, http://plan.geomatics.ucalgary.ca. ABSTRACT Degraded signal environments such as indoors and urban canyons typically limit the scope of standard GPS receiver operation. For instance, GPS signals can be attenuated by 20 dB or more under these adverse conditions. In degraded signal environments, enhancing the processing gain by 20 dB or more requires a significant increase in coherent integration. However, the coherent integration time is decisively limited to less than 20 ms in the legacy GPS L1 signal due to the presence of navigation data modulation. Besides, the detection of weak PRN signals is also an issue owing to the limited correlation suppression performance of the L1 C/A code. Hence, the legacy GPS is currently being modernized to include improved signals at L2 and L5 frequencies. In particular, GPS L2C signal is not only attractive due to its immediate availability but also for its role in civilian GPS applications. The introduction of new signal structures necessitates the development of new acquisition algorithms. In this paper, we introduce a novel detection scheme that collectively utilizes the legacy GPS L1 C/A and L2C CM code signals to enhance the acquisition sensitivity. The proposed acquisition scheme derives its major impetus from the fact that the data, code and carrier are coherently related on the GPS L1 and L2 signals for a given PRN satellite. Secondly, it also uses both the non-coherent and differential detection outputs in its implementation for further sensitivity enhancements. A modified design of the developed acquisition scheme is introduced, which readily allows for an efficient implementation. The acquisition sensitivity performance of the proposed acquisition scheme was evaluated along with the traditional non-coherent acquisition scheme using hardware simulated and live GPS signals. Preliminary analysis corroborates the acquisition sensitivity

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improvement of the proposed acquisition scheme over traditional non-coherent acquisition. INTRODUCTION Degraded signal environments such as indoors and urban canyons typically limit the scope of GPS receiver operation. For instance, GPS signals can be attenuated by 20 dB or more under these adverse conditions. In degraded signal environments, enhancing the processing gain by 20 dB or more requires a significant increase in coherent integration time. High sensitivity GPS (HS GPS) receivers utilize either assistance information or massive correlator architecture to accomplish enhanced sensitivity. For example, assisted GPS (AGPS) typically utilize Doppler and timing assistance to extend the coherent integration beyond navigation data bit duration. While it does not require extensive hardware resources, it is limited by network availability and the reliability of the assistance information. On the other hand, stand-alone HS GPS uses extensive hardware resources to increase the dwell period. However, they can still be limited in terms of coherent integration period. Consequently, GPS is now being modernized with new signals at L2 (for civilian) and L5 (for aviation) frequencies. The new signal structures are specifically designed to overcome the limitations faced by legacy GPS L1 C/A signal. The presence of pilot channel is of critical importance as it allows for long coherent integration periods. More specifically, the GPS L2C is of great interest owing to its immediate availability and for its role in civilian GPS applications.

still limited by 20 ms data symbol transition. On the other hand, for stronger signals, L1 C/A assisted L2 CM acquisition is more desirable as it reduces the CM code search space. Lim et al. (2006) proposed a fast acquisition scheme of L2C signals through the aid of L1 to accelerate CM code phase and frequency offset estimation. On the other hand, Psiaki (2004) developed a FFT-based acquisition scheme to acquire L2 CM and CL codes under weak signal conditions whereas Yang (2005) investigated acquisitions techniques on L2 CM alone, L2 CL alone and possible joint acquisition of CM/CL. Currently, three satellites are transmitting L2C as well as the usual L1 C/A signal, namely PRN 12, PRN 17 and PRN 31. Since the two signals are transmitted from the same satellites, most of the satellites and receiver errors are now correlated. Moreover, according to the Interface Control Document (ICD), the two codes are synchronized and even though the 20 ms long data bits are different on both channels, they are still aligned in terms of timing. Secondly, the relation between the Doppler on L1 and the Doppler on L2 should simply be the frequency ratio between L1 and L2. PROPOSED ACQUISITION METHOD The proposed acquisition method is designed to estimate both L1 C/A and L2 CM code delay and Doppler frequency while keeping the frequency bins size as small as possible by using only 1 ms coherent acquisition. As illustrated in Figure 1, the number of frequency bins to consider is a function of the coherent integration time used during the acquisition process.

The new L2C signal has data and pilot components. The data channel consists of a moderate ranging code namely the CM code, which is 10,230 chips long and clocked at 511.5 kHz. The data channel is further modulated with the 50 Hz navigation data. On the other hand, the pilot channel consists of long ranging code, the CL code, which is also clocked at 511.5 kHz. The long CL code is 727,250 chips long and offers substantial correlation suppression (~ 44 dB). However, L2C is limited to a single bi-phase carrier as it has to share the frequency with the military P(Y) code. Therefore, the CM and CL codes are time multiplexed at 1.023 MHz. The transmit power of L2C signal is 1.5 dB lower than that of L1 C/A and is further shared equally between the data and pilot channels. The presence of data-less channel and improved correlation properties benefit the GPS L2C signal in terms of signal acquisition and tracking.

Figure 1: effect of the coherent integration time on the frequency bins size to consider

Acquisition of the L2C signal is normally carried in two stages. The first stage includes a coarse acquisition of frequency offset alongside estimation of the CM code phase. The second stage includes finer frequency acquisition alongside CL code phase estimation. It should be emphasized here that the acquisition of CM code is

In order to use a 20 ms coherent acquisition, a minimum of 300 frequency bins has to be used to cover the entire Doppler frequency domain where as only 15 are necessary when a 1 ms coherent integration is used. Therefore, if no a priori information on the Doppler is available, the space search to consider is greatly enlarged.

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However, in order to keep the frequency bins as large as possible, the signal power required has to be fairly high. The proposed acquisition tries to make use of the fact that through the recent availability of L2C signal, the power available to civilian users has been increased. Indeed, since the noise statistics at the output of a non-coherent detector and differential detector are different, the detection outputs can be potentially combined to improve

the detection performance. For instance, the non-coherent and differential detection outputs from both L1 and L2CM signals can be combined. However, such an implementation would require four multiplications followed by three additions to obtain the final detection output. In contrast, the acquisition technique presented in this paper utilizes only two multipliers and five adders to obtain the same detection output (figure 2).

Figure 2: proposed acquisition scheme The combined L1/L2 acquisition presented in this paper makes used of the three assumptions already mentioned during the first part: 1.

2.

the navigation message even though it is different on L1 and L2 is still synchronized that is to say bits transition will occur at the same time on both channels

∆Dop L1− L 2 = Dop L1 ×

L2 − Dop L 2 L1

L1 = 1575.42 MHz L2 = 1227.60 MHz Residual of L1 Doppler - (L2/L1)L2 Doppler

the Doppler frequency on L1 is related to the one on L2 by the ratio L2/L1

0.008 PRN 9

0.006

the code delay on L1 C/A is the same than the one on L2 CM

Since it has been observed and confirmed by the United States Coast Guard Center that no navigation message is transmitted on L2C yet and since the ICD stipulates that the navigation message of L1 and the one of L2 should be synchronized, the first hypothesis is considered validated. Regarding the second hypothesis, data collection was performed using a NovAtel OEMv3 L2C capable receiver and the Doppler frequency tracked on L1 and L2 has been recorded. However, since only PRN 12 and PRN 31 were in view at this point, the Doppler information of all satellites, even non L2C ones, was used. Using this data, the Doppler residual obtained according to the following equation was plotted in Figure 3:

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Residual Doppler (Hz)

PRN 5

3.

PRN 12

0.004

PRN 18 PRN 22

0.002

PRN 31 PRN 30

0 1

4

7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55

-0.002

PRN 32 PRN 14 PRN 11

-0.004 Time (s)

Figure 3: residual Doppler obtained by differencing L1 Doppler times the ratio L2/L1 and L2 Doppler over 1 minute of real data tracked by a NovAtel OEMv3 L2C capable receiver Since the residuals found are minimal, the theoretical relationship relating L1 and L2 Doppler can then be considered verified.

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Finally, table 1 illustrates the fact that the L1 C/A code and L2 CM code are synchronized. Indeed, using an RF front end and collecting real data, it can be shown that the C/A and the CM code are separated by an integer number of milliseconds. This result makes sense considering the fact that the CM code is 20 ms long whereas the L1 C/A code is only 1 ms long. PRN 12 17 31

C/A code delay (ms) 0.8876 0.51705 0.1396

CM code delay (ms) 14.8876 16.51705 6.1396

Table 1: code delays found on L1 C/A and L2 CM using real data collecting through a NovAtel RF front end However, due to ionospheric activity, the time delay between L1 and L2 signals can vary and possibly invalidate this last assumption. This is especially important as the acquisition proposed makes used of the fact that L1 C/A code and L2 CM code are synchronized. Indeed, a delay of 0.5 chips between the two codes can lead to a 50 % loss compared to the synchronized case when adding the results (figure 4).

Figure 5: vertical TEC measured over Januray 2007 at 0° latitude and -180° longitude. 1 TECU = 1016 TEC. However, in order to represent the actual TEC encounters by the signal while traveling through the ionosphere, the elevation angle of the satellite has to be considered. The TEC encountered is then relation of the vertical TEC (VTEC) and the elevation angle E of the satellite through a mapping factor M(E):

TEC = M ( E ) × VTEC

M (E) =

1

    cos( E )   1−  h  1+  RE   E elevation angle Figure 4: effect of inter-code delay on the summation of the correlation peak. C/A code is in blue, CM code is in red.

2

h ionosphere altitude R E earth radius

In order to verify that the hypothesis still stands, a study of the ionospheric activity during January 2007 was performed. The data used was from the IGS website and represent the vertical TEC at 0° latitude and -180° longitude every two hours over the month and the vertical Total Electron Content (TEC) obtained are shown in Figure 5.

Figure 6: mapping factor to consider as a function of the elevation angle

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According to Figure 6, the worst case possible regarding the mapping factor to consider occurs when the elevation angle of the satellite is 0°. At this point, the VTEC has to be multiplied by three in order to estimate the TEC encounters by the signal along its path through the ionosphere. Then using this information the time delay between L1 and L2 can be deduced using equation 3 of the following:

∆t L1

∆R 1.34 × 10 −7 = = TEC (1) 2 c f1

∆t L 2 =

∆R 1.34 × 10 = 2 c f2

Therefore, the L1 C/A code and L2 CM code can be considered synchronized without engendering too much loss during the acquisition process.

−7

TEC (2)

THEORY

∆t L1− L 2 = ∆t L1 − ∆t L 2 f 2 − f1 2

⇒ ∆t L1− L 2 = 1.34 × 10 − 7 TEC

Under normal ionospheric conditions such as the one recorded during January 2007, the worst case possible was for the signal to encounter 105 TECU along its path which would result less than 4 % loss. Considering the case of the ionospheric storm with 185 TECU mentioned earlier, the worst TEC possibly encounters along the signal path is 555 TECU which corresponds to 20 % loss. Anyway, under such harsh conditions, most receivers will have a hard time to track any signals due to ionospheric scintillations usually occurring during the storms.

2

f1 f 2

First of all, the signals are assumed to be sampled at an integer multiple of the chip rate:

2

2

(3)

(1) Ionospheric time delay on L1 (2) Ionospheric time delay on L2 (3) Time delay between L1 and L2 due to the ionosphere

Tc = Ts N s where Tc is the chip duration, Ts is the sampling time and Ns is the number of samples per chip of the C/A code, the C/A code containing Nc = 1023 chips. Then beginning with the received signals already down converted to pseudo-baseband :

Therefore using equation (3), the loss experienced compared to the ideal case can be computed:

y1 (k ) = 2C1 d1 (k )c1 (k )e jφ1 ( k ) + w1 (k ) (1) for L1

Loss (%) = Delay (chip ) × 100

y 2 (k ) = 2C 2 d 2 (k )c 2 (k )e jφ2 ( k ) + w2 (k ) (2) for L2

As illustrated in Figure 7, in order to have 100% loss compared to the ideal case, it is necessary to encounter a TEC of 2800 TECU along the signal path that is a VTEC of 933 TECU. As a comparison, the strong ionospheric storm of July 16, 2000 had only a magnitude about 185 TECU and was already causing trouble to track the signals (Walter et al, 2004).

pN s ≤ k < ( p + 1) N s d (k )cm(k ) c2 (k ) =  2 ( p + 1) N s ≤ k < ( p + 2) N s  cl (k ) p being an even number where Ci is the carrier power and is assumed to be constant over the observation time, ci(k) represents the transmitted C/A code which has a period of 1 ms or the time-multiplexed L2C code, d1(k) is the data bit of the navigation message on L1 and lasts 20 ms and wi(k) is the complex additive white Gaussian noise samples. Φi(k) is the residual carrier phase with frequency and phase offset ∆Fi and θi and is defined as follow:

φi (k ) = 2π∆Fi k + θ i i being 1 or 2 and standing for L1 or L2.

Figure 7: signal loss experienced compared to the ideal case as a function of the TEC on the signal path

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As mentioned earlier in this paper, the CM code repeats itself every 20 ms and the CL code every 1.5 seconds. Note that the CM or CL code chip duration is equal to the C/A code chip duration and so one chip of the C/A code is 5/12

equal to one chip of CM code or one of CL code. However, due to the long period of the CL code, the L2C code consider for acquisition is formed as follows:

pN s ≤ k < ( p + 1) N s ( p + 1) N s ≤ k < ( p + 2) N s

cm(k ) c~2 (k ) =   0

As shown in figure 2, the proposed acquisition scheme uses the fact that both the CM and C/A codes measure the same quantities (i.e. code and frequency offset). The intermediate detection outputs at points 1, 2, 3 and 4 are given by:

z1 (n) = x1 (n) + x 2 (n) z 2 (n) = x1 (n) − x 2 (n)

p being an even number The baseband architecture of the proposed C/A-CM combined acquisition technique has been illustrated in Figure 2. In Figure 2, the upper and the lower halves pertain to the GPS L1 C/A and L2 CM detection modules. The same residual carrier is utilized to compensate for the residual frequency offset. The residual carrier frequency is scaled (by a factor 0.779) for the L2C detection module. The received samples after residual frequency compensation are correlated with the local C/A and modified CM code codes respectively. The modified CM code is obtained from the original CM code with every alternative sample being zero padded. The correlated samples are coherently integrated over the pre-detection integration time (PIT) (i.e. TPIT = NcTc). Then it can be shown that for a unique code offset l and frequency offset ∆F, the correlation/integration output can be expressed as:

x i ( n) =

nN c N s −1



k = ( n −1) N c N s

2C i d i (k )ci (k )e

j ( 2π∆Ferr , i k + Ω i )

ci (k − l )

+ wi (k )ci (k − l )e − j ( 2π∆Fk +θ r ) (5) where ∆Ferr,,i = ∆Fi – ∆F. Ωi = θi - θr is a random phase offset where θr is the arbitrary phase offset created by the local oscillator. The correlation/integration output is sampled every TPIT seconds with sample index being n. On substitution and further simplification, (5) can be reduced to:

x1 (n) = 2C i d i (n) Rl ,i (n)ψ i (n) + wi (n) (6) where di(n) is the integration output of d(k) over the predetection integration time and Rl,i is the auto-correlation function of the C/A code if i = 1 and the auto-correlation function of the modified CM code if i = 2 over the predetection integration time. ψi(n) is the frequency ambiguity function and is expressed as:

ψ i (n) ≈ sinc(π∆Ferr ,i (n) N c N s )e

z 3 (n) = x1 (n) + x 2 (n − 1) z 4 (n) = x1 (n − 1) − x 2 (n) The final detection output is then given by:

S (i, ∆F ) =

N −1

∑ z (n)z n =0

1

∗ 3

(n) + z 2 (n) z 4∗ (n) (7)

From (7), the individual signal components can be derived:

s13 (n) = 2C1 Rl2,1 (n) sinc 2 (π∆Ferr ,1 (n) N c N s ) + 2C 2 Rl , 2 (n − 1)ψ 2 (n)ψ 2∗ (n − 1) (8) and

s 24 (n) = 2C 2 Rl2, 2 (n) sinc 2 (π∆Ferr , 2 (n) N c N s ) + 2C1 Rl ,1 (n − 1)ψ 1 (n)ψ 1∗ (n − 1) (9) From equations (8) and (9), it is evident that the final detection output combines the individual non-coherent and differential detections from L1 C/A and L2 CM code signals. TEST METHODOLOGY In order to test the performance of the proposed acquisition technique, two sets of experiments were conducted, one using simulated data obtained through an RF simulator and one using actual data directly collecting through a GPS L1/L2 NovAtel Antenna (Figure 8). The tests performed using real data were limited due to the lack of satellites and were conducted primarily to validate the simulated results. The variable attenuator has only been represented in figure 8 in order to illustrate the fact that both simulated and real results where obtain with different C/N0.

j (π∆Ferr , i ( n ) N c N s +φi ( n ))

Where sinc(x) is the sinc function and Φ(n) is the phase at the beginning of the pre-detection integration.

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d2 =

[E (T / H 1 ) − E (T / H 0 ]2 var(T / H 0 )

The results obtained where then compared to the output SNR of non-coherent and coherent acquisition on L1 C/A signal. Moreover, the effect of the coherent integration on the combined acquisition was studied as well as the possibility to apply different weights on each channel. RESULTS USING REAL DATA During the real data collection, only PRN 31 and PRN 12 were visible and tracked at 48.8 dB-Hz and 35.6 dB-Hz on L1 by a NovAtel OEM4 receiver (Table 3).

Figure 8: test-bed used while using simulated or real data

L1

Intermediate frequency

Sampling frequency

70.42 MHz

20 MHz

70.1 MHz L2 Table: parameters of the RF frond end

20 MHz

As shown in Table 2, even though the IF frequencies were different for L1 and L2, the sampling frequencies were identical. Therefore most difficulties pertaining to resampling problems were avoided. The parameters used on the Spirent RF simulator during the first set of tests are described in Table 2. The signal power and navigation message transmitted by each channel are the ones defined in the Interface Control Document ICD-GPS-200C. The ionosphere was considered during the tests with a VTEC of 30 TECU. Under these conditions the worst TEC encounters along the signal path could be up to 90 TECU.

Signal power (dBW)

L1 C/A

L2C

-158.5

-160

Iono VTEC

30 TECU CNAV Navigation NAV with FEC message type Table 2: simulator parameters used during the tests

PRN

12

31

Frequency

L1 C/A

L1 C/A

Lock

Yes

Yes

SNR

35.6 dB-Hz

48.8 dB-Hz

-1023 Hz 1120 Hz Doppler Table 3: screenshot of the tracking parameters of PRN 12 and 31 followed through a NovAtel OEM4 receiver Given the availability of these two L2C PRNs with strong SNR differences, the analysis was conducted on both of them. 

PRN 31

The first attempt involved acquisition of the satellite using 1 ms coherent integration and 20 ms summation over the whole Doppler frequency range that is to say -5000 Hz to +5000 Hz around the central frequency using a frequency bin size of 666.66 Hz corresponding to the largest possible given the coherent integration time. Moreover, the CM code delay being unknown, each ms of the CM code has to be considered (Figure 9). The peak due to the presence of the CM code combined with L1 C/A code was found between millisecond 15 and millisecond 16 of the code. This result was expected given that the CM code delay found when using directly the 20 ms of the code to create a coherent acquisition was 15.0515 ms. Moreover, the combined acquisition outperformed the conventional L1 C/A non-coherent acquisition by 4 dB. However, as expected the performance was still inferior compared to the optimal L1 C/A coherent acquisition once it is synchronized with the data bits transition.

The performance of the proposed combined L1/L2 acquisition technique was evaluated through the SNR obtained through the deflection coefficient d2.

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synchronized with the boundary of the integration time considered.

Figure 9: Results for PRN 31. L1 C/A 20 ms coherent integration synchronized with the navigation message SNR, L1 C/A non-coherent integration of 1 ms with 20 ms summation SNR and proposed acquisition SNR for 1 ms coherent integration with 20 ms summation and covering the 20 possibilities of the CM code As expected, the proposed method actually performed the L1 C/A and L2C joint estimation of Doppler and code delays. Indeed, the output of the acquisition corresponds to the C/A code delay that can be found over 1 ms but also provide which millisecond of the CM code gave the desired combination. Therefore, by simply adding the C/A code delay over one millisecond to the millisecond of interest of the CM code, the code delay of the CM code can be found. Then using the knowledge that the CM code is synchronized with the data bits of L1, it is no longer necessary to perform a data bit synchronization on L1. Moreover, the proposed acquisition also outputs the Doppler frequency found on L1 (here 1000 Hz as expected given the frequency bin size used and the Doppler of the satellite 31) and using the fact that there is a direct relation between the Doppler on L1 and the Doppler on L2 as shown during the verification of the assumptions, both L1 Doppler and L2 Doppler are actually output by the combined L1/L2 technique. Secondly, a study of the effect of the coherent acquisition time was conducted (Figure 10). The two best cases obtained during this test were for 1 ms and 5 ms coherent integration times. These outperformed all other durations tested. This was to be expected given the fact that the CM code delay was 15.0515 ms; that is to say that after this time since the beginning of the RF data collected, a data bit transition was possible. This transition had actually happened and reduced the performance for 2, 4 and 10 ms coherent integration since for each of these cases, the transition occurred in the middle of the chunk of data considered to perform the integration. However, as expected for such a situation, 5 ms integration gives the best SNR since the transition is ION GNNS 2007, Fort Worth TX, 25-28 September 2007

Figure 10: effect of different coherent integration time on the proposed acquisition results for PRN 31 Finally, the effect of weighting the L1 or L2 channel is investigated and illustrated in Figure 11. As expected the best case possible occurs when both channels are weighted equally. Indeed, in any other weighting scheme, one would not benefit from the full level of additional signal power available.

Figure 11: effect of weighting the channel for PRN 31

Weight _ L 2 = 1 − Weight _ L1 

PRN 12

To confirm the previous results and in order to test the proposed combined acquisition under harsher conditions, the same series of tests were conducted on PRN 12 which was tracked only at 35.6 dB-Hz by the NovAtel OEM4 receiver used.

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First of all, a normal L2C CM acquisition was performed to determine the actual code delay of the code and compare it with the code phase output by the combined acquisition. The delay found was of 12.7655 ms and confirmed the results obtained on Figure 12 which shows that the correct CM code ms was the one between 12 and 13.

Figure 13: effect of different coherent integration time on the proposed acquisition results for PRN 12 Finally, Figure 14 confirms that the best choice possible is to use both signals equally during the acquisition process.

Figure 14: effect of weighting the channel for PRN 12 Figure 12: Results for PRN 12. L1 C/A 20 ms coherent integration synchronized with the navigation message SNR, L1 C/A non-coherent integration of 1 ms with 20 ms summation SNR and proposed acquisition SNR for 1 ms coherent integration with 20 ms summation and covering the 20 possibilities of the CM code Then following the same approach than for PRN 31, the effect of the coherent integration time was investigated (Figure 13). The best integration times obtained are 2 and 4 ms. Indeed, for both of these times, losses are minimal since the data bit transition occurs at 12.7655 ms. However, whereas 5 ms showed fairly good performance compared to what was expected. This could be explained by the fact that even if the transition occurred in the middle of a 5 ms chunk of data, three of the four of the coherent integrations are still maximal.

RESULTS USING SIMULATED DATA Two tests were conducted under a controlled C/N0 environment, one at 45 dB-Hz and one at 35 dB-Hz. A L1/L2 RF simulator was used to generate the signal transmitted by 9 satellites with equal power that is to say the signal-noise ratio received by the receiver was the same for each satellite. The only difference simulated on each satellite was the effect of the ionosphere through the elevation angle of the satellite considered and the navigation messages transmitted on L1 or L2. Indeed, since the between satellite and receiver distance was different for each satellite, the data bits transitions occurred at different instants for each of them. The 9 satellites were then used to create statistics on the SNR output by the proposed acquisition and compared to the results of a 20 ms coherent acquisition on L1 synchronized with the navigation message and a noncoherent acquisition on 20 ms with 1 ms coherent integration. 

Signals tracked at 45 dB-Hz on L1

The mean and standard deviation of the SNR obtained for a 20 ms test via the combined L1/L2 acquisition for different coherent integration time are illustrated on Figure 15.

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Figure 15: mean and standard deviation of conventional coherent and non-coherent acquisition on L1 compared to the proposed novel acquisition for different coherent integration time while L1 signal is tracked at 35 dB-Hz

Figure 16: mean and standard deviation of conventional coherent and non-coherent acquisition on L1 compared to the proposed novel acquisition for weight applied on the signals while L1 signal is tracked at 35 dB-Hz

The mean and standard deviation of conventional L1 C/A are also represented. For instance, using a 1 ms coherent integration followed by 20 non-coherent summation yields a mean SNR of 30.1 dB and a standard deviation of 0.61 dB whereas a full 20 ms coherent integration gave a mean SNR of 34.2 dB and a standard deviation of 0.5 dB. The proposed acquisition outperforms the performance of the conventional non-coherent acquisition on L1 while keeping the frequency bins size as small as possible. However, increasing the coherent integration time on the proposed method does not bring any improvement since the mean SNR found stayed approximately the same whereas the standard deviation increases. This was to be expected as the 1 ms coherent integration time is less affected by the data bit transition. Indeed, if a transition occurs while using only 1 ms coherent integration, only one twentieth of the 20 summations will be affected by it whereas it is one tenth for 2 ms, one fifth for 4 ms and so on. Finally, one should notice the strong correlation between the obtained statistics and the test performed using actual signals. Indeed, during the acquisition of PRN 31 tracked at 48.8 dB-Hz using real data, the SNR obtained was of 36.5 dB whereas the signals tracked at 45 dB-Hz during the simulation yield a 32.2 dB output SNR. This is a mean 4.2 dB difference in SNR for a 3.8 dB-Hz difference in C/ N0.

Once again, the best situation proved to be when both signals are weighted equally.

Secondly, the effect of weighting the signals was investigated and the statistical results are shown in Figure 16.

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Signals tracked at 35 dB-Hz on L1

A similar set of statistics was obtained using signals tracked at only 35 dB-Hz by the OEM4 NovAtel receiver. Once again the effects of the coherent integration time as well as the possibility of weighting L1 or L2 signal were investigated. On the other hand, the performances of the non-coherent and coherent acquisition on L1 were computed. The results where then compared between each other and the compared with the real case (PRN 12). Figure 17 and Figure 18 illustrate the results obtained for the effect of the coherent time and the weight respectively. The proposed acquisition proved to be able to perform better than conventional L1 C/A non-coherent acquisition (mean of 3 dB improvement). However, as was expected, it still remains below the performance of a full 20 ms coherent acquisition but this last one would need a total of 300 frequency bins whereas the combined method only requires 15. Increasing the coherent integration time used does not bring sufficient improvement. Indeed, even if the mean SNR is slightly improved, the standard deviation increases as well. On the other hand, obtained results are consistent with the tests performed using real data for the PRN 12 tracked at 35.6 dB-Hz; RF simulation yielding a SNR of 21.1 dB whereas actual data resulting in 21.6 dB.

Figure 17: mean and standard deviation of conventional coherent and non-coherent acquisition on L1 compared to the proposed novel acquisition for different coherent integration time while L1 signal is tracked at 35 dB-Hz

code phases and frequency offsets. However, whereas such combination would require four multiplications and four additions, the proposed algorithm needs only two multiplications and four additions to obtain the same results. In so doing, the processing time needed is almost divided by two since multiplications represent the critical factor compared to additions in terms of computational burden. All the assumptions required for the proposed method have been checked and validated before testing. Concerns were especially directed toward the assumption of synchronized L1/L2 codes due to the ionosphere effect. However, through a simple investigation of ionospheric “normal” conditions, it has been demonstrated that the combined could only be affected by less than 4 % loss compared to the ideal case. In order to verify the theory, several tests were conducted including tests using real data through the use of the three PRN already broadcasting L2C and simulation through the use of an RF software simulator to create a controlled C/N0 environment and perform a statistical study of the acquisition method’s performance. In both case, data collection included signals tracked at 45 dB-Hz and 35 dB-Hz by a NovAtel OEM4 receiver. During all of the tests, the combined acquisition outperformed the capability of common L1 C/A non-coherent acquisition by 2 to 3 dB while keeping a coherent acquisition time of only 1 ms. Under these conditions, the frequency bins size is kept at 666.66 Hz that is to say that only 15 bins are required to cover the entire Doppler space compared to 300 bins in the case of 20 ms coherent summation. This last point is especially important as it shows that the acquisition time can be greatly reduced under challenging conditions. ACKNOWLEDGMENTS

Figure 18: mean and standard deviation of conventional coherent and non-coherent acquisition on L1 compared to the proposed novel acquisition for weight applied on the signals while L1 signal is tracked at 35 dB-Hz Finally, using both signals equally during the acquisition process offers the best performance, far above the cases where only one of the two signals is used. This specific behavior is explained by the fact that the noise of a noncoherent acquisition and a differential acquisition are correlated to some extent whereas the noise on L1 and the noise on L2 are completely uncorrelated. CONCLUSION In this paper, a novel acquisition combining L1 and L2 civil signals has been proposed. The output obtained corresponds to the summation of non-coherent and differential acquisition performed on L1 and on L2 and allows performing a joint estimation of L1 C/A and L2C ION GNNS 2007, Fort Worth TX, 25-28 September 2007 11/12

The first author would like to thank Florence Macchi, PhD student in Geomatics Engineering, for her constant help and support, as well as the Informatics Circle Of Research Excellence and the GEOIDE Networks of Centres of Excellence for their financial support. REFERENCES Cho, D. J., C. S. Park, S. J. Lee (2004) “An Assisted GPS Acquisition Method using L2 Civil Signal in Weak Signal Environment,” Journal of Global Positioning Systems, vol 3, no 1-2:25-31 Lim, D.W., S.W. Moon, C. Park, S.J. Lee (2006) “L1/L2CS GPS Receiver Implementation with Fast Acquisition Scheme,” Position, Location, And Navigation Symposium, 2006 IEEE/ION, 25-27 April, pp 840- 844 Psiaki, M. L., L. Winternitz, M. Moreau (2004) “FFTBased Acquisition of GPS L2 Civilian CM and CL

Signals,” in Proceedings of the ION GNSS 2004, Long Beach, September 2004. Walter, T., S. Rajagopal, S. Datta-Barua, J. Blanch “Protecting Against Unsampled Ionospheric Threats,” in

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