ION ITM 2011, Session C4, San Diego, CA, 24-26 January 2011. 1 of 10 ... (20 ms for GPS L1 C/A), bit synchronization is required as is knowledge of the ...
Collaborative Tracking of Weak GPS Signals Using an Open-loop Structure Ping Luo and Mark G. Petovello Position, Location And Navigation (PLAN) Group Department of Geomatics Engineering Schulich School of Engineering University of Calgary
BIOGRAPHIES
INTRODUCTION
Ping Luo is a MSc. candidate in the Department of Geomatics Engineering, University of Calgary. He obtained his BSc from Huazhong University of Science and Technology in 1996, and MSc from Beijing Broadcasting Institute in 1999, both in Electrical Engineering. His previous working experience is mainly focused on wireless communications. He expects to complete his MSc in February 2011.
Weak GPS signal acquisition and tracking remains an active research area even though the GPS reception performance has been improved tremendously in the past. Various techniques and architectures are designed and implemented to utilize the time and spatial correlation of the GPS signal either to improve a GPS receiver’s sensitivity, the final positioning accuracy, or to reduce the time of outage of a receiver. The general way to exploit the time correlation of the GPS signal is to increase the integration time at the baseband signal processing stage as a longer integration time results in a higher signal to noise ratio for a given carrier to noise power density. As the integration time exceeds the navigation bit duration (20 ms for GPS L1 C/A), bit synchronization is required as is knowledge of the (relative) sign of the data bits. Another limiting factor is the dynamics of the receiver, which is equivalent to the stability of the carrier frequency viewed by the receiver. If the carrier frequency has a large dynamics over the integration time such that it cannot be tracked accurately, the advantage of the long integration time will be reduced dramatically. To overcome this drawback, modern GPS receivers use a separate set of sensors to track the dynamics, for example, inertial sensors to track the velocity and acceleration of a receiver such that the Doppler frequency and Doppler frequency rate can be estimated accurately. Examples could be found in Babu et al (2008), Cox (1980), and Petovello et al (2007, 2005).
Mark Petovello is an Associate Professor in the Position, Location And Navigation (PLAN) group in the Department of Geomatics Engineering at the University of Calgary. Since 1998 he has been involved in various navigation research areas including software receiver development, satellite-based navigation, inertial navigation, reliability analysis and dead-reckoning sensor integration. ABSTRACT Weak GPS signal tracking is studied in this paper. To utilize the spatial correlation of the GPS signal among local receivers, a collaborative signal tracking structure is proposed. More specifically, the GPS signal parameter, carrier Doppler from a nearby receiver is provided to the target receiver as reference. An open-loop batch processing technique is used in this study, mainly to take advantage of its high-sensitivity and immediate signal reacquisition. As the major limitation of the open-loop batch processing technique is its heavy computation due to the large uncertainty space in frequency and time domain, the reference signal parameters, that is, carrier Doppler and code phase are provided to limit the search range, and hence to reduce the complexity. In this paper, another benefit of the collaborative open-loop tracking, namely the capability to block a strong interference in a nearby frequency band, is presented, as well.
ION ITM 2011, Session C4, San Diego, CA, 24-26 January 2011
The general way to utilize the spatial characteristics of the GPS signals is to receive GPS signals from multiple antennas and to process the multiple GPS signals in either the signal processing domain or the navigation processing domain. The former takes advantage of signal combining methods to achieve spatial diversity or to perform beamforming (e.g. Brown and Gerein 2001), and thus to increase the overall signal to noise ratio. The latter shares measurements amongst receivers for correcting common errors such as satellite orbit error and atmosphere effects (RTO-AG-160-V21). 1 of 10
Despite the varieties of the above mentioned techniques, the baseband signal processing follows two major architectures, namely the closed-loop sequential processing architecture and the open-loop batch processing architecture. The main advantage of the closed-loop sequential processing is the reduced receiver complexity as only three correlators (in general) are required to track signals from one satellite. In this type of receiver the GPS signal acquisition and tracking are separated, and the results from the acquisition are used to initialize the tracking. This approach has historically been used in GPS receivers.
In this case, the level of uncertainty associated with the aiding information will have to increase.
A GPS receiver using the open-loop batch processing technique does not separate the signal acquisition and tracking (Van Graas et al 2009). A batch of GPS signals from a satellite is processed once, where the carrier Doppler, the code phase, and carrier phase are estimated independently from batch-to-batch. The advantage of this technique is its immediate re-acquisition when a GPS signal becomes available. Another advantage is the increased signal sensitivity as longer integration time can be used. The drawback of this technique is the largely increased receiver complexity mainly due to the large code phase and carrier Doppler uncertainty space.
The rest of the paper is organized as follows. First, the methodology used for this study is presented. The field test description is then given followed by the data analysis. The paper finishes with some conclusions based on the results obtained.
This paper is focused on a system with multiple locally distributed GPS receivers. The reception conditions of these receivers are similar in general. However, given a specific time period signals from the same satellite may have different reception conditions at different receivers. For example, signals at one receiver may maintain lineof-sight to the satellite while at another receiver the signal could be corrupted by multipath, or be attenuated by tree leaves. Nevertheless, as per our previous research (Luo and Petovello 2010), main signal parameters such as the carrier Doppler, code phase and navigation bit boundary are in-common from receiver to receiver.
The general structure of the GPS receiver used in this study is shown in Figure 1. The GPS L1 C/A signal received from the antenna is down-converted and digitized by the RF front-end. The I/Q data is then correlated with the local replica in the correlators. As the receiver has an open-loop structure, an acquisition-like processing is performed in the correlators, that is, the incoming signal is correlated with the local replicas associated with all the possible time-frequency bins in the time and frequency search space. The search space is determined by the frequency uncertainty space and time uncertainty space. After all the output (associated with each time-frequency bin) is calculated, either a global maximum or a local maximum of the output is generated, depending on the configuration of the receiver. The obtained maximum value is then used for code phase and carrier Doppler estimation. In case where the incoming signal is weak, and hence the integration time to exceed the bit duration (20 ms), bit boundary has to be determined.
With this in mind, in this paper, the Doppler frequency commonality is used to formulate the collaborative signal tracking. The carrier Doppler estimated from one receiver is provided to another receiver as reference. This reference then becomes the center of the frequency uncertainty space when performing carrier Doppler search. This concept is similar to assisted GPS (AGPS) but does not require a dedicated base station located in an open area. Furthermore, since the collaborating receivers are in relatively close proximity, a limited amount of power is needed to broadcast information between them. Another key difference from AGPS is that the reference receiver can be moving. As long as the position and velocity of this receiver is known, the effect of this motion can be removed before sending information to nearby users (this is the case assumed here). However, it is envisioned that in some environments, it may be difficult, if not impossible, to determine this information. ION ITM 2011, Session C4, San Diego, CA, 24-26 January 2011
The open-loop batch processing technique is used in this research, mainly because of its capacity of immediate reacquisition and high sensitivity. As the provided carrier Doppler aiding from other receiver can largely reduced the frequency uncertainty space (from 10 kHz to several hundred Hz), the complexity (number of calculations) can be largely reduced. As an important part of the open-loop batch processing technique, the navigation bit boundary estimation method is discussed, as well.
METHODOLOGY This section briefly reviews GNSS receiver methodology as it pertains to this paper. Receiver Structure
The incoming I/Q signal from the front-end can be expressed as
r (t ) = h(t )c(t − τ ) exp j 2π ( f IF + f d ) t + n(t )
(1)
where h(t ) is the amplitude of the received signal (including navigation data bits), c(t − τ ) stands for the delayed version of the GPS ranging code with τ 2 of 10
representing the time delay, f d is the Doppler frequency, and n(t ) is the combination of noise and interference. Note that for the simplicity of representation, only one channel of GPS signal is shown, that is, the GPS signal from other satellites are all absorbed by the noise term n(t ) . In normal conditions, as the power level of the target GPS signal is roughly at the same level as those from other satellites, this assumption is valid. However, if there are signals from other satellites with much higher received power (e.g., ~15 dB or more) than the target GPS signal, their impact is no longer background noise, and hence has to be taken into account.
Front-End
with r[n] = r (t ) |t = nTs and si , j [n] = si , j (t ) |t = nTs with
Ts
being the sampling time. Note that when the uncertainty (or search) range is large, equation (4) is implemented using a parallel code phase search technique, namely the circular convolution method (Tsui 2005). After all the correlator outputs Ri , j are calculated, the maximum value is found, and the code phase and carrier Doppler are then estimated. In collaborative signal tracking case, the reference carrier Doppler frequency can be sent from a nearby receiver, which is then used to narrow the frequency uncertainty space. The benefit of this approach is mainly the complexity reduction, wherein the typical 10 kHz of frequency uncertainty could be reduced to several hundred Hertz.
Code phase estimate
Correlators
Carrier Doppler estimate
Local Signal (NCO)
Bit synchronization
Finally, it is noted that although this paper only looks at the interaction between two receivers, the approach is scalable to more receivers. However, in this case, the approach adopted herein would have to be updated to accommodate multiple inputs. This will be investigated in a future paper. Bit Boundary Estimation
Time & Frequency Uncertainty
Figure 1: General structure of the receiver used in this paper The local replica signal can be expressed by
si , j (t ) = c(t − τ i ) exp − j 2π ( f IF + f d , j ) t
(2)
where the subscripts i and j stand for the index of the code phase bin and the carrier Doppler bin, respectively. The correlators are used to calculate the correlation of the incoming signal and the local replicas, as per T
Ri , j =
∫ r (t )s
i, j
(t )dt
To achieve bit synchronization in this type of situation, a sliding window with 20 ms width is used, where each time the sliding window is shifted by 1 ms (i.e., one C/A code period). By comparing the correlator’s output with an output pattern, the bit boundary can then be determined.
(3)
t =0
Equation (3) is the analytical expression. In the receiver, as both the incoming signal and local replicas are digitized, a more realistic expression is N
Ri , j = ∑ r[n]si , j [n]
To achieve higher sensitivity, the integration time in a GPS receiver has to be increased such that the signal to noise ratio (SNR) is sufficiently large for signal tracking even if the carrier to noise power ratio is low. In a weak signal environment, the required integration time is normally longer than the bit duration. In this case, the bit boundary should be estimated in order to maximize the SNR. In this study, 20 ms of coherent integration time is used followed by several (selectable) non-coherent integrations.
(4)
n =1
ION ITM 2011, Session C4, San Diego, CA, 24-26 January 2011
The schematic illustration of the bit boundary estimation method is shown Figure 2. For a given random bit sequence with 200 ms duration (top subplot), the correlator output (amplitude) for different shifts of the sliding window is as shown in the bottom subplot. It can be observed that when the input sequence within the sliding window has the same sign, the correlator output has its maximum output. This can be used to determine the start of the new bit. Note that in Figure 2, the assumptions made are that the carrier frequency is perfectly known and there is no noise or interference in 3 of 10
the incoming signal. In reality, this will never happen, and hence the correlator output will never reach zero.
7
3
x 10
2.8
2.6
Correlator Output
Figure 3 shows a real correlator’s output with an open-sky reception condition. It can be observed that as the bit transition happens, the correlators’ output matches well with the simulated result in Figure 2. The amplitude starts to decrease as the bit transition first appears in the sliding window, and the peak appears as the transition (bit boundary) is passed; the period between two peaks is 20 ms, as should be expected.
20 ms
2.4
2.2
2
1.8
With this method, the exact start time of a CDMA code is not required, although a more accurate estimation of the code start will give a sharper peak of the correlator output. Considering the open-loop receiver structure, and the long integration time (200 ms to 1 s in this study), the performance gain achieved by a more accurate code start is marginal. Note that the method reported in Soloviev (2009), which was developed for possible bit sign combinations in a multi-bit coherent integration case, could be used for bit boundary estimation, as well. The accuracy of the detected bit boundary will be the same as that of the sliding window. 2
Sliding Window
Bit Sign
1 0 -1
Correlator Output
-2
0
20
40
60
80
120 100 time (ms)
140
160
180
200
0
20
40
60
80
120 100 time (ms)
140
160
180
200
20
10
1.6
0
10
20
30
60
70
80
90
Figure 3: Correlator output with 20 ms of sliding window for PRN 02 Frequency Resampling (Interpolation) The GPS receiver structure adopted in this study uses an open-loop batch processing technique, where the code phase and carrier Doppler are estimated mainly by searching the time and frequency uncertainty space. In this case, only limited samples in both frequency and time domain are obtained. In other words, the estimated code phase and carrier Doppler by this technique have limited resolutions. To increase the resolution, other techniques have to be used. For code phase, a DLL-like technique can be used by taking advantage of the triangle shape of the autocorrelation output of the CDMA code, which is not going to be discussed in this paper. Assuming that the code phase is accurately estimated, the frequency offset causes the correlator’s output to follow approximately the Sinc function, which can be written as (Borio and O’Driscoll 2009)
0
Figure 2: Schematic illustration of bit boundary estimation using a sliding window
50 40 time (ms)
R(δ f ) ∝
sin(πδ f NTs )
πδ f Ts
(5)
where δ f is the offset between the local and incoming carrier frequencies, NTs is the coherent integration time, and Ts is the sampling period. Realizing this fact, a frequency domain interpolation scheme can be used to estimate the carrier Doppler with a higher resolution. The upsampling method introduced in Tan (2008) is used for this purpose. An example of the frequency interpolation is shown in Figure 4, where the original frequency resolution is 10 Hz and 10 times of re-sampling is used, resulting in a refined frequency resolution of 1 Hz.
ION ITM 2011, Session C4, San Diego, CA, 24-26 January 2011
4 of 10
12
14
x 10
Original output Resampled output
12
Correlator Output
10
8
6
Note that as the antennas passes near the trees (Figure 5), the trajectory obtained by a traditional software receiver (the GSNRx™ software receiver; details below) is no longer continuous since the signal is greatly attenuated by the dense tree leaves, which will be shown below.
4
2
0 420,940
side by side, as shown in Figure 6. In the test, the raw complex IF GPS data is collected using a National Instruments front-end with a sampling rate of 5 MHz and an intermediate frequency of 420 kHz. Only the GPS L1 C/A signal is collected. When collecting the data, the signals from the two antennas are not synchronized, and each receiver has its own on-board clock.
420,980
421,020 421,060 Frequency (Hz)
421,100
Figure 4: An example of frequency re-sampling (interpolation) of the correlator’s output Note that to have an accurate re-sampled output, at least the main lobe of the Sinc function has to be included in the frequency search range, that is, δ f NTs > 2 . For 20 ms
The post-processing of the raw GPS signal was mainly conducted using the GSNRx™ software receiver developed in the PLAN group at the of University of Calgary (O’Driscoll et al 2009, Petovello et al 2008), modified to include the changed described above.
of coherent integration time ( NTs = 0.02 ), the search range shall be at least 100 Hz. Aiding Strategy The core concept of the proposed collaborative signal tracking scheme is to provide Doppler aiding from nearby receivers. As each receiver has its own onboard clock, the clock drift difference among receivers has to be taken into account. In this study, the clock drift difference is assumed to be within 100 Hz. Therefore, in the data analysis part, as the Doppler aiding is provided to the target receiver, ± 100 Hz uncertainty is allowed. Normally, once the clock drifts between the receivers is computed, the uncertainty level could be reduced. However, in this work, it remains unchanged in order to account for different dynamics of the two receivers.
Figure 5: Trajectory of the data collection (extracted from Google Map), where “S” and “E” are the start and end of the data collection, respectively
Realizing that in two successive epochs (e.g. in 2 seconds), the receiver’s position does not change much and so a between epoch code phase aiding method is used for time-domain uncertainty reduction. That is, the code phase estimation from previous epoch is used as the code phase search center in the current epoch. The uncertainty space is ± 1 chip (or 300 m in space). TEST DESCRIPTION To test the proposed approach, GPS data was collected on the campus of the University of Calgary in a kinematic condition. The environment for data collection is shown in Figure 5, where the building shown is the CCIT building. The trajectory is shown by the green line. Two antennas were used for this test and they were mounted ION ITM 2011, Session C4, San Diego, CA, 24-26 January 2011
Figure 6: GPS antennas used for data collection (this picture was not taken at the time of data collection; however the configuration is the same)
5 of 10
DATA ANALYSIS 2000 Open-loop with Int. time = 1 s Closed-loop Int. time 0.02 s 1500
Carrier Doppler (Hz)
In this section, the collaborative GPS signal tracking results are presented and compared with those obtained by a standard receiver (i.e., a receiver based on a closed-loop structure). The performance of the open-loop batch processing-based receiver with different configurations is present, as well. The performance is mainly accessed by the accuracy of the carrier Doppler estimation. An inherent problem from the open-loop processing technique, namely near band interference is also discussed.
In Figure 7, two carrier Doppler estimations are shown, one from the standard receiver with a closed-loop structure and another from the receiver based on an openloop batch processing technique. Note that in this plot, the comparison is not fair as the integration time for the two cases is not the same. However, the intention is to show that as the signal quality drops due to multipath and signal attenuation (caused by the dense tree leaves), a traditional receiver based on a closed-loop structure can no longer track the signal, as the coherent integration time of such receiver is limited the bit duration (i.e. 20 ms) and hence the signal to noise ratio cannot be sufficiently increased by increasing the integration time. On the other hand, the open-loop structure based receiver can easily increase the integration time (mainly the number of the non-coherent integration) to ensure a sufficient signal to noise ratio. It is noted that non-coherent integration in the closed-loop case is also possible and would improve signal tracking. However, this approach would still suffer from having a limited view of the signal space since typically only three correlators spaced in the time domain would be used.
500
0
Carrier Doppler Estimation: Closed vs. Open-Loop In this subsection, the carrier Doppler estimation using a standard receiver and an open loop approach are shown. Note that the collaborative aspect whereby one receiver aids another is not shown here. Rather, the focus is on demonstrating that the open loop approach is working properly.
1000
-500
0
50
100
150
250 200 time (s)
300
350
450
400
Figure 7: carrier Doppler comparison between openloop receiver and closed-loop receiver Carrier Doppler Estimation: Different Integration Times
Open-Loop
with
In this subsection, the carrier Doppler estimation from the open-loop receiver is presented. Different integration times are examined, as shown in Figure 8. As expected, the longer the integration time the better the estimation performance. As the reception condition starts from an open-sky case, at the start of the data set (0-50 s), all three curves show good quality of carrier Doppler estimation. As the signal quality gets worse, it is observed that results with the shortest integration time degrade first. The results obtained from 1 s of integration have no visible penalty due to the signal quality change. Of interest is that for the 0.1 s and 0.2 s integration cases, if the frequency estimate is grossly wrong, with an error typically around 200 Hz. Upon further examination, this is due to a strong signal from another satellite which ultimately acts as an interferer. This will be discussed in more detail in the next subsection. 1100 1 s Int. Time 0.1 s Int. Time 0.2 s Int. Time
1000
Doppler (Hz)
900
800
700
600
500
0
50
100
150
200 250 Time (s)
300
350
400
450
Figure 8: open-loop carrier Doppler estimation with different integration time (coherent integration time = 20 ms) ION ITM 2011, Session C4, San Diego, CA, 24-26 January 2011
6 of 10
Carrier Doppler Estimation: Open-Loop with Carrier Doppler Aiding from Another Antenna
search range in time domain, as well as in the frequency domain.
The key concept of collaborative signal tracking is to use the provided aiding information (carrier Doppler) from a nearby GPS receiver. This information is then used to limit the frequency search range of the target receiver. However, as different receivers have different clock drifts, when using this information the clock drift at each receiver has to be taken into account when determining the frequency search range. Assuming that the target receiver has at least one high-quality signal from a satellite, the simplest way to compensate the different clock drifts is to difference the carrier Doppler from the aiding receiver from the locally estimated carrier Doppler. This difference can then be used to compensate the clock drift for other satellites. It is noted that this is still an approximation since user motion will introduce additional Doppler differences. However, for the data investigated here, this is a reasonable approach since the two receivers are fixed relative to each other and so their relative velocities are nearly zero. The case where the receivers are moving in different directions will be the topic of another paper.
As stated previously, the parallel code phase search technique is used in the software receiver used in this work and hence correlator outputs at all possible time samples are available. As such, the receiver was modified to only search the code phase bins within ±1 chips of the previous epoch. In other words, instead of a global maximum search across all code phases, a local maximum search is performed in case of code phase aiding.
Doppler estimation with/without aiding for PRN2: 200 ms Integration time 1800 With Doppler Aiding from Ant 2 No aiding 1600
1800 Code Phase + Doppler Aiding Doppler Aiding Only
1600
1400 Estimated Doppler (Hz)
Figure 9 shows the Doppler estimation with and without carrier Doppler aiding when using 200 ms of integration. As can be observed, with Doppler aiding the carrier Doppler is more accurate. However, due to the low signal quality and the relatively short integration time, there are still errors. Nevertheless, compared to the case without aiding, the reception quality has noticeable improvements.
Figure 10 shows the results where in one case only Doppler aiding from nearby antenna is used, and in the other case both Doppler aiding from the other receiver and code phase aiding from previous epoch are used. For the convenience of analysis, the associated code phase estimation of these two cases is shown in Figure 11. By comparing Figure 10 and Figure 11, one can conclude that the code phase aiding can be used to improve the reception performance (i.e., reduce the Doppler estimation error) as long as it is accurate. However, if the code phase reference is incorrect, it will cause a large error on carrier Doppler estimation. This is seen starting around time 320 s, at which point the code phase of the signals starts to drift from the true value.
Code Phase starts to drift 1200
1000
800
1400
Estimated Doppler (Hz)
600
1200 400 X: 160 Y: 930
1000
200
800
0
50
100
150
200 250 Relative Time (s)
300
350
400
450
Figure 10: Carrier Doppler estimation with two different aiding schemes (200 ms of integration)
600
400
200
0
50
100
150 200 Relative Time (s)
250
300
Figure 9: Doppler estimation with and without Doppler aiding from a nearby antenna In the test case, the GPS antennas’ speed is not high. Therefore, the code phases from two consecutive epochs are expected to be similar. This fact is used to limit the ION ITM 2011, Session C4, San Diego, CA, 24-26 January 2011
7 of 10
suggests that the error may due to the interference from PRN 16.
1200 Code Phase + Doppler Aiding Doppler Aiding Only
Code Phase (chips)
1000
800
Code Phase Starts to drift 600
400
200
0
0
50
100
150
200 250 300 Relative Time (s)
350
400
450
Figure 11: Code phase estimation with two different aiding schemes (200 ms of integration) Impact of Strong Near Band Interference In the previous subsections, the results have shown a systematic error in almost all the cases wherein an obvious frequency error of approximately 200 Hz was observed. In this section, it will be shown that this is due to a strong interference from another satellite. First, we show that the carrier Doppler from that satellite is the same as the wrongly detected carrier Doppler. Doppler estimation with/without aiding for PRN2: 200 ms Integration time 1800 Code Phase + Doppler Aiding Doppler Aiding Only Carrier Doppler from PRN 16
1600
Estimated Doppler (Hz)
1400
1200
Next the relative power levels from these two satellites are shown. In Figure 13 the power difference between PRN 02 and PRN 16 is shown. It can be observed that most of the time the signal from PRN 16 is at least 10 dB stronger than PRN 02. Relating Figure 12 to Figure 13, it is observed that when PRN16 is around 16 dB stronger than PRN02, there will be a wrong carrier Doppler estimation for PRN02. The theoretical analysis for this could be found in Jovancevic et al (2007), that is, the interference’s power shall be 15.6 dB lower than the desired signal to have a correct detection. Note that the relative power shown in Figure 13 is obtained by comparing the correlator amplitude obtained with integration time of 1 s (20 ms of coherent integration and 50 non-coherent integrations) for the two satellites. Inaccuracy may exist as the carrier Doppler in 1 second may change. The limited frequency and time resolution may contribute to the inaccuracy as well. The estimated carrier to noise density (C/N0) of PRN02 is shown in Figure 14. In producing this plot, one second of integration time is used. The correlator output for PRN 16 (the satellite in good reception condition) and PRN 02 are both generated and their power difference is calculated. C/N0 of PRN 16 is estimated by the GSNRxTM software receiver. Based on the relative power, C/N0 of PRN 02 in the first second is then estimated. The rest of the C/N0 in the data set is calculated based on the relative power to that in the first second (as determined by the amplitude of the correlator outputs). In Figure 14 the lowest C/N0 is about 18.2 dB-Hz, where the open-loop receiver with one second of integration time still tracks. This indicates that the sensitivity of the receiver is at least 18.2 dB-Hz.
1000
800
600
400
200
0
50
100
150
200 250 300 Relative Time (s)
350
400
450
Figure 12: Estimated Doppler with difference collaborative schemes, and carrier Doppler from an interference satellite. Figure 12 is the same as Figure 10 with an additional plot of the carrier Doppler estimation from an interfering satellite (PRN 16). It is shown that the carrier Doppler from PRN 16 is exactly located at the frequency where the systematic error happens for PRN 2. This result
ION ITM 2011, Session C4, San Diego, CA, 24-26 January 2011
To further understand the impact of the self-interference (cross correlation from another satellite), the correlator’s output from two epochs are shown in Figure 15 and Figure 16. Figure 15 shows the case where the cross correlation is visible, however as the cross correlation is weaker than the auto correlation of PRN 02, it has very little (if any) impact on the code phase and carrier Doppler estimation results. Figure 15, on the other hand, shows that the cross correlations are stronger. In this case, even if an accurate Doppler aiding is applied, as the ±100 Hz frequency uncertainty is allowed, it is likely to have a wrong code phase and carrier Doppler estimation. Note that Figure 15 provides a partial explanation of why the code phase drifted in Figure 11.
8 of 10
24
Relative power ratio: PRN16/PRN02 (dB)
22 20 18 16 14 12 10 8 6
0
50
100
150
200 250 time (s)
300
350
400
450
Figure 13: Power difference between PRN16 and PRN02. 36
Figure 16: Correlator’s output in case where the cross correlation (PRN02 and PRN 16) is stronger power than the desired signal (PRN02).
34
CONCLUSIONS AND FUTURE WORK
32
0
C/N (dB.Hz)
30 28 26 24 22 20 18
0
50
100
150
200 250 Time (s)
300
350
400
450
Figure 14: Carrier-to-noise power density of PRN02.
In this paper, collaborative signal tracking using an openloop structure is presented. It shows that in the weak signal environment, the receiver sensitivity can be improved by increasing the integration time, while the carrier Doppler aiding can be easily used incorporated with the open-loop structure. The accuracy of the aiding information is not stringent, as well. The paper also shows that a near band interference is harmful for a stand-alone open-loop receiver. By using the carrier Doppler reference from nearby receiver, this impact can be reduced. Future work will focus on the methods of further reducing the impact of the cross-correlation effects. Other data sets have also been collected and will be analysed in order to better characterize the overall performance of the proposed approach. ACKNOWLEDGMENTS Alberta Ingenuity, now Alberta Innovates – Technology Futures, is acknowledged for having supported this research. REFERENCES
Figure 15: Correlator’s output in case where the cross correlation (PRN02 and PRN16) is visible but weaker than the desired signal (PRN02).
ION ITM 2011, Session C4, San Diego, CA, 24-26 January 2011
Babu, R., Jinling Wang and G. Rao (2008) Analysis of ultra-tight GPS/INS integrated system for navigation performance, IEEE International Conference on Signal Processing, Communications and Networking, Chenmai, India, Jan. 2008, pp.234-237.
9 of 10
Borio, D. and C. O’Driscoll (2009) GNSS Receiver design, ENGO 638 lecture notes, Department of Geomatics Engineering, University of Calgary. Brown, A. and N. Gerein (2001) Test Results of a Digital Beamforming GPS Receiver in a Jamming Environment, Proceedings of ION GPS 2001, Salt Lake City, Utah, September 2001. Cox, D. B. (1980) Integration of GPS with Inertial Navigation Systems, reprinted in Collected GPS papers, Institute of Navigation; Alexandria, VA, 1980, pp. 144153.
Tan, L. (2008) Multirate DSP, Part 1: Upsampling and Downsampling, http://www.eetimes.com/design/signalprocessing-dsp/4017637/Multirate-DSP-part-1Upsampling-and-downsampling. Tsui, J. Bao-Yen (2005) Fundamentals of Global Positioning System Receivers: A Software Approach, 2nd Edition, John Wiley & Sons, Inc. Van Graas, F., A. Soloviev, M. U. de Haag, and S. Gunawardena (2009), Closed-Loop Sequential Signal Processing and Open-Loop Batch Processing Approaches for GNSS Receiver Design, IEEE Journal of Selected Topics in Signal Processing, Vol. 3, No. 4.
Jovancevic, A., N. Bhatia, J. Noronha, B. Sirpatil, M. Kirchner, and D. Saxena (2007) Piercing the Veil, GPS World, http://www.gpsworld.com/defense/navigation/piercingveil-3155 Luo, P. and M.G. Petovello (2010) Collaborative Acquisition of Weak GPS Signals, Proceedings of IEEE/ION PLANS 2010, Indian Wells (Palm Springs), California. O’Driscoll, C., D. Borio, M. Petovello, T. Williams and G. Lachapelle (2009) The Soft Approach: A Recipe for a Multi-System, Multi-Frequency GNSS Receiver, Inside GNSS Magazine, Volume 4, Number 5, pp. 46-51. Petovello, M.G., C. O'Driscoll and G. Lachapelle (2007) Ultra-Tight GPS/INS for Carrier Phase Positioning in Weak Signal Environment, NATO RTO SET-104 Symposium on Military Capabilities Enabled by Advances in Navigation Sensors, Antalya, Turkey. Petovello, M.G., C. O’Driscoll, G. Lachapelle, D. Borio and H. Murtaza (2008) Architecture and Benefits of an Advanced GNSS Software Receiver, Positioning, 1, 1, pp. 66-78. Petovello, M.G., G. Lachapelle and M.E. Cannon (2005) Using GPS and GPS/INS Systems to Assess Relative Antenna Motion Onboard an Aircraft Carrier for Shipboard Relative GPS, CD-ROM Proceedings of NTM 2005, San Diego, 24-26 January, The Institute of Navigation. RTO-AG-160-V21 (2009) Differential Global Positioning System (DGPS) for Flight Testing, Chapter 1, http://www.rta.nato.int/pubs/rdp.asp?RDP=RTO-AG-160V21 Soloviev, A., F. Van Graas, S. Gunawardena (2009) Decoding Navigation Data Messages from Weak GPS Signals, IEEE Transactions on Aerospace and Electronic Systems, Vol. 45, No. 2 April 2009. ION ITM 2011, Session C4, San Diego, CA, 24-26 January 2011
10 of 10
