Daniele Borio European Commission, Joint Research Centre (JRC), Melania Susi Topcon Positioning Systems Inc.

Several Global Navigation Satellite System (GNSS) receivers now support at least two frequencies. This includes the availability of dual-frequency measurements from smartphones capable of processing both L1 and L5 frequencies. Effective signal processing from different frequencies is still an active research field with implications both at the transmitter and receiver sides. The second-generation Galileo signals may include a new component into the L1/E1 frequency band, denoted as E1D. While E1D should be shifted at a Radio Frequency (RF) different from the L1 center frequency, its selection will also depend on a receiver’s ability to fully exploit the benefits of signals from different frequencies.

A promising approach to simultaneously deal with signals from different frequencies is based on the so-called meta-signal concept [1] where components from different frequencies are treated as a single entity characterized by common parameters. Recent work from the authors [2] shows that components from two different RFs can be effectively represented using bicomplex numbers. Such representation, which is briefly reviewed in the article, allows the isolation of the three components: a code, a carrier and a subcarrier term. These components can be effectively tracked using a triple-loop architecture, which can benefit from the introduction of a Kalman Filter (KF) exploiting the fact that related dynamics are experienced by the code, carrier and subcarrier components. Moreover, a KF can significantly improve receiver performance under dynamic conditions. This is mainly due to the dynamic model embedded in the KF.

This article, which is based on a recent work of the authors [3], describes the KF tracking architecture developed for GNSS meta-signals using bicomplex numbers. Tests performed under dynamic conditions show the benefits of this type of approach.

Bicomplex Signal Representation

In previous work from the authors [2], it was shown that two GNSS signals modulated into two different RFs can be effectively expressed as the real part of the product of three terms: a code component, a complex carrier and a subcarrier term:

In Equation 1, x(t) and y(t) are the RF signals, which form the sideband components of u(t), the final GNSS meta-signal. f₀ and f_sub are the center and subcarrier frequencies of u(t) and are obtained as the average and semi-difference of the RFs of the two sideband components, respectively.

Representations (Equation 1) is possible only using bicomplex numbers, which are a four-dimensional extension of complex numbers characterized by two imaginary units, i and j, which square to -1, and a hyperbolic unit, k, which squares to 1 [4]. u_bbb(t) is the bicomplex baseband representation of u(t), which is obtained by combining the (complex) baseband representations of x(t) and y(t). Additional details on the bicomplex representation of a GNSS meta-signal can be found in [2].

Signal representation (Equation 1) has fundamental implications for processing a GNSS meta-signal. Indeed, it implies the three components in product (Equation 1) can be processed using three independent tracking loops: a Delay Lock Loop (DLL), a Phase Lock Loop (PLL) and a Subcarrier Phase Lock Loop (SPLL). Each loop tracks one of the three factors isolated in the product in Equation 1. This is a direct extension of standard receiver processing where an additional loop, used to track the subcarrier component, is introduced. The SPLL aligns in phase the power received from the two sideband components leading to a form of coherent signal combining.

In the previous work from the authors [2], the triple-loop tracking architecture was implemented and tested using Galileo AltBOC signals collected with a Software Defined Radio (SDR) front-end. The three loops featured dedicated discriminators operating on the bicomplex correlators obtained by jointly processing the input samples from x(t)and y(t), which were used to reconstruct u_bbb(t). Each loop operated independently using separate loop filters. While the advantages with respect to separate sideband processing were clearly demonstrated, this type of architecture does not exploit the relationship between the different Doppler frequencies estimated by the three loops. Moreover, performance can be further improved by assuming a dynamic model describing the time evolution of the different system parameters. For this reason, a KF tracking loop is developed and analyzed.

Triple-Loop Kalman Filter Tracking

A schematic representation of the triple-loop architecture obtained using bicomplex numbers and a single KF is provided in Figure 1. The input samples, z[n], are a baseband bicomplex representation of the digital signals obtained from the sideband components, x(t) and y(t). In particular,

where y_bb[n] and x_bb[n] are the complex baseband samples obtained from x(t) and y(t) and e₁ and e₂ are defined as

In the previous equation, k is the hyperbolic bicomple unit. e₁ and e₂ are orthogonal and idempotent and their properties are useful to reduce the complexity of bicomplex number operations. Note that y_bb[n] and x_bb[n] are affected by residual delays and Doppler frequencies, which are estimated by the three loops depicted in Figure 1. z[n] is correlated with local replicas of the incoming signal codes and carrier and subcarrier components. In this way, three bicomplex correlators are obtained: the early, prompt and late correlators. They are processed by the code, carrier and subcarrier discriminators that provide as output noisy estimates of the residual code, carrier and subcarrier errors. Unlike previous work, where three independent loop filters were used, a single KF is adopted in this case to provide the Doppler estimates used to drive local code, carrier and subcarrier generation.

The KF implemented features a five-dimensional state vector:

where h is the time index and Δτ, Δφ_sub and Δφ are the code delay, subcarrier and carrier errors, respectively. Common Doppler frequency and acceleration errors, Δf and Δa, are also considered. Equation 4 is a direct generalization of the state vectors used in KF tracking loops operating on a single signal. In this case, an additional state, Δφ_sub, has been included in the KF state vector. 

The state vector is propagated in time using the following dynamic model

where A is the state transition matrix defined as

where β_code is the ratio between the code and carrier nominal frequencies. β_sub is the ratio between the subcarrier and carrier nominal frequencies and T_c is the coherent integration time and update rate of the loop.

w_h is a noise vector modeled as white and Gaussian. The covariance matrix of w_h depends on several factors including the signal line-of-sight acceleration, code-carrier and subcarrier-carrier divergences and the properties of the local oscillator of the front-end used to down-convert and digitize the input signal x(t) and y(t). Details on the construction of the covariance matrix associated to w_h can be found in [3]. 

The predictions made by the KF using Equation 5 are corrected using the three discriminator outputs that are grouped into the observation vector:

where D_code, D_sub and D_car are the code, subcarrier and carrier discriminator outputs. Also, in this case h denotes the time index.

The observation vector is related to the state vector by the following observation model:

with

In Equation 8, v_h is the observation noise vector: it is assumed zero mean and Gaussian with independent components. The covariance matrix of v_his determined by the variances of the discriminator outputs, which can be found in [3].

Experimental Setup

The KF triple-loop architecture has been implemented in a custom Python software receiver able to jointly process signals from two different frequencies.

Several tests were conducted to verify the effectiveness of the KF architecture developed. Both static and dynamic conditions were considered. The same datasets authors analyzed in previous work are considered for the static tests. Specific focus is given to the AltBOC modulation, which was collected using a wide-band SDR front-end configured according to the parameters reported in the upper part of Table 1.

The effectiveness of meta-signal KF filtering under dynamic conditions was studied through dedicated data collections performed using a low-cost SDR front-end mounted inside a car. Views of the experimental setup adopted for these tests are shown in Figure 2. The left part of the figure shows the interior of the car with the SDR platform, and a mass-market receiver adopted to collect reference data. Both devices were connected to a laptop and to a patch antenna mounted on the roof of the car. The right part of the figure provides a view of the place selected for the experiment: a long road in an industrial zone close to Turin, Italy. The driver performed several loops along this road reaching speeds around 50 km/hour. Buildings on both sides of the road introduced multipath and other propagation effects. 

The dynamic tests focused on the BeiDou B1 meta-signal obtained by combining the BeiDou B1I and B1C components. These components have different spectral characteristics and are received with different power levels. In this respect, the BeiDou B1 combination is one the most general forms of GNSS meta-signals without any specific structure or symmetry. The parameters adopted for configuring the low-cost SDR front-end used for tests are reported in the bottom part of Table 1. A center frequency of 1,568 MHz was selected as it is also at the middle of the center frequencies of the B1I and BIC components, which are 14.322 MHz spaced apart. It is noted that this frequency is the nominal value used to configure the SDR platform. It is well-known that in such low-cost devices a slightly different frequency is actually used for the signal down-conversion [5]. Without proper compensation, the difference between the nominal value and the actual center frequency adopted by the device will lead to a residual Intermediate Frequency (IF), which, in turn, can prevent proper KF tracking loop operations. For this reason, the residual IF was estimated and taken into account in the actual implementation of the KF tracking loop.

Experimental Results

Results obtained for the static dataset with AltBOC signals are considered at first. Figure 3 provides a comparison between the Doppler estimates obtained using triple-loop architectures with standard loop filters and with the KF approach. The two cases are considered in the two parts of the figure. In each part, the code, subcarrier and carrier Doppler estimates are provided, and each component is 
normalized by its nominal rate. The results obtained using separate loop filters are shown in the left part of the figure. A third order PLL with a 15 Hz bandwidth was considered along with a second order DLL and SPLL with 2 and 3 Hz bandwidths, respectively. An integration time of 5 ms is adopted after secondary code synchronization. Under static conditions, the standard triple-loop architecture is able to effectively track the different signal components, which overlap justifying the adoption of a KF with single Doppler frequency and acceleration states. KF tracking is analyzed in the right part of Figure 3. After an initial transient, where standards Frequency Lock Loop (FLL)/PLL are used to achieved frequency and phase lock conditions, KF operations are started. A single estimate for the three Doppler components is obtained as it clearly emerges from the right part of Figure 3. The case of signal from the satellite with Pseudo-Random Number (PRN) 13 is considered.

The use of joint Doppler states does not affect lock conditions as it clearly emerges from the analysis of the Carrier-to-Noise power spectral density ratio (C/N₀) provided in Figure 4. The C/N₀ has been estimated considering the ability of triple-loop architectures to align in phase the signals and correlators from the two sidebands. The C/N₀ is used here as a lock indicator showing the SPLL’s ability to effectively align in phase the two sideband prompt correlators. In this case, the two loop architectures achieve similar performance and practically identical C/N₀ values are found in the two cases. This is expected as the real advantages of a KF tracking loop are found under dynamic conditions. A static scenario has been considered mainly to preliminary check the proper functioning of the implemented KF tracking loop.

During the dynamic test, a total of 10 BeiDou satellites were visible. Three of them, the ones with PRN 11, 12 and 13, broadcast only the BI1 component and thus are not considered. The signals from satellite PRN 37 were very weak and received in a discontinuous way. While it was possible to acquire them, stable tracking was never achieved with any of the methods implemented. For this reason, only the remaining six signals are considered. The C/N₀, obtained for the different BeiDou B1 meta-signals, is depicted as a function of time in Figure 5. Satellites with PRN 34, 42 and 43 have high-elevations and are only marginally impacted by buildings. Periodic drops in the C/N₀ of the signal from satellite PRN 43 are clearly visible and correspond to the maneuvers made by the car to invert the direction of motion and perform the loops. During these maneuvers, the vehicle approaches the buildings on the roadside and signal reception is further impaired. A periodic pattern, corresponding to the different loops performed by the vehicle, is also visible in the C/N₀ time series of the signal from PRN 42.

Signals from satellites with PRN 22, 23 and 25 are much weaker and significantly impacted by vehicle dynamics. Despite this fact, the proposed tracking architecture allows one to maintain the lock on the three meta-signals.

This is because of the combined use of bicomplex signal tracking, which allows recovery of all the available signal power, and KF, which allows one to cope with dynamics and continue tracking even when very low signal power is available. This is the case of the signal from PRN 23, which experiences severe drops in the C/N₀ values. Even if these drops last a few seconds, lock conditions are not lost and the KF successfully propagates the signal parameters allowing the recovery of C/N₀ values above 35 dB-Hz. When such medium-high C/N₀ are realized, valid code, carrier and subcarrier discriminator values are obtained and allow for effective KF measurement updates. The ability of the proposed KF meta-signal tracking architecture to maintain signal lock under challenging conditions is further studied in Figure 6, which shows the Doppler variations of the different BeiDou B1 meta-signals tracked during the dynamic test. Doppler variations have been obtained by removing the median value from each Doppler frequency profile estimated during the experiment. Doppler variations have been considered only to improve Figure 6’s clarity and highlight the periodic patterns generated by the loops the vehicle performed. Indeed, the Doppler frequencies estimated by the KF for each signal assume very different values and, without removing the median values, would have hidden the variations due to the vehicle motion. The fact lock on signal with PRN 23 was maintained during the full duration of the test clearly emerges from Figure 6. The corresponding Doppler variations are smooth and have the same period of those obtained for the other signals.

It was not possible to obtain similar results using the triple-loop architecture with separate loop filters. Even if different loop bandwidth and coherent integration time combinations were tested, it was not possible to achieve continuous tracking for the signals with PRN 22, 23 and 25 and in all cases, an early loss of lock occurred. This is highlighted in Figure 7, where the case of a signal with PRN 22 is considered.

A 25 Hz bandwidth with a 1 ms coherent integration was adopted to improve the dynamic loop response. Despite this fact, loss of lock occurs after about 17 seconds from the start of the experiment: the C/N₀ assumes low values and the estimated Doppler frequencies (not displayed in this article) diverges. As already mentioned, several bandwidth/coherent integration time combinations were tested, always achieving results similar to those shown in Figure 7. KF tracking, on the contrary, can maintain lock on the signal even if a coherent integration time equal to 10 ms was adopted. These results show the real advantages of triple-loop KF tracking.

Conclusions

In this work, the performance of a triple-loop architecture, designed using the bicomplex number paradigm, has been further improved by introducing a KF, which exploits a state transition model to track dynamics and jointly process the code, carrier and subcarrier components resulting from the bicomplex representation. While bicomplex numbers are effective for jointly representing and processing signals from different frequencies, the KF fully exploits the fact that related dynamics are experienced by the different signal components.

The proposed architecture has been implemented and tested using real Galileo AltBOC and BeiDou B1I/B1C meta-signals, under both static and dynamic conditions. The data collected have been processed using a custom Python software receiver implementing KF tracking. The analysis clearly shows the advantages of KF tracking for processing GNSS meta-signals. This fact is particularly evident from the tests conducted under dynamic conditions: the KF allows one to continuously track weak GNSS signals received from a moving vehicle. These results are not achievable using standard loops, which require large bandwidths and short integration times to cope with high dynamic conditions.

Manufacturers

The wideband front-end adopted for the AltBOC data collection is a Universal Software Radio Peripheral (USRP)-2944R from National Instruments. The front-end adopted for the dynamic tests with the BeiDou B1 signals is a HackRF One from Great Scott Gadgets. The mass-market receiver used as reference is a Ublox F9R.

References 

(1) Issler J.-L., Paonni M., and Eissfeller B. (2010), “Toward Centimetric Positioning Thanks to L- and S-band GNSS and to meta-GNSS Signals”. Proc. of the ESA Workshop on Satellite Navigation Technologies and European Workshop on GNSS Signals and Signal Processing (NAVITEC), Noordwijk, Netherlands.

(2) Borio D. (2022), “Adopting Bicomplex Numbers for GNSS Meta-Signal Processing”. Inside GNSS, November/December, Vol. 17, No. 6, pp. 48-53.

(3) Borio D., Susi M. (2023), “Bicomplex Kalman Filter Tracking for GNSS Meta-Signals”. Proc. of the ION International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+), Denver, CO.

(4) Alpay D., Luna-Elizarrarás M. E., Shapiro M., and Struppa D. C. (2014). “Basics of Functional Analysis with Bicomplex Scalars, and Bicomplex Schur Analysis.” Springer Briefs in Mathematics. Springer, Cham, Switzerland AG.

(5) O’Driscoll C. and Curran J. T. (2018). “Carrier Phase Tracking Considerations for Commodity SDR Hardware.” Proc. of the International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+), Miami, Florida (FL)

Authors

Daniele Borio received an M.S. degree in communications engineering from Politecnico di Torino, Italy, and an M.S. degree in electronics engineering from ENSERG/INPG de Grenoble, France, in 2004. He received a doctoral degree in electrical engineering from Politecnico di Torino in April 2008. From January 2008 to September 2010, he was a senior research associate in the PLAN group of the University of Calgary, Canada. Since October 2010, he has been with the European Commission Joint Research Centre (JRC). He is currently a scientific technical officer in the JRC Food Security Unit where he supports the European Common Agricultural Policy (CAP) through the European satellite programs, Galileo and Copernicus.

Melania Susi received her B.E. in Mathematical Engineering from the Università TorVergata di Roma, Italy, and M.Sc.s in Telecommunication Engineering and Geomatic Engineering, from the Università of L’Aquila, Italy, and from the University of Calgary, Canada. She holds a Ph.D. in Engineering Surveying and Space Geodesy from the University of Nottingham, UK, where she was also a Marie Curie fellow. After being a scientific technical officer at the Joint Research Centre (JRC) of the European Commission, she is now a GNSS senior researcher at Topcon in Concordia, Italy.

The post Coping with Dynamics Using Bicomplex Numbers and Kalman Filter Tracking appeared first on Inside GNSS - Global Navigation Satellite Systems Engineering, Policy, and Design.

With the rethinking of the Galileo Commercial Service (CS), the E6B signal will disseminate Precise Point Positioning (PPP) corrections whereas the E6C component will be encrypted for authentication purposes. Different processing options for the E6 signals are investigated and it is shown that the sensitivity gap between data and pilot processing can be bridged by introducing non-coherent integrations and inter-frequency aiding. Extended integrations mitigate the impact of noise while inter-frequency aiding reduces the dynamics perceived by the E6B tracking loop.

After the rethinking of its Commercial Service (CS), Galileo will offer High Accuracy (HA) corrections that will be disseminated through the E6B signal. As stated in Commission Decision (EU) 2018/321 and discussed in the article by P. Gutierrez listed in Additional Resources, it will be possible to achieve accuracies in the order of a few decimeters (approximately 20 centimeters) without the need for ground communication infrastructures or for base stations providing differential corrections. In this way, the user will be able to access measurements from a third frequency and enjoy the benefits of a signal with intermediate characteristics between the AltBOC and the Galileo E1 Open Service (OS) modulation. While the E6B signal, which is modulated by a 1 ksymbol/s navigation message, will provide Precise Point Positioning (PPP) corrections, the E6C component will be encrypted so to render the signal robust against spoofing attacks and will be used to provide an authentication service. In this way, it will not be possible to use the E6C signal as a pilot component for most users. Although the presence of a pilot component can provide increased receiver sensitivity (see for example the papers by Curran et Melgard 2016 and Göhler et al. 2016, Additional Resources), specific approaches exist to improve the performance of data-only processing. Moreover, Galileo satellites broadcast several pilot components in frequency bands different from the E6 one. These pilot components can be used to improve the processing performance of the E6B signal when the E6C component is unavailable. 

In this article, the authors investigate different processing options for the E6B signal and analyze different data-only tracking strategies, which take advantage of pilot components from different frequencies and operate in the presence of fast bit/symbol transitions.

The analysis is performed using a combination of Commercial Off-The-Shelf (COTS) and Software Defined Radio (SDR) receivers. In this respect, an E6B/C capable SDR receiver was developed to test different tracking schemes for the processing of the E6B signal, which was considered in standalone mode or in combination with the Galileo E1 pilot component. The results provided by a COTS receiver implementing E6C pilot processing were used as comparison term for the findings obtained using the SDR receiver.

For the analysis, three types of scenarios were considered: static open-sky conditions, a simulated test with progressively decreasing Carrier-to-Noise Power Density Ratio (C/N0) conditions and live dynamic experiments conducted in the presence of foliage and building blockage. The data collected under open-sky conditions were used to verify the proper functioning of the SDR receiver and to provide an initial comparison with the results obtained using the COTS receiver. The tests performed using a hardware simulator were conducted to determine the sensitivity limits of the different tracking approaches in the presence of noise alone. This type of test was also used to analyse the E6B demodulation performance and to determine the associated Bit Error Rate (BER). Finally, dynamic tests were used to analyze the receiver performance in a challenging, realistic environment.

While pure pilot processing is the most effective approach for reducing the impact of noise, the analysis shows that the sensitivity gap between data and pilot tracking can be effectively compensated by implementing high-sensitivity tracking approaches and by adopting inter-frequency aiding that reduces the dynamics perceived by the E6B tracking loop.

E6B Tracking Approaches

Different approaches exist for tracking the E6B signal and increasing the receiver sensitivity even in the presence of bit transitions. In particular, two problems need to be solved: 1) increase the integration time taking into account possible bit transitions and 2) reduce the signal dynamics perceived by the tracking loop. We have tackled these problems using extended integrations and inter-frequency channel aiding. A general scheme representing the tracking approach adopted in this paper is depicted in Figure 1 that shows a tracking loop implementing additional integrations after data symbol removal and implementing inter-frequency aiding. The figure only describes the Phase Lock Loop (PLL) that is considered as the weakest element of signal tracking. A similar processing scheme is adopted for the Delay Lock Loop (DLL) that also implements long integrations. The E6B signal, y_E6B[n], is at first multiplied by the E6B local code generated by the DLL. In the following, we will assume that analog GNSS signals have been filtered, amplified, down-converted and digitized by the receiver front-end. Thus, y_E6B[n], is the digital sequence obtained at the output of the receiver front-end sampled with a sampling frequency, f_s. The variable n, is the time index.

The E6B signal, y_E6B[n], is also multiplied by the local carrier generated by the PLL using previous estimates of the Doppler frequency and signal carrier phase. After code and carrier removal, the signal is integrated for 1 millisecond (ms), i.e. the duration of one E6B code period. In this way, the prompt correlator outputs, P_k, is obtained. Index k is used here to indicate the 1 ms epochs corresponding to each code period. The correlators, P_k, are modulated by the E6B navigation message and thus cannot be further integrated without removing at first the data symbols. In general, the removal of the navigation message is performed by multiplying the prompt correlator outputs by a quantity, S_k, proportional to the data symbols. In particular, an extended correlator output is obtained as:

We have considered two forms of extended integrations:

• non-coherent integrations (see the paper from Borio and Lachapelle,Additional Resources), where the effect of the data navigation message is removed through squaring, and 

• Decision Directed (DD) PLL (a description of the associated principle can be found in the classic book from Meyer and Ascheid on Synchronization): where the data symbols are estimated directly from the correlator outputs and removed to further extend the integration time.

In the non-coherent case,

whereas in the DD case,

i.e., S_k is the sign of the real part of the prompt correlator. The extended correlator, P^ext, is used to compute the PLL discriminator output that, after filtering, is used to drive the Numerically Controlled Oscillator (NCO) and generate a new replica of the signal carrier for the next processing epoch of the PLL. In this article, we considered standard Proportional-Integrate (PI) filters used for smoothing the PLL discriminator output. Other approaches, for example based on the Kalman Filter, can be used. 

The signal dynamics perceived by the PLL is reduced by injecting an estimate of the Doppler frequency at the output of the loop filter, indicated in Figure 1 by its transfer function, F(z). This estimate is obtained by scaling the Doppler frequency estimated from another signal transmitted by the same satellite. In this work, we considered the case where both E1 and E6 signals are processed at the same time. The Doppler frequency estimated from the E1C signal, which is a pilot component, is scaled by

Frequency aiding reduces the actual dynamics that the E6B tracking loop has to track. More specifically, when frequency aiding is implemented, the E6B PLL only needs to track the residual frequency difference between the E1 and the E6 signals. These frequency differences may be caused by ionospheric propagation and by residual effects due to different implementations in the E1/E6 transmission and reception chains. More details on the processing implemented for the E6B signal can be found in our paper presented at the 2018 ION GNSS+ conference (see again Borio and Susi 2018, Additional Resources).

In addition to the non-coherent and DD PLL, the authors have considered pure pilot processing as a comparison term. Note that pure pilot processing also can be represented according to the general scheme provided in Figure 1. In this case, S_k, is the secondary code value corresponding to the specific correlator output and known after secondary code synchronization. Results for pilot processing have been obtained using our custom SDR receiver and the COTS device that implements this type of approach. Pure pilot processing is obtained using the E6C signal that will be encrypted.

Experimental Setup 

Three sets of tests were performed to assess the approaches described above:

• static live E6B/C signals collected under open-sky conditions using a rooftop antenna,

• simulated data using a hardware Radio Frequency (RF) simulator,

• live signals collected under dynamic conditions using an antenna mounted on the roof of a van.

The first type of tests was performed to tune the processing implemented by the SDR receiver and compare the results obtained with that achieved using the COTS receiver. The signal from the rooftop antenna was split between the SDR front-end and the commercial receiver.

The use of a hardware simulator for the second type of tests allowed us to collect signals in a controlled environment considering only the effects of noise and of the front-end local oscillator. A scenario where the C/N₀ of all the signals was progressively reduced was considered. The signals generated by the hardware simulator were provided to two SDR front-ends and to the COTS receiver.

For the SDR case, commercial SDR front-ends with a poor local oscillator were used for data recording. The built-in clocks of these platforms have biases of about 10 kilohertz with respect to the Galileo E6 centre frequency (about 8 parts per million (ppm)) and large frequency drifts. This type of clock induces a significant apparent dynamic on the received signal, preventing the use of narrow loop bandwidths and/or long integration times. Tests were conducted using two of such platforms connected using a Multiple-Input-Multiple-Output (MIMO) cable for synchronization purposes. In this way, it was possible to simultaneously collect data from two frequencies and implement inter-channel frequency aiding.

The clock of the platform configured as master was used to drive both devices. Views of the experimental setup adopted for the hardware simulator tests are provided in Figure 2. The signal provided by the hardware simulator is split between the two identical low-end SDR front-ends connected through the MIMO cable. Additional experiments were conducted using a second type of SDR front-end of better quality. These tests are described in the authors’ paper mentioned above and presented at the ION GNSS+ conference.

Finally, the third type of tests were conducted using the van shown in Figure 3a that was equipped with a multi-frequency high-end geodetic antenna capable of receiving E6 signals. The antenna, mounted on the van’s roof was connected to one of the low-end SDR front-ends and to the COTS receiver placed inside the van, as shown in Figure 3b. An external 10 megahertz rubidium oscillator has been used to drive the SDR front-end in order to have a stable clock reference. The van was driven around the two paths indicated in Figure 4a and located inside the Joint Research Centre (JRC) campus in Ispra, Italy. As shown in Figure 4b, the paths were characterized by the presence of very tall trees with rich foliage rendering the signal reception challenging. Also small buildings were present on the road sides from time to time. This harsh environment has been selected to assess signal tracking performance under challenging propagation conditions. 

Experimental Analysis 

During the open-sky test conducted using a roof-top antenna, five Galileo satellites were in view. All five signals were characterized by high C/N₀ values ranging from 42 to 55 dB-Hz. Under these conditions, stable tracking was easily achieved even when the data channel was used without inter-frequency aiding. Figure 5 shows the C/N₀ time series obtained for the five signals visible during the experiment using both the COTS device and the custom SDR receiver. A difference of less than 1 dB was observed between the C/N₀ values estimated by the COTS device and by the custom SDR receiver. This difference was removed to improve the clarity of the plot and highlight the similar trend of the time series estimated by the two receivers. This difference is small and can be justified by hardware differences, leading to different signal losses, and by different approaches for the estimation of the C/N₀.

The results shown Figure 5 were obtained using data-only processing with 10 non-coherent integrations. With this configuration, the SDR receiver was able to maintain stable signal lock over the whole duration of the experiments. The C/N₀ is used here as a lock indicator and for signal quality monitoring: under open-sky conditions data-only processing achieves performance similar to that obtained using pilot tracking. 

The test with the RF simulator was carried out to assess the sensitivity of the SDR and COTS receivers using different tracking configurations. For this purpose, the C/N₀ of all simulated signals was progressively reduced at steps of 1 dB per minute. Figure 6 compares the C/N₀ values provided by the COTS device and estimated by the SDR receiver for the different tracking algorithms. Pure pilot processing achieves a tracking threshold of about 24 dB-Hz whereas standard data processing, with a 1-ms coherent integration time, loses signal lock for a C/N₀ of about 30 dB-Hz. For pure pilot processing, a coherent integration time of 10 ms was adopted. For all configurations, a third order PLL with a 15 hertz bandwidth was used. 

When 10 non-coherent integrations are introduced, the tracking limit of the data processing is around 27.5 dB-Hz and therefore, the sensitivity gap between data and pilot processing is reduced.

The DD PLL does not significantly improve the performance of standard data processing and shows a lower sensitivity with respect to the tracking algorithm adopting 10 non-coherent integrations. Furthermore, no benefit is achieved by extending the non-coherent integrations from 10 to 50 ms. The above result is due to the clock dynamics limiting the maximum number of integrations.

As for the previous test case, the difference between the C/N₀ provided by the COTS device and the one estimated by the SDR receiver is within 1 dB-Hz. Moreover, the COTS device, adopting pure pilot tracking, achieves a tracking threshold close to that of pure pilot processing implemented by the SDR receiver.

In order to reduce the dynamics introduced by the poor clock embedded in the SDR front-end, inter-frequency aiding was implemented. Figure 7 reports the C/N₀ values obtained using data-only processing with inter-frequency aiding and the non-coherent squaring PLL. The C/N₀ obtained using pure pilot tracking on the E1C signal is also shown. For the E1C pure pilot tracking, an integration time of 12 ms was used. The E1C primary code lasts 4 ms and 12 ms is the smallest multiple of this duration larger than 10 ms. The latter integration time was used for the previous experiments on E6C.

Inter-frequency aiding allows longer non-coherent integrations and narrow loop bandwidths. In this case, a 5 hertz bandwidth and 50 non-coherent integrations were adopted. This configuration is able to track the E6B signal down to 24 dB-Hz obtaining performance similar to that of pilot processing. Note that, in this case, the E6B signal was lost because loss of lock occurred on the E1C channel used for inter-frequency aiding.

The Galileo E6B signal currently broadcast a dummy message that is known as a priori. The hardware simulator was configured to transmit the same dummy message. For this reason, it was possible to use the received correlator outputs to estimate the Bit Error Rate (BER) and Symbol Error Rate (SER) as a function of the received C/N₀. The SER is estimated before decoding the convolutional code used to protect the E6B signal whereas the BER reflects the final E6B data demodulation performance. 

The BER and SER curves are shown in Figure 8 for pure pilot processing with a 10-ms coherent integration. When the PLL is tracking the signal phase and frequency, the empirical SER is close to its theoretical value.

Even if pure pilot processing is able to track signals down to 24 dB-Hz, the SER is above 0.1 for C/N₀ values lower than 30 dB-Hz, in agreement with the findings of Göhler et al. (2016, Additional Resources). Therefore the ability to track weak signals does not improve demodulation capabilities. This fact is confirmed by the BER shown in Figure 8 for the COTS device that implements pure pilot processing and soft Viterbi decoding. A BER of about 0.1 is obtained for the C/N₀ values lower than about 28 dB-Hz. The COTS device and the SDR receiver achieve similar demodulation performance.

Data demodulation performance is analysed in Figure 9 for the data processing case when 10 non-coherent integrations are adopted. As for the previous case, under lock conditions the empirical BER and SER curves closely follow the theoretical one. In correspondence of loss of lock, at about 27.5 dB-Hz, a jump in the BER (SER) values can be clearly observed. After loss of lock, the SER converges to 0.5, which corresponds to a random choice of the symbols, which are correctly guessed half of the time. However, when the loss of lock occurs, the SER achieved using pilot processing is above 0.1, implying that the data demodulation performance is already quite poor in these conditions. Thus, data-only processing does not significantly degrade data demodulation performance of E6B standard receivers even when inter-frequency aiding is not used.

Dynamic Tests

Sample results obtained for the dynamic tests are provided in Figure 10 that considers parts of the trajectory shown in green in Figure 4 a. During this test, four Galileo satellites were in view. All four signals were acquired and tracked by both COTS and SDR receivers. The corresponding C/N₀ values are compared in Figure 10 that considers three cases:

• pilot processing implemented using the SDR receiver (continous lines),

• pilot processing implemented by the COTS device (dashed lines) and

• data processing with 10 non-coherent integrations (dashed circled lines).

In general, data and pilot processing provide similar results that are coherent with the C/N₀ estimates provided by the COTS receiver. In the dataset, the signal from Satellite Vehicle (SV) 9 is very strong and is characterized by C/N₀ values in the order of 55 dB-Hz. This signal was tracked continuously by both SDR and COTS receiver. Moreover, no significant differences were observed between data and pilot processing. For the other three signals, both SDR and COTS receiver experienced frequent loss of locks. Since the loop shown in Figure 4a was performed several times, it was possible to verify that loss of lock always occurred in the same portion of the trajectory, in the proximity of obstacles or when the van was passing under deep foliage. In this case, pilot processing did not provide significant improvement with respect to data-only tracking and loss of lock also occurred using this type of processing strategy. Pilot processing on the SDR receiver adopted 10 coherent integrations and a 15 hertz PLL bandwidth. These were the same parameters used for data-only processing that adopted 10 non-coherent integrations. 

Note that the scenario selected was very challenging, and with the completion of the Galileo constellation, more satellites will be available increasing the possibility of having signals characterized by favorable reception conditions as for the signal from SV 9 in our experiment.

These results confirm the fact that the absence of a pilot channel can be compensated, at least partially, by using advanced signal processing techniques such as the usage of non-coherent integrations. In this case, we used a stable clock reference to drive the SDR front-end. Applications that require an even better performance can use E1-E6 inter-frequency aiding which, as demonstrated before, can further reduce the signal dynamics perceived by the E6B PLL.

Conclusions

This article investigated several approaches for tracking the E6B signal without exploiting the E6C pilot component that will be encrypted. The use of non-coherent integrations and of a DD PLL was analyzed along with the adoption of inter-frequency aiding. The different approaches were analyzed using live static data, hardware simulated signals and live experiments under dynamic conditions. The analysis shows that the sensitivity gap between data and pilot processing can be bridged by adopting non-coherent integrations and inter-frequency aiding. Non-coherent integrations are effective in mitigating the impact of noise whereas inter-frequency aiding reduces the dynamic experienced by the E6B tracking loop. This allows one to increase the integration time and reduce the loop bandwidth.

Future work includes additional testing with COTS receivers, the adoption of frequency aiding for dynamics conditions, and the implementation of non-coherent integrations in adaptive tracking loops.

Manufacturers

The hardware simulator used for the tests is a Spirent GSS9000 multi-constellation simulator from Spirent, Crawley, United Kingdom, and the SDR front-ends used for data recording are Universal Software Radio Peripherals (USRPs) 2 by Ettus Research, Austin, Texas, USA. The multi-constellation multi-frequency COST GNSS receiver is the AsteRx4 device from Septentrio, Leuven, Belgium and Torrance, California, USA.

Additional Resources

(1) orio, D., and G. Lachapelle, “A non-coherent architecture for GNSS digital tracking loops,” Annals of Telecommunications, vol. 64, pp. 601–614, Oct. 2009

(2) orio, D., and M. Susi, “Non-coherent processing of E6B signals”, in Proc. of the 31st International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+), Miami, FL, pp. 1–13, Sept. 2018.

(3) urran, J., and T. Melgard, “The particular importance of Galileo E6C,” Inside GNSS, vol. 11, pp. 57–63, Sep/Oct 2016.

(4) uropean Commission, Implementing Decision (EU) 2018/321 of 2 March 2018, Available on-line at https://eur-lex.europa.eu/eli/dec_impl/2018/321/oj

(5) öhler, E.,I. Krol,M. Bodenbach, J. Winkel,G. Seco-Granados, and I. Fernandez-Hernandez, “A Galileo E6-B/C receiver: signals, prototype, tests and performance,” in Proc. of the 29th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS+), Portland, OR, pp. 486–496, Sept. 2016.

(6) utierrez, P. “Fundamental Rethink for Galileo Commercial Service” Inside GNSS, Nov./Dec. 2017, pp. 26-32  

(7) eyr, H. and G. Ascheid, “Synchronization in Digital Communication: Phase-, Frequency-Locked Loops, and Amplitude Control,” John Wiley and Sons, Mar. 1990

Authors

Daniele Borio received the M.S. degree in communications engineering from Politecnico di Torino, Italy, and the M.S. degree in electronics engineering from ENSERG/INPG de Grenoble, France, in 2004. He received the doctoral degree in electrical engineering from Politecnico di Torino in April 2008. From January 2008 to September 2010, he was a senior research associate in the PLAN group of the University of Calgary, Canada. He is currently a scientific policy officer at the Joint Research Centre of the European Commission (EC) in the fields of digital and wireless communications, location and navigation.

Melania Susi received her B.E. in Mathematical Engineering from the Universita` TorVergata di Roma, Italy, and M.Sc.s in Communication Engineering and in Geomatic Engineering, respectively, from the Università di L’Aquila, Italy, and from the University of Calgary, Canada. She holds a Ph.D. from the University of Nottingham where she was a Marie Curie fellow. Currently, she is a contract agent at the Joint Research Centre of the European Commission.

Em. Univ.-Prof. Dr.-Ing. habil. Dr. h.c. Guenter W. Hein is Professor Emeritus of Excellence at the University FAF Munich. He was ESA Head of EGNOS & GNSS Evolution Programme Dept. between 2008 and 2014, in charge of development of the 2nd generation of EGNOS and Galileo. Prof. Hein is still organizing the ESA/JRC International Summerschool on GNSS. He is the founder of the annual Munich Satellite Navigation Summit. Prof. Hein has more than 300 scientific and technical papers published, carried out more than 200 research projects and educated more than 70 Ph. D.´s. He received 2002 the prestigious Johannes Kepler Award for “sustained and significant contributions to satellite navigation” of the US Institute of Navigation, the highest worldwide award in navigation given only to one individual each year. G. Hein became 2011 a Fellow of the US ION. The Technical University of Prague honoured his achievements in satellite navigation with a Doctor honoris causa in Jan. 2013. He is a member of the Executive Board of Munich Aerospace since 2016. 

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