Putting the Synthetic Global Navigation Satellite System Meta-Signal Paradigm into Practice: Application to Automotive Market Devices ^†

Abstract

The synthetic meta-signal reconstruction approach enables the generation of wideband Global Navigation Satellite System (GNSS) measurements from side-band observations. This approach is of particular interest for automotive market devices where, for instance, hardware constraints do not allow full-band Galileo Alternative Binary Offset Carrier (Alt-BOC) processing. In this paper, the applicability of the synthetic GNSS meta-signal paradigm is extended by introducing a half-cycle ambiguity detector for the reconstructed carrier phases and a jump detector for the pseudoranges. These accessories make the reconstruction approach more robust and suitable for mass market devices. Tests conducted using the STMicroelectronics TeseoV receiver demonstrate the validity and potential of this approach.

1. Introduction

The concept of Global Navigation Satellite System (GNSS) meta-signals, which relies on the coherent processing of two components broadcast on different frequencies, is gaining significant interest in modern receivers. The resulting meta-signal has a wide Gabor bandwidth leading to high-accuracy pseudoranges (PSRs) and consequently high-accuracy code solutions. An example of GNSS meta-signal is the Galileo Alternative Binary Offset Carrier (Alt-BOC) modulation, which combines the E5a and E5b side-band components.

Recent research has shown that Galileo Alt-BOC PSRs can be produced through the synthetic meta-signal reconstruction approach [1], where high-accuracy PSRs are obtained as the combination of side-band code measurements smoothed using the side-band wide-lane linear Carrier Phase (CP) combination. In the original reconstruction approach, meta-signal CPs were obtained as the average of the side-band CPs. When forming meta-signal carrier phases, the averaging operation requires a division by a factor two, which introduces half-cycle ambiguities in the reconstructed measurements [1].

This limitation is solved here by using a Half-Cycle Ambiguity Resolution (HCAR) detector, which is based on the Hatch–Melburne–Wübbena (HMW) combination [2] formed using side-band observations. The HMW combination provides an unbiased estimator for the integer ambiguities of the side-band wide-lane CP combination and this property is exploited for the meta-signal CP HCAR.

In this way, this paper extends the applicability of the meta-signal synthetic reconstruction approach: the HCAR rule enables the generation of meta-signal CP observable usable for Precise Point Positioning (PPP) users.

In addition to the HCAR detector, a jump detector is also introduced to reduce the occurrence of artefacts on the PSRs originating from the side-band reconstruction in noisy environments.

The proposed approach has been implemented on the STMicroelectronics TeseoV (STA8135GA) (Naples, Italy) [3], triple band multi-constellation receiver able to track the Galileo E1, E5a and E5b signals. This serves as a special feature in automotive devices where the limited front-end bandwidth and hardware correlation constraints do not allow for direct full Alt-BOC tracking and make it usable for the mass market [4].

Several tests have been conducted in order to demonstrate the benefits of reconstructed wide-band meta-signals and analyze the new capabilities of the STA8135GA receiver. In the measurements’ domain, the synthetic E5 Alt-BOC measurements have been analyzed in a zero-base line test using a geodetic grade receiver as reference. Experimental results confirm the effectiveness of the HCAR and jump detectors that complete the synthetic meta-signal reconstruction approach.

The remainder of this paper is organized as follows: Section 2 introduces the concepts behind GNSS meta-signals with the reconstruction formulas for CPs and PSRs meta-signals. Reconstruction accessories that extend the usability of the method are detailed in Section 3. Section 4 introduces the TeseoV receiver, the processing chain adopted for meta-signal support and the experimental setup. Experimental results are reported in Section V, and Section VI finally concludes the paper.

2. Synthetic Meta-Signal Observation Reconstruction

According to the meta-signal observation reconstruction paradigm [1], meta-signal CP measurements can be reconstructed as:

$${\phi }_0={\displaystyle \frac{1}{2}}\left({\phi }_1+{\phi }_2\right)$$

(1)

where ${\phi }_0$ is the reconstructed meta-signal CP and ${\phi }_1$ and ${\phi }_2$ are the CP side-band observations. All quantities in Equation (1) are expressed in cycles. The averaging operation in (1) reduces the overall variance of the resulting CP; however, it also introduces a half-cycle ambiguity that will be solved in the following using the proposed HCAR detector.

Meta-signal PSRs are mixed code–carrier measurements and are obtained as [1]:

$${\rho }^{+}={\mathsf{\Phi }}_{sub}+{\lambda }_{wl}round\left({\displaystyle \frac{{\rho }_0-{\mathsf{\Phi }}_{sub}}{{\lambda }_{wl}}}\right),$$

(2)

where ${\rho }^{+}$ is the final high-accuracy meta-signal PSR. ${\mathsf{\Phi }}_{sub}$ is the meta-signal subcarrier phase expressed in meters and obtained as the wide-lane combination of the side-band CPs with wavelength, ${\lambda }_{wl}$. ${\rho }_0$ is the raw PSR obtained as a weighted average of the side-band PSRs. For symmetric side-band components, such as in the Alt-BOC case, ${\rho }_0$ reduces to the average of the side-band PSRs. A full account for the reconstruction of meta-signal observations can be found in [1].

From Equation (2), it emerges that an ambiguity resolution process is implemented through the rounding operation that determines the closest integer to its argument. The code-carrier difference ${\rho }_0-{\mathsf{\Phi }}_{sub}$ degenerates to the HMW code carrier combination for closely spaced side-band components [5] and it used in (2) to estimate the integer number of cycles affecting the subcarrier phase ${\mathsf{\Phi }}_{sub}$. Given the presence of an ambiguity fixing process, cycle slips can occur inducing jumps in the reconstructed measurements and in the final position solution. This problem is addressed by including a PSR cycle slip jump detector.

3. Reconstruction Accessories

In order to complement the meta-signal measurement reconstruction approach, the following accessories have been introduced.

3.1. Half-Cycle Ambiguity Detector

From the previous section, it emerges that meta-signal measurement reconstruction heavily relies on the narrow- and wide-lane CP combinations of the side-band measurements. The reconstructed meta-signal CP is obtained as half the narrow-lane CP combination (see Equation (1)). To solve the half-cycle ambiguity problem, it is necessary to determine if the sum ${\phi }_1+{\phi }_2$ is even or odd. When even, no half-cycle ambiguity is present. Otherwise, a half-cycle correction has to be introduced. In general, if the sum of two integers is odd, their difference is also odd. Similarly, if their sum is even, their difference is also even. This fact can be exploited to design a HCAR detector based on CP difference rather than on their sum. Working on the difference is more practical since it is characterized by a much wider wavelength, ${\lambda }_{wl}$. The HMW code–carrier combination is an unbiased estimator for the cycle ambiguity of the wide-lane CP combination. Thus, it can be used for HCAR. More specifically, the following quantity (already introduced in (2)) is computed:

$$S^{\ast }=round\left({\displaystyle \frac{{\rho }_0-{\mathsf{\Phi }}_{sub}}{{\lambda }_{wl}}}\right)$$

(3)

and tested for oddness/evenness. In (3), it is assumed that side-band components are close in frequency and that the code-carrier combination, ${\rho }_0-{\mathsf{\Phi }}_{sub}$, corresponds to the HMW one. Finally, a half-cycle is added to ${\phi }_0$ depending on the following condition:

$$D=\left\{\begin{array}{c}1 if S^{\ast } is odd\\ 0 if S^{\ast } is even\end{array}\right..$$

(4)

Thus, the final CP measurement of the meta-signal is reconstructed as

$${\phi }^{+}={\displaystyle \frac{1}{2}}\left({\phi }_1+{\phi }_2+D\right).$$

(5)

3.2. Cycle Slip Detector in High Accuracy PSRs

A cycle slip on the high-accuracy PSRs, ${\rho }^{+}$, can be detected comparing time differences of high-accuracy and raw PSRs. In particular, consider

$$\mathsf{\Delta }{\rho }_0\left[n\right]={\rho }_0\left[n\right]-{\rho }_0\left[n-1\right]$$

(6)

where the time index n has been included to denote measurements from different epochs. Similarly, it is possible to define

$$\mathsf{\Delta }{\rho }^{+}\left[n\right]={\rho }^{+}\left[n\right]-{\rho }^{+}\left[n-1\right].$$

(7)

The two rates should differ only for different noise components, and the difference

$$\mathsf{\Delta }{\rho }_0\left[n\right]-\mathsf{\Delta }{\rho }^{+}\left[n\right]$$

(8)

should be close to zero. Note that (8) only depends on the code-minus-carrier difference, ${\rho }_0-{\mathsf{\Phi }}_{sub}$ introduced for meta-signal reconstruction. In particular, it is possible to show that (8) is an estimate of the rate of change of the ambiguities that should be constant over time. Thus, (9) can be used to detect and correct cycle slips in the reconstructed measurements:

$${\rho }_{adj}^{+}[n]={\rho }^{+}[n]+{\lambda }_{wl}floor\left({\displaystyle \frac{\mathsf{\Delta }{\rho }_0\left[n\right]-\mathsf{\Delta }{\rho }^{+}\left[n\right]}{{\lambda }_{wl}}}\right)$$

(9)

where ${\rho }_{adj}^{+}$ is the high-accuracy PSRs corrected for possible cycle slips between two consecutive epochs. Symbol floor(.) denotes the floor operator.

4. Experimental Setup

In this section, the experimental setup used to assess the performance of the reconstructed meta-signal measurements is presented. First, the receiver used is presented; then, the zero-baseline test is described; and finally, the architecture used for the position domain analysis is introduced.

4.1. The TeseoV (STA8135GA) Receiver

Figure 1 reports the functional block diagram of the STA8135GA receiver, which is a member of the STMicroelectronics TeseoV 5th generation family of GNSS receivers introduced for triple-band applications in automotive environment and used for synthetic Galileo Alt-BOC measurement delivery. It is a Multi-Chip-Module (MCM) combining in a single package both an STA8100GA receiver and STA5635A frontend, which has 80 multi correlator tracking channels and four fast-acquisition channels compatible with different frequency bands [3,4].

When dealing with meta-signal reconstruction on this STMicroelectronics hardware platform, no specific constraints have been introduced in terms of side-band tracking loops but a common clock chain to drive front-end heterodyne and local correlation is used. Independent code and frequency loops are used for both side-band components and independent measurements are provided in terms of PSR, Doppler frequency and CP. Possible inter-frequency receiver bias is assumed as compensated at measurement building level. CPs are aligned to the respective PSRs at the start-up of tracking.

The reference scheme for side-band signal processing, measurement delivery and meta-signal production of the Galileo E5 Alt-BOC is reported in Figure 2.

The reconstruction formulas for GNSS meta-signal observations, as proposed in Section 2 and Section 3, have been successfully implemented in the STA8100 v5_8_23 TeseoV software platform’s library. This enhancement notably extends the number of observables without necessitating extra hardware and, importantly, adds the capability to manage wideband signals previously unsupported due to limited frontend bandwidth.

4.2. Zero-Baseline Tests

The proper reconstruction of the Galileo Alt-BOC has been verified using a zero-baseline test [6]. For the test, a Trimble BD990 (Trimble Inc., Westminster, CO, USA) [7] was used as reference receiver. The device provides both E5a and E5b components and the full Alt-BOC measurements. In the test, the Trimble device acted as base and the STA8135GA equipped with a dedicated firmware with meta-signal support as rover. The two devices were let run in parallel fed by a common geodetic antenna (Thimble Zephyr 3 [8]).

For the two devices, E5a and E5b observables were recorded along with the native Alt-BOC output of the Trimble receiver and its synthetic version provided by the STA8135GA device. Note that Alt-BOC synthetic reconstruction is now fully integrated within the ST Teseo Suite Tool [9]: Figure 3 provides a snapshot of the modified software tool, which displays Alt-BOC signal information along with the sideband components. The Alt-BOC Carrier-to-Noise Power Spectral Density Ratio (C/N₀) is conventionally displayed on vertical bars as the average of the side-band C/N₀s.

The antenna was placed on the rooftop of the office building in the STM premises located in Arzano (Naples, Italy). The antenna was located under open sky conditions, and it was accurately referenced also allowing the analysis of the positioning error.

The Trimble receiver’s noise level was assumed to be far lower than that of a consumer receiver; PSRs and CPs have been double-differentiated to eliminate both receiver-specific (e.g., TXCO clock) and satellite-specific common errors.

In the zero-baseline configuration using double differences, common errors (receiver clock bias) are removed using the first differentiation between pair of satellites, while second differentiation removes spatial correlated errors (e.g., ionosphere and troposphere). CP ambiguity is integer provided that has been correctly resolved on both the receivers.

4.3. Position Domain Analysis

The analysis in the position domain was performed using a common Single Point Positioning (SPP) algorithm, in single-frequency mode. For the assessment, performance was evaluated in terms of mean and standard deviation of the horizontal and vertical errors. The solution obtained using the side-band components singularly and the synthetic E5 Alt-BOC measurements are compared to assess the benefits of the reconstruction approach. PSR measurements have been modeled as:

$$\rho =d-cd{t}_S-\gamma TGD+{\sigma }_{Rel}+T+\gamma I+cd{t}_R,$$

(10)

where:

• $d$ is the satellite-receiver geometric distance;
• $cd{t}_S$ is the satellite clock error corrected using the parameters of the navigation message;
• $TGD$ is the time group delay corrected using the information in the Galileo navigation message;
• ${\sigma }_{Rel}$ is the term including Sagnac and relativistic effects;
• $T$ is the tropospheric delay modeled with the Saastamoinen model;
• $I$ is the ionospheric delay estimated using the Klobuchar model;
• $cd{t}_R$ is the receiver clock offset estimated in the navigation solution;
• Frequency-dependent errors, such as the Ionospheric one and TGD, are adapted for the different frequencies using the scaling factor $\gamma ={\left(E1/UsedFreq\right)}^2$.

5. Experimental Results

5.1. Zero-Baseline Test 1: Carrier Phase Results with/Without HCAR Rule

A three-device test was run with two STA8135GA running in parallel with/without the HCAR detector enabled. The test was conducted to verify the HCAR effectiveness to resolve the CP half-cycle ambiguity in nominal conditions. The results for this test are reported below in Figure 4.

5.2. Zero Baseline Test 2: HCAR Stress Test

A test was conducted where the front-end of the TeseoV receiver, with the HCAR algorithm enabled, is periodically switched “on” and “off” to simulate signal blockage conditions occurring for instance when passing under a bridge or in a tunnel. The professional receiver used in the test, acting as base, was always left on [4].

The analysis of the carrier phase double differences obtained in this trial confirms the consistency of the half-cycle ambiguity recovery method for meta-signals observables. CP measurements align around integer values every time the receiver front-end is turned on. This supports the effectiveness of the proposed HCAR detector. Results are reported in Figure 5.

5.3. Zero Baseline Test: PSR Results

For the PSR analysis, a 3 h test was carried out (Figure 6). Multipath effects are evident on E5a and E5b double difference result (center and right subplots), while synthetic Alt-BOC measurements are aligned (no jump) to the BD990 true version with a 95-percentile noise deviation in the 20 cm range (left subplot).

5.4. Impact of PSR Cycle Slip Detector

Since meta-signal PSR reconstruction requires the ambiguity resolution of the side-band wide-lane carrier phase combination, jumps in the reconstructed measurements can occur. This is addressed using the jump detector introduced in Section 3.2. An example of the ability of the jump detector to identify and remove jump effects is shown in Figure 7.

5.5. Positioning Results

In Figure 8, the horizontal positioning errors obtained using single-frequency SPP algorithms using the PSR from E1 (blue markers), E5a (orange markers), E5b (yellow markers) and Alt-BOC synthetic measurements (purple markers) are shown. From the figure, it can be noted that the solutions are centered on the origin of the axes and no specific biases can be appreciated for the different solutions. All the solutions have a similar behavior, but the solutions obtained with the synthetic observables are more accurate: the purple cloud is more concentrated than the others showing the clear benefits of the synthetic approach also with respect to the classical E1 solution.

The time evolution of the vertical error is shown in Figure 9. Also, for the vertical components, the solutions have a similar behavior, and clear noise reduction can be noted using the synthetic Alt-BOC measurements.

6. Conclusions

The generation of wideband GNSS measurements from side-band observations, specifically referring to the Galileo Alt-BOC case, has been presented. Additionally, two novel tools—a HCAR and a PSR jump detector—have been introduced to complement the meta-signal reconstruction paradigm and enable implementation in automotive devices. This paper detailed several test outcomes and proposed a promising position domain analysis. Future work will focus on extending this approach to the BDS3 Asymmetric Constant Envelope Binary Offset Carrier (ACE-BOC) case and enhancing the potential of meta-signal CP for PPP users.