Toward Context-Aware GNSS Positioning: A Preliminary Analysis ^†

Abstract

The vast majority of GNSS users move in urban areas, where the signal conditions are highly unstable and multipath or gross errors make GNSS navigation unreliable or plainly unfeasible. In this study, features from real GNSS data collected by different grades of receivers have been compared to find candidate statistical indicators of the context that allow the automatic recognition of open sky or obstructed environments. The features considered are all pre-PVT and snapshot-based and hence suitable for real-time applications. They are namely the number of visible satellites, the dilution of precision, multipath linear combination with dual-frequency measurements, and the C/N0 difference between each couple of satellites in the same epoch at the same frequency. All measurements have been gathered both in open sky and in obstructed scenarios. The evidences suggest multipath linear combination and the C/N0 difference between couples of satellites as the most promising baselines for an environment classifier based on Machine Learning.

1. Introduction

The use of GNSS (Global Navigation Satellite System) in different environmental conditions presents challenges in employing a uniform positioning method in real-time navigation. In open-sky scenarios, the good visibility of the satellites, favorable geometric positioning, and strong signal quality contribute to highly accurate and reliable PVT (Position, Velocity, Time) solutions. Conversely, navigating through densely built-up urban areas can lead to issues like multipath interference and an increase in GNSS measurement anomalies. To counteract these outlier effects, integrity strategies, also known as FDE (Fault Detection and Exclusion), have been developed over time. These techniques aim to identify and eliminate significant errors from the positioning calculations, thus improving the accuracy and reliability of the solution [1,2,3]. Nevertheless, these techniques require a level of redundancy that is not always available in challenging environments where satellite signals may be limited, hindering the effectiveness of FDE.

Given these limitations, researchers have increasingly focused on characterizing the GNSS environment, especially for adaptive navigation. In this context, research on features that enable a clear distinction in outdoor environments is essential; common features used for this purpose are the C/N0 (Carrier-to-Noise Power Spectral Density Ratio) and satellite visibility [4,5], together with the constellation geometry [6], the satellites’ azimuth and elevation [7], the pseudorange residuals [8], and the multipath indicator [9]. As can be seen from [10], such features can distinguish between position dependence and independence.

The aim of this research is to inspect various features and their potential constraints while also seeking out new and practical metrics for categorizing the environment. To distinguish the fundamental contrasts between unobstructed and obstructed scenarios, GNSS data from receivers of different qualities, i.e., consumer-grade, automotive, and geodetic, were collected. This evaluation is performed at the level of raw measurements, before the calculation of PVT, to aid in developing an adaptive strategy that can be implemented for real-time navigation. This investigation primarily focuses on the satellite visibility, satellite geometry, signal intensity, and the impact of multipath effects, introducing unique metrics for the latter two to underscore the differences between the environments being examined.

The findings suggest that satellite visibility and geometry metrics can occasionally yield analogous values at certain times in different scenarios, thus proving to be unreliable for accurate environmental detection. In contrast, metrics related to signal strength and multipath effects are shown to vary significantly with the environment, demonstrating their potential as more effective indicators for contextual analysis.

This paper is organized as follows: in Section 2, the features and the proposed methodology are explained; in Section 3, a brief description of the adopted device and the data collection is provided. Section 4 presents the features; finally, Section 5 concludes the paper.

2. Materials and Methods

2.1. Features Definition

A GNSS receiver provides various measurements, such as code, carrier phase (CP), and C/N0 observables [2], which serve as the foundational raw data of investigation for this research. At first, metrics based on the number of satellites and their geometry distribution are described; then, metrics based on multipath linear combination (MLC) and C/N0 are covered.

2.1.1. Satellite Visibility and Geometry

Satellite visibility and constellation geometry are quite common features used in GNSS environment classification.

In this work, the satellite visibility is measured using the number of satellites involved in the PVT estimation at each epoch, i.e., those whose elevation is greater than 10 degrees and C/N0 is larger than 20 dB-Hz.

The constellation geometry is evaluated in terms of DOP (dilution of precision); specifically, the Positional DOP (PDOP) is considered [1,2,11].

2.1.2. Multipath Linear Combination

GNSS provides two measurements that can be used for positioning purposes: code (or the pseudorange) and the carrier phase [1]. Code observables are susceptible to multiple error sources, including delays caused by the ionosphere and troposphere, as well as discrepancies in the satellite and receiver clocks, alongside multipath errors. In contrast, carrier-phase observables leverage the phase of the carrier signal for a more accurate assessment of the satellite-to-receiver distance than that which code observables can offer. Nevertheless, the challenge lies in pinpointing the precise distance, as the exact count of the full carrier wavelengths between the satellite and the receiver remains uncertain, so the CP measurements are inherently ambiguous. Exploiting the distinct characteristics of the code and carrier-phase measurements, it is possible to formulate different linear combinations to counter specific errors. Considering multipath errors, for instance, they can distort the carrier-phase measurements by up to a quarter of the carrier wavelength (approximately 5 cm for GPS L1) and the code measurements by up to several meters. A technique known as code minus phase (CMP) comparison can detect multipath interference; it was introduced for the first time in [12]. CMP is a valuable tool for validating the data integrity and rectifying errors with sophisticated GNSS data processing methodologies. It assists in assessing the signal quality and detecting irregularities that may not be immediately evident through the examination of the code or carrier-phase data alone. Notably, the CMP combination leads to the consideration of a double ionospheric delay since the ionosphere induces a delay in code observables and an advance in carrier-phase observables. Different strategies have been employed to address this aspect: in [13], the authors neutralized the ionospheric effect by averaging it out over a time window, while this study eliminates the ionospheric error by capitalizing on its frequency dependence. Consequently, the CMP for the L1 frequency is calculated using the subsequent formula:

$$CM{P}_{L1}={\rho }_{L1}-\left({\varphi }_{L1}{\lambda }_{L1}\right)-2K\left({\varphi }_{L1}{\lambda }_{L1}-{\varphi }_{L2}{\lambda }_{L2}\right)$$

(1)

In this equation, the subscripts indicate the frequency, $\rho$ is the pseudorange, $\varphi$ is the carrier phase, $\lambda$ is the wavelength, and $K={\displaystyle \frac{f_1^2}{f_1^2-f_2^2}}$, with $f_1$ and $f_2$ indicating the L1 and L2 signal frequencies.

To mitigate the effect of cycle slips on the CMP observables, a cycle slip detector based on geometry-free combination is used to detect and exclude CP measurements affected by a cycle slip.

2.1.3. C/N0 Differences

C/N0 is a critical parameter in GNSS signal processing, and it represents the strength of the received signal in relation to the level of background noise [14]. This parameter provides insight into the performance of the signal reception and tracking processes within a GNSS receiver. A higher C/N0 value indicates a stronger signal relative to the noise, which typically results in a better signal tracking accuracy and more reliable measurements [2]. One significant factor influencing C/N0 is multipath interference, where environmental reflections can disrupt the signal integrity. When multipath effects occur, these reflections mingle with the direct signal, prompting swift changes in the signal power and consequently variations in the C/N0 ratio perceived by the receiver. This can cause the average C/N0 to decline. In this study, a metric is introduced that utilizes pairing of the available C/N0 values at each time point. For any given epoch t and for two distinct satellites i and j, the following metric is defined:

$${(\mathsf{\Delta }C/N_0)}_t^{i,j}=\left|{(C/N_0)}_t^i-{(C/N_0)}_t^j\right|$$

(2)

All of the satellite pairings are calculated to generate pairs, which results in an increased sample count for each epoch (for example, with 5 satellites, 10 pairs are obtained). Furthermore, any abnormal C/N0 values associated with a particular satellite are distributed across multiple samples, yielding higher statistical figures. Consequently, this enhances the suitability of the metric for the purpose of detecting the environmental conditions.

2.2. Processing Steps

In this section, the steps for obtaining the MLC reference distribution and all of the statistical strategies applied to the data are detailed.

2.2.1. Reference Distribution Building

The process of building a reference distribution for multipath effects began with the collection of publicly available open-sky data from 37 IGS stations [15]. These datasets were acquired via FTP and consist of 24 h of multi-GNSS and multi-frequency data, recorded at 30 s intervals using high-quality receivers and antennas. As specified before, only GPS data were considered.

For each selected IGS station, an empirical probability distribution of multipath effects on the L1 frequency was generated. These distributions were then transformed using a Box–Cox transformation [16] and trimmed at the 95th percentile, both to increase their Gaussianity and to reduce the effect of outliers.

This study explored two different strategies:

Case A: Averaging the binned data from all 37 stations to generate the empirical multipath reference distribution;

Case B: Considering as a reference multipath distribution a single Gaussian with the average of the parameters of the 37 best-fitting Gaussians estimated based on the empirical probability distribution of each station as its parameters.

For both approaches, the Kullback–Leibler (KL) divergence was used as the metric to quantify the differences between the reference distribution(s) and the test distributions.

2.2.2. Box–Cox Transformation

The Box–Cox transformation is a statistical transformation used to make a distribution as close as possible to a Gaussian. In such technique, a datum $y$ is transformed into $y^{\left(\lambda \right)}$, with $\lambda$ referred to as a transformation parameter. For $y>0$, it is possible to define the transformation equations as follows [16]:

$$y^{\left(\lambda \right)}=\left\{\begin{array}{c}\left(y^{\lambda }-1\right)/\lambda \mathrm{for}\lambda \ne 0\\ \log y\mathrm{for}\lambda =0\end{array}\right.$$

(3)

Due to the presence of the logarithm operator in (4), the data must be positive.

In this study, at first, a shift in the data into the positive domain is performed, and then the Box-Cox transformation is applied. This two-step process involves first adding a constant to all of the data points to ensure positivity and then applying the Box–Cox transformation. After processing, the data are back-shifted.

2.2.3. Trimming

After the Box–Cox transformation, trimming [17] at the 95% point of the central data is applied in order to mitigate the effect of possible outliers.

Trimming is quantile-based: two thresholds are identified through the 0.025 and 0.975 quantiles, and data overpassing these thresholds are rejected.

2.2.4. Kullback–Leibler Divergence

Given two probability distributions $A$ and $B$, the statistical distance between them can be calculated using the asymmetric Kullback–Leibler divergence, which expresses the divergence of A from B and vice versa [18].

$$\left\{\begin{array}{c}{D}_{KL}\left(A\right|\left|B\right)={\displaystyle \sum _i}A\left(x\right)\log \left({\displaystyle \frac{A\left(x\right)}{B\left(x\right)}}\right)\\ D_{KL}\left(B\right|\left|A\right)={\displaystyle \sum _i}B\left(x\right)\log \left({\displaystyle \frac{B\left(x\right)}{A\left(x\right)}}\right)\end{array}\right.$$

(4)

In order to have a symmetric KL indicator, the J-Divergence, defined as the average of $D_{KL}\left(A\right|\left|B\right)$ and $D_{KL}\left(B\right|\left|A\right)$, is determined. The KL indicator is used to evaluate the divergence of a test multipath distribution from the reference multipath distribution(s) [19].

3. The Experimental Setup and Data

For the tests, three different devices were used, i.e., a TeseoV multi-GNSS automotive-grade receiver manufactured by STMicroelectronics based in Ginevra Switzerland [20,21,22,23]; a u-Blox F9P multi-GNSS low-cost receiver manufactured by u-Blox based in Thalwil, Switzerland [24]; a Novatel SPAN multi-GNSS high-grade receiver manufactured by Hexagon/Novatel based in Calgary, Canada [25].

Data collection using the aforesaid devices was carried out in both urban and open-sky scenarios. Each device was connected to a separate antenna.

For the uBlox open-sky scenario, the open data retrieved from [26] were used.

4. The Test and Results

In this section, the experimental results are discussed. Firstly, the satellite visibility and geometry have been analyzed and are reported in Figure 1. Only the TeseoV case is presented to avoid the repetition of similar findings. From the figure, it can be noted that in the urban scenario, the number of visible satellites and the PDOP are strongly variable, while in open-sky contexts, these values are characterized by near constancy. In some cases, the features have very similar values in both environments, making these features unreliable for context detection using only their pure values.

In the upper box of Figure 2, $\mathsf{\Delta }C/N_0$ as a function of the absolute value of the elevation differences ($\mathsf{\Delta }El)$ is reported for each pair of satellites. Also, in this case, only the dataset related to the TeseoV receiver is considered. As clearly shown by the linear interpolators, clear differences can be detected in the two scenarios. This approach exploits the full dataset, making it suitable for static surveys where the conditions are similar in the entire data collection, but in urban navigation, a different approach needs to be adopted to face the continuous variation in the environment. For real-time urban navigation, the standard deviation of $\mathsf{\Delta }C/N_0$ for each epoch is considered. The lower part of Figure 2 shows the standard deviation of $\mathsf{\Delta }C/N_0$ as a function of time. From the figure, it can be noted that in open-sky conditions, the STD has a lower value than that in the urban case. But also in this case, some of the epochs in obstructed conditions have lower values, showing the limitations of this approach.

Moving the focus to the multipath analysis, the MLC probability distributions of the open-sky and urban canyon data have been compared to the MLC probability distributions for the 37 selected IGS stations. In Figure 3, the KL indicators for the TeseoV are shown. It clearly emerges that the KL indicator assumes higher values when the IGS station distributions (which are referred to as open-sky) are compared with those in the urban canyon environment. For the open-sky case (blue bars), the KL divergence assumes lower values, with most of them being about one. For some stations, it can be noted that the KL divergence indicator is larger in the open-sky case (see the station UCAL); this phenomenon is probably due to an anomalous distribution for the specific station. Further analyses are required for this specific case.

This approach has also been applied to open-sky and obstructed data for a high-grade Novatel receiver (referred to as “SPAN”) and a low-cost uBlox receiver. In Figure 4, box charts for the 37 KL indicators for the considered devices are shown. For the TeseoV and uBlox, the standard deviation of the KL indicators in the urban canyon case is higher with respect to that in the open-sky case. For the SPAN device, the KL indicators seem to assume very similar values in both cases; one possible explanation for such evidence is the automatic application of an effective multipath mitigation technique embedded into the high-grade receiver.

The same data are used for the second approach, which compares the test MLC probability distribution with a single, perfectly Gaussian reference distribution (Case B). Figure 5 shows the KL indicators for the abovementioned devices, for which the same conclusions can be drawn. In all cases, except for the TeseoV and uBlox in an urban environment, the indicator assumes values below one. For the automotive device and the mass-market receiver in an urban scenario, the KL value is about 6 and 2, respectively, confirming the results obtained using all 37 stations singularly.

5. Conclusions

This paper has focused on analyzing various metrics for environmental detection to refine adaptive navigation algorithms. The commonly used metrics, based on satellite visibility and the PDOP, in different contexts using devices of different grades have been investigated and their limitations explored. A novel metric based on ΔC/N0 has been proposed and its effectiveness for environmental characterization assessed. Two distinct approaches for static and dynamic scenarios have been considered.

Additionally, a statistical strategy for establishing a reliable reference distribution for open-sky conditions was developed and tested. To measure the divergence between the reference distribution and test cases, a statistical indicator (the symmetrized KL divergence) was chosen. The analyses revealed that the KL divergence indicator facilitates a proper distinction between environments when using mass-market and automotive devices. However, when applying a high-grade device equipped with possible advanced multipath mitigation preprocessing techniques, the indicator did not show significant differences between open-sky and obstructed scenarios.

In summary, these findings indicate that while the KL divergence can effectively distinguish between different environments for certain devices, this advantage may become negligible when high-grade receivers with advanced preprocessing techniques are used.

These insights are crucial for the development of reliable and context-aware GNSS-based navigation systems, particularly in urban settings, where the environmental conditions can drastically affect the signal quality and positioning accuracy.