Abstract
The accuracy of global navigation satellite system (GNSS) signal reception is crucial for precise navigation and geodetic positioning. Signal interactions with objects near the receiving antenna can cause multipath errors and distort GNSS antenna group delays, thereby reducing the achievable positioning accuracy. To mitigate these effects, the distortions can be predicted in advance and subsequently reduced through a calibration approach. This approach is possible, for example, for static errors, such as those caused by interactions between the antenna and the installation platform, for instance, on a car.
This paper addresses the accurate prediction of distortions caused by the installation of the antenna on a car in automotive scenarios. This work introduces a hybrid calibration approach that combines real-world data and simulations to enhance GNSS antenna performance predictions. This approach allows the simulation to reconstruct the effect of the mounting platform on the data of an individual antenna previously measured in an anechoic chamber, thereby predicting the final error of the installed antenna on the platform. This methodology is then validated and compared with a GNSS-based calibration of the antenna performed directly on a car, i.e., inherently including installation effects. The results show that approximately 48% of the sky plot region exhibits a code phase variation difference within ±25 cm, indicating a high level of accuracy and consistency.
1 INTRODUCTION
Global navigation satellite system (GNSS) technology has become an essential component across a diverse range of applications, including maritime, vehicle, and aeronautical navigation (European Union Agency for the Space Programme, 2024). Among these, vehicle-based applications represent an important category, wherein the precise real-time localization of road users is gaining increasing importance, for instance, in the development of partially and fully autonomous driving (Khalil, 2024).
To achieve high-precision positioning, it is imperative to reduce all possible error sources at the global, regional, and local level (Li et al., 2023). The placement of an antenna in a specific scenario can significantly impact its nominal characteristics, resulting in distortions due to interactions between the antenna’s fields and surrounding objects (Addo et al., 2024; Caizzone et al., 2021). These distortions occur because the antenna receives signals not only from the intended direction but also from various other directions, including reflections from the platform surface on which the antenna is installed. When GNSS signals reflect off the platform surface and reach the antenna, a phenomenon known as multipath occurs, as described by Smyrnaios et al. (2013).
In automotive scenarios, the effect of the car structure has a relevant impact on the antenna pattern, distorting it significantly with respect to the pattern experienced by a stand-alone antenna.
Moreover, GNSS parameters are significantly impacted by multipath effects or reflections coming from the mounting platform (often called “near-field multipath” effects).
This impact can be well estimated by analyzing the distortions of antennaintrinsic errors, i.e., for the group delay error in pseudorange-based positioning (Caizzone et al., 2022). Specifically, the antenna group delay refers to the time delay that each frequency component of the received signals experiences during the transduction process of the antenna. These delays vary depending on the elevation (θ) and azimuth (ϕ) of the signal’s direction of arrival, resulting in group delay variations (GDVs) or, in the GNSS context, code phase variations (CPVs). The group delay is an intrinsic antenna error and can be removed by means of proper antenna calibration (Kersten et al., 2017; Caizzone et al., 2022; Kersten et al., 2022).
For carrier phase observations, an ideal receiver antenna is characterized by a spherical radiation pattern. However, in reality, deviations from this ideal pattern occur; these deviations are referred to as phase center variations (PCVs) or phase center corrections. Analogous effects on the code are known as CPVs, which are derived from the antenna GDV after an appropriate weighting of the different frequency components with the signal spectra. This property is heavily dependent on the characteristics of the receiving antenna. In applications such as ambiguity resolution and the determination of geodetic parameters, which strongly rely on the accuracy of received signal code phases, precise information about the receiving antenna’s GDVs has become increasingly important. In other words, an accurate knowledge of the antenna’s GDVs is crucial for achieving high precision in these applications, and it is essential to consider the antenna’s characteristics when designing and implementing these systems. When the antenna pattern is distorted by installation on a (car) platform, the GDVs and CPVs will be altered as well, reducing the validity of the stand-alone antenna calibration.
Geo++ has reported their technique for a GNSS-based calibration of an antenna after installation on a car (Wübbena et al., 2021). The technique is powerful but time-consuming and is impractical to perform, for instance, when the performance of the antenna in various car setups/variants must be assessed. In fact, each car configuration (e.g., panoramic roof, special lacquers, spoilers, etc.) interacts differently with the GNSS antenna on the roof and would theoretically require an ad-hoc calibration, making this technique impractical for such analyses.
“Accurauto” (accurate prediction of GNSS antenna performance in automotive scenarios), a joint project of Geo++, German Aerospace Center (DLR), and Leibniz University of Hannover as project partners, is dedicated to advancing GNSS antenna-on-vehicle calibration techniques. Specifically, the project aims to find a practical method for calibrating the group delay of antennas installed on cars, utilizing not only measurements but also a hybrid approach combining measurements and simulations, exploiting the digital twin approach developed at DLR for aviation applications (Caizzone et al., 2021).
The goal of this study is to create a more efficient and cost-effective calibration process that can be rapidly applied for different car configurations. Thus, in this project, a demonstration and validation of the digital twin approach was performed, comparing the predicted installed antenna error with errors obtained by GNSS measurement at the Geo++ VehiCal facility.
This paper is organized into five sections. Section 2 delves into the details of the Geo++ in situ car calibration, offering a comprehensive discussion of the concept. The hybrid calibration scheme is thoroughly explained in Section 3, highlighting its key features and benefits. In Section 4, the calibration of stand-alone antennas and installed antennas on a digital twin is discussed and compared with Geo++ in situ calibration, providing valuable insights into the differences and similarities between these approaches. Finally, the conclusions and key takeaways from the study are presented in Section 5, summarizing the main findings and implications of this research.
2 IN SITU CALIBRATION
To accurately measure near-field multipath effects caused by the installation of an antenna on a car, the antenna must be mounted on a vehicle and calibrated in situ.
For this purpose, a vehicle was placed on a rotating platform developed by Geo++ (Wübbena et al., 2021), as shown in Figure 1. The platform completes one full rotation every 90 s, allowing the collection of GNSS signals from all azimuthal directions relative to the vehicle within a short time frame. Each full calibration session lasts approximately 6 h to ensure sufficient data coverage.
Antenna calibration on a rotating platform
A nearby reference station, equipped with a multi-frequency geodetic antenna (TWIVC6050) and a Javad GNSS receiver (JAVAD OMEGA), was installed a few meters from the platform. The GNSS observations from the vehicle-mounted antenna are processed together with the reference station data using a short-baseline kinematic processing mode, which effectively eliminates satellite orbit and clock errors, as well as ionospheric and tropospheric delays. All carrier phase ambiguities above a 5° elevation cutoff are resolved, and a processing rate of 1 Hz is used. A forward-only Kalman filter is used, simultaneously processing all multi-frequency multi-GNSS code and phase observables. After the application of phase wind-up corrections, the remaining residuals predominantly contain the GDV/PCV and multipath effects.
The resulting code and carrier phase residuals, observed from different signal directions, are transformed into the vehicle coordinate system and can be subsequently applied as antenna corrections in the processing of positioning solutions. After approximately ten iterations, the observation residuals converge, indicating the completion of processing and the effectiveness of the correction model. In this paper, only code residuals are used to calibrate the antenna errors.
A Volkswagen Passat B8 Variant was used as the test vehicle, and the performance of an automotive-grade shark-fin antenna mounted on the test vehicle was analyzed.
3 HYBRID CALIBRATION SCHEME
In addition to the in situ calibration, the performance of a GNSS antenna installed on a car was also determined via a full-wave hybrid simulative approach, a method that has been well described for aircraft by Caizzone et al. (2022). The full workflow is represented in Figure 2, where the installation environment, for this study, is a 2014 VW Passat B8 Variant, as used by Geo++, equipped with an inbuilt rooftop Global Positioning System (GPS) antenna operating in the L1 band. The process begins with calibration of the stand-alone antenna at the DLR facility. DLR houses a semi-anechoic chamber developed by Microwave Vision Group, where the antenna under test (AUT) is measured on a circular metallic plate with a 40-cm diameter, as shown in Figure 3.
Hybrid calibration scheme; NF: near-field
Antenna measurement in an anechoic chamber
This approach involves extracting a near-field source (NFS) of the AUT, modeled as surface currents on a Huygens’ box positioned on top of the car, from measurements taken in an anechoic chamber using the equivalence principle (Futter et al., 2018).
The NFS is then simulated using a digital twin of the installation scenario via an electromagnetic (EM) ray-tracing solver in SIMULIA CST Studio Suite®, a three-dimensional (3D) EM field and multiphysics modeling and simulation tool (Dassault Systemes, 2024). The interaction between the stand-alone antenna characteristics and the scattered multipath ray properties causes distortions in the effective antenna radiation pattern, which are then processed to obtain the installed CPVs.
This methodology provides a comprehensive and precise assessment of how the antenna behaves in real-world automotive scenarios, considering the complex interactions between the antenna and its surrounding environment.
The proposed approach is most effective when the digital twin representation of the scenario has sufficient information regarding the materials and objects around the antenna to represent the real-world conditions with high fidelity. In contrast, approximations, such as treating the structure of the vehicle or the surroundings as a perfect electric conductor (PEC), can lead to overestimations of the reflection error.
4 ANTENNA CHARACTERIZATION
4.1 Stand-Alone Calibration
For a stand-alone antenna, the antenna complex response (over frequency, elevation, and azimuth) can be directly extracted from measurements acquired in an anechoic chamber and then used to calculate the group delay.
Figure 4 displays the antenna’s radiation characteristics for 1575 MHz, when measured on a metallic plate. The data are presented using a left-hand topocentric coordinate system, where ϕ = 0° indicates the antenna’s “north” direction, i.e., the direction that points to the front of the car in the installed case.
Radiation pattern of the stand-alone antenna
Figure 5 illustrates the GDV along the elevation and azimuth angles for 1575 MHz (L1 band). The GDV yields the antenna’s transfer function of the GNSS band as a function of frequency, elevation, and azimuth angles and, as a measure of the time delay of the signals, is expressed in nanoseconds. Upon examining the gain pattern of the antenna, it can be noticed that in certain regions of the upper hemisphere (for instance, toward the south, i.e., an azimuth of ∼150°–180°), the received gain of the antenna is low; hence, the satellite signals received in that area will be weak. The group delay plots demonstrate that the group delay has a high absolute value in those same areas (around an azimuth of 150°–180°). Although calibration data are available for these areas as well, their relevance is reduced, owing to the poor GNSS signal trackability (due to low gain).
GDV of the stand-alone antenna
To accurately evaluate the antenna-induced errors across the GNSS frequency band (the L1 band in this case), it is necessary to appropriately weight the antenna transfer function with the GNSS signal spectrum. For this, the antenna transfer function was processed through an ideal receiver tracking error model, following the methodology outlined by Vergara et al. (2016). The obtained errors (now in the form of CPVs) are depicted in Figure 6. The plot indicates that the GNSS code error expected for the automotive-grade antenna can reach up to ±2 m, significantly impacting the overall achievable accuracy.
CPV of the stand-alone antenna
4.2 Hybrid Calibration on a Simplified Digital Twin
Following the initial calibration, a simplified digital twin is constructed by combining EM measurements of the antenna with a computer-aided design (CAD) model of the test vehicle (see Figure 7), obtained through a publicly available database (3DModels.org, 2024). In the CAD car model, the body of the vehicle is represented as a PEC, depicted in green, whereas the side, front, and back windows are represented as glass, depicted in light blue.
Simulated CAD car model with the antenna as a source
When the performance of the installed antenna is assessed via the hybrid approach described above, the extracted gain and phase data now include the effects of the antenna mounted on the vehicle. The resulting radiation pattern, which illustrates the realized gain of the right-hand circularly polarized (RHCP) signal in the presence of reflections from the vehicle’s body, is depicted in Figure 8. Figure 9 presents the corresponding GDV and CPV obtained from the simplified digital twin.
Radiation pattern of the installed antenna for a simplified digital twin
GDV and CPV obtained from a simplified digital twin
The results show how the performance of the installed antenna exhibits oscillations and ripples due to the reflections of nearby objects.
4.3 Generation of CAD Model to be Integrated in the Digital Twin
Interactions between the antenna’s EM fields and the surrounding objects (not only the car) can significantly affect the antenna’s nominal characteristics. Thus, to properly compare the results of the digital twin with those obtained at Geo++’s automotive calibration facility, it is crucial to develop a comprehensive digital twin CAD model of the environment of the vehicle calibration platform. To create this model, terrestrial geodetic measurements, which include distance and horizontal and vertical angles, were conducted using a tachymeter, as depicted in Figure 10.
Image of CAD model creation of the automotive calibration station through tachymeter-based terrestrial geodetic measurements
For instrument placement, two distinct locations were selected in order to survey the entire area of interest. A common frame and datum were realized in an Earth-centered, Earth-fixed (ECEF) system by four markers whose coordinates were determined with GNSS real-time kinematic (RTK) technology, including the coordinates of the two instrument locations.
Although the primary interest of this project lies in the relative distances between object coordinates (using a local coordinate system), the coordinates are first determined in the ECEF system to allow for potential ray-tracing tasks by taking into account the positions of GNSS satellites in the same frame.
Subsequently, object acquisition is performed via terrestrial tachymetric measurements on two faces on the reflectors when possible and, alternatively, via reflector-less techniques. Additional metadata, such as temperature, air pressure, and surface material information, are also gathered. Surface material information is crucial for the EM simulations (see Section 4.4), whereas physical measurements aid in correcting the tachymeter measurements.
In total, the polar elements of 139 distinct points were measured and then transformed into a common frame. The environmental geometry was modeled with geometric primitives, and additional points on 3D bodies were computed to form solid objects.
Because the exact model type of the vehicle is accessible in a publicly available database (as shown in Figure 7), this model is integrated into the digital twin by selecting key points measured on the car. Finally, the detailed digital twin, including the vehicle, is provided in the Standard for the Exchange of Product Data (STEP) format, as illustrated in Figure 11. Additionally, a comprehensive file, including the materials of the objects, is produced.
4.4 Hybrid Calibration on the Detailed Digital Twin
The comprehensive CAD model generated at the calibration station was imported in the digital twin and integrated with the CAD car model, for a more precise representation of the actual scenario. In addition to object geometries, information on object materials was also added: for instance, the car measurement platform was modeled as metal, the fence at the boundary of the lot was modeled as wood, and the tower for the reference antenna was modeled as aluminum. The ground surface was modeled as a wet sandy soil (with εr = 13, μr = 1, and electric loss tangent = 0.29). This detailed assignment of materials is illustrated in Figure 11. High-fidelity digital twins, incorporating realistic material properties, are essential for accurate/precise reflection modeling. Simplifying structures as PECs can lead to overestimated reflection errors, which would later contribute to overall antenna errors.
Detailed digital twin, including the structures in the vicinity of the car, each considered with the corresponding material
Figure 12 displays the predicted radiation pattern of the antenna installed on the car, taking into account the specific scenario of the detailed digital twin. The pattern represents the antenna’s radiation characteristics when the car is stationary, facing the x-direction. Figure 13 provides the corresponding GDV and CPV from the detailed digital twin.
Radiation pattern for the detailed digital twin in the installed case
GDV and CPV obtained from the detailed digital twin
In this case, the patterns exhibit more oscillations over the upper hemisphere, and a few peculiar phenomena appear, such as shadowing at low elevations for an azimuth of ~10° or 160°, with corresponding low gain values and high GDV oscillations.
4.5 Comparison with in Situ Calibration
The installed CPV pattern obtained by the calibration on Geo++’s rotating platform is shown in Figure 14. This figure presents the in situ calibrated CPV of GPS L1 from an antenna installed on a VW Passat in the vehicle coordinate system, where the zero-azimuth of the antenna points to the front of the car and the units are centimeters. While most of the CPVs have magnitudes within ±50 cm, peaks of ±2 m can be observed from the right front and right rear of the car.
Calibrated CPV for GPS L1
A general similarity between the CPVs obtained from the detailed digital twin and those obtained by the Geo++ facility can be observed, but some differences are still visible. These differences might be due to the fact that, during the calibration at the Geo++ facility, the car was not static; instead, it was rotated, effectively changing the multipath geometry.
To facilitate a comprehensive comparison with the in situ calibration results, we conducted multiple simulations in which the car was rotated on the platform by 90° to resemble the actual geometry experienced during the Geo++ calibration; we then calculated the mean of the CPVs obtained from each simulation. Figure 15 presents the mean CPV, now exhibiting an even better match with the errors obtained through the in situ calibration for the Geo++ setup, as shown in Figure 14.
Mean GDV and CPV obtained from the detailed digital twin
The difference between the simulated installed performance results and the in situ calibration is shown in Figure 16. It is evident that the strong effect of the tree close to the 10° azimuth is reduced by this method. Taking the mean of the installed performance can improve the result, bringing it closer to the in situ result. For both the mean and static cases, approximately 48% of the region exhibited a difference within ±25 cm. Furthermore, the percentage of the region with an absolute difference of 25-50 cm was approximately 31% for the mean case and 29% for the static case. Additionally, the percentage of the region with an absolute difference of 50-100 cm was approximately 18% for the mean case and 19% for the static case. The larger differences are predominantly observed in regions where the antenna experiences a lower gain. Overall, these results suggest that one static simulation result can potentially lead to a calibration result that is very close to the in situ calibration.
Difference between installed performance and in situ calibration: (left) difference with respect to a static car in one position; (right) difference with respect to the mean of different positions
4.6 Impact of Calibration on Positioning
To assess the effect of antenna calibration on positioning accuracy, a kinematic driving test was carried out on day of year 043, 2025. At the start of the experiment, the vehicle was kept stationary for several minutes in front of the Geo++ building, after which the vehicle performed multiple runs along a single route. The route included urban sections, a highway segment, and a tree-lined rural road, as shown in Figure 17.
Trajectory of the driving test
Because the shark-fin antenna installed on the Volkswagen Passat B8 is capable of receiving only L1 signals, an additional multi-frequency Tallysman antenna was mounted on the windshield at a distance of approximately 1.95 m from the shark-fin antenna. The reference trajectory was obtained using dual-frequency multi-GNSS RTK positioning. Owing to signal blockages caused by buildings in the parking area and tree obstructions along the rural-road sections, RTK fixing was degraded during these periods. Therefore, the coordinates obtained under such conditions were excluded from the coordinate comparison.
The coordinates of the shark-fin antenna were determined by differential GNSS (DGNSS) processing, both with and without application of GDV correction. Figure 18 presents the coordinate deviations with respect to the reference trajectory in the east (top) and north (bottom) components. The red line represents the solution with GDV correction, whereas the blue line corresponds to the solution without GDV correction. The results of the DGNSS evaluation indicate that application of GDV correction significantly reduces both the systematic and stochastic components of the positioning error. In the east component, the mean error is reduced from +0.19 m without GDV correction to 0.00 m with GDV correction, while the root mean square (RMS) decreases from 0.38 m to 0.27 m. In the north component, the mean error decreases from -0.08 m to 0.02 m, and the RMS is reduced from 0.57 m to 0.38 m. These improvements correspond to approximately 29% in the east component and 33% in the north component. The results confirm that GDV correction for vehicle-installed GNSS antennas provides a substantial improvement in positioning accuracy for precise navigation applications.
Difference in DGNSS solutions for the east and north directions with respect to the reference trajectory with (red) and without (blue) GDV correction
5 CONCLUSION
This paper has shown a hybrid measurement-simulation approach (“digital twin”) for predicting the GNSS errors of an antenna mounted on an automobile. The approach was validated against calibration values obtained through GNSS measurements.
Good agreement between the two methods was found, with ~48% of the region demonstrating a CPV difference within ±25 cm. This correlation serves to validate the approach, providing confidence in its accuracy and reliability. Residual differences are attributed to the difficulty of precisely incorporating the real environment (and its characteristics, for instance, in terms of material properties) in the digital twin environment and because only a selected number of simulations with different car orientations are used.
The proposed approach is a valuable tool that can potentially enable efficient, scalable calibration of various vehicle/antenna combinations, paving the way for the use of open correction data services in the mobility sector. The approach presented herein is not limited to automotive applications, but can also be applied to other types of mounting platforms, such as aircrafts, rooftops, ships, or any other mounting platforms.
HOW TO CITE THIS ARTICLE:
Tripathi, V., Ren, L., Kröger, J., Wübbena, J., Schön, S., & Caizzone, S. (2026). Hybrid GNSS antenna characterization for improved vehicle localization. NAVIGATION, 73. https://doi.org/10.33012/navi.777
ACKNOWLEDGMENTS
We extend our thanks to Wahid Elmarissi for his assistance in performing the measurements. The work presented in this paper was carried out as part of the Accurauto project, funded in the framework of the innovation initiative mFUND by the German Federal Ministry of Transport and Digital Infrastructure - Project No. 19F1189C.
This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.
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