Abstract
Reference stations constitute important elements within the global navigation satellite system (GNSS) infrastructure, as they provide valuable measurements for performance monitoring. For high-quality measurements from such stations, local error sources should be properly characterized and compensated for or minimized. Multipath remains a major contributor to these errors. In severe occurrences, multipath can cause critical errors in sensitive systems such as those utilized for code-dependent applications.
This paper discusses a method for GNSS multipath characterization in challenging installation scenarios, based on a dual-polarization antenna and its integration in a hybrid measurement–simulation framework. A dedicated dual-polarized probe, which houses both an effective geodetic antenna and a multipath-susceptible antenna, was designed, manufactured, and assessed. The dual-sensing nature of the probe allows auxiliary information to be acquired about multipath generated by nearby objects and can be used to infer a plausible range of expected multipath-induced code error at a GNSS sensor station. In addition, a ray-tracing method is discussed, in which antenna measurements are integrated into digital-twin simulations of installations for characterizing multipath conditions. Finally, this study demonstrates that by combining the DPA with digital-twin simulations, it is possible to predict multipath error bounds at an installation in advance. This combined technique presents a flexible tool that is useful for planning system performance with respect to multipath, site layout/selection, and even optimal receiving antenna placement at a given installation.
The proposed simulative method is validated through field experiments, and tests with commercial geodetic-grade antennas are presented to confirm the capability of this method to predict their performance ranges.
1 INTRODUCTION
Satellite-based positioning systems have become an indispensable element of modern life, supporting a wide array of applications in domains ranging from navigation to surveying, among others. In recent years, advances in global navigation satellite system (GNSS) technology have focused on pushing towards higher precision, targeting subcentimeter accuracy (Schaefer & Pearson, 2021). For GNSS-enabled navigation, position–velocity–time (PVT) information estimation involves measuring the distance from a minimum of four satellites to the user through time differences. By implication, not only is the communication between two GNSS segments affected by the satellite–receiver radio link quality but the ability to measure these distances (and by extension, to determine the actual PVT itself) also bears an intrinsic dependence on the quality of this link. Thus, understanding the various satellite–user channel disruptions is of great importance. Typical related error sources include tropospheric and ionospheric refractions. It naturally follows then that to improve positioning accuracy, attempts should be made to mitigate these errors as much as possible. With the use of corrective methods such as dual-frequency measurements and differential pseudorange evaluation, most of the aforementioned errors, as well as several timing-related errors, can be completely eliminated or greatly reduced, as demonstrated by Karaim et al. (2018). Nonetheless, in the very last few meters of downlink propagation, another error source emerges: multipath. Here, incoming right-hand circularly polarized (RHCP) satellite wave fronts, interacting (through reflection/diffraction) with objects in vicinity of the GNSS receiver system, produce signal replicas that reach the antenna together with the direct signals but through paths other than the line-of-sight (LoS) path. The resultant multipath-contaminated signals typically have different polarizations, delays, and amplitudes. In some cases, the LoS signal may be completely blocked by an obstacle, and only indirect signals reach the antenna. Effects of these far- and near-field signal interactions can cause significant system performance degradation as attempts to track the superimposed signals create distortions in the receiver system and introduce biases into collected GNSS observables. In extreme occurrences, severe multipath can render GNSS measurements collected from reference station networks unusable, particularly for code-dependent applications such as time and frequency transfer, where multipath errors can dominate the overall residual error budget. The net multipath effect depends on several factors, the most crucial of which are signal characteristics, antenna installation environment, geometries of reflected signal paths, antenna properties, and receiver design. Although a well-documented phenomenon, multipath remains a major source of error, whose remedy is often largely limited to the design of certain receiving antenna properties and the choice of installation location (Lau, 2021).
Reference stations constitute critical elements within the GNSS infrastructure, as they provide valuable measurements for monitoring the space segment of the satellite navigation chain. In the code observation domain, biases resulting from multipath range from a few decimeters to several meters for typical reference stations. Such biases can translate into severe degradations in positioning/timing accuracy. To obtain high-quality measurements from such stations, these local error sources should be properly characterized and compensated for or minimized. As primary elements in the GNSS receiver chain, antennas significantly influence the received signal quality and, ultimately, navigation precision. Therefore, interactions between antennas and multipath require adequate investigation and characterization. Antenna parameters that influence multipath susceptibility have been discussed extensively by Caizzone et al. (2018). To achieve higher-precision navigation, a proper prior estimation of an antenna’s expected (multipath) performance in situ is of significant importance in site planning. In existing installations, an assessment of antenna responses to multipath conditions is also useful for error troubleshooting and calibration. The natural approach, of course, would be to measure the electromagnetic (EM) behavior of the antenna, once it has been set upon its final platform. However, it can be extremely expensive, difficult, and sometimes impossible to undertake such studies, especially for cases in which the platform/scene is very large. To address this problem, new techniques such as using drone-bound aerial EM probes, are currently being developed; see, e.g., the work by Faul & Eibert (2021). However, this technology is still in its infancy and not yet fully available. Another interesting technique is the fully simulative analysis of installed antenna performance. Although a viable solution, this method is limited by the availability of design files for antennas to be installed, which are uncommon for commercial-off-the-shelf (COTS) types.
In this paper, a method for GNSS multipath characterization in challenging installation scenarios is presented, based on a dual-polarization antenna (DPA) and its integration in an hybrid measurement–simulation framework. For this study, a dedicated dual-polarized probe, which houses both an effective geodetic antenna and a multipath-susceptible antenna, was designed, manufactured, and assessed. The dual-sensing nature of the antenna allows for reliable capture of both LoS and reflected signals for evaluation. Next, a ray-tracing method is discussed, in which anechoic chamber antenna measurements are integrated into digital-twin simulations of installations for characterizing multipath conditions. With this approach, sources of multipath that the antenna will experience in situ can be predicted with reasonable accuracy and analyzed. Moreover, by considering actual antenna characteristics, the proposed method more closely models the real installed performance. A combination of the DPA with digital-twin simulations makes it possible to predict multipath error bounds at an installation in advance. Furthermore, this combined technique presents a flexible tool for system performance planning with respect to multipath and for optimal receiver placement at a given installation.
The proposed method is validated through field experiments, and tests with COTS-grade geodetic-grade antennas are performed to confirm the ability of the proposed method to predict multipath performance ranges. This paper builds upon and augments the findings of an earlier conference publication (Addo & Caizzone, 2023) and includes new results from simulations and experiments, with an elaborate description of the characterization method.
2 CHARACTERIZING GNSS MULTIPATH CONDITIONS AT REFERENCE STATIONS
2.1 Multipath–Antenna–Receiver Interactions
When signals transmitted by satellites approach the earth, they reflect or diffract off objects in the vicinity of the GNSS receiving system. In the presence of multipath, replicas of the direct signal arrive at the receiving system through multiple paths other than the LoS path. Ordinarily, the phenomenon is studied geometrically, whereas EM or physical properties of the indirect signals are not often discussed. However, in contrast to the LoS, the form assumed by multipath signals is directly related to the EM nature of signal interactions in the scene, satellite– reflector–receiver geometry, signal frequency, and reflector material properties. These non-LoS (NLoS) signals vary in terms of signal strength, phase, delay, and polarization (Braasch, 2017). Moreover, the different multipath interaction types (and their combinations) result in diverse multipath propagation effects, particularly in complex installation scenarios. Generally, reflections may be specular or diffused or a mix of the two, depending on the reflector. For specular reflections, signals reach the receiving antenna from only one direction, and the distortion of the signals can be described by the Fresnel reflection coefficients (Najibi & Jin, 2013):
1
2
3
where ϵ, ϵr, and σ are the complex permittivity, relative permittivity, and conductivity of the reflector material, respectively. The carrier wavelength and signal incidence angle are denoted by λ and α, respectively, whereas Γv and Γh represent the respective reflection coefficients of the individual linear (vertical, horizontal) components of the signal (Equation (2)). It should be noted that the descriptions of Γv and Γh in Equation (2) refer to specular reflections off a horizontal surface and may take different forms for other orientations of reflecting surfaces and scattering regimes. These coefficients change for different reflecting angles and different reflector materials. Generally, the two orthogonal components of the GNSS signal undergo dissimilar attenuation and polarity changes when reflected. Γh amplitudes increase steadily for increasing α and maintain a near-constant phase shift for all signal incidences. In contrast, the magnitude of Γv decreases to zero with increasing incidence angle until α reaches the so-called Brewster incidence angle γB, after which it reaches a value similar to that of Γh. Additionally, Γv undergoes a phase reversal at γB. For α < γB, an RHCP signal reverses polarization sense, producing a left-hand circularly polarized (LHCP) or left-hand elliptical signal with some attenuation, the degree of which depends on the material. The eccentricity of the signal increases as α approaches γB and becomes linearly (horizontally) polarized at α ≈ γB. For α > γB, an RHCP signal becomes right-hand elliptical upon reflection (Appleget & Bartone, 2019; Smyrnaios et al., 2013). Diffuse scattering occurs on irregular surfaces and is statistically random with a Rayleigh distribution, but can be treated as a further attenuation of the specular case. In contrast, the diffraction mechanism, which occurs on the edges of shadowing objects and can cause deep fading of LoS signal amplitudes, is often described by the uniform theory of diffraction or physical optics. These methods quantify the ray-bending phenomena in the form of diffraction coefficients for source–object combinations (Nicolás et al., 2012).
At the receiving antenna, the superposition of direct and multipath signals yields compound signals. These signals can impinge on the antenna from any direction within its local upper or lower hemisphere (Figure 1). As spatio-polarimetric filters, GNSS antennas are required to offer as much inherent multipath discrimination as possible and, for this reason, are designed as RHCP antennas. For instance, at zenith, a well-designed GNSS reference station antenna is at least 20 dB more sensitive to RHCP signals than to LHCP signals. However, as discussed above, some multipath signals, entering the antenna at low elevation angles, may retain RHCP properties depending on the reflection regime and thus bypass this filtering process. Furthermore, antennas are usually capable of effective LHCP rejection only in a limited range of angles and can therefore still receive LHCP signals impinging from other directions. Such antenna properties strongly influence the amount of multipath passed to the receiver. Depending on these characteristics, LHCP and other mixed-polarized signals may nonetheless be collected by a receiving antenna. The various categories of GNSS antenna abilities for suppressing impinging multipath signals have been studied extensively by Caizzone et al. (2018). The interference on the LoS signal, whether constructive or destructive (depending on the relative amplitude and phase differences), results in a deformed correlation between the received signal and the local PRN replicas in the receiver during signal tracking (Vergara et al., 2016). Code autocorrelation peaks are distorted, and consequently, accurate determination of LoS code phases cannot be guaranteed by signal power equalization methods in receiver correlation channels. Induced biases propagate through to tracking loops and signal strength estimation algorithms, thus contaminating all related observables (carrier phase, code phase, and carrier-to-noise power ratio [C/N0]). In severe cases, these interferences can also cause erratic tracking loop locking and a degraded acquistion/quality of ranging observations. Resulting tracking errors can be up to half a code chip (Jiang & Groves, 2014).
Multipath and LoS signal interactions with a GNSS receiving antenna in an installation scene
2.2 DPAs as Multipath Characterization Tools
2.2.1 Background
A study of GNSS multipath at a given site necessitates the use of sensors, in the form of antennas, that are capable of collecting all of the varied signal forms. Intuitively, the use of an LHCP antenna to sense the predominantly oppositely polarized reflected satellite signals would be beneficial for characterizing multipath. Such antennas receive a greater reflected power than an RHCP antenna. However, with a “pure” LHCP antenna alone, satellite–receiver radio link tracking cannot be sustained on commercial receivers. With the low number of stable observables on an LHCP channel in such cases, it becomes very difficult to fully resolve multipath sources. One solution is to consider harnessing the potential of antenna polarimetry (Aloi & Van Graas, 2004; Emmanuele et al., 2019). Exploiting diversity in the polarization domain affords additional degrees of freedom to better estimate multipath conditions. In this approach, it is possible to consider the composite circularly polarized signals or, in contrast, the different individual linearly polarized signal components. The latter requires the use of complex and specialized receiver front-ends, as in the study reported by Hahn et al. (2023). This work adopts the first method in order to enable the use of commercially available high-performance receivers and minimize the risk of introducing additional error sources from custom hardware into signal processing/analysis. An antenna with the capability to sense and produce outputs of both RHCP and LHCP signal responses was envisioned. By collecting, processing, and comparing the two outputs, it is possible to characterize multipath in a given installation scene.
2.2.2 Dual-Polarized Multipath Probe
For this study, the GNSS antenna based on a broadband, multifeed dielectric-resonator design discussed by the authors in Caizzone et al. (2021) was augmented to be used as a multipath probe. This probe is dual-circularly polarized with opposite-sense RHCP and LHCP outputs. The two polarization states of the DPA are hereafter referred to as DPA-RHCP (DPA-R) and DPA-LHCP (DPA-L). It should be noted that the desired polarization for a given antenna’s response is its co-polarization (co-pol) component whereas the naturally occurring and typically unwanted counter-polarization is referred to as cross-polarization (cross-pol). For example, the co-pol response of DPA-L is LHCP, and its cross-pol is RHCP. The difference in the two gain responses is termed cross-polarization discrimination (XPD), which is a measure of the polarization purity of an antenna. DPA-R and DPA-L are the output ports of the DPA (Figure 2(a)).
In-house-developed DPA mounted in the DLR semi-anechoic chamber for EM characterization (a) DPA output ports (b) DPA in an anechoic chamber
For a DPA to function effectively as a multipath characterization probe, its design must satisfy three requirements:
The two polarization states must co-locate in space, i.e., their mean antenna phase centers (APCs) must be very similar. This requirement ensures that multipath signals in a given installation reach both antenna states similarly. Their relatively unbiased responses can then be used as a basis for the multipath characterization technique.
DPA-R should have very pure RHCP polarization and strong backlobe suppression for optimal conventional GNSS receiver performance. The former requirement indicates that it is desirable for DPA-R to have a near-azimuthally-uniform RHCP radiation pattern whilst exhibiting high XPD. A high XPD reduces the sensitivity of DPA-R to NLoS signals reaching it from the upper hemisphere whereas strongly suppressed backlobes shield DPA-R from signals arising from lower-hemisphere reflections when it is installed (Caizzone et al., 2018).
DPA-L should have a high co-pol response, preferably as high as that of DPA-R. This allows for DPA-L to act as a “focusing lens” for probing the predominantly LHCP multipath. However, the cross-polar gain of DPA-L must also be kept sufficiently high, to allow for continuous tracking of satellite signals by the receiver. This requirement helps mitigate the challenges of poor and erratic signal tracking observed on LHCP channels in previous studies with DPAs (Groves et al., 2010). Finally, the co- and cross-polarization patterns on DPA-L should exhibit as little azimuthal variance as possible. This feature ensures a uniform collection of each class of signals, LoS (RHCP) or reflected (~LHCP), from all azimuths of arrival, ϕ, for a given elevation, θ (Caizzone et al., 2017).
Generally, one must balance the need for a probe that is capable of acting as an effective representative of the reference/geodetic class of GNSS antennas while being vulnerable to multipath signals in its vicinity, all in one antenna (housing). Proper design techniques allowed us to satisfy all three requirements. The use of a single antenna element to generate the two polarization states satisfies Requirement 1. Because the focus of this work is to characterize, rather than to mitigate, multipath, the use of a single element is sufficient (Ray et al., 1999; Sgammini et al., 2019). The application of manifold element feed and effective grounding techniques satisfies Requirement 2. Requirement 3 is satisfied by using the solution to Requirement 2, coupled with special polarization generation circuitry. The antenna has a 40-cm diameter and is 50 cm high.
To verify the efficacy of these solutions, we fabricated and assessed the proposed antenna. Moreover, to develop a tractable multipath characterization technique, it was imperative to obtain information on related EM properties of the antenna, i.e., gain and group delay variations (GDVs). Deviations in these “standalone” EM properties of the antennas or their related GNSS observables can then be analyzed to derive the presence/nature/effects of multipath in an installation scene. For instance, the C/N0 of received signals is strongly dependent on the antenna gain, and high C/N0 levels are important for proper receiver-side operation. Additionally, the relative levels of co- and cross-pol antenna gain responses are indicative of an antenna’s susceptibility to multipath. Therefore, the varied signal strengths and polarizations of multipath can be observed via the C/N0 measured at the antenna. In contrast, the group delay, as described by Equation (4), refers to the different angular-dependent time delays experienced by each frequency component of received signals while being transduced by the antenna:
4
where Ψ is the (RHCP) far-field radiation phase response of the antenna as a function of frequency, f, and signal direction-of-arrival (θ, ϕ). The GDV of the receiving antenna influences the pseudorange determination, as such variations cause distortions in signal correlations at the receiver (Caizzone et al., 2019). Provided that the GDV of a receiving antenna is properly characterized, these effects on measured GNSS observables can be fully corrected. However, the different signal delays of LoS replicas generated by multipath phenomena introduce code variations that remain even after the antenna’s intrinsic group delay has been calibrated out. By examining these residual deviations, it is possible to analyze the effects of multipath and derive the resultant pseudorange error induced by multipath effects.
For the EM characterization, the DPA was mounted and measured in a semi-anechoic near-field chamber (Starlab by MVG) available at DLR’s premises (Figure 2(b)). This antenna calibration provides the transfer function (amplitude and phase) of the antenna dependence on frequency, elevation, and azimuth angles. The transfer functions of DPA-R and DPA-L were evaluated over the full GNSS L1/E1 (1563–1587 MHz) and L5/E5a (1164–1189 MHz) bands at a 1-MHz resolution. Measurements were referenced to the DPA base (antenna reference point [ARP]) and were sampled over a 2° aspect-angle grid. Figure 3 shows the per-elevation gain responses of the DPA polarization states measured at the central frequencies of the two bands: 1575 and 1176 MHz. The plots indicate that DPA-R and DPA-L possess near-identical uniform co-pol patterns and gain roll-offs. Pattern uniformity is signified by how closely the gain traces are bound. Naturally, it is observed that the polarization responses of both DPA-R and DPA-L became progressively linear towards the horizon, down to the lower hemisphere. Additionally, DPA-R exhibits high polarization purity (~ 22-dB XPD at zenith) and significant backlobe suppression (Requirement 2). The DPA-L patterns show sufficiently strong co-pol and cross-pol responses in both bands of study (Figures 3(b) and 3(d)). Although a difficult design parameter to control, the obtained cross-pol on the DPA-L shows good uniformity along the azimuth in both GNSS bands (Requirement 3, obtained using special polarizers). For the DPA-R cross-pol, a focus was placed on XPD levels rather than uniformity as a requirement. Lastly, the measured APCs of DPA-R and DPA-L were also found to be similar, satisfying Requirement 1. For instance, their APCs were offset by 31.82 cm and 31.78 cm, respectively, above the DPA ARP at 1575 MHz. From the DPA measurement results, it is clear that the goal of developing an effective geodetic antenna (DPA-R) and a multipath-susceptible antenna (DPA-L), all in one housing, was achieved. Measured antenna GDVs will be presented and discussed in the next sections.
Realized gain vs. elevation for DPA-R and DPA-L, measured at the central frequencies of the GNSS L1/E1 and L5/E5a bands: 1575 MHz and 1176 MHz, respectively (a) DPA-R (b) DPA-L (c) DPA-R (d) DPA-L
Different lines represent azimuthal values with a resolution of 2°, with RHCP responses in blue and LHCP in red. (The gain is shown in dBiC, i.e., referring to a circularly polarized isotropic radiator.)
2.3 DPA-Enabled Hybrid Simulative Approach for Multipath Characterization
To elucidate the physical processes involved in multipath phenomena, wave propagation models are very useful. However, several factors render the full characterization of multipath in intense installation scenes through analytical methods, summarized in Section 2.1, a challenging task. These factors include the unknown number/nature of different multipath signal components, the varying EM interactions, and the complex geometries of their paths coupled with antenna–receiver system properties. A possible solution is to harness the potential of EM simulators (Addo & Caizzone, 2022). By combining the output responses of a DPA with the capabilities of ray-tracing-based EM solvers, it is feasible to achieve a holistic modeling of multipath propagation and to assess the effect of this phenomenon on GNSS performance. An even better extension of this idea is the hybrid simulative approach, which is considered in this work.
In this method, chamber measurements of the actual DPA (discussed in Section 2.2.2) are integrated with EM simulations of a digital twin of a given installation scene. The underlying principle is that the effects of multipath can be expressed as aberrations in the effective characteristics of the DPA when compared with the standalone states, and by examining these distortions, the multipath error can be quantified. To do this, the so-called Huygens’ boxes (near-field equivalent sources [NFSs]) of the DPA are first extracted from the anechoic chamber measurements. Then, the DPA NFSs are simulated both standalone and when inserted into a three-dimensional (3D) computer-aided design model of the anticipated installation site. The former generates far-field properties akin to what is obtained in chamber measurements, whereas simulation of the installed case produces distorted DPA gain and phase patterns due to interactions of the antenna with multipath and nearby near-field structures (the Fresnel region in this case is approximately 1 m wide). The simulations were performed in SIMULIA CST Studio Suite®, a 3D EM field and multiphysics modeling and simulation tool (Dassault-Systèmes, 2022). Analyses of these pattern perturbations with respect to the standalone case allow one to predict sources of multipath that the DPA (and GNSS antennas in general) will experience when installed. Moreover, by considering actual DPA characteristics, the actual installed performance can be analyzed much more closely. In particular, this performance can be evaluated in terms of the antenna gain, linked to C/N0 observables and/or the group delay, which is related to pseudoranges. The two evaluation methods are complementary or can be utilized alone for multipath characterization. The group-delay-based method will be used in this paper, because of its stronger correlation to code multipath error compared with the gain-based method.
Studies by Murphy et al. (2007) and Caizzone et al. (2022) have demonstrated that the intrinsic contributions of GNSS antennas to pseudorange errors are strongly related to GDVs with respect to observation angles. Thus, for a group-delay-based evaluation of the purely-multipath-induced pseudorange errors passed on by the antenna(s) to the receiver, the related error contributions of the DPA itself should be determined and calibrated out. These systematic DPA code biases can be obtained by passing the simulated antenna responses through a software receiver that projects onto the antennas, corresponding to GNSS signal spectral properties. This calibration process was achieved using a multi-frequency GNSS receiver model adapted from the framework described by Vergara et al. (2016). This receiver implements mathematical models of various blocks in the basic receiver chain. The outputs of this receiver model are the DPA antenna-generated pseudorange errors, which are then de-embedded from the simulated responses prior to statistical processing in another in-house software tool for generating 3D code multipath error maps. In this way, the multipath suppression capability of the DPA can still be considered while its intrinsic code error contribution is eliminated. This separation allows for the prediction and analysis of antenna-bias-free multipath-induced error on pseudorange measurements. A functional diagram of the DPA-enabled hybrid simulative multipath characterization process is presented in Figure 4. It is important to note that multipath determination using ray-tracing in an EM simulator has some inherent practical challenges. First, GNSS signals are not simply rays. Additionally, predicting signal phase delays to within a fraction of a wavelength is impossible; hence, an exact determination of (the signs of) multipath errors is difficult. Such accuracy requires that the digital-twin mapping and receiving antenna placement be as precise as possible. Furthermore, surface reflectivity information is difficult to fully obtain. Generally, only approximations are possible. The closer the model is to the actual scene, the better the approximation. Nonetheless, with a reasonably good model fidelity, the method remains a very useful tool for obtaining a fairly accurate first-order understanding of the multipath propagation.
Flow diagram of the digital-twin-enabled code multipath characterization scheme
3 EXEMPLARY STUDY
3.1 Test Scenario and Digital Twin
An antenna farm located on the roof of an office building at DLR’s Oberpfaffenhofen campus was chosen as the test environment for this study. The in-house-developed DPA was used to assess the multipath conditions in the scene. As shown in Figure 2, the antenna platform sits on an elevated midsection of the roof (7 m above the main roof level) and is surrounded by numerous reflecting/diffracting/obstructing objects. Thus, the scenario under characterization is a multipath-intense scene, comparable to rooftop installations in many GNSS monitoring networks. Prominent reflectors in the vicinity of the setup included a 5-m parabolic dish antenna (with its support structure), the antenna-farm platform, and an observatory dome. The dome is located a distance of approximately 10 m at an azimuth of ≈130° and is nearly submerged in the lower hemisphere of the setup, whereas the dish antenna, tilted eastward and elevated 30°, is located approximately 20 m away at an azimuth of ≈300°. From visual inspection, the dish antenna’s reflector body, which was static during our experimentation, constituted the main upper hemisphere obstacle within 50 m of the test setup. Many smaller lower-elevation reflectors also exist in the scene.
The multipath environment in the test scene was studied with the aid of the digital-twin analyses discussed in Section 2.3. A 3D model of the installation site was first constructed using available information on the surrounding structures, taking into account the presence, geometry, and material properties of in-scene objects (Figure 6). The materials used in the model and their related EM properties at GNSS frequencies are summarized in Table 1. The mean phase centers of the Huygens’ boxes of the DPA were positioned such that they coincided with the test setup position shown in Figure 5 and the origin of the digital twin’s local coordinate system. The analysis was conducted on a aspect-angle grid with 2° resolution.
Digital twin of the test scenario (a) Top view (b) Perspective view The mean DPA phase center is located at the origin of the local coordinate system.
EM Properties of Materials of Test Scene Objects Modeled in the Digital Twin (Source: Mitchell (2003))
Test installation scenario to be characterized (a) Aerial view (credit: Google Maps) (b) Side view
The antenna setup position is indicated by red markers.
3.2 Prediction of Multipath Conditions in the Test Scene
The distortions that the DPA-R and DPA-L patterns undergo after installation are each used to examine multipath conditions. These multipath-induced effects are estimated by de-embedding the standalone GDV patterns from the patterns obtained when the antenna is installed in the scenario. The “standalone” and “installed” GDV patterns of the DPAs, GDValone and GDVinstall, as well as a measure of the changes that they undergo (ΔGDV = GDVinstall – GDValone) are summarized in polar plots in Figure 7. GDValone refers to the GDV of the DPA obtained through calibration in a benign environment (an anechoic chamber in this case). In contrast, GDVinstall is the GDV of the DPA when installed in the scene. The maps show the portions of the sky from which signals transmitted by satellites will be affected by multipath propagation and the degree of this effect. Strong GDV perturbations are observed at most lower elevations of the eastern hemisphere of the map and some regions of the western hemisphere. A much larger distortion is visible for DPA-L, confirming the hypothesis that most of the reflections are LHCP and therefore mostly affect the pattern of DPA-L, while being suppressed by DPA-R. Analyses in this study are restricted to the GNSS L1/E1 band for brevity. However, with appropriate modifications to the NFS, material dispersive properties, etc., these analyses can be applied to any of the current GNSS bands. All skyplots, including antenna patterns, are presented in the topocentric coordinate system.
Standalone and distorted GDV patterns (in ns) of the DPA polarization outputs at the GNSS L1/E1 band (a) G DValone (b) G DVinstall (c) ΔG DV (d) G DValone (e) G DVinstall (f) ΔG DV
For antenna-induced pseudorange error calibration, would-be received satellite signals were represented with BPSK(1) modulated signals for L1 C/A and CBOC(6,1,1/11,-) for E1-OS in the receiver model. The receiver delay-locked loop (DLL) discriminators were configured to have a correlator chip spacing of 0.1 for L1/E1 over a 24-MHz bandwidth. The antenna-bias-free multipath-induced pseudorange error maps obtained post-calibration for both DPA-R and DPA-L are shown in Figure 8. These errors are related to ΔGDV. This evaluation demonstrates that DPA-L exhibits much more susceptibility to code multipath and confirms its usability as a multipath “zooming lens” to estimate the worse-case multipath to be expected at the receiver. Together with DPA-R, the responses at the two DPA output ports can be used to assess the nature of the multipath conditions, i.e., the upper and lower bounds on multipath error in a given installation scene. A comparison with the GNSS measurement results is shown later in Section 4.2.
Absolute multipath-induced code error (in meters) experienced by the DPA, predicted through digital-twin analyses (a) DPA-R (b) DPA-L
3.3 Investigating Contributions of In-Scene Objects
An added advantage of the presented DPA-enabled hybrid simulative method for multipath characterization is that it can serve as a valuable tool for assessing the contributions of objects to the residual multipath error at existing reference station sites. For a test scenario, the dish antenna and observatory dome are studied, as they constitute the two most prominent disturbing objects in the vicinity of the GNSS receiving system. Three variations of the test scenario were investigated: one without the observatory dome, one without the dish antenna (with its base), and one without either. Because the DPA-L responses represent a view of the worst-case multipath environment, only DPA-L error maps were studied in this analysis and are presented here for brevity. These three variants of the scene were compared with the full scene (Figure 6). The delta-error maps shown in Figure 9 present the various influences of the dome and/or dish antenna on the residual multipath error. These maps bolster the assertion that the two large objects contribute significantly to the bulk of multipath error in the scene (cf. Figure 8(b)). It is observed that the presence of these objects primarily influences multipath errors in lower elevations of the western quadrant and most of the eastern hemisphere of the skyplot. These contributions could be destructive or constructive to the residual multipath error. For instance, in Figures 9(g)–9(i), bluish points denote negative contributions, i.e., multipath errors that are strongly reduced or completely eliminated (from the error map of the full scene) because of the presence of the object(s). The opposite is true for reddish points, which represent positive contributions, i.e., introduction of or strong increase in multipath error. With such information, post-installation corrective measures such as the work by Caizzone et al. (2023) could be explored to electromagnetically filter out effects of such disturbing scene objects, if they cannot be physically removed.
Contributions (in meters) of scene object presence to residual multipath-induced pseudorange error (on DPA-L) (a) Scene model without observatory dome (b) Scene model without dish antenna (+ base) (c) Scene model without dish antenna or dome (d) Error map of “domeless” scene (e) Error map of “dishless” scene (f) Error map of “dishless” and “domeless” scene (g) Contributions of observatory dome (h) Contributions of dish antenna (+ base) (i) Combined contributions of dome and dish
The antenna mount positions are indicated by red arrows.
3.4 Receiving Antenna Placement and System Performance Planning
A natural evolution of the analyses in Section 3.3 is the possibility of using the presented characterization method preemptively as a tool for site layout and/or antenna placement planning for critical reference installation stations. Thus, this method is useful for system performance prediction from the viewpoint of multipath-induced error. For sensitive applications, it is possible to undertake a priori assessments of candidate receiving-antenna placements to ascertain whether they allow for operation below multipath tolerances.
For the purpose of this study, we introduce two parameters: the multipath tolerance, Tm (in meters), and the usable coverage, uC = (uCw, uCb), which refers to the fraction of collected measurement data from available GNSS coverage that can be used by the system, subject to Tm. The parameters uCw and uCb represent the worst- and best-case uC, characterized by DPA-L and DPA-R, respectively. The [Tm, (uCw, uCb)] tuple provides a descriptive tag for comparing and selecting sites. Moreover, flagged maps can be created for a given installation to determine skyplot areas from which incoming satellite transmissions are severely affected by multipath (i.e., with values beyond Tm). Green points signify usable observation sources whereas black spots represent unusable sources (Figure 10). Collected observables linked to the black points can then be discarded from sensitive post-processing or targeted for selective refining. In this work, the tuple definition is based on uniform thresholding. Furthermore, because the 3D hemispherical space is sampled uniformly (on a 2° grid), a cosθ weighting profile was applied for cell aggregation in the computation of uC because higher-elevation cells subtend smaller solid angles compared with cells corresponding to a smaller θ. More complex criteria can also be employed.
Predicted usable GNSS coverage of Mount 0, based on application-specific multipath tolerances (Tm = 1.0 m here) (a) “Worst-case” usable GNSS coverage (b) “Best-case” usable GNSS coverage
Three alternatively sited antenna mounts, Mounts 1–3, were studied as candidates for potential improved antenna installation locations in the scene with respect to multipath error (Figure 11). The multipath environments at Mounts 1–3 were compared to that of the current test mount in the actual installation scene (Figures 5 and 6), denoted as Mount 0. Two conservative Tm values, 0.5 m and 1.0 m, were used for the analyses. The results are summarized in Table 2, showing that siting the antenna with Mount 3 gives the best performances among the four options, with [0.5, (71.8, 85.6)] and [1.0, (81.3, 90.9)].
Alternatively sited antenna mounts (indicated by red arrows) and their projected uCw maps for Tm = 1.0 m (a) Mount 1 (b) Mount 2 (c) Mount 3 (d) uCw map for Mount 1 (e) uCw map for Mount 2 (f) uCw map for Mount 3
Projected in Situ Error Performance Bounds for Different Antenna Mount Locations and Multipath Tolerances
4 EXPERIMENTAL VALIDATION: TESTS, RESULTS, AND DISCUSSIONS
4.1 Field Tests
Field tests were conducted to verify the test scene’s characterized multipath environment obtained through the hybrid simulative approach (discussed in Section 3.2). The DPA was installed on the antenna mount and allowed to collect GNSS observables over a 10-day period to achieve full skyplot coverage for the analysis of multipath effects. In this way, mapping of the multipath signatures in the scene is enhanced, and repeatable examination of test antenna responses is possible. Each DPA output was connected to two identical Septentrio PolaRx5TR multi-frequency, multi-constellation GNSS receivers. Thus, GNSS measurements were collected concurrently for both outputs, at a 1-Hz observation rate for both hardware receivers. For the purpose of this study, DPA-R and DPA-L were treated as independent channels. The phase and DLL bandwidths on both receivers were set to 0.25 and 15 Hz, respectively. Furthermore, chip receiver correlator spacings of 0.1 and 1 were used for L1/E1 and L5/E5a DLL discriminators, respectively, for reduced code tracking errors and sufficient noise reduction. Measurement data from DPA-R and DPA-L were time-matched, and satellite tracking corrections were performed in the post-processing stages for comparison purposes.
4.2 Predicted vs. Measured Multipath Error
The multipath-induced code error at the receiver was estimated from the collected data via the dual-frequency code-minus-carrier (CMC) method described by Circiu et al. (2020). This technique allows for the isolation of multipath contributions to the code error by using measured carrier phases to remove (a majority of) other residual GNSS error factors, such as ionospheric divergences in collected pseudoranges. Skyplot representations of the estimated multipath error in the L1 band, as measured by DPA-R and DPA-L, are summarized in Figures 13(c) and 13(d), respectively. Multipath error maps predicted for the DPA outputs using the group-delay-based method (Section 3.2) are shown in Figures 13(a) and 13(b). For better comparison, the maps (same as Figure 8) are masked by using binned satellite coordinates recorded in the respective GNSS field measurements described above. Because of its higher multipath susceptibility, DPA-L acts as a “zooming lens” for the multipath conditions present in the test environment and enables us to obtain worst-case predictions of the amount of multipath that GNSS antennas will experience in the installation scenario. The empty low-elevation zones in the DPA-L maps are due to the low-gain values of the cross-polar (RHCP) component in those regions. A comparison between the predicted and measured multipath-induced pseudorange error maps obtained for both DPA-R and DPA-L shows good agreement. The differences between the predicted and measured error maps can be attributed to a combination of several factors. Among these is the hemispheric sampling of skyspace for the predicted maps compared with the finer observation points obtained in measurements along satellite trajectories. These discrepancies appear to be prevalent at higher elevations because of the smaller corresponding cells. Furthermore, the predictions obtained through simulations approximate real measurements simply from an EM viewpoint (as described in Section 2.3) and do not consider influences such as receiver and signal dynamics or noise. Thus, the simulation predictions tend to underestimate the error. This effect is clear in DPA-L maps, whose measurements are more susceptible to these noisy reflected signals. However, the predicted and measured multipath hotspots (e.g., regions with azimuth angles of 30°–90°and elevations up to 40°) show good agreement. The per-elevation root-mean-square (RMS) “raw’’ L1/E1 multipath errors sensed by DPA-R and DPA-L are summarized in Figure 14. The “worst-case’’ error values range from approximately 0.3 m at zenith to upwards of 1.0 m at low elevations. The multipath RMS error predictions obtained through simulation also show good agreement with the errors measured with both DPA-R and DPA-L, validating the hybrid simulative multipath characterization method. Furthermore, as discussed in Section 3.2, the responses of DPA-R and DPA-L could be used as indicators for the upper and lower bounds of reference antenna responses to multipath conditions in a GNSS installation. These multipath bounds can be characterized by using the DPA either through measurements or in the case of an a priori characterization, predicted through the discussed hybrid simulative approach. The bounds for the multipath conditions at Mount 0 in the test installation scene (Figure 5) obtained from the simulative method are indicated by the shaded region in Figure 13.
DPA installed in the test scene for GNSS measurements; perspective views of the setup with respect to large disturbing objects
Skyplots of multipath environment measured for the DPA setup at the test site, compared with predictions from digital-twin simulations at the GNSS L1/E1 band (a) Predicted DPA-R response (b) Predicted DPA-L response (c) Measured DPA-R response (d) Measured DPA-L response
RMS multipath (in meters) measured at DPA outputs, indicating the characterized bounds for multipath conditions in the test scene at the GNSS L1/E1 band
4.3 Responses of Different Installed COTS Reference Antennas to Multipath
To validate the characterized multipath bounds derived for the scene, three International GNSS Service-level COTS antennas were studied: NovAtel’s GNSS750, Septentrio’s PolaNt, and Trimble’s Zephyr-2. These three antennas are geodetic antennas equipped with different design technologies for strong multipath suppression. PolaNt uses a slightly modified version of the classic choke ring, GNSS750 has a 3D conical choke ring structure, and Zephyr-2 employs Trimble’s patented resistive ground plane. The COTS antennas were each installed on the test mount in the scene (Mount 0), where their multipath responses were measured using the same hardware receiver listed in Section 4.1 and estimated using the CMC method. Multipath error skyplots of the respective antennas are shown in Figure 15. Each of the antennas exhibited varied multipath error maps according to the efficacy of their individual multipath-limiting capabilities, with PolaNt showing the strongest suppression. Compared with the DPA analysis, the skyplot regions that were determined to show intense multipath signatures were consistent in all three maps. Figure 16 shows the RMS multipath error of the three COTS antennas together with those of the DPA. Among the tested antennas, DPA-R and PolaNt passed on the lowest multipath error to the receiver for all elevations. However, DPA-R exhibited slightly better performance at intermediate to low elevations. Additionally, it can be observed that the RMS errors of the test geodetic antennas fell within the error bounds defined by the DPA measurements. This trend was also observed for the multipath bounds predicted using the DPA through the discussed simulative technique. Therefore, with DPA measurements, it is possible to characterize the upper and lower bounds of the multipath conditions that will be experienced by geodetic antennas at the GNSS reference installation site. This ability is useful for planning system performance with respect to multipath, particularly in the case of very sensitive code-dependent applications. Furthermore, by combining this ability of the DPA with the presented hybrid simulative method, a priori characterization of the multipath environment can be achieved, even for installations that cannot be tested beforehand through measurements. Optimal receiving antenna placement or even site layout planning is possible with the presented method, as was demonstrated in Sections 3.3 and 3.4.
Multipath skyplots (in meters) for different COTS antenna setups at the test site, estimated at the GNSS L1/E1 band (d) NovAtel GNSS750 (e) Septentrio PolaNt (f) Trimble Zephyr-2
RMS multipath error responses of COTS reference antennas, compared with the characterized multipath bounds predicted using the hybrid simulative method
5 CONCLUSIONS
In this paper, a method for characterizing GNSS multipath by means of a DPA and its integration in a hybrid measurement–simulation framework has been presented. DPAs allow us to obtain auxiliary information of the multipath generated by objects in the vicinity of the antenna and to thus extend the characterization of multipath levels in such scenarios further than that achieved by a conventional (RHCP) reference station antenna. A dedicated DPA was designed, fabricated, and assessed for this purpose. This dual-polarized probe combines an effective geodetic antenna and a multipath-susceptible antenna in one housing. It has been shown that with the use of this probe, a plausible range of expected multipath at a GNSS receiver installation can be inferred through the responses of the probe outputs. Furthermore, it has been demonstrated that by integrating the abilities of the manufactured DPA with a digital twin of the real-life installation scenario, one can predict in advance the installation effects and multipath levels at the antenna position. This technique is useful for site layout and system performance planning with respect to multipath, especially for installations that cannot be tested beforehand through measurements. This method can also be used to determine, in a flexible way, optimal placements for a GNSS receiving antenna in a given scene. Field tests using the discussed antenna, as well as commercial geodetic-grade antennas, confirmed the validity of the proposed approach.
HOW TO CITE THIS ARTICLE
Addo, E. O., Elmarissi, W., & Caizzone, S. (2024). Digital twin-enabled characterization of GNSS multipath in challenging reference stations using a dual-polarized probe. NAVIGATION, 71(2). https://doi.org/10.33012/navi.644
DISCLAIMER
The opinions expressed herein are those of the contractor alone and do not represent the contracting authorities’ official position. Furthermore, the authors do not recommend any of the commercial products used in this study. Commercial products are named only for scientific transparency. Please note that a different antenna/receiver unit from the same manufacturer and/or of the same type may show slightly different characteristics/results.
The dual-polarized antenna used in this study was designed, fabricated, and calibrated by DLR and is the property of DLR.
CONFLICT OF INTEREST
The authors declare no potential conflicts of interest.
ACKNOWLEDGMENTS
Part of the work presented in this paper was performed within the framework of the project MAESTRO, funded by the German Research Foundation (Deutsche Forschungsgemeinschaft - DFG) (Project No. 470510446). The authors thank Dr. C. Enneking for his support with the receiver model and GMV for providing the PolaNt antenna.
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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