METHOD FOR REDUCING THE EFFECTS OF ANTI-CHARGE SUSPENSION ON THE MEASUREMENT OF THE CARRIER PHASE OF A SATELLITE NAVIGATION SIGNAL AT THE PLACE OF ITS RECEPTION, AND APPLICATIONS OF THIS METHOD

Description

[0001] The present application claims priority from German patent application 10 2022 101 576.9 dated January 24, 2022.

[0002] The invention relates to a method for reducing the effects of interference suppression on the measurement of the carrier phase of a satellite navigation signal at the point of reception. Furthermore, the invention relates to a method for determining the pseudo-distance of a satellite navigation signal receiver to a satellite, and to a method for determining the position of a satellite navigation signal receiver, wherein both of these methods employ the method for reducing the effects of interference suppression on the measurement of the carrier phase of the satellite navigation signal.

[0003] Receivers of Global Navigation Satellite Systems (GNSS) are susceptible to interference. A successful method for mitigating interference is the use of multi-antenna systems, which superimpose the input signals of the individual antenna channels in a suitable manner, thereby suppressing the interference signal. For this purpose, the signals are multiplied by a complex factor (beamforming weight) and then summed. The interference signal can thus be suppressed by pre-whitening or by setting a spatial zero (nulling). Additionally, the desired signal can be amplified by suitable superposition (e.g., using an intrinsic beamformer).

[0004] A GNSS signal typically consists of a modulated code signal, which is upmixed to a target frequency (e.g., the L1 band) using a carrier signal. The code signal contains the PRN code and (if present) a navigation message. A conventional GNSS receiver removes the carrier signal and uses the code signal to determine the pseudorange and thus the position. For such a receiver, it is only relevant that the carrier signal can be removed, not its (absolute) phase at a specific time. However, for highly accurate positioning, the carrier phase or its phase at a specific time is still used. Spatial filtering, in conjunction with noise suppression, modifies the carrier phases of the satellite navigation signals.After interference suppression, the carrier phases of the various satellite navigation signals can no longer be related to a specific point in space. However, this is necessary for position determination using the carrier phase. The code phase is less problematic, as its accuracy (typically around 3 m) is significantly lower, and the code phases are shifted by a maximum of one wavelength of the carrier phase (typically around 19 cm) due to spatial filtering.

[0005] One disadvantage of interference suppression is that the superposition of the input signals distorts the carrier phase of the input signals depending on the direction, making it impossible to accurately determine the original carrier phases. However, the exact carrier phase (as an absolute value) is required for determining the receiver's position when used in high-precision positioning algorithms such as Real-Time Kinematics (RTK) or Precise Point Positioning (PPP). Carrier phase information is also used to determine the direction of incidence of the received signal. For this purpose, however, the relative value is sufficient, i.e., the carrier phase shift at the location of the individual antennas in the array relative to each other.

[0006] In the current state of the art, there are two different approaches to correct the distorted carrier phase: 1. The directional dependence of an antenna array can be characterized by its so-called spatial phase signature (steering vector). This describes the phase of the incident signal at the various antenna elements relative to a fixed point. If the spatial phase signature of the incident signal is known, the phase error can be calculated and the carrier phase of the incident signal corrected. There are several approaches to calculating the phase signature: a. The multi-antenna system is measured in a test chamber, and the direction-dependent phase signature (or a correction value derived from it) is stored in a table. Knowing the directions of incidence of the signals and the position of the antenna array, the phase error can then be determined and corrected. The disadvantage of this approach is that the antenna array must be measured. This is usually only possible in an antenna test chamber at high cost.Furthermore, the spatial phase signature of the antenna array changes significantly with changes in the near field, meaning that a measurement is only valid for a predefined environment. Additionally, the directions of incidence of the signals must be known, and the antenna array used must be calibrated. Both of these factors involve additional effort and thus increased costs. (Calibration is necessary to compensate for the different signal propagation times in the front end and other components.) b. Assuming that the desired signal has the highest power, the spatial phase signature can be estimated during receiver operation. For GNSS signals, this assumption is met after correlation with the satellite-specific spreading code, provided there is no interference. However, if interference is present, it must first be suppressed to estimate the phase signature. Mitigation by pre-filling or setting a spatial zero, in turn, changes the phase vector.Known methods first determine the altered phase vector and then calculate the mitigation. This approach has the disadvantage that the mitigation must then be subtracted from the estimated phase signature. This reintroduces the previously suppressed interference signal into the estimate, causing the estimated phase signature to deviate from the actual phase signature of the incoming signal. This, in turn, alters the calculated correction of the carrier phase. This approach only works as long as either the interference signal is very small or the phase vector of the incoming signal is perpendicular to the phase vector of the interference signal. 2. The arrangement of the array's antenna elements is restricted to specific systems. This usually assumes a point-symmetric arrangement of the antenna elements with the point of symmetry at the center of the array.Depending on the approach, there must also be an antenna element in the center of the array, or the choice of weights must be restricted. Assuming idealized, isotropic antenna elements, any influence on the carrier phase can be completely prevented. If the antenna elements deviate only slightly from this ideal, a phase error of the carrier phase occurs, but it is relatively small. The disadvantage here is that the arrangement of the antenna elements is predetermined. Therefore, not arbitrary antenna arrays can be used. If the antenna elements also deviate from idealized, isotropic radiators, the carrier phase is distorted more significantly. Known approaches also reduce the number of degrees of freedom for suppressing interference signals by a factor of 2. This means, for example, that an antenna array with four elements can only suppress one interference signal instead of three.

[0007] From US patent A-2002 / 0169578, a method for interference suppression and position determination of a satellite navigation signal receiver is known. The signal resulting from the interference suppression is processed in a conventional, i.e., code-phase-based, GNSS receiver. According to the known method, a common beamforming is performed for all satellite navigation signals, which causes individual, direction-dependent phase errors for the different satellite navigation signals.

[0008] WO-A-02 / 051028 discloses the suppression and amplification of a useful signal using a combination of different methods. However, this method does not stabilize the carrier phases after the suppression. Therefore, this method is also only suitable for code-phase-based GNSS receivers.

[0009] US Patent 2017 / 0102445 concerns the combination of antenna signals from an antenna array into a single signal (beamforming). According to the known method, the resulting signal is compared with the signal from a reference antenna, with the weights adjusted so that the desired signal is strongest and differs as little as possible from the signal at the reference antenna. However, a comparison with the reference antenna is only possible as long as the desired signal at the reference antenna is still usable. If, in addition to the desired signal, there is also a noise signal that is significantly stronger than the desired signal, this noise signal can no longer be evaluated with a single antenna, and thus a comparison with the reference antenna is no longer possible.

[0010] WO-A-98 / 032239 describes a method for interference suppression using notch filters and the subsequent combination of the filtered signals for additional spatial interference suppression by means of spatial filtering. The aim is to ensure the amplification of the individual signals as in the case of an isotropic antenna, meaning that the satellite signal is attenuated as little as possible by the filter. BAMBERG TOBIAS ET AL "Mitigation of Carrier Phase Distortions Induced by Spatial Filtering using Antenna Arrays" describes a method for GNSS interference suppression using spatial filters and intrinsic beamformers.

[0011] The object of the invention is to further reduce the negative effects of interference signal suppression in satellite navigation signals on the measurement of the carrier phase.

[0012] To solve this problem, the invention proposes a method for reducing the effects of interference suppression on the measurement of the carrier phases of satellite navigation signals at the point of their reception, wherein the method a one- or multi-dimensional antenna array with multiple receiving antennas is provided, satellite navigation signals received by the receiving antennas are processed in a signal processing unit, an intrinsic beamformer is applied to one or each of the received satellite navigation signals and parameters describing it are calculated, the parameters of the intrinsic beamformer of the one or each satellite navigation signal are measured or determined at times when no interference suppression is required, the parameters being initialized such that the satellite navigation signal received by a previously defined receiving antenna of the antenna array is passed through unchanged, the received satellite navigation signals are processed in the signal processing unit by means of a spatial filter, i.e., by means of spatial filtering, such as...The signals are subjected to interference suppression by a power inversion (PI) filter or a projection filter, after which the carrier phases of the satellite navigation signals are distorted. Following interference suppression, the signal processing unit modifies the carrier phase of at least one or each of the satellite navigation signals by calculating parameters from the current and previous eigenbeamformers associated with the respective satellite navigation signal, thus correcting the distortions of the carrier phases caused by the interference suppression.

[0013] The concept according to the invention eliminates the distortion of the carrier phase caused by the application of an interference suppression method by applying an intrinsic beamformer to each received satellite navigation signal, or by proceeding in this manner for at least one of the received satellite navigation signals, initially when no interference suppression is required. If, following, for example, the last application of an intrinsic beamformer without interference suppression of the satellite navigation signals, interference is then applied in order to subsequently or simultaneously with the interference suppression, a correction of the carrier phase is made based on the resulting distorted carrier phase and the previously applied intrinsic beamformers.In other words, the intrinsic beamformer applied to a satellite navigation signal before interference suppression serves as a source of information for describing the carrier phase before interference suppression. Assuming that the spatial configuration of the antenna array and satellite remains unchanged, the distorted carrier phase can then be modified by calculating parameters from the current and previous intrinsic beamformers, thus correcting the distortions in the carrier phase caused by the interference suppression.

[0014] Should the configuration of the antenna array and satellite have changed during the interference suppression period, which will be the normal case since the satellites continue to move during the interference suppression period, this can also be taken into account, as the satellites' orbits are known.

[0015] The interference suppression (together with the intrinsic beamformers) thus alters the (measurable) carrier phases in the summed signals calculated for each satellite navigation signal, depending on the direction of incidence. This alteration must be compensated for. The absolute carrier phase in the interference-free state does not need to be known for the procedure. Only (indirect) information about the direction of incidence of the satellite signal is required so that this alteration can be calculated accordingly. This information is stored in the intrinsic beamformers at times when no interference suppression is being performed.

[0016] Even without interference suppression, a certain degree of design flexibility remains when creating the intrinsic beamformer. The intrinsic beamformer (as a vector) can only be determined up to a complex factor. To enable position determination from the measurable phase angles of the summed signals, the intrinsic beamformers of all satellites must have the same shape (e.g., antenna 1 is defined as having a positive real value).

[0017] The parameters from the current and previous eigenbeamformer are calculated; however, the carrier phase change discussed here is achieved by manipulating the current eigenbeamformer. The previous carrier phase correction is therefore already incorporated into the last eigenbeamformer and is thus accumulated.

[0018] In a receiver implementing the inventive method, the input signals (satellite navigation signals) received by the receiving antenna for each satellite are mixed at two different points. First, during interference suppression, which mixes the signals in such a way that the interference signal is canceled out, and then again during beamforming, in which the already mixed signals are individually combined with each satellite navigation signal so that the satellite navigation signal to be used is amplified as much as possible.

[0019] Accordingly, in an exemplary concrete implementation of the invention, the signal path can look like this, where N is assumed to be the number of receiving antennas of the antenna array, M i with i = 1, 2, ... the individual received satellite navigation signals and S i with e = 1, 2, ... the sum signal for the satellite navigation signal M i resulting after correlation and beamforming.

[0020] Antennas 1, 2, ..., N receive the satellite signal M1 and transmit it through antenna channels 1, 2, ..., N in the front end. An analog-to-digital conversion (ADC) is then performed for each channel to carry out interference suppression. In this process, each channel, i.e., the signal of each channel, is correlated with the PRN code of the satellite navigation signal M1. After each correlation, beamforming is performed, and then the summed signal S1, corresponding to the satellite navigation signal M1, is generated.

[0021] The same procedure is followed for each additional received satellite navigation signal M i, so that a sum signal S i corresponding to this satellite navigation signal is obtained.

[0022] In total, there are N * M correlators and consequently also S i different sum signals after beamforming with the same number of different beamformers as the number of received satellite navigation signals.

[0023] Therefore, if interference suppression takes place, the correlation can no longer be described as being correlated with the antenna signal of, for example, antenna 1. At this point, each of the N channels contains a mixture of all N antenna channels, which have been blended to minimize interference. Mathematically, this is a complex linear combination of the antenna channels. Correlation with each PRN code still occurs for N channels. Therefore, after interference suppression, N different signal channels are still required.

[0024] The invention proceeds, for example, in such a way that the respective interference suppression is defined by a set of signal processing parameters for application to the satellite navigation signals to be suppressed, wherein this parameter set changes when interference affecting the satellite navigation signals changes, which arise from interference signals in the vicinity of the receiver or due to infrastructure in the vicinity of the receiver, and that when the interference changes For the at least one satellite navigation signal or for each satellite navigation signal, the parameters of a new eigenbeamformer are calculated so that the previously calculated phase of the at least one satellite navigation signal or each satellite navigation signal is obtained when applying the new eigenbeamformer in question, and to compensate for the change in the phase of the at least one satellite navigation signal or each satellite navigation signal calculated by the new eigenbeamformer, which results from the changed parameter set of the interference suppression, the parameters of the new eigenbeamformer in question are further changed to correct the phase by shifting it, i.e. by rotating the phase.

[0025] To define the reception location, one approach can be to define complex weights for each in-beamformer's parameters. These weights are used to assign weights to the respective signals emitted by the receiving antennas. The reference location of the antenna array, representing the reception location, can then be either one of the receiving antennas, with the weight for that antenna being positive and real-valued (e.g., 1), or a position within the antenna array that does not coincide with any of the receiving antennas. In this case, the weights for the receiving antennas of the antenna array can be chosen such that the carrier phase of the summed signal (after weighting) corresponds to the carrier phase of the satellite navigation signal belonging to the in-beamformer at that position; that is, the carrier phase at a virtual antenna at that position. It should be noted that the in-beamformer weights are complex-valued.If a receiving antenna is weighted with 1, this does not mean that all other receiving antennas receive a weight of 0, but only that the signal from that antenna is passed through without any phase shift. If the weight were, for example, 1i (90°) or 0.7 + 0.7i (45°), the phase would be rotated, i.e., shifted, by 90° or 45°, respectively.

[0026] In an advantageous embodiment of the invention, the method can be provided that the parameters of the intrinsic beamformer define complex-valued weights with which the respective signals output by the receiving antennas are weighted, and that either one of the receiving antennas is selected as the reference position, wherein the weight for this receiving antenna is chosen to be positive and real-valued (e.g., 1), or a position within the antenna array is selected that does not coincide with one of the receiving antennas, wherein the complex-valued weights for the receiving antennas of the antenna array are chosen such that the carrier phase of a resulting sum signal after weighting is equal to the carrier phase of the satellite navigation signal assigned to the intrinsic beamformer, which would reach an antenna at the said reference position of the antenna array.

[0027] In a further advantageous embodiment, it can also be provided that the beamforming weights of the intrinsic beamformer are initialized with undisturbed satellite navigation signals by passing the satellite navigation signal unchanged at the reference position, whereby no direction-dependent carrier phase error arises with respect to this reference position due to the beamforming, whereby in subsequent interference suppression the intrinsic beamformer to be calculated is adapted on the basis of the previous intrinsic beamformer with the aim that the phase of a resulting sum signal remains equal to the carrier phase of the satellite navigation signal at the reference position.

[0028] The resulting sum signal is typically the sum of the complex-valued, weighted, noise-suppressed receive antenna signals, where these noise-suppressed receive antenna signals are a complex-valued linear combination of the individual digitized receive antenna signals and are calculated from the input signals by applying noise suppression, and where the eigenbeamformer defines the complex-valued weights of the sum.

[0029] The inventive method uses a one- or multi-dimensional (e.g., two- or three-dimensional) antenna array with multiple receiving antennas. The signals received by the receiving antennas and present at their outputs (channels of the antenna array) are processed in a signal processing unit, for example, a signal processor. First, interference suppression is performed, which separates the individual satellite navigation signals from the interference signal. Unfortunately, this procedure results in the loss of information about the phases at which the individual satellite navigation signals reach the antenna array, because the signals from the individual receiving antennas are made in phase during interference suppression. This must then be compensated for in the calculation of intrinsic beamformers, whereby one intrinsic beamformer is generated / calculated for each satellite navigation signal.The resulting phase error is not compensated for by calculating the eigenbeamformer, but by a term that is in turn applied to the eigenbeamformer as a phase rotation or phase shift.

[0030] With every change in interference to the satellite navigation signals, resulting from the environment or movement of the receiver, the calculation of the eigenbeamformers changes. At successive intervals or points in time, both the interference suppression and each eigenbeamformer are recalculated. This iterative process proceeds in such a way that the eigenbeamformer to be recalculated at a given time x is calculated in such a way that its resulting phase initially remains unchanged compared to the phase previously calculated (i.e., at time x-1). This effectively reverses the (temporary) phase change resulting from the change in interference (between time x-1 and x) and thus from the recalculated interference suppression.The (temporary) phase change caused by the new change in interference suppression must also be compensated, which is done by means of a phase shift applied to the phase calculated by the new eigenbeamformer.

[0031] The method according to the invention requires a multi-antenna receiver with interference suppression and subsequent beamforming by means of an intrinsic beamformer. In the undisturbed case, the method initializes the beamforming weights such that the signal from the reference antenna (a predefined element of the array) is passed through unchanged (complex-valued weight = 1). With respect to this element, no direction-dependent phase error arises from the beamforming in this procedure. If an interference signal is present, the intrinsic beamformer to be calculated is adjusted based on the previous intrinsic beamformer with the aim that the phase of the resulting summed signal (after application of the intrinsic beamformer) still corresponds to the phase of the signal at the reference antenna (before application of the interference suppression).

[0032] According to the invention, the carrier phase is modified after interference suppression to ensure that the carrier phase behaves after interference suppression as it would in the undisturbed state. This means that a carrier phase measurement that, in the undisturbed state, referred to, for example, receiving antenna 1, can also refer to receiving antenna 1 in the undisturbed state. However, the measured carrier phase changes over time because the antenna array under the satellite(s) move relative to each other.

[0033] The adaptation is carried out in a two-stage process according to the invention: 1. The parameters of the new intrinsic beamformer are adjusted to those of the previous intrinsic beamformer as described above. Simultaneously, the (temporary) phase shift caused by the previous change in interference suppression is reversed. 2. The (temporary) phase shift resulting from the (new) change in interference suppression is compensated for by applying a phase shift to the new intrinsic beamformer.

[0034] The method according to the invention calculates the correction of the distorted carrier phases in a multi-antenna receiver from the current and the last intrinsic beamformer as well as the current and the last interference suppression matrix. This calculation is performed without information about the antenna array used and is therefore essentially "blind." A two-stage process is employed, which applies the calculated phase correction directly to the beamformer used. In contrast to the prior art, the method according to the invention does not calculate the spatial phase signature. The calculation of such a signature is severely distorted by interference signals. Unlike a comparable prior art method, the method according to the invention can also be used in receivers that employ a projection filter for interference suppression.Furthermore, the inventive method can also be used in receivers in which the eigenbeamformer is calculated on one data set and only applied to the next data set.

[0035] Compared to the known method mentioned above in section 1a, the invention has the advantage that the method functions blindly, i.e., it does not require any measurement of the antenna array. Furthermore, no knowledge of the directions of incidence of the signals is required.

[0036] In contrast to the method mentioned above in section 1b, the spatial phase signature does not need to be explicitly calculated according to the invention. Instead of inverting the interference suppression, only the change in interference suppression needs to be taken into account. This allows the method to be used even in environments with strong interference signals. Furthermore, this significantly reduces drift in the phase correction.

[0037] Compared to the known method described above in section 2, the invention has the advantage that the arrangement of the antenna elements can be arbitrary. Furthermore, the performance of the method according to the invention is not impaired if the antenna elements deviate from the ideal of an isotropic antenna.

[0038] The invention can be used, for example, to determine the distance of a receiver for satellite navigation signals to a satellite, wherein the previously described method for reducing the effects of interference suppression on the measurement of the carrier phases of satellite navigation signals at the place of their reception is carried out, and wherein the so-called pseudo-distance of the receiver to the satellite is calculated on the basis of the calculated carrier phase of the satellite navigation signal.

[0039] The invention can be used, for example, to determine the position of a receiver for satellite navigation signals, wherein the previously described method for reducing the effects of interference suppression on the measurement of the carrier phases of satellite navigation signals at the place of their reception is carried out, whereby the position of the receiver is determined based on the distances of the receiver to several satellites.

[0040] Possible commercial applications include GNSS receivers requiring high accuracy, GNSS reference stations, and GBAS stations.

[0041] The invention is explained in more detail below with reference to an exemplary embodiment and the drawing. Specifically, the drawing shows: Figures 1a and 1b show a measurement setup on the roof of the UMIC research center at RWTH Aachen University. The antenna group in the front... Abb. 1a and at the back Abb. 1b (DLR UNITAS) is used to receive satellite signals, and the antenna is located at the rear. Abb. 1a and at the front Abb. 1b for the radiation of the jamming signal. Fig. 2 shows a signal tracking structure of a multi-antenna receiver with N antenna channels and the proposed compensation unit, where M is the number of satellites. Fig. 3 shows the movement of the jamming antenna around the UNITAS antenna array in Scenario 2. Fig. 4 shows the power of the eigenvalues ​​of the precorrelation covariance matrix estimated by the receiver. Fig. 5 shows Scenario 1: Carrier phase residues over UTC time. Fig. 6 shows Scenario 1: Position deviation over time. Fig. 7 shows Scenario 2: Moving jammer with constant power level. Fig. 8 shows Scenario 2: Position deviation over time.

[0042] Global Navigation Satellite Systems (GNSS) are widely used for positioning and timing. These systems are used by almost all land, air, and watercraft for navigation. With the increasing number of private and commercial drones and the advent of autonomous vehicles, the number of systems relying on GNSS will continue to rise. Therefore, ensuring the availability and integrity of the position, velocity, and time (PVT) solution, even in the presence of interference, disturbances, or spoofing, is becoming increasingly critical. Furthermore, these new applications demand higher precision in the PVT solution. This requirement can be met by precise point positioning (PPP) and real-time kinematics (RTK) techniques. A key element of these methods is the integration of carrier phase measurements into the PVT estimation.Carrier phase measurements enable much more accurate distance measurements because the wavelength of a GNSS carrier, e.g. 19 cm for GPS L1, is much smaller than the corresponding length of a PRN code chip when propagating in free space, e.g. 293 m for the C / A code of GPS L1.

[0043] An advanced approach to protection against jamming and spoofing involves the use of adaptive antenna arrays and spatial signal processing. These antenna arrays can be used to detect and mitigate jamming transmitters [1] and spoofers [2], [3]. Furthermore, an antenna array can increase the C / N0 value of a satellite signal by directing a beam in the direction of arrival (DoA). Mitigation is typically achieved using spatial filters such as the power inversion (PI) filter or the minimum variance distortionless response (MVDR) filter. These filters can be divided into deterministic and blind approaches. In a deterministic approach, the steering vector of the incoming satellite signal must be known. The steering vector of an incoming signal is its spatial signature, which contains the phase information of the signal at each antenna element.To obtain the steering vector, the antenna's reception pattern must be known. In practice, a blind approach is often desired. A blind approach works without prior knowledge of the antenna gain / phase matrix, the calibration matrix, and the arrival direction of the disturbance. However, common implementations of blind spatial filters and beamformers introduce an error into the carrier phase measurements.

[0044] The problem of induced error in carrier phase measurements has been addressed by other researchers. Two different strategies for mitigating the phase error caused by blind spatial filtering are described in the literature: One strategy aims to preserve the continuity of the phase measurement in noisy scenarios. Jia et al. [4] presented such an algorithm, which works well for short-term scenarios. However, Jia et al. did not validate the proposed algorithm with recorded real-word signals and did not evaluate the impact of the resulting phase errors on the positioning solution. In particular, the stability of the carrier phase measurements over short time periods is problematic. Further investigations show that approaches using this strategy generally fail to preserve phase continuity over long time periods [5].The second strategy is based on the use of additional constraints on the spatial filter to avoid phase errors. This approach was demonstrated by Daneshmand et al. [6] in both simulations and with recorded signals, clearly showing its advantages over a standard implementation. However, the additional constraints reduce the degrees of freedom of the spatial filter by half. Therefore, an antenna array would require twice the number of antenna elements to suppress the same number of interfering sources as the standard implementation. Furthermore, the algorithm only works with centrosymmetric array geometries; that is, it is not directly applicable to real antenna arrays without significant performance degradation due to asymmetries in the antenna characteristics caused by imperfections, tolerances, near-field object interference, or installation problems.

[0045] The aforementioned limitations of the prior art were the reason for the research described in [7] and [5]. In [7], the induced carrier phase error was evaluated for four different implementations of a spatial filter. The analysis was performed in three different scenarios to characterize the error both in the absence and presence of a disturbance signal. In addition, the influence of the antenna was evaluated using an isotropic antenna and a simulated antenna array diagram. The results show that the MVDR filter produces the smallest phase error. It can be shown that this filter is theoretically even free of carrier phase distortion [4]. The simulations performed assumed that the approach had inaccurate knowledge. However, it is still a deterministic approach that requires a priori knowledge. The three remaining approaches in [7] are blind.In these approaches, the carrier phase distortion depends on the DoA of the satellite and the DoA of the interfering signal. One approach was to summe the incoming signals after suppressing the interfering signal, i.e., to use beamforming where each line contains a one. This approach results in only a small phase distortion but suppresses low-altitude satellite signals. Nevertheless, PPP / RTK remains a challenge in rapidly changing environments even with these approaches. In [5], these results were used to develop two new blind approaches for reducing the carrier phase error during spatial filtering. The basic idea of ​​these approaches is to reduce the distortion of the tracked carrier phase by comparing the mean phase of the applied beamformer either with the previous beamformer or with the beamformer of the approach mentioned above, which is known to have a minimal effect on the phase.The reduction of carrier phase error using these approaches is promising, but the evaluation was limited to numerical simulations with synthetic satellite signals. The approaches were not tested with realistic signal data, and furthermore, the impact of the phase error on the positioning solution was not investigated.

[0046] The proposed invention extends the research from [7] and [5] to practical experiments using recorded realistic signals and an RTK positioning algorithm. The analysis in [7] and [5] focused on the carrier phase shift caused by adaptive spatial filtering at the signal plane. The proposed invention investigates the resulting effect of such an error on the RTK positioning solution. To this end, GNSS signals from realistic scenarios are recorded by a software-defined radio system (SDR) and processed by a software receiver. The receiver's observables are then passed to RTKlib [8], an open-source software package for GNSS positioning, to obtain an RTK positioning solution and to evaluate the induced errors in the positioning domain.The filtering and averaging of carrier phase errors occurring in the receiver's carrier tracking loops are inherently taken into account in this approach. The performance of the carrier phase measurements (carrier range) and the positioning solution is analyzed in various scenarios, ranging from interference-free to moving jamming sources. These scenarios are addressed using classical spatial filtering implementations and the approach proposed in [5]. The description concludes with a recommendation regarding which RTK positioning approach is suitable for performing spatial filtering of interference, multipath, or spoofing signals. Using the results obtained, the invention aims to close the gap in the use of GNSS array receivers with RTK positioning techniques, particularly considering the limitations arising from real-world inadequacies.It will pave the way for the use of GNSS group receivers in applications that require a combination of high positioning accuracy and high reliability. NOTE

[0047] This description uses the following notation: Small bold letters represent vectors; large bold letters represent matrices; the symbols -T< and -H< represent transposition and Hermitian transposition, respectively; arg{-} represents the angle of a complex number; E[-] and var[-] represent the statistical expected value and variance, respectively. SYSTEM MODEL AND SPATIAL SIGNAL PROCESSING

[0048] This section introduces the signal model and the theoretical background for the spatial filters and the beam shaper. Signal model

[0049] We assume an antenna array with N Antennas off. This group receives M Satellite andL Interference signals. The incoming signal is: ℂ N × 1 ∋ x t = ∑ m = 1 M Ca m s m t + ∑ l = 1 L Ca l j l t + n 1 = s + j + n 2 a m ∈ C N ×1< and a l ∈ C N ×1< describes the steering vectors of the satellite or the interfering signals. A steering vector is the spatial signature of a signal and depends on the direction of arrival (DoA) of the incoming signal and the orientation of the antenna array. For a simplified, isotropic antenna array, this describes a = e − 1 , … , e − i k T r N the control vector of an incoming wave. k is the wave vector and r 1,..., rN describes the spatial positions of the antenna elements. In practice, the control vector (in phase and amplitude) deviates from this simplified model because the array antenna elements are typically not isotropic or even azimuthally invariant, due to electromagnetic coupling between the array elements. Several other practical effects, such as manufacturing tolerances and the presence of other objects in the near field, also cause the antenna patterns of an installed array to differ from those calculated with antenna modeling tools or measured in an anechoic chamber. In equation (1), some of these effects are represented by the term C This matrix takes into account different cable lengths and component tolerances in the NAntenna processing channels and crosstalk between different channels. It is the same for all incoming signals and is not affected by the DoA of a signal. Its inverse. C -1< is referred to as the calibration matrix.

[0050] It should be emphasized here that the control vector also depends on the choice of the reference coordinate system. The origin of this reference system is the spatial reference for the modeled signal. s m (t) and j(t). Unless otherwise specified, the origin point is the center of the antenna array, determined as the average of all antenna positions. s m (t) This describes the satellite signal. It contains the data bits, the spreading code, and the carrier signal. j l stands for the interference signal and n ∈ C N ×1< represents the additive noise component. It is described as Gaussian noise with a mean of zero and a variance of σ n 2 modeled. Spatial filter and beamformer

[0051] The combination of the received antenna signals offers the possibility of amplifying or suppressing various DoAs (Differences of Ambient Signals). For this purpose, the received signals are multiplied by a complex number (phase and amplitude variation) and summed. The resulting beamformed signal can be expressed as y = w H x .

[0052] The weight vector w is defined by the user's needs. A common method for suppressing unwanted signals is the use of the minimum variance (MV) filter, which minimizes the variance of the unwanted signals in the output signal. Assuming that the unwanted signals have a mean of zero and are uncorrelated with the satellite signal, we can write: min w var w H j + n = E w H j + n 2 = w H E j + n j + n H w = w H R j + n w

[0053] R j+n is the covariance matrix of the unwanted signal and the noise. To find the trivial solutionw = 0 To exclude the other option, another condition must be added. The additional condition w H< a m A value of 1 results in the MVDR filter. The solution for this filter is given by: w MVDR = R j + n − 1 a m a m H R j + n − 1 a m

[0054] The GNSS satellite signals are far below the background noise. Therefore, the covariance matrix of the unwanted signal can be approximated without prior knowledge by: R ˜ j + n = 1 K ∑ k = 1 K x k x k H , where K describes the number of samples used and x [k] the read sample values ​​at time t k = kT with the sampling interval T represents.

[0055] Estimating the control vector for the desired satellite signal is more difficult: If the receiver system's reception pattern, the location, and the position of the antenna array are known, the DoA and the control vector of the incoming signal can be calculated using the ephemeris data. This approach is classified as a deterministic filter. In practice, this approach is quite challenging due to the time-varying nature of the required information. A promising attempt to estimate the time-varying components together is described by Zorn in [9] and

[10] . Self-beam shaper

[0056] Another way to estimate the steering vector is to estimate it using scattering / correlation. Correlation amplifies the useful signal above the background noise, making it possible to extract its spatial signature.

[0057] This approach can even be used in the presence of an interfering signal that overlays the satellite signal. To suppress strong interference, a spatial filter is applied before the correlation. P = R j + n − 1 2 applied. This process is called pre-whitening. The filtered signal is: x ¯ t = Px t = Ps + Pj + Pn

[0058] The signal following the correlation can be expressed as: y m = G m PCa m + n pc , m where the factor G m the scaling of the correlation with the local replica and n PC m This is the noise after the correlation process. This noise includes the other satellites, the suppressed jamming signals, and the pre-correlation noise.

[0059] The post-correlation covariance matrix for satellite m is: R y m = E y m y m H

[0060] If one calculates the eigenvalue decomposition and takes the eigenvector that belongs to the strongest eigenvalue, one obtains the following vector: b m = α m e i ϕ m PCa m + e m

[0061] Eigenvectors are only fixed to a scale factor, which in equation (10) is given by the complex term ( α m egg ϕ m The eigenvector is represented by < ). Normally, the eigenvector is scaled so that it has a norm of one. The phase factor (ei) ϕm <) is still arbitrary, however. The term e m represents the errors in estimating the control vector.

[0062] Because of the use of the eigenvector, this beamformer is called an eigenbeamformer. The approach requires no information about the antenna array and is therefore classified as a blind filter. The eigenbeamformer is described in more detail in

[11] and [4]. The weighting vector for the restricted MV filter with an eigenbeamformer is given by: w MVEig = P H b m b m H P H Pb m PHASE ERROR AND PHASE COMPENSATION MECHANISMS

[0063] The previously described beamformer suppresses unwanted interference and amplifies a desired satellite signal. This is achieved by summing the phase-shifted signals. The resulting summed signal is then passed to the PLL / DLL used for pseudo-distance and carrier phase measurements. This section analyzes the influence of the described intrinsic beamformer on the carrier phase. Furthermore, two methods for reducing this effect are presented. Phase error

[0064] Mathematically, beamforming can be described by combining equations (3) and (1): y = w H x = ∑ m = 1 M w H Ca m S m t + ∑ l = 1 L w H Ca ljl + w H n .

[0065] The phase shift of a single satellite signal induced by spatial signal processing s m can be described as the phase of the product of the weighting vector, the inverse calibration matrix, and the true control vector of this particular satellite: Δ φ m = arg w H Ca m .

[0066] The induced phase shift of the MVEig beamformer can be calculated. Using equation (11), equation (13) is obtained: Δ φ MVEig , m = arg w MVEig H Ca m 14 = arg b m H PCa m b m H P H Pb m 15 = arg b m H PCa m 16

[0067] For technical reasons, the eigenbeamformer is normally estimated from samples of the previous iteration, while the spatial filter is applied in the same iteration in which it was generated. To account for this, we add an index indicating the time dependency: h and h, respectively. h-1 (e.g. a h and a h -1). To maintain readability, we no longer specify the satellite dependency, i.e., we no longer show the index m. With these adjustments and with equation (10), equation (16) reads: Δ φ MVEig = arg α h − 1 e i ϕ h − 1 P h − 1 C h − 1 a h − 1 + e h − 1 H P h C h a h 17 = arg α h − 1 e − i ϕ h − 1 a h − 1 H C h − 1 H P h − 1 H P h C h a h + e h − 1 H P h C h a h 18 = − ϕ h − 1 + arg a h − 1 H C h − 1 H P h − 1 H P h C h a h + arg 1 + e h − 1 H P h C h a h α h − 1 e − i ϕ h − 1 a h − 1 H C h − 1 H P h − 1 H P h C h a h 19 compensation

[0068] To prevent spatial signal processing from interfering with distance measurements, the phase error must be zero, i.e., Δ φ MVEig = 0 !< . The proposed compensation algorithm aims to prevent a phase jump between two successive estimates of the beam shaper or the space filter. Compensation is achieved by changing the phase of the estimated intrinsic beam shaper (10) before it is used in the beam shaping process. Mathematically, the weighting vector after compensation for the satellite is m : w ^ MVEig , m = e i φ Comp , m P H b m b m H P H Pb m with the compensation phase φ Comp.

[0069] The compensation phase is estimated in two steps. The first step is defined by the multiplication of two consecutive intrinsic beam shapers: φ c 1 : = arg b h H b h − 1 21 = arg α h − 1 e i ϕ h − 1 P h − 1 C h − 1 a h − 1 + e h − 1 H α h − 2 e i ϕ h − 2 P h − 2 C h − 2 a h − 2 + e h − 2 22 = − ϕ h − 1 + ϕ h − 2 + arg a h − 1 H C h − 1 H P h − 1 H P h − 2 C h − 2 a h − 2 23 + arg 1 + e h − 2 H e h − 2 + α h − 2 e i ϕ h − 2 e h − 1 H P h − 2 C h − 2 a h − 2 + α h − 1 e − i ϕ h − 1 a h − 1 H C h − 1 H P h − 1 H e h − 2 α h − 1 e − i ϕ h − 1 α h − 2 e i ϕ h − 2 a h − 1 H C h − 1 H P h − 1 H P h − 2 C h − 2 a h − 2 24

[0070] The second step takes into account the changing pre-whitening matrix. It is defined by φ c 2 : = arg b h H P h P h − 1 − 1 b h 25 = arg α h − 1 e i ϕ h − 1 P h − 1 C h − 1 a h − 1 + e h − 1 H P h P h − 1 − 1 α h − 1 e i ϕ h − 1 P h − 1 C h − 1 a h − 1 + e h − 1 26 = arg a h − 1 H C h − 1 H P h − 1 H P h C h − 1 a h − 1 27 + arg 1 + e h − 1 2 + α h − 1 e i ϕ h − 1 e h − 1 H P h C h − 1 a h − 1 + α h − 1 e − i ϕ h − 1 a h − 1 H C h − 1 H P h − 1 H P h P h − 1 − 1 e h − 1 α h − 1 α h − 1 a h − 1 H C h − 1 H P h − 1 H P h C h − 1 a h − 2 28

[0071] We assume the following: 1) The calibration matrix and the control vector do not change significantly over three iterations, i.e. a h = a h -1 = a h -2 and C h = C h- 1 = C h -2. This can be assumed if the interval between iterations is small compared to the motion of the satellites and the receiver. If the receiver is stationary or moving slowly, a reasonable interval for the iterations is 50 ms. 2) The error in estimating the eigenbeamformer is vanishingly small, i.e., ∥ e ∥ ≪ ∥ a ∥.

[0072] Using these postulates, the phase compensation is given by: φ Comp = φ c 1 + φ c 2 29 ≈ − ϕ h − 1 + ϕ h − 2 + arg a h − 1 H C h − 1 H P h − 1 H P h − 2 C h − 2 a h − 2 + arg a h − 1 H C h − 1 H P h − 1 H P h C h − 1 a h − 1 30 ≈ − ϕ h − 1 + ϕ h − 2 − arg a h − 2 H C h − 2 H P h − 2 H P h − 1 C h − 1 a h − 1 + arg a h − 1 H C h − 1 H P h − 1 H P h C h a h 31

[0073] Applying this compensation to the beam shaper (20) yields: arg Δ φ ^ MVEig , m = arg Δ φ MVEig − φ Comp 32 ≈ − ϕ h − 2 + arg a h − 2 H C h − 2 H P h − 2 H P h − 1 C h − 1 a h − 1 33 ≈ − ϕ h − 2 + arg a h H C h H P h − 2 H P h − 1 C h a h 34

[0074] The phase error induced by the new weighting vector is the same as the phase error of the previous weighting vector, except that the phase shift caused by the previous change to the pre-brightening filter is removed. If we assume that the pre-brightening matrix did not change in the previous iteration, i.e., P h -2 = P h -1, the second term becomes zero, i.e. arg a h H C h H P h − 2 P h − 1 C h a h = 0 This can be used to prevent phase shifts caused by spatial signal processing in a changing environment.

[0075] However, the dependence on the previous weighting vector is also the biggest disadvantage of this approach: A phase error in the previous iteration is carried over to the next phase compensation. Therefore, the induced phase will drift over time with this compensation approach. Furthermore, we need to know (or estimate) the initial phase error. PROCESSING OF THE SIGNALS AND IMPLEMENTATION OF THE PROPOSED ALGORITHM

[0076] To analyze the proposed compensation algorithm, we acquire and process GNSS satellite signals. We perform the following steps: 1) Recording the GNSS signals with a suitable multi-channel data streamer. 2) Using a software receiver to process the signals and generate code and carrier space observations in RINEX format. 3) Reading the RINEX file using RTKlib to estimate an RTK position solution. Recording of signals

[0077] The Ettus USRP x300 platform is used for digitizing and storing GNSS signals. The most important settings are: Center frequency: 1575.42 MHz Intermediate frequency of digitized signals: 0 Hz (complex I&Q sampling) Sampling rate: 5 MHz Number of recording channels: 4

[0078] The four channels are connected to the UNITAS antenna array developed and manufactured by DLR, which is located in the foreground of Abb. 1a It can be seen as a uniform rectangular 2x2 antenna array with a spacing of the antenna elements of approximately half a wavelength L1 (approximately λ L1 = 19.04 cm). λ L 1 2 = 9.52 cm The recorded signal samples are stored on a hard drive and then processed by a multi-antenna software receiver. Processing of the recorded signal

[0079] The GNSS software receiver used is implemented in MATLAB. Abb. 2 The receiver's function diagram is shown. NInput signals are buffered to estimate a spatial covariance matrix, the so-called pre-correlation covariance matrix (see equation (6)). This covariance matrix is ​​used to estimate the pre-whitening filter matrix, which serves to attenuate noise. The filter matrix is ​​then applied to the input signal (see equation (7)). The signal is spread-out is performed individually for each satellite. The post-correlation beamforming operates using the N outputs of the spread-out / correlation unit. The outputs are buffered over several correlation epochs to compute the post-correlation covariance matrix (see equation (9)). To ensure that this covariance matrix does not contain signals with different pre-correlation filter matrices, the pre- and post-correlation buffers are synchronized.The post-correlation covariance matrix is ​​used to calculate the eigenbeamformer weighting vector (see equation (10)). The proposed compensation approach, as described in previous sections, is used to adjust the eigenbeamformer phase. The adjusted eigenbeamformer is applied to the output of the spread-out / correlation unit, and the result is fed into the PLL / DLL tracking loops. The PLL and DLL are implemented as in a conventional single-antenna receiver (e.g.,

[12] ). The states of the PLL and DLL are further used to generate the pseudo-range and the accumulated Doppler range (ADR). These are stored in the RINEX observation file, which is passed to the RTKlib. RTK positioning

[0080] The RTKlib (version 2.4.3 b34) is used to obtain an RTK position solution from the RINEX observation file. Additionally, a RINEX navigation file is downloaded to provide the epherizer and clock data. The RTKlib is configured to process the file in "Static Position" mode and fix integer ambiguities in "Continuous" mode. If the RTKlib can correct at least four integer ambiguities and the validation ratio is greater than 3, we refer to the solution as "RTK Fix". Otherwise, we refer to it as "RTK Float". Furthermore, an RTK position solution requires a reference station. For the evaluations in this work, a reference station of the Satellite Positioning Service of the German State Survey Offices in Aachen (SAPOS®)

[13] was used. TABLE I: Jamming events in scenario 1. ID Start Time (UTC) Stop Time (UTC) rel. Power [dB] 1 13:01:28 13:02:20 20 2 13:02:20 13:02:50 26 3 13:02:50 13:03:20 32 4 13:03:20 13:03:50 38 5 13:03:50 13:04:22 44 6 13:04:22 13:04:50 50 7 13:04:50 13:05:19 56 8 13:05:19 13:05:50 62 9 13:05:50 13:06:20 68 10 13:06:20 13:06:50 74 11 13:06:50 13:07:19 80 12 13:07:19 13:07:51 86 SCENARIOS AND EVALUATION STEPS Scenarios

[0081] For the evaluation, we consider two different scenarios. Both scenarios are recorded on the roof of the UMIC research center at RWTH Aachen University on September 21, 2021. Two images of the measurement setup are included in Fig. 1 to be seen. Each scenario includes a noise signal that is specific to that particular scenario: 1) In scenario 1, a jammer with gradually increasing signal power is investigated. The direction of incidence of the jamming signal on the antenna array remains constant. The jamming power is increased by 6 dB every 30 seconds. Table I shows the relative power of the individual stages as well as the start and stop times. Fig. 4a shows the eigenvalues ​​of the precorrelation covariance matrix calculated by the receiver. As can be seen in the figure, the dispersion of the eigenvalues ​​can be used to estimate the power of the incoming jamming signal relative to the receiver's noise floor. 2) In scenario 2, a moving jamming source with a constant power level is investigated. The jamming antenna is moved in a semicircle around the UNITAS antenna array and then towards the UNITAS antenna array. This movement is in Fig. 3 shown. The movement was performed manually, so it is not as perfect as depicted. The jamming event begins at 13:38:16 UTC and ends at 13:42:04. Using the same relative power scale as in Table I, the jammer radiates 62 dB (level 8). However, due to the antenna movement, the received power of the jamming signal varies. This variation can be illustrated by plotting the power of the eigenvalues ​​of the precorrelation covariance matrix, as shown in Fig. 4b As shown. It can be observed that the power of the received signal starts at a value comparable to level 8 in scenario 1 and increases to a value comparable to level 11. Evaluation

[0082] Each scenario is processed in three different modes: 1) Single antenna: In this mode, neither pre-whitening nor beamforming is used. Instead, only the signal from the first array element is processed by the software receiver, which operates like a conventional single-antenna receiver. 2) Without phase compensation: In this mode, the receiver uses pre-whitening and beamforming but does not compensate for any potential phase shift. Pre-whitening is only activated if the largest eigenvalue of the pre-correlation covariance matrix is ​​10 dB higher than the smallest eigenvalue. This ensures that the filter does not affect the carrier phase of the satellite signals as long as no serious interference is present. The weights of the eigenbeamformers are normalized so that the first element (corresponding to antenna 1) remains equal to 1, i.e., positive and real-valued. Without interference, this results in a position determination similar to that in single-antenna mode.The beamformed signal, however, has a better C / N0 because it superimposes the input signal from N antennas. 3) with phase compensation: In this mode, the receiver uses pre-whitening and beamforming, as well as the proposed algorithm for phase deviation compensation. As in the mode without phase compensation, the pre-whitening matrix is ​​applied only if the largest eigenvalue of the pre-correlation covariance matrix is ​​10 dB higher than the smallest eigenvalue. The beamformer phase is estimated using the proposed algorithm. However, for initializing the beamformer, or if the room filter is not applied, the beamformer phase is estimated as in the mode without phase compensation; that is, the first element of the beamformer is equal to 1. RESULTS AND DISCUSSION Scenario 1: Jammer with gradually increasing signal power

[0083] Fig. 5 Figure 5 shows the carrier phase residuals as written by the RTKlib for the three different modes: single antenna (5a), without phase compensation (5b), and with phase compensation (5c). The graphs show only the results for the fixed RTK solution. The beginning and end of each phase, as defined in Table I, are highlighted in red. Due to the interference, the single antenna has difficulty tracking the satellite signals in phase 8; with two or more satellites, a cycle error occurs. In the next phase (phase 9), the single antenna receiver is no longer able to track the satellite signals and loses them all.

[0084] The use of the pre-whitening filter makes it possible to maintain an RTK-FIX solution up to level 12 ( Fig. 5b In stage 12, some satellites are lost, and the residual values ​​of the remaining satellites increase. The main reason for this is the clipping effect that occurs during the digitization process, as the recording system (USRP X300) does not use automatic gain control (AGC).

[0085] In this scenario, the phase compensation algorithm cuts ( Fig. 5c ) only slightly better than the receiver without phase compensation ( Fig. 5b The residuals in stages 8, 9, 10, and 11 are somewhat smaller, and the jump in some residuals in stage 12 is not as large as it would be without phase compensation. However, in this scenario with static receiver-jammer geometry, phase compensation is not explicitly necessary, but it is also not detrimental.

[0086] Fig. 6 This shows the relative position offset for the three modes separately for east, north, and altitude. The results are referenced to the average position of the single-antenna processing. Similar to the previous diagrams, it can be observed that the single antenna struggles to track the signals at stage 8 (leading to a clearly visible position offset) and loses them at stage 9. Using the pre-whitening filter allows for the estimation of an RTK-FIX solution up to stage 12. However, from stage 11 onward, the receiver loses contact with some satellites, which is evident from the small jumps in the position estimates. In this static scenario, the drift of the position solution is comparable with and without carrier phase compensation. Scenario 2: Mobile jammer with constant power level

[0087] Fig. 7 Figure 2 shows the carrier phase residuals for Scenario 2 for the different processing modes. In this scenario, the power of the radiated jamming signal remains constant, but the direction in which the jamming signal arrives at the receiving antenna changes over time due to the movement of the jamming antenna. Additionally, the received jamming power at the antenna array varies due to the changing distance between the jamming source and the receiving antenna (see 3b). The time at which the jam is activated is indicated by two vertical lines in all relevant figures.

[0088] Similar to Scenario 1, the single-antenna mode is unable to track the satellite signals while the jamming signal is active. Using the pre-brightening filter enables tracking of the satellite signals throughout the entire signal recording. This scenario clearly demonstrates the advantage of the proposed phase compensation algorithm: while without phase compensation the carrier residuals increase significantly during the jamming period, they remain low when using the proposed compensation approach. Without phase compensation, the RTK-FIX solution is even unavailable for several seconds.

[0089] The results for the position deviation in Abb. 8This also supports the conclusion regarding the usefulness of the proposed approach. Without phase compensation, the position solution drifts significantly when the jammer is activated. As can be seen in the previous diagrams, the RTK-FIX solution is even lost. With phase compensation, however, the estimated position solutions exhibit only minor deviations, which are of the same order of magnitude under both interference-free and interference-prone conditions.

[0090] Within the scope of this invention, an algorithm for compensating carrier phase shifts that occur during "blind" spatial signal processing is proposed. "Blind" in this context means that the user does not need any prior information about the phased antenna pattern or the front end. The proposed algorithm was tested in two different scenarios using a proprietary software receiver in combination with the RTKlib, which was used to estimate an RTK solution. In the first scenario, the signal power of a jammer was incrementally increased from a constant DoA (Dead On Array), and in the second scenario, a jammer with a constant signal power was moved around the receiving antenna array. For both scenarios, the proposed algorithm was compared with a multi-antenna system without phase shift compensation and with single-antenna processing.

[0091] As expected, the single-antenna receiver is unable to estimate a position solution once the interfering signal becomes too strong. The multi-antenna system suppresses the interference through pre-brightening and is able to track the satellite signals during periods of interference. It generates continuous code and carrier-space observations that provide a position solution. However, without compensation for phase deviations, the carrier phase residuals estimated by the RTKlib begin to grow in the rapidly changing environment (moving jammer). Consequently, the RTKlib can no longer estimate an RTK-FIX solution, but only a FLOAT solution. Furthermore, the position solution begins to drift, even though we analyzed a static scenario. The invention mitigates this problem.The carrier phase residues do not increase compared to the interference-free period, and the RTK-FIX solution can be maintained throughout the entire recorded period.

[0092] The invention makes it possible to leverage the advantages of an antenna array (without relying on detailed information about the antenna pattern) together with an RTK positioning solution. It is best suited for situations where a medium- to high-accuracy solution (dm to cm accuracy) must be insensitive to interference. A very accurate solution (cm to mm accuracy), comparable to a geodetic receiver that utilizes variations in the antenna phase center, cannot be achieved with this algorithm. This is not surprising, since the algorithm does not use or require detailed information about the antenna pattern. An alternative solution for such a scenario would be the use of a deterministic beamforming approach, which, however, would be highly dependent on knowledge of the amplitude and phase patterns of the array antennas. REFERENCES

[0093] [1] M. Cuntz, A. Konovaltsev, M. Sgammini, et al., "Field test: Jamming the DLR adaptive antenna receiver", in Proceedings of the 24th International Technical Meeting of The Satellite Division of the Institute of Navigation (ION GNSS 2011), Portland, OR, USA, vol. 2023, 2011, p. 384392. [2] M. Meurer, A. Konovaltsev, M. Appel, and M. Cuntz, "Direction-of-Arrival Assisted Sequential Spoofing Detection and Mitigation", p. 12, 2016. [3] A. Konovaltsev, M. Cuntz, C. Hättich, and M. Meurer, "Autonomous Spoofing Detection and Mitigation in a GNSS Receiver with an Adaptive Antenna Array", presented at the ION GNSS+ 2013, Nashville, TN, USA: The Institute of Navigation, Sep. 30, 2013. [4] Q. Jia, R. Wu, W. Wang, D. Lu, and L. Wang, "Adaptive blind antijamming algorithm using acquisition information to reduce the carrier phase bias", GPS Solutions, vol. 22, no. 4, p. 99, Jul. 19, 2018, ISSN: 1521-1886. DOI: 10.1007 / s10291018-0764-4. [5] T. Bamberg, A. Konovaltsev, and M.Meurer, "Mitigation of Carrier Phase Distortions Induced by Spatial Filtering using Antenna Arrays", in Proceedings of the 33rd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2020), Oct. 28, 2020, pp. 3120-3131. DOI: 10.33012 / 2020.17707. [6] S. Daneshmand, T. Marathe, and G. Lachapelle, "Millimetre Level Accuracy GNSS Positioning with the Blind Adaptive Beamforming Method in Interference Environments", Sensors (Basel, Switzerland), vol. 16, no. 11, Oct. 31, 2016, ISSN: 1424-8220. DOI: 10.3390 / s16111824. pmid: 27809252. [7] T. Bamberg and M. Meurer, "Characterizing the Carrier Phase Distortions for Different Interference Mitigation Approaches using an Antenna Array", in Proceedings of the 32nd International Technical Meeting of the Satellite Division of The Institute of Navigation (ION GNSS+ 2019), Miami, Florida, Oct. 11, 2019, pp. 3517-3527. DOI: 10.33012 / 2019. 16933. [8] T. Takasu and A.Yasuda, "Development of the low-cost RTK-GPS receiver with an open source program package RTKLIB", International Symposium on GPS / GNSS, Jan. 1, 2009. [9] S. Zorn, M. Niestroj, S. Caizzone, M. Brachvogel, and M. Meurer, "Selfcontained Antenna Crosstalk and Phase Offset Calibration by Jointly Solving the Attitude Estimation and Calibration Problem", in ION GNSS 2017, Portland, Orgeon, USA, Jul. 7, 2017.

[10] S. Zorn, T. Bamberg, and M. Meurer, "Accurate Position and Attitude Determination in a Jammed or Spoofed Environment Using an Uncalibrated Multi-Antenna-System", Proceedings of the 2018 International Technical Meeting of The Institute of Navigation, p. 13, 2018.

[11] M. Sgammini, F. Antreich, L. Kurz, M. Meurer, and T. G. Noll, "Blind Adaptive Beamformer Based on Orthogonal Projections for GNSS", presented at the ION GNSS 2012, Nashville, USA, Sep. 2012.

[12] E. Kaplan and C. Hegarty, Understanding GPS: Principles and Applications. Artech House, 2005, 718 pp., ISBN: 978-1-58053-895-4.

[13] "Satellite Positioning Service of the German State Surveying Agencies - SAPOS®." (), [Online]. Available: https: / / www.bezregkoeln.nrw.de / brk_internet / geobasis / raumbezug / sapos / index.html (visited on 11 / 29 / 2021). . US-A-2002 / 0169578 WO-A-02 / 051028 US-A-2017 / 0102445 WO-A-98 / 032239

Claims

1. A method of reducing the effects of interference suppression on the measurement of the carrier phases of satellite navigation signals at the location of their reception, in which method a) a one- or multi-dimensional antenna array with a plurality of receiving antennas is provided, b) satellite navigation signals received by the receiving antennas are processed in a signal processing unit, c) an eigenbeamformer is applied to one or each of the received satellite navigation signals and parameters describing the same are calculated, d) the parameters of the eigenbeamformer of the one satellite navigation signal or of each satellite navigation signal are measured or determined at times when no interference suppression is to be performed, the parameters being initialized such that the satellite navigation signal received by a predetermined receiving antenna of the antenna array is passed unchanged, e) the received satellite navigation signals are subjected to interference suppression in the signal processing unit by means of a spatial filter, i.e. by means of spatial filtering, such as a power inversion (PI) filter or a projection filter, after which the carrier phases of the satellite navigation signals are distorted, f) after the interference suppression by means of the signal processing unit, the carrier phase of at least one or each of the satellite navigation signals is changed by calculating parameters from the current eigenbeamformer associated with the respective satellite navigation signal and the preceding eigenbeamformers associated with the respective satellite navigation signal, including the eigenbeamformer according to feature d), so that the distortions of the carrier phases resulting from the interference suppression are corrected.

2. The method according to claim 1, characterized in that the respective interference suppression is defined by a set of signal processing parameters for application to the satellite navigation signals to be suppressed, this set of parameters changing when interference affecting the satellite navigation signals, which interference arises from interference signals in the vicinity of the receiver or due to infrastructure in the vicinity of the receiver, changes, and that, when the interference changes, - the parameters of a new eigenbeamformer are calculated for the at least one satellite navigation signal or for each satellite navigation signal, so that the previously calculated carrier phase of the at least one satellite navigation signal or of each satellite navigation signal results when the respective new eigenbeamformer is applied, and - to compensate for the change in the carrier phase of the at least one satellite navigation signal or each satellite navigation signal calculated by the new eigenbeamformer resulting from the changed interference suppression parameter set, the parameters of the relevant new eigenbeamformer are further changed to rotate the calculated carrier phase.

3. The method according to claim 1 or 2, characterized in that, at times when no interference suppression is to be performed, the parameters of the at least one eigenbeamformer define complex-valued beamforming weights with which the respective signals output by the receiving antennas per satellite navigation signal are weighted, in that either one of the receiving antennas is selected as the reference position, the weight for this receiving antenna being selected to be positive, real-valued (e.g. 1), or a position within the antenna array which does not coincide with one of the receiving antennas is selected, and in that the complex-valued weights for the receiving antennas of the antenna array are selected such that the carrier phase of a sum signal resulting per satellite navigation signal after weighting is equal to the carrier phase of the satellite navigation signal assigned to the eigenbeamformer, which arrives at the receiving antenna selected as the reference position of the antenna array or which would reach an antenna at the reference position of the antenna array not coinciding with a receiving antenna, the resulting sum signal being calculated as the sum of the complex-valued weighted, interference-suppressed receiving antenna signals, which in turn result from a complex-valued linear combination of the individual digitized receiving antenna signals and which are calculated from the receiving antenna signals by applying the interference suppression.

4. The method according to one of claims 1 to 3, characterized in that the beamforming weights of the at least one eigenbeamformer are initialized with undisturbed satellite navigation signals by passing the satellite navigation signal at the reference position unchanged, whereby no direction-dependent carrier phase error arises in relation to this reference position as a result of the beamforming, the eigenbeamformer to be calculated being adapted, during a subsequent interference suppression, based on the previous eigenbeamformer with the aim that the phase of a resulting sum signal is still equal to the carrier phase of the satellite navigation signal at the reference position, the resulting sum signal being calculated as the sum of the complex-valued, interference-suppressed receiving antenna signals, which in turn result from a complex-valued linear combination of the individual digitized receiving antenna signals and which are calculated from the receiving antenna signals by applying the interference suppression.

5. A method for determining the distance of a receiver for satellite navigation signals from a satellite, in which method - the method in accordance with one of claims 1 to 4 is performed, and - the so-called pseudo-distance of the receiver to the satellite is calculated using the calculated phase of the satellite navigation signal.

6. A method for determining the position of a receiver for satellite navigation signals, in which method - the method in accordance with claim 5 is performed, and - the position of the receiver is determined using the distances between the receiver and several satellites.