Method for reducing the effects of interference suppression on the measurement of a phase shift of a satellite navigation signal at the location of its reception and applications of this method

Abstract

Method for reducing the effects of interference suppression on the measurement of the phase shift of the carrier signal of satellite navigation signals at the location of their reception, wherein the method - a one- or multi-dimensional antenna array with several receiving antennas is provided, - satellite navigation signals from one or more satellites received by the receiving antennas are processed in a signal processing unit, - the received satellite navigation signals are subjected to interference suppression at the multiple receiving antennas in the signal processing unit by means of a spatial filter, i.e. by means of spatial filtering, - after interference suppression by means of the signal processing unit, the phase shift of the carrier signal of the satellite navigation signal of one or each satellite is corrected by calculating parameters of an eigenbeam former assigned to the satellite whose satellite navigation signal is received, wherein the eigenbeam former shifts the satellite navigation signal of the satellite assigned to it several times with respect to its carrier signal phase and thus generates several phase-shifted satellite navigation signals, - where the parameters of the eigenbeam former define complex-valued weights with which the respective signals emitted by the receiving antennas are weighted, - where the reference location of the antenna array, which represents the location of reception, - either one of the receiving antennas is selected, whereby the weight for this receiving antenna is chosen to be positive, real-valued (e.g. 1), - or a position within the antenna array that does not coincide with one of the receiving antennas is selected and - wherein the complex-valued weights for the receiving antennas of the antenna array are selected such that the phase shift of the sum signal formed as the sum of the phase-shifted satellite navigation signals of the eigenbeamformer, after weighting, corresponds to the phase shift of the satellite navigation signal belonging to the eigenbeamformer which would reach the antenna array at the reference position.

Description

The invention relates to a method for reducing the effects of interference suppression on the measurement of a phase shift of a satellite navigation signal at the location of its reception. The invention further relates to a method for determining the pseudo-distance of a receiver for satellite navigation signals from a satellite and to a method for determining the position of a receiver for satellite navigation signals, wherein the method for reducing effects of interference suppression on the measurement of the phase shift of the satellite navigation signal is used in these two methods.Global satellite navigation system (GNSS) receivers are susceptible to interfering signals. One successful method for mitigation of interference signals is multi-antenna systems, which suitably superimpose the input signals of the individual antenna channels. For this purpose, the signals are multiplied by a complex factor (beamforming weight) and then added up. The interference signal can thus be suppressed by pre-whitening (pre-whitening) or setting a spatial zero (nulling). In addition, the useful signal can be amplified by suitable superposition (e.g. self-beam former).However, a disadvantage of this method is that the superposition of the input signals distorts the absolute phase shifts of the carrier signal of the satellite signals (hereinafter sometimes referred to as carrier phase) depending on the direction, and an exact determination of the original carrier phases is therefore no longer possible. The exact carrier phase is required, for example, in highly accurate positioning algorithms such as real time kinetics (RTK) or precise point positioning (PPP).In the prior art, there are two different approaches to correct the corrupted carrier phase: 1. the directionality of an antenna array can be characterized by the so-called spatial phase signature (steering vector). This describes the phase position 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 various approaches to calculating the phase signature: a. The multi-antenna system is measured in a measurement chamber and the directional phase signature (or a correction variable derived therefrom) is stored in a table. Knowing the directions of incidence of the signals and the position of the antenna array, the phase error can thus be determined and corrected. The disadvantage of this approach is that the antenna array has to be measured. This is usually only possible with high costs in an antenna measurement chamber. In addition, the spatial phase signature of the antenna array changes very strongly in the case of changes in the near field, so that a measurement is valid only for a predefined environment. In addition, the directions of arrival of the signals must be known and the antenna array used must be calibrated. Both entail additional outlay and thus increased costs. (Calibration is required to compensate for the different signal propagation times in the front end and the other components.) b. Assuming that the useful signal has the greatest power, the spatial phase signature can be estimated during operation of the receiver. Without interfering signal, this assumption is fulfilled with GNSS signals after the correlation with the satellite-type spreading code. However, if an interfering signal is present, this must first be suppressed for estimating the phase signature. Mitigation by pre-whitening or setting a spatial null back varies the phase vector. Known methods first determine the changed phase vector and then calculate the mitigation. This approach has the disadvantage that the mitigation has to be calculated out again from the estimated phase signature. As a result, the previously suppressed interference signal is again included in the estimate, so that the estimated phase signature deviates from the actual phase signature of the incoming signal. This in turn changes the calculated correction of the carrier phase. This approach works only as long as either the perturbation signal is very small, or the phase vector of the incident signal is perpendicular to the phase vector of the perturbation signal. 2. the arrangement of the antenna elements of the array is limited to fixed systems. In this case, a point-symmetrical arrangement of the antenna elements with the point of symmetry in the center of the array is usually assumed. 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 idealised, isotropic antenna elements, an influence on the carrier phase can thus be prevented completely. If the antenna elements deviate only slightly from this ideal, a phase error of the carrier phase occurs, which is however relatively small. A disadvantage here is that the arrangement of the antenna elements is predefined. Thus, any antenna arrays cannot be used. If the antenna elements also deviate from idealised, isotropic radiators, the carrier phase is again more strongly distorted. Known approaches also reduce the number of degrees of freedom in the suppression of interference signals by a factor of 2.US 2002 / 0169578 A1 discloses a method for interference signal suppression and position determination of a satellite navigation signal receiver. The signal resulting from the interference signal suppression is processed in a conventional GNSS receiver, i.e. a GNSS receiver based on code phases. According to the known method, a common beamforming is performed for all satellite navigation signals, which causes individual, directional phase errors for the different satellite navigation signals.WO 02 / 051028 A2 discloses the suppression of interference signals and amplification of a useful signal using a combination of different methods. A stabilization of the carrier phases after the interference signal suppression does not take place in this method. This method is therefore also suitable only for code phase-based GNSS receivers.US 2017 / 0102445 A1 relates to the combination of antenna signals of an antenna array to form a single signal (beamforming). According to the known method, the resulting signal is compared with the signal of a reference antenna, wherein the weights are adjusted such that the useful 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 useful signal can still be used at the reference antenna. If, in addition to the useful signal, there is also an interference signal which is significantly stronger than the useful signal, this signal can no longer be evaluated with an individual antenna and thus a comparison with the reference antenna is also no longer possible.WO 98 / 032239 A9 describes a method for interference signal suppression using notch filters and the subsequent combination of the filtered signals for additional spatial interference signal suppression by means of spatial filtering. Attempts are made to ensure the amplification of the individual signals as in the case of an isotropic antenna, which means that the satellite signal is as far as possible not attenuated by the filter.It is an object of the invention to further reduce the negative influences of the interference signal suppression in satellite navigation signals on the measurement of the carrier phase.To achieve this object, the invention specifies a method having the features of claim 1. Individual embodiments of the method are the subject matter of the dependent claims.The invention proposes a method for reducing the effects of interference suppression on the measurement of the phases of satellite navigation signals (also referred to below as carrier phase) at the location of their reception, the method being characterized in that it includes the method.providing a one- or multi-dimensional antenna array having a plurality of receiving antennas,satellite navigation signals of one or more satellites received by the receiving antennas are processed in a signal processing unit,the received satellite navigation signals at the plurality of receiving antennas in the signal processing unit are subjected to interference suppression by means of a spatial filter, i.e. by means of spatial filtering,after the suppression of interference by means of the signal processing unit, the phase shift of the carrier signal of the satellite navigation signal of one of the or each satellites is corrected by calculation of parameters of a respective self-operator which is assigned to the satellite whose satellite navigation signal is received, wherein the self-operator shifts the satellite navigation signal of the satellite assigned to it multiple times with respect to its carrier signal phase and thus generates a plurality of phase-shifted satellite navigation signals,wherein the parameters of the self-beam former define complex-valued weights with which the respective signals output by the receiving antennas are weighted,wherein the reference location of the antenna array representing the location of reception is,either one of the receiving antennas is selected, 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, andwherein the complex-valued weights for the receiving antennas of the antenna array are selected such that the phase shift of the sum signal formed as the sum of the phase-shifted satellite navigation signals of the self-beam former corresponds, after the weighting, to the phase shift of the satellite navigation signal belonging to the self-beam former which would reach the antenna array at the reference position.After the application of the respective self-beam former per satellite, the phase shift of the resulting sum signal is conventionally calculated / tracked, for example, via a PLL, wherein the phase shift calculated / tracked in this way is now corrected, however, by the compensation according to the invention (calculation of the parameters mentioned here) of a corruption given as a result of the interference suppression.To define the reception location, the procedure is such that the parameters of each self-operator define complex weights with which the respective signals output by the reception antennas are weighted, and that either one of the reception antennas is selected as the reference location of the antenna array, which represents the location of the reception, wherein the weight for this reception antenna is selected to be positive, real valued (for example 1), or a position within the antenna array, which does not coincide with one of the reception antennas, is selected, wherein the weights for the reception antennas of the antenna array are selected such that the carrier phase of the sum signal (after the weighting) corresponds to the carrier phase of the satellite navigation signal belonging to the self-operator at said position; that is to say the carrier phase at a virtual antenna at this position. It should be noted that the weights of the self-beam formers are complex valued. If a receiving antenna is weighted with 1, this therefore does not mean that all other receiving antennas receive the weight 0, but rather only that the signal of the corresponding receiving antenna is transmitted without a phase change. If the weight were, for example, 1i (90°) or 0.7+0.7i (45°), the phase would be rotated, i.e. displaced, by 90° or 45°, respectively.According to the invention, the respective suppression of interference is defined by a set of signal processing parameters for application to the satellite navigation signals to be suppressed of interference, this parameter set changing when interference affecting the satellite navigation signals, which noise arises from interference signals in the vicinity of the receiver or due to infrastructure in the vicinity of the receiver, changes, and when the interference changesthe parameters of a new self-operator are calculated for the at least one satellite navigation signal or for each satellite navigation signal, so that the previously calculated phase of the at least one satellite navigation signal or each satellite navigation signal results when the respective new self-operator is used, andcompensating 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 phase results from the changed parameter set of the interference suppression, the parameters of the respective new eigenbeamformer can be changed further for the correction of the phase by means of their displacement, i.e. by rotation of the phase.In the method according to the invention, a one- or multi-dimensional (for example two- or three-dimensional) antenna array with a plurality of receiving antennas is used. The signals which are received by the receiving antennas and are present at their outputs (channels of the antenna array) are processed in a signal processing unit with a signal processor, for example. First, the interference suppression is carried out, whereby the individual satellite navigation signals can be separated from the interference signal. Unfortunately, this approach loses the information about the phases at which the satellite navigation signals of the individual satellites reach the antenna array; this is because the signals of the individual receiving antennas are made in phase with the suppression of interference. This must now again be compensated for when calculating self-beam formers, wherein one self-beam former is generated / calculated per satellite navigation signal. In this case, the phase error which has occurred is not compensated for by the calculation of the self-beam former, but by a term which is in turn applied to the self-beam former as a phase rotation or phase shiftWith each change in interference from the satellite navigation signals resulting from the environment or motion of the receiver, the calculation of the self-beam formers changes. In successive sections in time or at successive points in time, the disturbance suppression as well as each self-operator is recomputed. In this iterative process, the method is now such that the self-beam former to be recomputed at a time x is calculated in such a way that the phase resulting from it initially remains unchanged compared to the phase calculated previously (namely at the time x-1). In this case, the (temporary) phase change resulting from the change in the disturbance (between the time x- 1 and x) and thus from the newly calculated disturbance suppression is reversed again. The (temporary) phase change which arises as a result of the new change in the interference suppression must also be compensated, which takes place by means of a phase rotation which is applied to the phase calculated by the new self-former.The method according to the invention presupposes a multi-antenna receiver with interference suppression and subsequent beam shaping by means of an eigenbeamformer. In the undisturbed case, the method initializes the beamforming weights such that the reference antenna signal (a predefined element of the array) is passed unchanged (complex valued weight=1). With respect to this element, no directional phase error arises due to beam forming in this procedure. If an interference signal is present, the self-beam former to be calculated is adapted on the basis of the previous self-beam former with the aim that the phase of the resulting sum signal (after application of the self-beam former) still corresponds to the phase of the signal at the reference antenna (before application of the interference suppression).The adaptation is carried out in a two-stage method: 1. the parameters of the new self-beam former are adapted in the above sense to those of the previous self-beam former. At the same time, the (temporary) phase change caused by the previous change of the interference suppression is reversed again. 2. the (temporary) phase change which arises as a result of the (new) change of the interference suppression is compensated by means of phase rotation applied to the new self-beam former.The method according to the invention calculates the correction of the corrupted carrier phases in a multi-antenna receiver from the current and the last self-beam former and the current and the last interference suppression matrix. The calculation for this is carried out without information about the antenna array used and thus quasi "blind". A two-stage method is applied 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 signal is greatly distorted by interference signals. In contrast to a comparable method of the prior art, the method according to the invention can also be used in receivers which use a projection filter for interference suppression. In addition, the method according to the invention can also be used in receivers in which the self-operator calculates on one data record and is only applied to the next data record.Compared to the known method mentioned above under 1a, the invention has the advantage that the method works blindly, i.e. it does not require any measurement of the antenna array. In addition, no knowledge about the directions of incidence of the signals is required.Compared to the method mentioned above under 1 b, according to the invention the spatial phase signature does not have to be explicitly calculated. Instead of inverting the interference suppression, only the change in the interference suppression has to be taken into account. This allows the method to be used even in environments with strong interference signals. Furthermore, a drift of the phase correction is thus significantly reduced.Compared to the known method described above under 2, the invention has the advantage that the arrangement of the antenna elements can be effected as desired. Also, the performance of the method of the invention does not suffer if the antenna elements deviate from the ideal of an isotropic antenna.The method according to the invention can be advantageously used in determining the pseudo-distance of a receiver for satellite navigation signals from a satellite, wherein after carrying out the aforementioned method, the pseudo-distance of the receiver from the satellite is then calculated using, inter alia, the phase of the satellite navigation signals calculated by at least one of the self-formers.Finally, the method according to the invention can also be used for determining the position of a receiver for satellite navigation signals, wherein after carrying out the method described above for determining the pseudo-distance on the basis of said pseudo-distance, the position of the receiver is determined.Possible commercial applications are GNSS receivers that require high accuracy, GNSS reference stations, and GBAS stations.The invention is explained in more detail below on the basis of an exemplary embodiment and with reference to the drawing. In detail, the following show: Figures 1a and 1b show a measurement setup on the roof of the UMIC research center of the RWTH Aachen University. The antenna group at the front in FIG. 1 aand at the back in FIG. 1 b(DLR UNITSAS) serves to receive the satellite signals and the antenna at the back in FIG. 1 aand at the front in FIG. 1 b serves to emit the interference 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 motion of the interfering antenna around the UNITAS antenna group in scenario 2. Figure 4 shows the power of the eigenvalues of the pre-correlation covariance matrix estimated by the receiver. FIG. 5 shows scenario 1: Residues of the carrier phase over the UTC time. FIG. 6 shows scenario 1: position deviation over time. FIG. 7 shows scenario 2: moving jamming transmitter with constant power level. FIG. 8 shows scenario 2: position deviation over time.Global navigation satellite systems (GNSS) are frequently used for position determination and time measurement. The systems are used by almost all land, air and watercraft to navigate. As the number of private and commercial drones and the volume of autonomous driving vehicles increases, the number of systems that rely on GNSS will increase even further. Therefore, it is becoming increasingly important to ensure position, velocity and time solution (PVT) availability and integrity even in the event of interference, interference, or even snooping. In addition, the new applications require higher precision of the PVT solution. This requirement can be met by the techniques of precise point positioning (PPP) and real time kinematics (RTK). A key element of these methods is the inclusion of carrier phase measurements in the PVT estimate. Carrier phase measurements allow much more accurate range measurements because the wavelength of a GNSS carrier, e.g., 19 cm for GPS L1, is much less 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.An advanced approach to jamming and grooming protection is to use adaptive antenna arrays and to use spatial domain signal processing. The antenna groups can be used for detecting and containing jamming transmitters [1] and radio receivers [2], [3]. Moreover, an antenna array enables the C / N0value of a satellite signal to be increased by directing a beam in the direction of arrival (DoA). The mitigation is generally performed by 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 control vector of the incoming satellite signal must be known. The steering vector of an incident signal is its spatial signature, which contains the phase information of the signal at each antenna element. In order to obtain the steering vector, the reception pattern of the antenna must be known. In practice, a blind approach is often desired. A blind approach works without prior knowledge of the antenna gain / phase matrix, calibration matrix and direction of arrival of the perturbation. However, current implementations of blind spatial filters and beamformers induce an error in the carrier phase measurements.The problem of induced error in carrier phase measurements has been dealt with by other researchers. Two different strategies are found in the literature for attenuating the phase error arising from blind spatial filtering: one strategy aims to preserve the continuity of phase measurement in disturbed scenarios. Jia et al. [4] have presented for this an algorithm that works well for short-term scenarios. However, Jia et al. have not validated the proposed algorithm with recorded real word signals and did not evaluate the effects of the phase errors that occurred on the positioning solution. In particular, the stability of the carrier phase measurements over short periods of time is problematic. Further studies show that approaches using this strategy generally cannot maintain phase continuity over long periods of time [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, with its advantages over a standard implementation becoming evident. However, the additional constraints reduce the degrees of freedom of the spatial filter by half. Thus, an antenna array bumled twice the number of antenna elements to suppress the same number of jamming transmitters as the standard implementation. In addition, the algorithm works only with centrosymmetrical array geometries, i.e. it is not directly applicable to real antenna arrays without significant performance losses due to asymmetry in the antenna characteristics caused by imperfections, tolerances, near field object effects or installation problems.The above-mentioned limitations of the prior art have been 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 fault in both the absence and presence of a perturbation 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 least phase error. It can be shown that this filter is theoretically even free from carrier phase distortions [4]. In the simulations performed, it was assumed that the approach has inaccurate knowledge. However, this is still a deterministic approach that requires a priori knowledge. The three remaining approaches in [7] are blind. In these approaches, carrier phase distortion depends on the DoA of the satellite and the DoA of the interfering signal. One approach has been to sum the incoming signals after suppression of the interference, i.e. to use beamforming in which a one is present in each row. This approach results in only low phase distortion, but suppresses satellite signals at low altitude. Nevertheless, even with these approaches, PPP / RTK remains a challenge in rapidly changing environments. In [5], these results were used to develop two new blind approaches to reduce carrier phase error in 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 to either the previous beamformer or the beamformer of the above approach known to hardly affect the phase. The reduction of carrier phase error by these approaches is promising, but the evaluation has been limited to numerical simulations with synthetic satellite signals. The approaches were not tested with realistic signal data and, moreover, the effect of phase error on the positioning solution was not studied.With the proposed invention, the research works from [7] and [5] are extended to practical experiments with recorded realistic signals and using an RTK positioning algorithm. The analysis in [7] and [5] focused on the carrier phase offset caused by the adaptive spatial filtering on the signal plane. The proposed invention examines the resulting effect of such error on the RTK positioning solution. For this purpose, 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 the RTKlib [8], an open source package for GNSS positioning, to obtain an RTK positioning solution and evaluate the induced errors in the positioning area. The filtering and averaging of the 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 interference transmitters. The scenarios are processed using the classical implementations of spatial filtering and the approach proposed in [5]. The description concludes with a recommendation as to which approach is suitable for RTK positioning to perform spatial filtering of interference, multipath, or grooming signals. With the help of the obtained results, the invention aims to close the gap when using GNSS antenna array receivers with RTK positioning techniques, in particular taking into account the limitations resulting from the deficiencies of the real world. It will debate the way for the use of GNSS group receivers in applications that require a combination of high positioning accuracy and high reliability.NOTEIn this specification, the following notation is used:Small bold letters represent vectorsLarge bold letters stand for matricesSymbols - T and - H represent the transpose and Hermitian transpose, respectively- arg{-} represents the angle of a complex numberE[-] and var[-] represent the statistical expectation value and variance, respectivelySYSTEM MODEL AND SPATIAL SIGNAL PROCESSINGIn this section, the signal model and theoretical background for the spatial filters and beamformer are presented.Signal modelWe proceed from an antenna array with N antennas. This group receives M satellite and L interfering signals. The incident signal is: a m ∈C N×1 and a l ∈C N×1 describe the control vectors of the satellite and the interfering signals, respectively. A steering vector is the spatial signature of a signal and depends on the direction of arrival (DoA) of the incident signal and the orientation of the antenna array. For a simplified, isotropic antenna array, a=(e -1,..., e-ikTrN) describes the control vector of an incident wave. k is the wave vector and r1,...,rNdescribes the spatial positions of the antenna elements. In practice, the control vector (in phase and amplitude) deviates from this simplified model, since the antenna elements of the arrays are usually not isotropic or even not azimuthal invariant, which is due to the electromagnetic coupling of the array elements. Also, some other practical effects such as manufacturing tolerances and the presence of other objects in the near field result in the antenna patterns of an installed array deviating from the patterns calculated with antenna modeling tools or measured in a sonic chamber. In equation (1), some of these effects are taken into account by the term C. This matrix models different cable lengths and component tolerances in the N antenna processing channels as well as crosstalk between different channels. It is the same for all incoming signals and is in particular not affected by the DoA of a signal. Its reciprocal C -1 is referred to as a calibration matrix.At this point, it should be emphasized that the control vector also depends on the selection 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 stated, the origin point is the center of the antenna array, which is determined as the mean of all antenna positions. s m( t) 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 stands for the additive noise component. It is modeled as zero mean Gaussian noise with variance of zero.Spatial Filter and BeamformerThe combination of the received antenna signals offers the possibility of amplifying or suppressing different DoAs. For this purpose, the received signals are multiplied by a complex number (phase and amplitude change) and summed up. The beamformed signal can be expressed asThe weight vector w is defined by the needs of the user. A common method for suppressing unwanted signals is to use the minimum variance filter (MV) which minimizes the variance of the unwanted signals in the output signal. Assuming that the unwanted signals have a mean value of zero and are uncorrelated with the satellite signal, we can write:R j+n is the covariance matrix of the unwanted signal and noise. To exclude the trivial solution w=0, a further condition must be added. The additional condition w H a m= 1 yields the MVDR filter. The solution for this filter is given by:The GNSS satellite signals are far below the noise floor. Therefore, the covariance matrix of the unwanted signal can be approximated without prior knowledge by: where K describes the number of samples used and x[k] represents the read samples at time t k= kT with the sampling interval T.Estimating the steering vector for the desired satellite signal is more difficult: If the receiver system receive pattern, the location and position of the antenna array are known, the DoA and the incident signal steering vector can be calculated from the ephemeris data. This approach is classified as a deterministic filter. In practice, this approach is quite demanding due to the temporal change of the required information. A promising attempt to jointly estimate the time-varying components is described by Zorn in [9] and

[10] .EigenbeamformerAnother way to estimate the steering vector is to estimate it after the diffusion / correlation. The correlation amplifies the useful signal beyond the noise floor, so that it is possible to extract its spatial signature.This approach can be used even in the presence of a perturbation signal that overlays the satellite signal. In order to suppress strong noise, a spatial filter is applied before the correlation. This process is referred to as prewhitening. The filtered signal is:The signal after correlation can be expressed as: where the factor G m represents the scaling of the correlation with the local replica and n pc,m is the noise after the correlation process. This noise contains both the other satellites and the suppressed jamming and pre-correlation noise.The post-correlation covariance matrix for satellite m is:If the eigenvalue decomposition is calculated and the eigenvector belonging to the strongest eigenvalue is taken, the following vector is obtained:Eigenvectors are fixed only to a scale factor represented in equation (10) by the complex term (α m e iϕm). Normally, the eigenvector is scaled to have a norm of one. However, the phase factor (e iϕm) is still arbitrary. The term e m represents the errors in the estimation of the control vector.Due to the use of the eigenvector, this beamformer is referred to as an eigenbeamformer. The approach does not require information about the antenna array and is therefore classified as a blind filter. The self-beam former is described in more detail in

[11] and [4]. The weight vector for the constrained MV filter with an eigenbeamformer is given by:PHASE ERROR AND PHASE COMPENSATION MECHANISMSThe beamformer described above suppresses unwanted interference signals and amplifies a desired satellite signal. This is done by summing the phase shifted signals. The resulting sum signal is then passed to the PLL / DLL used for pseudorange and carrier phase measurements. In this section, the influence of the described self-beam former on the carrier phase is analyzed. In addition, two methods are presented for reducing this effect.Phase ErrorsMathematically, beamforming can be described by the combination of equations (3) and (1):The spatial signal processing induced phase shift of a single satellite signal, s m can be described as the phase of the product of the weight vector, the inverse calibration matrix, and the true control vector of that particular satellite:The induced phase shift of the MVEig beamformer may be calculated. Equation (11) yields equation (13):For technical reasons, the self-beam former 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 take this into account, we add an index indicating the time dependence: h and h-1, respectively (e.g., a h and a h-1). In order to obtain readability, we no longer indicate the satellite dependency, i.e. we no longer indicate the index m. With these adjustments and with equation (10), equation (16) is:CompensationTo prevent the spatial signal processing from affecting the range measurements, the phase error must be zero, i.e. Δφ MVEig= 0!. The proposed compensation algorithm aims to prevent phase jumping in two successive estimates of the beamformer or spatial filter. The compensation is done by changing the phase of the estimated eigenbeam former (10) before it is used in the beam forming process. Mathematically, the post-compensation weighting vector for the satellite m is: with the compensation phase φ Comp.The compensation phase is estimated in two steps. The first step is defined by the multiplication of two successive eigenbeam formers:The second step takes into account the changing pre-whitening matrix. It is defined byWe proceed from the following:1) The calibration matrix and 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 when the interval between iterations is small compared to the movement of the satellites and the receiver. If the receiver is stationary or is moving slowly, a reasonable interval for iterations is 50ms.2) The error in the estimation of the self-beam former is negligibly small, i.e. ||e|<<|a||.With these postulats, the phase compensation results in:Applying this compensation to the beamformer (20) obtains:The phase error induced by the new weight vector is the same as the phase error of the previous weight vector, but the phase offset is removed by the previous change of the pre-lightening filter. If we assume that the pre-lightening matrix has not changed in the previous iteration, i.e., P h-2= P h-1, the second term becomes zero, i.e., this can be used to prevent a phase change caused by spatial signal processing in a changing environment.However, the dependence on the previous weight vector is also the greatest disadvantage of this approach: a phase error in the previous iteration is transferred to the next phase compensation. Therefore, the induced phase will drift over time in this compensation approach. In addition, we must know (or estimate) the initial phase error.PROCESSING OF THE SIGNALS AND IMPLEMENTATION OF THE PROPOSED ALGORITHMTo analyze the proposed compensation algorithm, we pick up and process GNSS satellite signals. To do this we perform the following steps:1) recording the GNSS signals with a suitable multi-channel data streamer.2) Use of a software receiver for processing the signals and generating code and carrier domain observations in RINEX format.3) Read in the RINEX file using the RTKlib to estimate an RTK position solution.Recording of SignalsThe Ettus USRP x300 platform is used for digitizing and storing the GNSS signals. The most important settings are:• Center frequency: 1575.42 MHz• Intermediate frequency of digitized signals: 0Hz (complex I&Q sampling)• Sampling rate: 5MHz• Number of recording channels: 4The four channels are connected to the UNITAS antenna array developed and manufactured by the DLR, which can be seen in the foreground of FIG. 1 a. It is a uniform rectangular 2x2 antenna array with antenna element spacing of about one-half wavelength L1 (approximately The recorded signal samples are stored on a hard disk and then post-processed by a multi-antenna software receiver.processing of the recorded signalThe GNSS software receiver used is implemented in MATLAB. Figure 2 shows the functional diagram of the receiver. The N input 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 interfering signals. The filter matrix is then applied to the input signal (see equation (7)). The despreading of the signal is performed for each satellite individually. The post-correlation beamforming operates on the N outputs of the despreading / correlation unit. The outputs are buffered via several correlation epochs to calculate the covariance matrix of the post-correlation (see equation (9)). To ensure that this covariance matrix does not contain signals with different pre-correlation filter matrices, the buffers for the pre- and post-correlation are synchronized. The post-correlation covariance matrix is used to calculate the eigen-former weight vector (see equation (10)). The proposed compensation approach as described in the previous paragraphs is used to adjust the phase of the self-beam former. The matched self-beam former is applied to the output of the despreading / 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 pseudorange and the accumulated Doppler range (ADR). These are stored in the RINEX observation file, which is passed to the RTKlib.RTK PositioningThe RTKlib (version 2.4.3 b34) is used to obtain an RTK position solution from the RINEX observation file. In addition, a RINEX navigation file is downloaded to make the ephemeris and clock data available. The RTKlib is set to process the file in the "static position" mode and fix the integer ambiguity in the "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 them as "RTK Float". For further details on the options used, a digest from the rtkpost.ini can be found in the appendix.In addition, 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 Land Survey Office in Aachen (SAPOS® )

[13] was used. TABLE I: Jamming events in scenario 1. TABLE I: Jamming events in scenario 1.113:01:2813:02:2020213:02:2013:02:5026313:02:5013:03:2032413:03:2013:03:5038513:03:5013:04:2244613:04:2213:04:5050713:04:5013:05:1956813:05:1913:05:5062913:05:5013:06:20681013:06:2013:06:50741113:06:5013:07:19801213:07:1913:07:5186SCENARIOS AND EVALUATION STEPSScenariosFor the evaluation we consider two different scenarios. Both scenarios are recorded on the roof of the UMIC Research Center of the RWTH Aachen on Sep. 21, 2021. Two images of the measurement setup can be seen in FIG. 1. Each scenario includes an interfering signal specific to the respective scenario:1) In scenario 1, a jamming transmitter with gradually increasing signal power is studied. The direction of incidence of the interference signal on the antenna field remains constant in this case. The interference power is increased by 6 dB after each 30 s. Table I shows the relative performance of the individual stages as well as the start and stop times. FIG. 4a shows the eigenvalues of the pre-correlation covariance matrix calculated by the receiver. As can be seen in the figure, the spread of eigenvalues can be used to estimate the power of the incoming interfering signal in relation to the lower noise limit of the receiver.2) In scenario 2, a moving jamming transmitter with constant power level is studied. The interfering antenna is moved in a semicircle around the UNITAS antenna group and then in the direction of the UNITAS antenna group. This movement is shown in FIG. 3. The movement was performed manually, therefore it is not as perfect as shown. The fault event begins at 13:38:16 UTC and ends at 13:42:04. Using the same relative power scale as in Table I, the jamming transmitter radiates 62 dB (stage 8). However, due to the movement of the antenna, the received power of the interfering signal varies. The variation can be illustrated by plotting the power of the eigenvalues of the pre-correlation covariance matrix, as shown in Figure 4b. It can be observed that the power of the received signal starts at a value comparable to stage 8 in scenario 1 and rises to a value comparable to stage 11.EvaluationEach scenario is processed in three different modes:1) Single Antenna: In this mode neither pre-whitening nor beamforming is used. Instead, only the signal of 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 a possible phase offset. Prewhiteting is only activated when the largest eigenvalue of the pre-correlation covariance matrix 10dB is higher than the smallest eigenvalue. This ensures that the filter does not affect the carrier phase of the satellite signals as long as there are no serious disturbances. The weights of the self-beam formers are normalized such that the first element (corresponding to antenna 1) remains equal to 1, i.e. positive and real valued. Without interference signal, this leads to a similar position determination as in the single antenna mode. However, the beamformed signal has a better C / N 0because it overlays the input signal from N antennas.3) w / Phase Compensation: In this mode, the receiver uses pre-whitening and beamforming as well as the proposed algorithm for compensating phase deviations. As in the mode without phase compensation, the pre-whitening matrix is only applied when the largest eigenvalue of the pre-correlation covariance matrix is 10 dB higher than the smallest eigenvalue. The phase of the beamformer is estimated using the proposed algorithm. However, for initialization of the self-beamformer or when the spatial filter is not applied, the phase of the beamformer is estimated as in the mode without phase compensation, i.e. the first element of the beamformer is equal to 1.RESULTS AND DISCUSSIONScenario 1: Jamming Transmitter with Gradually Increasing Signal PowerFigure 5 shows the residues of the carrier phase 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 RTK solid solution. The beginning and end of each phase as defined in Table I are highlighted in red. Because of the interfering signal, the single antenna in phase 8 has difficulty tracking the satellite signals; a cycle error occurs with two or more satellites. In the next phase (phase 9), the single antenna receiver is no longer able to track the satellite signals and loses all them.The use of the prewhitening filter makes it possible to maintain an RTK-FIX solution up to stage 12 (FIG. 5 b ). 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 digitizing process, since the recording system (USRP X300) does not use automatic gain control (AGC).In this scenario, the phase compensation algorithm (FIG. 5 c) only cuts slightly better than the receiver without phase compensation (FIG. 5 b): the residues in stages 8, 9, 10 and 11 are slightly less and the jump of some residues in stage 12 is not as great as without phase compensation. In this scenario with static receiver-Jammer geometry, however, the phase compensation is not explicitly necessary, but is also not harmful.Figure 6 shows the relative position offset for the three modes separated for east, north and altitude. The results are related to the average position of the single antenna processing. Similar to the previous diagrams, it can be observed that the single antenna has difficulty tracking the signals in stage 8 (resulting in a clearly visible position offset) and losing them in stage 9. The use of the pre-whitening filter allows estimation of an RTK-FIX solution up to stage 12, however, from stage 11 the receiver loses connection to some satellites, which can be seen 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: Moving Jamming Transmitter with Constant Power LevelFIG. 7 shows the carrier phase reidues for scenario 2 for the various processing modes. In this scenario, the power of the radiated interfering signal remains constant, but the direction of the interfering signal arriving at the receiver antenna changes over time due to the movement of the interfering antenna. In addition, the received interference power at the antenna group varies due to the changing distance between the interference transmitter and the receiving antenna (see 3b). The time at which the disturbance is activated is indicated by two vertical lines in all relevant images.Similar to scenario 1, single antenna mode is unable to track the satellite signals while the interfering signal is active. The use of the pre-illumination filter allows the satellite signals to be tracked throughout the length of the signal record. In this scenario, the advantage of the proposed phase compensation algorithm can be clearly demonstrated: while without phase compensation the carrier reliabilities increase significantly in the time the jamming transmitter is active, they remain low when using the proposed compensation approach. Without the phase compensation, the RTK-FIX solution is not available even for several seconds.The results for the positional deviation in Figure 8 also support the conclusion about the benefit of the proposed approach. Without phase compensation, the position solution drifts significantly when the interference transmitter is activated. As can be seen in the previous diagrams, the RTK-FIX solution is even lost. With the phase compensation, on the other hand, the estimated position solutions have only slight deviations which are of the same order of magnitude under interference-free and interference-afflicted conditions.CONCLUSION AND INSIGHTIn this application we have proposed an algorithm for compensating for carrier phase rotations occurring with blind spatial signal processing. Blind in this context means that the user does not need to know any prior information about the phased array antenna or the front end. The proposed algorithm was tested in two different scenarios using a proprietary software receiver in combination with the RTKlib used to estimate an RTK solution. In the first scenario, the signal power of a transmitter was increased stepwise by a constant DoA, and in the second scenario, a transmitter with constant signal power was moved around the receiving antenna group. For both scenarios, the proposed algorithm was compared to a multi-antenna system without phase rotation compensation and single antenna processing.As expected, the single antenna receiver is unable to estimate a position solution as soon as the interference signal becomes too strong. The multi-antenna system suppresses the interference due to pre-illumination and is capable of tracking the satellite signals during the interference influences. It produces continuous code and carrier range observations which provide a positioning solution. Without compensating for the phase deviations, however, the carrier phase residues estimated by the RTlibegin to grow in the (rapidly) changing environment (moving jamming transmitter). As a result, the RTKlib can no longer estimate an RTK-FIX solution, but only a FLOAT solution. In addition, the position solution begins to drift even though we have analysed a static scenario. This problem can be alleviated with the proposed approach. The residues of the support phase do not increase compared to the undisturbed period of time, and the RTK-FIX solution can be maintained throughout the recorded period of time.The proposed algorithm allows to take advantage of the advantages of an antenna array (without relying on detailed information about the antenna diagram) together with an RTK position solution. It is best suited for situations in which a solution with medium to high accuracy (dm to cm) must be insensitive to disturbances. A very accurate solution (cm to mm) comparable to a geodetic receiver using antenna phase center variations cannot be achieved with this algorithm. This is not surprising because the algorithm does not use or require detailed information about the antenna diagram. An alternative solution to such a scenario would be to use a deterministic beamforming approach, which would, however, be highly dependent on knowledge of the amplitude and phase embedded patterns of the array antennas.In this work, the time for signal recording and processing was limited to less than one half hour. The carrier phase shift produced by the proposed algorithm can become larger with longer observation time. This is to be evaluated as part of the future work.REFERENCES[1] M. Cuntz, A. Konovaltensev, 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. Konovaltensev, M. Appel, and M. Cuntz, "Direction-of-Arrival Assisted Sequential Grooming Detection and Mitigation", p.12, 2016.[3] A. Konovaltensev, M. Cuntz, C. Hettich, and M. Meurer, "Autonomous Grooming Detection and Mitigation in a GNSS Receiver with an Adaptive Antenna Array", present 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 / s1029018-0764-4.[5] Bamberg, T., Konovaltensev, A., and Meurer, M., "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 (Basle, Switzerland), vol. 16, no. 11, Oct. 31, 2016, ISSN: 1424-8220. DOI: 10.3390 / s16111824. pmid: 27809252.[7] Bamberg, T. and Meurer, M., "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, "Self-contained Antenna Crosstalk and Phase Offset Calibration by Joint Releasing the Constituent 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 Customized Environment Using an Uncalibrated Multi-Antenna System", Proceedings of the 2018 International Technical Meeting of The Institute of Navigation, p.13, 2018.

[11] Sgammin, M., Antria, F., Kuntri, L., Meurer, M., and Noll, T.G., "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 Antennas - SAPOS®." (), [Online]. Available: https: / / www.bezregkoels.nrw.de / brk_intert / geobase / space reference / sapos / index.html (visited on 11 / 29 / 2021).

Claims

Method for reducing the effects of interference suppression on the measurement of the phase shift of the carrier signal of satellite navigation signals at the location of their reception, wherein in the method - a one- or multi-dimensional antenna array having a plurality of reception antennas is provided, - satellite navigation signals of one or more satellites received by the reception antennas are processed in a signal processing unit, - the received satellite navigation signals at the plurality of reception antennas are subjected to interference suppression in the signal processing unit by means of a spatial filter, i.e. by means of spatial filtering, - after the interference suppression by means of the signal processing unit, the phase shift of the carrier signal of the satellite navigation signal of one of the or each satellite is corrected by calculation of parameters of a respective self-operator which is assigned to the satellite whose satellite navigation signal is received, wherein the self-operator shifts the satellite navigation signal of the satellite assigned to it multiple times with respect to its carrier signal phase and thus generates a plurality of phase-shifted satellite navigation signals, - wherein the parameters of the self-operator define complex-valued weights with which the respective signals output by the receiving antennas are weighted, - wherein as the reference location of the antenna array, which represents the location of the reception, - either one of the receiving antennas is selected, wherein the weight for this receiving antenna is 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 - wherein the complex-valued weights for the receiving antennas of the antenna array are selected, the phase shift of the sum signal formed as the sum of the phase-shifted satellite navigation signals of the self-beam former after the weighting corresponds to the phase shift of that satellite navigation signal which would reach the antenna array at the reference position and which belongs to the self-beam former.Method according to Claim 1, characterized in that a power inversion (PI) filter or a projection filter is used as the spatial filter.Method according to one of Claims 1 or 2, characterized in that the respective suppression of interference is defined by a set of signal processing parameters for application to the satellite navigation signals to be suppressed of interference, this parameter set changing when interference which influences the satellite navigation signals and arises from interference signals in the vicinity of the receiver or owing to infrastructure in the vicinity of the receiver is changed, and in that, when the interference is changed, - the parameters of a new self-operator are calculated for the at least one satellite navigation signal or for each satellite navigation signal, with the result that the previously calculated phase shift of the carrier signal of the at least one satellite navigation signal or each satellite navigation signal arises when the new self-operator in question is used, and for compensating the change in the phase shift of the carrier signal of the at least one satellite navigation signal or each satellite navigation signal calculated by the new self-operator, which phase shift results from the changed parameter set of the interference suppression, the parameters of the respective new self-operator are further changed in order to rotate the calculated phase shift of the carrier signal.Method for determining the distance of a receiver for satellite navigation signals from a satellite, wherein - the method according to one of Claims 1 to 3 is carried out in the method, and - the so-called pseudo-distance of the receiver from the satellite is calculated on the basis of the calculated phase shift of the carrier signal of the satellite navigation signal.Method for determining the position of a receiver for satellite navigation signals, wherein - the method according to Claim 4 is carried out and - the position of the receiver is determined on the basis of the distances of the receiver to a plurality of satellites.

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