Method for determining a position and an orientation of a receiver array by estimation

Abstract

The invention relates to a method for determining a position and / or orientation of a receiver array with multiple receiving antennas by estimation, in particular with N A Receiving antennas, wherein the following steps are carried out in the procedure: Broadcasting a respective signal by at least one transmitter at different positions, in particular at N R Positions, and Evaluating a spatially characteristic phase response of the wave fields of the respective radiated signals using the multiple receiving antennas of the receiver array, wherein At the receiver, at least one measured difference phase of at least one pair of receiving antennas is compared with hypothetical difference phases of the same pair of antennas, which result from the positions and orientation of the receiver.

Description

[0001] The present invention relates to a method for determining the position and / or orientation of a receiver array, based on the evaluation of different phase differences between at least two receiving antennas of the receiver array. The present invention is therefore based on the PDOA (phase-difference-of-arrival)-based determination of the position and orientation of receiver arrays.

[0002] There are already several providers of angle-based positioning systems, particularly using the Bluetooth standard, e.g., Quuppa, infsoft, Bluelot, u-blox. These systems use PDOA measurements from multiple receiver arrays distributed throughout the room, the positions of which are known in advance, to first estimate the angle to the transmitter at each receiver array and then to locate the transmitter using multiangulation. Such a system is in Fig. 1 illustrated.

[0003] It is known from the prior art that the localization accuracy of PDOA systems depends directly on the aperture size of the receiver arrays relative to the measurement distance; see Sippel, Erik; Geiss, Johanna; Brückner, Stefan; Gröschel, Patrick; Hehn, Markus; Vossiek, Martin: Exchanging Bandwidth With Aperture Size in Wireless Indoor Localization - Or Why 5G / 6G Systems With Antenna Arrays Can Outperform UWB Solutions. In: IEEE Open Journal of Vehicular Technology Vol. 2 (2021), pp. 207-217.

[0004] Known angle-based PDO localization approaches do not work optimally for large receiver arrays because the transmitter to be located is typically in the receiver's near field. This contradicts the assumption of plane received waves used by angle estimators. Due to the spherical waves emitted by the transmitter, this assumption only holds true for small spatial regions (namely the far field) and can therefore only be considered valid for small receiver arrays. The near field is often referred to in the literature as the Fresnel region, where the Fresnel approximation applies, but not the Fraunhofer approximation. The far field, on the other hand, is often referred to as the Fraunhofer region, where the Fraunhofer approximation applies.

[0005] Furthermore, according to current technology, receiver arrays for angle estimation are typically fully populated with receiving antennas, so that the entire area is covered with antennas, usually spaced half a wavelength apart. This becomes very complex and expensive for large receiving arrays. Therefore, sparsely populated receiver arrays are often used for positioning with large arrays; see Pavlenko, T.; Reustle, C.; Dobrev, Y.; Gottinger, M.; Jassoume, L.; Vossiek, M.: Design and Optimization of Sparse Planar Antenna Arrays for Wireless 3-D Local Positioning Systems. In: IEEE Transactions on Antennas and Propagation Vol. 65 (2017), No. 12, pp. 7288-7297.

[0006] Consequently, for precise and cost-efficient PDOA-based positioning systems, the evaluation of raw data (for example, complex amplitudes of the received signals) without angle estimation is necessary.

[0007] It is known, for example, from DE102019110512A1, that the position of the transmitter can be efficiently determined by recursively evaluating the phase differences between the spatially distributed receiving antennas of the receiving arrays. This is usually done by applying recursive filters, in particular the Extended Kalman Filter in the form of the Holographic Extended Kalman Filter (HEKF).

[0008] However, current technology does not yet allow for the inversion of the known measurement process, which would be advantageous in principle for determining the position and orientation of, for example, a single receiver array in a measurement system with many transmitters, instead of the position of transmitters in a measurement system with many receivers. Such a setup is described in Fig. 2 illustrated.

[0009] The object of the present invention is to determine the position and orientation of a receiver array with multiple receiving antennas using multiple transmitters distributed in space. This is achieved by a method according to independent claim 1, wherein advantageous embodiments of the present invention are set forth in the dependent claims.

[0010] The present invention relates to a method for determining the position and orientation of a receiver array with multiple receiving antennas by estimation, in particular with N A Receiving antennas, wherein the following steps are carried out in the procedure: Broadcasting a respective signal by at least one transmitter at different positions, in particular at N R Positions, and Evaluating a spatially characteristic phase response of the wave fields of the respective radiated signals using the multiple receiving antennas of the receiver array, wherein At the receiver, at least one measured difference phase of at least one pair of receiving antennas is compared with hypothetical difference phases of the same pair of antennas, which result from the positions and orientation of the receiver.

[0011] According to the present invention, the position and orientation of a receiver array with at least two receiving antennas are determined by receiving the signals of several transmitters distributed throughout space and comparing them with respect to the phase difference of the receiving antennas arranged in the receiver array. To estimate the position and orientation of the receiver array, hypothetical phase differences related to the position and orientation of the receiver array are used and compared with the actually measured phases or phase differences of the signals emitted by the various transmitters.An estimation algorithm can be used to assess the different hypothetical phase differences, so that the set of estimated phase differences that provides an optimal result with respect to a cost function is used to determine position and orientation.

[0012] For many applications, such as driverless transport systems, knowledge of the target's orientation (in the case of this invention, the receiver or receiver array) is essential. According to the invention, this orientation can be determined very precisely by evaluating the relative phases of the receiver. In comparison, implementing rotation estimation with multiple transmitters (as known from the prior art) on, for example, a transport system and spatially distributed receiver arrays is significantly less accurate, since these do not share a common frequency reference and consequently their transmitted signals cannot be evaluated coherently.

[0013] Just as with HEKF, the accuracy of determining position and orientation depends on the size of the receivers, which is why the evaluation of angles represents a significant limitation; see Dobrev, Yassen; Reustle, Christoph; Pavlenko, Tatian; Cordes, Florian; Vossiek, Martin: Mobile robot 6D pose estimation using a wireless localization network. In: 2016 IEEE MTT-S International Conference on Microwaves for Intelligent Mobility (ICMIM), 2016, pp. 1-4 and Geiß, Johanna; Sippel, Erik; Gröschel, Patrick; Hehn, Markus; Schütz, Martin; Vossiek, Martin: A Wireless Local Positioning System Concept and 6D Localization Approach for Cooperative Robot Swarms Based on Distance and Angle Measurements. In: IEEE Access Vol. 8 (2020), pp. 115501-115514.

[0014] In PDOA-based localization systems consisting of many receiver arrays, as in Fig. As illustrated in Figure 1, the relative positions and orientations of the multiple receivers to each other must be precisely known. For this purpose, a calibration setup is required accordingly. Fig. 3 suitable, in which the position and orientation of a receiver is determined using measurements to known reference positions.

[0015] The estimation problem arising according to the invention is equivalent to the representation in Fig. 2.

[0016] According to the present invention, it can further be provided that the comparison of the measured difference phases and the hypothetical difference phases, which depend on an estimated position and an estimated orientation, is carried out within the framework of a general optimization problem in which a least-squares metric, a generalized least-squares metric, a method of convex optimization and / or an artificial neural network is used to obtain, depending on the method, the best possible estimates for the position and orientation of the receiver array.

[0017] Typically, a cost function is derived, which then needs to be minimized.

[0018] According to a further advantageous modification of the present invention, it can be provided that some or all receiving antennas of the receiver array are spaced at a distance of half a wavelength or 0.4 to 0.6 times a wavelength or less from at least one adjacent receiving antenna.

[0019] The advantage of this is that for an antenna pair where the distance is less than or equal to half a wavelength, the evaluated phase difference is unambiguous, while the area of ​​unambiguity decreases with a larger distance.

[0020] According to the invention, it can further be provided that the receiver is so large that at least one position of a transmitter is located in the near field of the receiver array.

[0021] Furthermore, according to the invention, the evaluated signal can be narrowband modulated, preferably less than or equal to 2 MHz, more preferably less than or equal to 1 MHz. Furthermore, according to the invention, the bandwidth of the narrowband signal can be less than 500 kHz, more preferably less than 200 kHz, and more preferably less than 75 kHz.

[0022] According to the invention, it can also be provided that the comparison, preferably the search for the solution of the optimization problem, is carried out iteratively, preferably in such a way that the evaluated difference phases change in the iteration steps.

[0023] According to an optional further development of the present invention, it can be provided that the orientation of the receiver array is represented by a rotation matrix, quaternions or Euler angles.

[0024] The basic idea of ​​the present invention does not depend on how the alignment or orientation of the receiver array is mathematically described. It is clear to those skilled in the art that there are numerous possibilities for this, all of which can be used to implement the present invention.

[0025] Furthermore, according to the present invention, an estimation algorithm for obtaining estimates for the position and orientation of the receiver array, in which the comparison of at least one measured difference phase of at least one antenna pair of the receiving antennas is compared with hypothetical difference phases of the same antenna pair, can start on several different hypotheses.

[0026] According to an advantageous embodiment of the present invention, it can be provided that an estimation algorithm for obtaining estimates for the position and orientation of the receiver array, in which the comparison of at least one measured difference phase of at least one antenna pair of the receiving antennas is compared with hypothetical difference phases of the same antenna pair, starts recursively on the previous estimate.

[0027] The recursive design of such an estimation algorithm is particularly efficient and resource-saving, while at the same time enabling the obtaining of very good and accurate results.

[0028] Furthermore, according to the present invention, it may be provided that a Kalman filter, extended Kalman filter, unscented Kalman filter or particle filter is used in the comparison, preferably in the execution of the optimization problem.

[0029] According to a further optional embodiment of the present invention, it can be provided that the position of the receiver array is known in advance of at least one spatial direction and / or the rotation of the receiver array with respect to at least one axis of rotation is known in advance.

[0030] For example, if the receiver array is not movable in all three spatial directions, this can be used to reduce the complexity of the estimation algorithm. Since the receiver's position relative to the vertical axis is known beforehand, this knowledge can be used when executing the estimation algorithm, thus reducing the estimation's complexity.

[0031] Furthermore, according to the present invention, it can be provided that a phase difference evaluation matrix T is used during the comparison, preferably during the execution of the optimization problem. i with rank (N A - 1)N R is used, whereby N Rthe number of receiving antennas of the receiver array and N R the number of different signal emission positions.

[0032] Advantageously, according to the invention, it can be provided that the phase difference evaluation matrices T nR,i First, evaluate the phase differences of closely adjacent receiving antenna pairs, whose phase difference is typically unique due to a distance of less than or equal to half a wavelength, and then successively include more distant receiving antennas until all phase difference evaluation matrices T nR,i the required rank (N) for each individual measurement A - 1) and thus the phase difference evaluation matrix T i the rank (N A - 1)N R owns.

[0033] According to an optional further development of the present invention, it can be provided that several transmitters are used at only one position each to emit a respective signal, or that only one transmitter is used at different positions to emit a respective signal, and / or that several of the respective signals are sent simultaneously or sequentially.

[0034] According to a further advantageous embodiment of the present invention, it can be provided that the different positions of the at least one transmitter for emitting a respective signal are known and form reference positions, preferably N R Reference positions exist,

[0035] Advantageously, it can be provided that the reference positions are determined by a tachymeter, a motion capture system, a robot with SLAM function (Simultaneous Localization And Mapping function), an existing radio tracking system and / or inertial sensors.

[0036] According to the invention, a concept for determining the global position and orientation of a single PDOA receiver array with N is provided. A The concept is based on the evaluation of linear combinations of phases at different receiving antennas, but unlike the previously known state of the art, it locates the receiver instead of the transmitter and also determines its orientation.

[0037] The measurement concept is based on Fig. 3. Here, a transmitter emits at N RKnown reference positions, at which it is positioned one after the other, each generating a wave field which is received at the receiving antennas. Instead of a transmitter at N R known reference positions can also be N R Transmitters are used at a known reference position, as in Fig. Figure 2 illustrates this. Furthermore, any combination of fixed and moving transmitters can be used. The reference positions can be established by any measurement system. These include, among others, optical systems such as total stations or motion capture systems, robots with SLAM (Simultaneous Localization and Mapping) functionality, existing radio tracking systems, or inertial sensors. The position and orientation of the receiver can then be determined from the received wave fields. For this purpose, the transmitter emits [wave fields] during the [phase]. R tenth position any narrowband signal sTX,nR(t)=sTX,BB,nR(t)exp(j(ω0t+φnR)), where s TX,BB,nR (t) the narrowband baseband signal, ω0 = 2πf0 the angular frequency used and φ nR represents the unknown transmission phase. The signal is received at the n A ten antenna time-delayed as sRX,nR,nA(t)=anR,nAsTX,BB,nR(t)exp(j(ω0(t−τnR,nA)+φnR)) received, whereby a nR,nA represents the attenuation of the transmission and the delay τnR,nA=‖pTX,nR−pnA‖c using the transmitter positions p TX,nR , the antenna positions p nA and the wave propagation speed c in the medium between transmitter and receiver (typically the speed of light). Depending on the signal shape s TX,BB,nR (t) can now either directly determine the signal phase φnR,nA=mod2π'(−ω0τnR,nA+φnR) extract or correlate the phase difference between the arbitrarily selectable antenna pairs of the receiver array ΔφnR,nA,nA'=arg(∫ sRX,nR,nA(t)sRX,nR,nA'*(t)dt)≈mod2π'(ω0τnR,nA'−ω0τnR,nA) evaluate, whereby mod2π'(⋅) the ambiguous phases with mod2π'(θ)={mod2π(θ)if mod2π(θ)≤πmod2π(θ)−2πif mod2π(θ)>π maps to (-π,π]. For simplicity, the following calculations will use the evaluation of absolute phases. These are first converted into vectors for each measurement. φnR=(φnR,1φnR,2⋯φnR,NA)T combined. Thus, any phase difference evaluation matrices T can be used. nR,i can be used to determine any phase differences ΔφnR=mod2π'(TnR,iφnR) to calculate. The index i allows for the variation of the phase difference evaluation matrices T. nR,i This is the iterative step of a potentially iterative or recursive optimization algorithm, but it is not yet relevant for the current explanation. Such an iterative optimization algorithm will be shown later in the exemplary implementation.

[0038] The evaluation of difference phases via the phase difference evaluation matrices T nR,i This enables both the elimination of the unknown transmission phase φ nR as well as the improvement of the uniqueness range, depending on the phase difference considered. For an antenna pair separated by half a wavelength, the evaluated phase difference is unambiguous, while the uniqueness range decreases with increasing antenna spacing. To evaluate all the information from a measurement, the phase difference evaluation matrices T must be used. nR,i rank N A -1, since one degree of freedom is lost for the unknown transmission phase, cf. Brückner, Stefan; Sippel, Erik; Lipka, Melanie; Geiss, Johanna; Vossiek, Martin: Phase Difference Based Precise Indoor Tracking of Common Mobile Devices Using an Iterative Holographic Extended Kalman Filter. In: IEEE Open Journal of Vehicular Technology Vol. 3 (2022), pp. 55-67.

[0039] By combining the phases of the reference measurements and the phase difference evaluation matrices used T nR,i further results Δφ=mod2π'(Tiφ) with φ=(φ1 φ2⋯φNR)T and Ti=(T1,i0⋯00T2,i⋱⋮⋮⋱⋱00⋯0TNR,i).

[0040] To describe the algorithm below, the hypothetical phases resulting from the previously introduced equations are denoted by the subscript "hyp", while the measured phases are denoted by the subscript "mess". The measured phases are derived from the hypothetical phases by... φmess=mod2π'(φhyp+n), where the vector n describes any measurement errors that are additively superimposed on the measured phases. The goal of the algorithm is to estimate the position and orientation of the receiver. While the position of the receiver is directly determined by the vector p RXAs described, there are many possibilities for orientation, e.g., rotation matrices, quaternions, or Euler angles. Here, the orientation of the receiver is described by the rotation matrix R. RX described, but this is arbitrarily interchangeable. The position of the n A The ten receiving antenna in the room thus results in pnA=pRX+RRX⋅pnA,local, where p nA,local The relative antenna positions are represented in the receiver's local coordinate system. To calibrate the receiver's position and orientation, the optimization problem must generally be solved. minpRX,RRXCost(mod2π'(Δφhyp(pRX,RRX)−Δφmess)) to be solved, where Cost(·) represents an arbitrarily definable cost function.

[0041] To include all information in estimating the receiver's position and orientation, the phase difference evaluation matrix T must be used. nR,i Rank N for each individual measurement A- 1 and therefore T i the rank (N A - 1)N R On the other hand, evaluating the phase differences of closely adjacent antenna pairs provides unambiguous information. Therefore, it is advantageous to solve the optimization problem by using the phase difference evaluation matrices T. nR,i First, evaluate the phase differences of closely adjacent antenna pairs, and then successively include more distant antennas until all T nR,i Rank N for each individual measurement A - 1 and therefore T i the rank (N A - 1)N R have.

[0042] It is conceivable that in some application scenarios not all parameters need to be determined; for example, the height might be known, or the rotation might only occur around one or two axes. Many different metrics are possible for the cost function, especially the least-squares metric or the generalized least-squares metric. The optimization problem can be solved in any number of ways, particularly using convex optimization methods or an artificial neural network. The position and orientation of the receiver can be estimated recursively, starting from the previous estimate, if the receiver is continuously moving. Kalman filters, extended Kalman filters, unscented Kalman filters, or particle filters are particularly suitable for this purpose. The transmitters do not necessarily have to transmit simultaneously.Instead, the successively measured phase differences can be processed successively within the filters.

[0043] Further features, details and advantages of the invention will become apparent from the following description of the figures and the exemplary embodiment. These show: Fig. 1: Illustration of the state of the art with a localization environment in which three receivers, each with six antennas, locate a transmitter, Fig. 2: Illustration of the present invention, with a Fig. 1. Inverted localization process, in which the position and orientation of a receiver on a vehicle are determined using signals from multiple transmitters, and Fig. 3: Illustration of the measurement process at N R Reference position measurements are taken to determine the position and orientation of the receiver.

[0044] Fig. Figure 1 shows a conventional method for determining the position and orientation of a transmitter, requiring several receiver arrays distributed throughout space. The positions of the receiver arrays are known, and they use PDOA measurements to determine the angle of the signal emitted by the transmitter. Once an angle has been calculated for each of several receiver arrays, the transmitter's position is determined using multiangulation.

[0045] Fig. Figure 2, however, shows an implementation of the present invention in which several transmitters are arranged distributed in space and a receiver array with at least two receiving antennas can be determined with respect to its position and orientation. This is shown in Figure 2. Fig. 2. A vehicle equipped with the receiver array. According to the invention, it is possible to determine the position and orientation of a single receiver array based on a respective radiated signal from the multiple transmitters distributed throughout space.

[0046] Fig.Figure 3 shows a schematic representation of a measurement process in which a signal is emitted from a transmitter at several reference positions, the positions of which are known. According to the invention, the position and orientation of the receiver can be determined by emitting the signals at the multiple reference positions. For the present invention, it is irrelevant whether the signals emitted at the respective reference positions are emitted simultaneously or sequentially. Thus, according to the invention, the signals from the transmitters arranged at the different positions can have different transmission frequencies, or, if they do not, can be temporally resolved by sequential transmission.

[0047] In the following, an iterative optimization algorithm for estimating the position and orientation of a receiver will be shown using an embodiment of the present invention.

[0048] A typical assumption of modern algorithms is that the measurement of mean-free additive uncorrelated normally distributed noise n~N(0,σ) 2 I) is superimposed, where σ 2 Let represent the noise power and I be the identity matrix. This usually results in a simple least-squares metric for the optimization problem, which can be solved efficiently using modern algorithms. However, once the least-squares metric has been found, the optimization problem can also be solved using methods other than the example least-squares metric.

[0049] In the case of evaluating difference phases, calculating the difference phases results in noise correlated with a covariance matrix. Ci=σ2TiTiT. This results in the cost function as follows: minpRX,RRX mod2π'(Δφmess−Δφhyp(pRX,RRX))TCi mod2π'(Δφmess−Δφhyp(pRX,RRX)).

[0050] While the position of the transmitter p RX The rotation matrix R can be directly estimated in this form. RX nine entries with only three degrees of freedom. One possible representation of the rotation matrix R RX From these three degrees of freedom, the Rodrigues formula yields RRX=I+sin|γ||γ|[γ]×+1−cos|γ||γ|2[γ]×2 with γ=(γxγyγz) and [γ]×=(0−γzγyγz0−γx−γyγx0).

[0051] The algorithm is designed to iteratively estimate the position and rotation of the receiver. Since the Rodrigues formula describes a non-linear relationship between γ and R RX Since this represents the problem, directly estimating the entries of γ is difficult. Instead, the rotation matrix is ​​estimated by R RXThe rotation matrix is ​​iteratively corrected for "small" rotations ΔR, with each "small" rotation being expressed by its corresponding Δγ. The estimated rotation matrix is ​​then obtained in the iteration R. RX,i from the i - 1st iteration to RRX,i=ΔR⋅RRX,i−1.

[0052] Since the rotation matrix ΔR represents a small rotation, the entries of the corresponding Δγ are also small. Consequently, the rotation matrix can be expressed as ΔR≈I+[Δγ]× approximate. As can be seen here, ΔR is now approximately linearly dependent on Δγ, which enables a stably converging algorithm. Now, if we take a pre-estimation of the rotation matrix R RX,i-1 and position p RX,i-1 Therefore, the cost function for a single iteration of the calibration algorithm can be determined as follows: minΔp,Δγ mod2π'(Δφmess−Δφhyp(pRX,i−1,RRX,i−1,Δγ))TCi mod2π'(Δφmess −Δφhyp(pRX,i−1,Δp,RRX,i−1,Δγ) with RRX≈(I+[Δγ]×)⋅RRX,i−1=RRX,i−1+[Δγ]×⋅RRX,i−1 and pRX=pRX,i−1+Δp modify. Thus, the hypothetical global positions of the antennas can be modified to pnA=pRX+RRXpnA,local≈pRX,i−1+Δp+(RRX,i−1+[Δγ]×⋅RRX,i−1)pnA,local adjust. For ease of description, the parameters to be estimated are: x=(ΔpΔγ) In summary, this allows us to calculate the hypothetical phase differences with Δφhyp≈h(x)≈Δφhyp,i−1(RRX,i−1,pRX,i−1)+Hx approximate, where Δφ hyp,i-1 (R RX,i-1 , p RX,i-1 ) the hypothetical phase differences in the i-1st iteration with R RX,i-1 and p RX,i-1 as an assumption and H being the Jacobian matrix of h(x) at R RX,i-1 and p RX,i-1 This approximation allows us to represent the phase deviation in the cost function. mod2π'(Δφhyp−Δφmess)≈devi−1−Hx with devi−1=mod2π'(Δφhyp,i−1(RRX,i−1,pRX,i−1)−Δφmess) Rewrite it. Substituting this into the cost function yields minx(devi−1−Hx)TCi(devi−1−Hx).

[0053] This represents a generalized least squares problem, which is characterized by x^=(HTCi−1H)−1HTCi−1devi−1 can be solved closed. From x̂, Δp and Δγ can now be extracted to estimate the position and rotation of the receiver. pRX,i=pRX,i−1+Δp and RRX,i=ΔR⋅RRX,i−1 with ΔR=I+sin|Δγ||Δγ|[Δγ]×+1−cos|Δγ||Δγ|2[Δγ]×2 improve.

[0054] The formulas established now enable the execution of a structured estimation algorithm with the following steps: 1. Creating an initial assumption for R RX,0 and p PX,0These can, for example, be chosen randomly within a specific, pre-known range or be determined by a prior estimate. The iteration index is initialized with i = 1. 2. Selection of the current phase difference evaluation matrix T i This initially evaluates only the measurements of closely adjacent antenna pairs and then includes more and more antennas until the rank (N) A - 1)N R has been reached 3. Calculation of the corresponding measured phase differences Δφmess=mod2π / (Tiφmess) 4. Calculation of the current deviation devi−1=mod2π'(Δφhyp,i−1)(RRX,i−1,pRX,i−1)−Δφmess) 5. Calculating the update x^=(HTCi−1H)−1HTCi−1devi−1 6. Update of the estimated rotation matrix R RX,i = ΔR · R RX,i-1 , where ΔR is obtained from Δγ using the Rodrigues formula 7. Update of the estimated position p RX,i = p RX,i-1+ Δp 8. Verification that the currently estimated position and rotation are reasonable. This can be done, in particular, by obtaining prior information about the receiver's possible position range. a. If the currently estimated position and rotation do not make sense: continue at step 1. b. If the currently estimated position and rotation make sense: Verification that the estimation algorithm has fully converged. This can be done in particular using the rank of the phase difference evaluation matrix T. i , the number of iterations i and the size of the update x̂ i. If the estimation algorithm is not yet finished: Increase the iteration level i = i + 1 and continue at step 2. ii. If the estimation algorithm is complete: Save R RX,i and p RX,i QUOTES INCLUDED IN THE DESCRIPTION

[0000] This list of documents cited by the applicant was automatically generated and is included solely for the reader's convenience. The list is not part of the German patent or utility model application. The DPMA accepts no liability for any errors or omissions. Cited patent literature

[0000] DE 102019110512A1

[0007] Cited non-patent literature

[0000] Sippel, Erik; Geiss, Johanna; Brückner, Stefan; Gröschel, Patrick; Hehn, Markus; Vossiek, Martin: Exchanging Bandwidth With Aperture Size in Wireless Indoor Localization - Or Why 5G / 6G Systems With Antenna Arrays Can Outperform UWB Solutions. In: IEEE Open Journal of Vehicular Technology Vol. 2 (2021), pp. 207-217

[0003] Pavlenko, T.; Reustle, C.; Dobrev, Y.; Gottinger, M.; Jassoume, L.; Vossiek, M.: Design and Optimization of Sparse Planar Antenna Arrays for Wireless 3-D Local Positioning Systems. In: IEEE Transactions on Antennas and Propagation Bd. 65 (2017), Nr. 12, S. 7288-7297

[0005] Dobrev, Yassen; Reustle, Christoph; Pavlenko, Tatian; Cordes, Florian; Vossiek, Martin: Mobile robot 6D pose estimation using a wireless localization network. In: 2016 IEEE MTT-S International Conference on Microwaves for Intelligent Mobility (ICMIM), 2016, S. 1-4

[0013] Geiß, Johanna; Sippel, Erik; Gröschel, Patrick; Hehn, Markus; Schütz, Martin; Vossiek, Martin: A Wireless Local Positioning System Concept and 6D Localization Approach for Cooperative Robot Swarms Based on Distance and Angle Measurements. In: IEEE Access Bd. 8 (2020), S. 115501-115514

[0013] Brückner, Stefan; Sippel, Erik; Lipka, Melanie; Geiss, Johanna; Vossiek, Martin: Phase Difference Based Precise Indoor Tracking of Common Mobile Devices Using an Iterative Holographic Extended Kalman Filter. In: IEEE Open Journal of Vehicular Technology Bd. 3 (2022), S. 55-67

[0038]

Claims

[1] Method for determining a position and / or orientation of a receiver array with multiple receiving antennas by estimation, in particular with N A Receiving antennas, wherein the following steps are carried out in the procedure: Broadcasting a respective signal by at least one transmitter at different positions, in particular at N R Positions, and Evaluating a spatially characteristic phase response of the wave fields of the respective radiated signals using the multiple receiving antennas of the receiver array, wherein At the receiver, at least one measured difference phase of at least one pair of receiving antennas is compared with hypothetical difference phases of the same pair of antennas, which result from the positions and orientation of the receiver. [2] Method according to claim 1, wherein the comparison of the measured difference phases and the hypothetical difference phases, which depend on an estimated position and an estimated orientation, is carried out within the framework of a general optimization problem in which a least-squares metric, a generalized least-squares metric, a convex optimization method and / or an artificial neural network is used to obtain, depending on the method, the best possible estimates for the position and orientation of the receiver array. [3] Method according to one of the preceding claims, wherein some or all of the receiving antennas of the receiver array are spaced at a distance of 0.4 - 0.6 times the wavelength, preferably half a wavelength or less, of the signal emitted by the at least one transmitter from at least one adjacent receiving antenna. [4] Method according to any of the preceding claims, wherein the receiver is so large that at least one position of a transmitter is located in the near field of the receiver array. [5] Method according to any of the preceding claims, wherein the evaluated signal is narrowband modulated. [6] Method according to one of the preceding claims, wherein the comparison, preferably the execution of the optimization problem according to claim 2, is carried out iteratively, preferably in such a way that the evaluated difference phases change in the iteration steps. [7] Method according to any of the preceding claims, wherein the orientation of the receiver array is represented by a rotation matrix, quaternions or Euler angles. [8] Method according to one of the preceding claims, wherein an estimation algorithm for obtaining estimates for the position and orientation of the receiver array, in which the comparison of at least one measured difference phase of at least one antenna pair of the receiving antennas is compared with hypothetical difference phases of the same antenna pair, starts on several different hypotheses. [9] Method according to one of the preceding claims, wherein an estimation algorithm for obtaining estimates for the position and orientation of the receiver array, in which the comparison of at least one measured difference phase of at least one pair of antennas of the receiving antennas is compared with hypothetical difference phases of the same pair of antennas, starts recursively at the previous estimate. [10] Method according to one of the preceding claims, wherein a Kalman filter, extended Kalman filter, unscented Kalman filter or particle filter is used in the comparison, preferably in the performance of the optimization problem according to claim 2. [11] Method according to one of the preceding claims, wherein the position of the receiver array is known in advance of at least one spatial direction and / or the rotation of the receiver array with respect to at least one axis of rotation is known in advance. [12] Method according to one of the preceding claims, wherein, in the comparison, preferably in the execution of the optimization problem according to claim 2, a phase difference evaluation matrix T i with rank (N A - 1)N R is used, whereby N A the number of receiving antennas of the receiver array and N R the number of different signal emission positions. [13] Method according to one of the preceding claims, wherein several transmitters are used at only one position each to emit a respective signal, or only one transmitter is used at different positions to emit a respective signal, and / or several of the respective signals are sent simultaneously or sequentially. [14] A method according to any of the preceding claims, wherein the different positions of the at least one transmitter for emitting a respective signal are known and form reference positions, wherein preferably N R Reference positions exist, [15] Method according to the preceding claim 14, wherein the reference positions are determined by a tachymeter, a motion capture system, a robot with SLAM function, an existing radio tracking system and / or inertial sensors.

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