Method for determining the position and / or orientation of a receiver array by means of an estimation

Abstract

The invention relates to a method for determining the position and / or orientation of a receiver array having a plurality of receiving antennas, in particular N A receiving antennas, by means of an estimation, wherein the following steps are carried out in the method: emitting a respective signal by means of at least one transmitter at different positions, in particular at N R positions, and evaluating the spatially characteristic phase progression of the wave field of each emitted signal with the aid of the plurality of receiving antennas of the receiver array. At least one measured differential phase of at least one antenna pair of the receiving antennas is compared at the receiver with hypothetical differential phases of the same antenna pair resulting from the positions and orientation of the receiver.

Description

[0001]000172-25 He Friedrich-Alexander-University Erlangen-Nuremberg DE - 91054 Erlangen ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Method for determining a position and an orientation of a receiver array by estimation ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ The present invention relates to a method for determining a position and / or an orientation of a receiver array, which method is 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. There are already several providers of angle-based positioning systems, in particular in the Bluetooth standard, e.g.: Quuppa, infsoft, BlueIot, u-blox.These use PDOA measurements at several receiver arrays distributed in space and whose positions are known in advance to first estimate the angle to the transmitter at each receiver array and then to localize the transmitter using multiangulation. One such system is illustrated in Fig. 1. It is known from the state of the art that the localization accuracy of PDOA systems depends directly on the aperture size of the receiver arrays in relation 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. Known angle-based PDOA localization approaches do not work optimally for large receiver arrays, since the transmitter to be located is usually located in the near field of the receiver.This, however, contradicts the assumption of plane receive waves by angle estimators. Due to the spherical waves emitted by the transmitter, this assumption only applies to 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, in which the Fresnel approximation, but not the Fraunhofer approximation, applies. The far field, on the other hand, is often referred to as the Fraunhofer region, in which the Fraunhofer approximation applies. Furthermore, according to the state of the art, receiver arrays for angle estimation are typically fully populated with receive antennas, so that the entire area is covered with antennas, usually at a distance of half a wavelength, which is very complex and cost-intensive for large receiver arrays. For location with large arrays, sparsely populated receiver arrays are therefore often used, cf. 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. Consequently, for precise and cost-effective PDOA-based positioning systems, the evaluation of raw data (e.g., complex amplitudes of the received signals) without angle estimation is necessary. 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 receive antennas of the receive arrays. This is usually achieved by applying recursive filters, in particular the extended Kalman filter in the form of the holographic extended Kalman filter (HEKF).However, the prior art has not yet succeeded in inverting the known measuring process, which would in principle be advantageous in order to determine the position and orientation of, for example, a single receiver array in a measuring system with many transmitters instead of the position of transmitters in a measuring system with many receivers. Such a setup is illustrated in Fig. 2. The aim of the present invention is to determine the position and orientation of a receiver array with multiple receiving antennas using multiple transmitters arranged in a spatial distribution. This is achieved with a method according to independent claim 1, wherein advantageous embodiments of the present invention are set out in the dependent claims. The present invention relates to a method for determining a position and an orientation of a receiver array with multiple receiving antennas by estimation, in particular with ^^^^. AReceiving antennas, wherein the following steps are carried out in the method: Radiating a respective signal by at least one transmitter at different positions, in particular at ^^^^ RPositions, and evaluating a spatially characteristic phase curve of the wave fields of the respective emitted signals using the plurality of receiving antennas of the receiver array, wherein at least one measured differential phase of at least one antenna pair of the receiving antennas is compared at the receiver with hypothetical differential phases of the same antenna pair, which result from the positions and orientation of the receiver. According to the present invention, it is therefore provided that the position and orientation of a receiver array with at least two receiving antennas is determined by receiving the signals of several transmitters arranged distributed in space and adjusting 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 various hypothetical phase differences, so that the set of estimated phase differences that delivers the optimal result in terms of a cost function is used to determine position and orientation. For many applications, such as driverless transport systems, knowledge of the orientation of the target (in the case of the invention, the receiver or receiver array) is essential. According to the invention, this can be determined very precisely by evaluating the relative phases of the receiver.In comparison, the implementation of rotation estimation with multiple transmitters (as known from the state of the art), for example, on a transport system and spatially distributed receiver arrays, is significantly less accurate, as these do not have a common frequency reference and consequently their transmitted signals cannot be evaluated coherently with each other. 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, cf. 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, p.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. In PDOA-based localization systems consisting of many receiver arrays, as illustrated in Fig. 1, the relative positions and orientations of the multiple receivers to one another must be precisely known. A calibration setup according to Fig. 3 is suitable for this purpose, in which the position and orientation of a receiver is determined using measurements to known reference positions. The resulting estimation problem according to the invention is equivalent to the representation in Fig. 2.According to the present invention, it can further be provided that the comparison of the measured differential phases and the hypothetical differential phases, which depend on an estimated position and an estimated orientation, takes place 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 the best possible estimates for the position and orientation of the receiver array. Typically, a cost function is derived that must be minimized.According to a further advantageous modification of the present invention, it can be provided that some or all of the receiving antennas of the receiver array are spaced from at least one adjacent receiving antenna by a distance of half a wavelength or 0.4 to 0.6 times the wavelength or less of the signal emitted by the at least one transmitter. 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, whereas the unambiguousness range decreases with a greater distance. According to the invention, it can further be provided that the receiver is large enough that at least one transmitter position is located in the near field of the receiver array. Furthermore, according to the invention, it can be provided that the evaluated signal is narrowband modulated, preferably less than or equal to 2 MHz, more preferably less than or equal to 1 MHz.Furthermore, according to the invention, it can be provided that the bandwidth of the narrowband signal is less than 500 kHz, preferably less than 200 kHz, and most preferably less than 75 kHz. According to the invention, it can also be provided that the comparison, preferably the search for a solution to the optimization problem, is carried out iteratively, preferably in such a way that the evaluated difference phases change in the iteration steps. According to an optional 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. For the basic idea of ​​the present invention, it is not important how the orientation of the receiver array is described mathematically. It is clear to a person skilled in the art that there are numerous possibilities for this, all of which can be used to implement the present invention.Furthermore, according to the present invention, it can be provided that an estimation algorithm for obtaining estimated values ​​for the position and orientation of the receiver array, in which the comparison of at least one measured differential phase of at least one antenna pair of the receiving antennas is compared with hypothetical differential phases of the same antenna pair, starts with several different hypotheses. According to an advantageous development of the present invention, it can be provided that an estimation algorithm for obtaining estimated values ​​for the position and orientation of the receiver array, in which the comparison of at least one measured differential phase of at least one antenna pair of the receiving antennas is compared with hypothetical differential phases of the same antenna pair, starts recursively with the previous estimate.The recursive design of such an estimation algorithm is particularly efficient and resource-saving, while simultaneously enabling the obtaining of very good and accurate results. Furthermore, according to the present invention, it can be provided that a Kalman filter, extended Kalman filter, unscented Kalman filter, or particle filter is used during the comparison, preferably during the implementation of the optimization problem. According to a further optional development of the present invention, it can be provided that the position of the receiver array in at least one spatial direction is known in advance and / or the rotation of the receiver array with respect to at least one rotation axis is known in advance. If, for example, the receiver array is not movable in all three spatial directions, this circumstance can be used to reduce the complexity of the estimation algorithm.Since the receiver's position relative to the vertical axis is already known in advance, this knowledge can be used when executing the estimation algorithm, thus reducing the complexity of the estimation. Furthermore, according to the present invention, a phase difference evaluation matrix ^^^^^^^^ with rank (^^^^A − 1)^^^^R is used during the comparison, preferably when implementing the optimization problem, where ^^^^A is the number of receiving antennas in the receiver array and ^^^^. R The number of different emission positions of the signals is advantageously provided according to the invention that the phase difference evaluation matrices first evaluate the phase differences of closely adjacent receiving antenna pairs, whose phase difference is typically unambiguous due to a distance of less than or equal to half a wavelength, and then successively more distant receiving antennas are included until all phase difference evaluation matrices ^^^^^^^^R,^^^^have the required rank (^^^^A − 1) for each individual measurement and thus the phase difference evaluation matrix ^^^^^^^^ has the rank (^^^^A − 1)^^^^R. According to an optional development of the present invention, it can be provided that several transmitters are used at only one position 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 transmitted simultaneously or one after the other.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, wherein preferably ^^^^. R Reference positions exist. Advantageously, the reference positions can be determined by a tachymeter, a motion capture system, a robot with SLAM (Simultaneous Localization and Mapping) functionality, an existing radio location system, and / or inertial sensors. According to the invention, a concept for determining the global position and orientation of a single PDOA receiver array with ^^^^ AReceiving antennas. The concept is based on the evaluation of linear combinations of phases at different receiving antennas, whereby, unlike the existing state of the art, this now locates the receiver instead of the transmitter and also determines its orientation. The measurement concept is based on Fig. 3. Here, a transmitter emits at ^^^^ R known reference positions, at which it is positioned one after the other, each with a wave field that is received at the receiving antennas. Instead of a transmitter at ^^^^ R known reference positions can also ^^^^ RTransmitters can be used at a known reference position, as illustrated in Fig. 2. Furthermore, any combination of fixed and movable transmitters can be used. The reference positions can be determined by any measuring system. These include, among others, optical systems such as tachymeters or motion capture systems, robots with SLAM (Simultaneous Localization and Mapping) functions, existing radio positioning 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(s) emit(s) during ^^^^ R ten position any narrowband signal ^^^^TX,^^^^R(^^^^) = ^^^^TX,BB,^^^^R(^^^^)exp�j�^^^^0^^^^ + ^^^^^^^^R, where ^^^^TX,BB,^^^^R(^^^^) is the narrowband baseband signal, ^^^^0 = 2^^^^^^^^0^ is the used angular frequency and ^^^^ ^^^^R the unknown transmission phase The signal is at the ^^^^ A ten antenna time delayed as = − received, where ^^^^^^^^R,^^^^A represents the attenuation of the transmission and the delay − ^^^^ using the transmitter positions ^^^^ TX,^^^^R , the antenna positions ^^^^ ^^^^A and the wave propagation speed ^^^^ in the medium between transmitter and receiver (typically the speed of light). Depending on the signal form ^^^^TX,BB,^^^^R ( ^^^^ ) you can now either directly adjust the signal phase ′ extract or by correlation the phase difference between the arbitrarily selectable antenna pairs of the receiver array ^^^^^^^^^^^^ ′R,^^^^A,^^^^A = arg ^^^^RX,^^^^R,^^^^A(^^^^)^^^^ ∗RX,^^^^R,^^^^′A (^^^^)d^^^^� ≈ mod ′ 2 ^^^^ �^^^^0^^^^^^^^R,^^^^′ A −^^^^0^^^^^^^^R,^^^^A� evaluate, where mod ′ 2 ^^^^ (∙) the ambiguous phases with falls mod2^^^^(^^^^) ≤ ^^^^− if mod2^^^^(^^^^) > ^^^^maps to (−^^^^,^^^^]. For a simpler illustration, the following calculations continue with the evaluation of absolute phases. These are initially calculated for each measurement in the vectors^^^^^^^ =�^^^^ T ^^^^^ ⋯ ^^^^ � combined. Thus, any phase difference evaluation matrices ^^^^^^^^R,^^^^can be used to calculate any phase differences ^ ^^^^^^^ = ′ to calculate. The index ^^^^ enables the variation of the phase difference evaluation matrices ^^^^^^^^R,^^^^in the ^^^^th step of a potentially iterative or recursive optimization algorithm, but is not yet relevant for the current explanation. Such an iterative optimization algorithm will be shown later in the embodiment. The evaluation of difference phases via the phase difference evaluation matrices ^^^^^^^^R,^^^^enables both the elimination of the unknown transmission phase ^^^^ ^^^^Ras well as the improvement of the unambiguousness range depending on the phase difference considered. For an antenna pair separated by half a wavelength, the evaluated phase difference is unambiguous, while the unambiguousness range decreases with increasing antenna separation. To evaluate the entire information of a measurement, the phase difference evaluation matrices ^^^^^^^^R,^^^^the rank ^^^^ A − 1, since one degree of freedom is lost for the unknown transmission phase, see 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. By combining the phases of the reference measurements and the phase difference evaluation matrices used ^^^^^^^^R,^^^^, we also obtain ^^^^^^^^ = mod ′ 2 ^^^^ (^^^^ ^^^^^^^^) with^^^^ =�^^^^ ^^^^ ⋯ ^^ T 1 2 ^^ and ^^^^1,^^^^ 0 … 0 To describe the algorithm below, the hypothetical phases resulting from the previously introduced equations are denoted by the index "hyp", while the measured phases are denoted by the index "mess". The measured phases result from the hypothetical phases by ′ where the vector ^^^^ 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 ^^^^ RX As described, there are many possibilities for the alignment, e.g. rotation matrices, quaternions, or Euler angles. In this case, the orientation of the receiver is determined by the rotation matrix ^^^^ RX described, which is interchangeable. The position of the ^^^^A The spatial distribution of the receiving antenna is thus ^^^^^^^^A = ^^^^RX + ^^^^RX ∙ ^^^^^^^^A,local, where ^^^^^^^^A,local represent the relative antenna positions in the local coordinate system of the receiver. To calibrate the position and alignment of the receiver, the optimization problem ^^^^ m Xin R X Cost�mod ′ 2^^^^�^^^^^^^^hyp(^^^^RX,^^^^RX) − ^^^^^^^^mess R ,^^^^ be solved, whereby Cost ( ∙ )represents an arbitrarily definable cost function. In order to include all information in the estimation of the position and orientation of the receiver, the phase difference evaluation matrix ^^^^^^^^R,^^^^must have the rank ^^^^A − 1 for each individual measurement and thus ^^^^^^^^ the rank (^^^^A − 1)^^^^R. On the other hand, the evaluation of the phase differences of closely neighboring antenna pairs provides unique information. Therefore, it is advantageous to solve the optimization problem by first evaluating the phase differences of closely neighboring antenna pairs then include successively more distant antennas until all ^^^^^^^^R,^^^^have the rank ^^^^A − 1 for each individual measurement and thus ^^^^^^^^ have the rank (^^^^A − 1)^^^^R.It is conceivable that in some application scenarios not all parameters need to be determined, e.g. the altitude may be known or the rotation may only take place around one or two axes. Many different metrics are conceivable for the cost function, in particular the least squares metric or generalized least squares metric. The optimization problem can be solved in any way, in particular using convex optimization methods or with the help of 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. The transmitters do not necessarily have to transmit at the same time. Instead, the phase differences measured one after the other can be processed successively within the filters. 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 prior 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 locating process inverted to Fig. 1, in which the position and orientation of a receiver on a vehicle are determined using the signals from several transmitters, and Fig. 3: Illustration of the measuring process in the case of the ^^^^. RReference position measurements are carried out in order to determine the position and orientation of the receiver. Fig. 1 shows a conventional method for determining the position and orientation of a transmitter, which requires several receiver arrays arranged in a spatial distribution. The receiver arrays have known positions and use PDOA measurements to determine an angle of the signal emitted by the transmitter. If a respective angle has been calculated for several receiver arrays, the position of the transmitter is determined using multiangulation. Fig. 2, on the other hand, shows an implementation of the present invention in which several transmitters are arranged in a spatial distribution and a receiver array with at least two receiving antennas can be determined with regard to its position and orientation. Fig. 2 shows a vehicle which is equipped with the receiver array.According to the invention, it is possible to determine the position and orientation of an individual receiver array based on a respective emitted signal from the multiple transmitters arranged in a spatial distribution. Fig. 3 shows a sketch of a measuring process in which a respective signal is emitted by a transmitter at multiple reference positions whose position is known. According to the invention, it is possible to determine the position and orientation of the receiver by emitting the signals at the multiple reference positions. For the present invention, it is irrelevant whether the respective signals emitted at the respective reference positions are emitted simultaneously or in succession.Thus, according to the invention, it can be provided that the respective signals of the transmitters arranged at the various positions differ from one another in their transmission frequencies, or, if they do not, can be resolved in time by sequential transmission. In the following, an iterative optimization algorithm for estimating the position and orientation of a receiver will be shown using an exemplary embodiment of the present invention. A typical assumption of modern algorithms is that the measurement of zero-mean additive uncorrelated normally distributed noise ^^^^~^^^^. ( 0,^^^^ 2 ^^^^ ) is superimposed, where ^^^^ 2represents the noise power and ^^^^ is the identity matrix. This usually provides a simple least-squares metric for the optimization problem, which can be solved efficiently using modern algorithms. However, once found, the optimization problem can also be solved using methods other than the least-squares metric chosen as an example. In the case of evaluating difference phases, calculating the difference phases produces correlated noise with a covariance matrix ^^^^ 2 T^^^^ = ^^^^ ^^^^^^^^^^^^^^^^ . This results in the cost function being ^^^^ �. While the position of the transmitter ^^^^ RX can be estimated directly in this form, the rotation matrix ^^^^ RX consisting of nine entries with only three degrees of freedom. A possible representation of the rotation matrix ^^^^ RX From these three degrees of freedom, the Rodrigues formula gives s in | ^^^^ |1 − cos |^^^^|^^^^RX = ^^^^ +| ^^^^ | [ ^^^^ ] × + | ^^^^ |2 [ ^^^^ ]2 × with and0 −^^^^^^^^ ^^^^^^^^ The algorithm should iteratively estimate the position and rotation of the receiver. Since the Rodrigues formula assumes a non-linear relationship between ^^^^ and ^^^^ RX , the direct estimation of the entries of ^^^^ is difficult. Instead, the rotation matrix is ​​estimated by ^^^^ RXis iteratively corrected for "small" rotations ∆^^^^, while each "small" rotation is expressed by the corresponding ∆^^^^. The estimated rotation matrix in the ^^^^th iteration ^^^^RX,^^^^ from the ^^^^ − 1st iteration is ^^^^RX,^^^^ = ∆^^^^ ∙ ^^^^RX,^^^^−1. Since the rotation matrix ∆^^^^ represents a small rotation, the entries of the corresponding ∆^^^^ are also small. Consequently, the rotation matrix can be approximated with ∆^^^^ ≈ ^^^^ + [∆^^^^]×. As can be seen here, ∆^^^^ is now approximately linearly dependent on ∆^^^^, which enables a stably converging algorithm. If one now takes a preliminary estimate of the rotation matrix ^^^^ RX,^^^^−1 and position ^^^^ RX,^^^^−1 , the cost function for a single iteration of the calibration algorithm can be with ^^^^RX ≈ (^^^^ + [∆^^^^]×) ∙ ^^^^RX,^^^^−1 = ^^^^RX,^^^^−1 + [∆^^^^]× ∙ ^^^^RX,^^^^−1and^^^^RX = ^^^^RX,^^^^−1 + ∆^^^^. Thus, the hypothetical global positions of the antennas can be modified to =+ ≈ + ∆^^^^ + ∙ For a simple description, the parameters to be estimated are This allows the hypothetical phase differences to be approach, whereby the hypothetical phase differences in the ^^^^ − 1st iteration with ^^^^RX,^^^^−1 and ^^^^RX,^^^^−1 as assumption and ^^^^ the Jacobian matrix of^^^^(^^^^) at ^^^^ RX,^^^^−1 and ^^^^ RX,^^^^−1 With this approximation, the phase deviation in the cost function can now be ^^^^^^^^^^^^^^^^−1 − ^^^^^^^^with ^^^^^^^^^^^^ ^ ^^^−1 − If you insert this into the cost function, you get min ^^^^(^^^^^^^^^^^^^^^^−1 − ^^^^^^^^ − .This represents a Generalized Least Squares Problem, which is characterized by can be solved in a closed form. From ^�^^^ we can now extract ∆^^^^ and ∆^^^^ to estimate the position and rotation of the receiver ^^^^RX,^^^^ = ^^^^RX,^^^^−1 + ∆^^^^and ^^^^RX,^^^^ = ∆^^^^ ∙ ^^^^RX,^^^^−1with sin|∆^^^^ The formulas established now allow the implementation of a structured estimation algorithm with the following steps: 1. Creation of an initial assumption for ^^^^ RX,0 and ^^^^ RX,0 These can, for example, be randomly selected within a certain pre-known range or be given by a prior estimate. The iteration index is initialized with ^^^^ =1. 2. Selection of the current phase difference evaluation matrix ^^^^ ^^^^. This initially evaluates only the measurements of closely adjacent antenna pairs and then includes more and more antennas until the rank (^^^^A − 1)^^^^R is reached. 3 Calculation of the corresponding measured phase differences ^^^^^^^^ mess = mod ′ 2 ^^^^ (^^^^ ^^^^ ^^^^ mess ) 4. Calculate the current deviation ^^^^^^^^^^^^ ^^^^−1 = 5. Calculating the update ^�^^^ Update the estimated rotation matrix ^^^^RX,^^^^ = ∆^^^^ ∙ ^^^^RX,^^^^−1, where ∆^^^^ results from ∆^^^^ using the Rodrigues formula. Update the estimated position ^^^^RX,^^^^ = ^^^^RX,^^^^−1 + ∆^^^^Check whether the currently estimated position and rotation are reasonable. This can be done in particular by providing advance information about the possible position range of the receiver. a. If the currently estimated position and rotation are not reasonable: Continue with step 1. b. If the currently estimated position and rotation are reasonable: Check whether the estimation algorithm has fully converged. This can be done in particular using the rank of the phase difference evaluation matrix ^^^^ ^^^^ , the number of iterations ^^^^ and the size of the update ^�^^^ i. If the estimation algorithm is not yet finished: increase the iteration level ^^^^ = ^^^^ + 1 and continue with step 2. ii. If the estimation algorithm is finished: save ^^^^ RX,^^^^and ^^^^ RX,^^^^

Claims

1 000172-25 He Friedrich-Alexander-University Erlangen-Nuremberg DE - 91054 Erlangen ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Method for determining a position and an orientation of a receiver array by estimation ^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^^ Claims 1. Method for determining a position and / or an orientation of a receiver array with a plurality of receiving antennas by estimation, in particular with ^^^^ A Receiving antennas, wherein the following steps are carried out in the method: Radiating a respective signal by at least one transmitter at different positions, in particular at ^^^^ RPositions, and evaluating a spatially characteristic phase profile of the wave fields of the emitted respective signals using the plurality of receiving antennas of the receiver array, wherein at the receiver 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, which result from the positions and orientation of the receiver.

2. The 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 method of convex optimization and / or an artificial neural network is used in order to - 2 - to obtain the best possible estimates for the position and orientation of the receiver array.

3. The method according to one of the preceding claims, wherein some or all of the receiving antennas of the receiver array are spaced from at least one adjacent receiving antenna by 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.

4. The method according to one of the preceding claims, wherein the receiver is large enough that at least one transmitter position is in the near field of the receiver array.

5. The method according to one 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 implementation of the optimization problem according to claim 2, is performed iteratively, preferably such that the evaluated differential phases change in the iteration steps.

7. Method according to one 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 estimated values ​​for the position and orientation of the receiver array, in which the comparison of at least one measured differential phase of at least one antenna pair of the receiving antennas is compared with hypothetical differential phases of the same antenna pair, starts with several different hypotheses. - 3 - 9. The method according to one of the preceding claims, wherein an estimation algorithm for obtaining estimated values ​​for the position and orientation of the receiver array, in which the comparison of at least one measured differential phase of at least one antenna pair of the receiving antennas is compared with hypothetical differential phases of the same antenna pair, starts recursively from the previous estimate.

10. The 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 implementation of the optimization problem according to claim 2.

11. The method according to one of the preceding claims, wherein the position of the receiver array in at least one spatial direction is known in advance and / or the rotation of the receiver array with respect to at least one axis of rotation is known in advance.Method according to one of the preceding claims, wherein in the comparison, preferably in the implementation of the optimization problem according to claim 2, a phase difference evaluation matrix ^^^^^^^^ with rank (^^^^A − 1)^^^^R is used, where^^^^. A the number of receiving antennas of the receiver array and ^^^^ R the number of different emission positions of the signals.

13. Method according to one of the preceding claims, wherein several transmitters are used at only one position for emitting a respective signal or only one transmitter is used at different positions for emitting a respective signal, and / or several of the respective signals are transmitted simultaneously or sequentially.

14. Method according to one of the preceding claims, wherein the different positions of the at least one transmitter for emitting a respective signal - 4 - are known, and form reference positions, preferably ^^^^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 location system and / or inertial sensors.

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