Method for forming an autocorrelation matrix of radio signal measurements for distance measurement and noise reduction

Description

[0001] The invention relates to the evaluation of properties of signal propagation of radio signals, in particular the determination of the distance and / or the provision of mathematical objects obtained from measured values ​​of radio signals for determining the properties of signal propagation.

[0002] It is known to generate an autocorrelation matrix from complex measured values ​​and to determine at least some of its eigenvalues ​​and / or eigenvectors in order to determine properties of signal propagation, such as the distance traveled and / or the direction of arrival of the signal. For this purpose, one of the methods known as MUSIC, CAPON's method, or MATRIX PENCIL is widely used.

[0003] It is also known from WO 2022 / 096509 A1 to calculate complex values ​​from runtime measurements and to use them in methods such as MUSIC, CAPON's method or MATRIX PENCIL.

[0004] It is also known to reduce a measurement value space by means of spatial smoothing and to determine a distance that a radio signal has traveled between two objects from an autocorrelation matrix of measured values ​​of received radio signals, whether generated with or without spatial smoothing.

[0005] For spatial smoothing, subspace matrices with the size gxa are formed from a measurement matrix of dimension fxa and thus, for example, a antenna measurement vectors with measurement values ​​at an at least approximately uniform frequency but a different antenna paths and f frequency measurement vectors with measurement values ​​at f different frequencies of each antenna path, with g < f. The number of subspace matrices is (f - g + 1)

[0006] The subspace matrices U(j) with j = 1 ... (f - g + 1) are then formed as follows: U(j) is formed from the frequency measurement vectors j to g + j - 1 of the measurement matrix, in the order of the frequency measurement vectors in the measurement matrix. The subspace matrices are then correlated with themselves. The autocorrelated subspace matrices are subsequently summed to form the autocorrelation matrix. Here, g, a, f, and j are positive integers. In particular, the autocorrelation matrix is ​​​​given by the result of the summation.

[0007] The autocorrelation matrix can then be used to apply well-known methods for treating autocorrelation matrices of measured values, for example, to reduce noise components and / or multiply test vectors by the autocorrelation matrix, its inverse, or its eigenvector space. For this purpose, one of the methods known as MUSIC, CAPON's method, or MATRIX PENCIL is widely used.

[0008] It is also known from "An Improved Spatial Smoothing Technique for DoA Estimation of Highly Correlated Signals", Avi Abu, Engineering Letters, 19:1, EL_19_1_02 (Advance online publication: 10 February 2011) to use the eigenvalues ​​of the subspace matrices otherwise used for spatial smoothing directly to determine the angle of incidence using MUSIC without summing the subspace matrices beforehand.

[0009] The task is to provide an improved derivation of an autocorrelation matrix that reduces the size of the autocorrelation matrix while still allowing for the most accurate evaluations. By selecting the number of subspace matrices, the computational effort can be chosen relatively freely, even for a given size of the ACM. With a small number, the computational effort can be significantly reduced, and with a large number, the accuracy of the information derived from the autocorrelation matrix can even be increased compared to the state of the art. However, excessive rounding errors in the calculation must be avoided.

[0010] The object is achieved by a method for determining at least one distance, comprising the provision of an autocorrelation matrix of measured values ​​of radio signals between a first and a second object for determining at least one property of the signal propagation of the radio signals between the first and second object, in particular the distance that the radio signals have traveled and / or between the first and second object, wherein a. f, in particular complex, measured value vectors, in particular frequency measured value vectors, each with a coordinates with a > = 1 and with f > 1, in particular with f > 3, in particular f > 10, are provided with a given sequence, in particular as a complex measured value matrix, in particular with f rows and a columns or f columns and a rows, which in particular span a measured value space, and wherein an autocorrelation matrix with a vector number lower than f, in particular with a smaller number of columns and / or rows than that of the measured value matrix is ​​formed from the set of measured value vectors, in particular measured value matrix, by means of spatial smoothing, wherein b. for carrying out the spatial smoothing, a plurality of subspace matrices each with a measured value vector number, in particular column or row vector number, lower than f, in particular a smaller number of columns and / or rows than that of the measured value matrix,is formed and wherein the subspace matrices are each correlated with themselves and the self-correlated subspace matrices are summed, in particular weighted, characterized in that the formation of the subspace matrices takes place in such a way that c. a selection with the same number of measured value vectors, in particular rows or columns of the measured value matrix, which are at least partially non-adjacent in the sequence for all subspace matrices, forms a subspace matrix and / or that a first subset of the subspace matrices is formed in such a way that a subspace matrix of the first subset is formed in each case by a selection with the same number of measured value vectors, in particular rows or columns of the measured value matrix, for all subspace matrices, wherein the arrangement of the selected measured value vectors in the subspace matrix is ​​as in the sequence and that a second subset of the subspace matrices is formed in such a way,that a subspace matrix of the second subset is formed by a selection with the same number of modified measured value vectors for all subspace matrices from a modified measured value vector set, in particular a modified measured value matrix, and that the modified measured value vector set, in particular a modified measured value matrix, is formed by selecting measured value vectors and reversing their order and inverting the complex or real part of all coordinates of the modified measured value vector set, wherein the arrangement of the selected measured value vectors in the subspace matrix of the second subset corresponds to the reversed order. In particular, only either the complex or the real part of a coordinate is inverted.

[0011] A measured value vector, which is given in particular by a frequency measured value vector, is in particular formed from at least a, in particular exactly a, in particular complex, measured values ​​of signals of a first object received at a second object or signals of a second object received at a first object, at at least approximately identical frequencies via a antenna paths. Different frequency measured value vectors differ in particular by different, i.e., in particular not approximately identical, frequencies of the signals at which their measured values ​​were taken.

[0012] A measured value matrix has, in particular, frequency measured value vectors and antenna measured value vectors as columns or row vectors.

[0013] An antenna measurement value vector is in particular formed from at least f, in particular exactly f, in particular complex, measured values ​​of signals of a first object received at a second object or signals of a second object received at a first object, at f different frequencies via a common antenna path. Different antenna measurement value vectors differ in particular in the antenna path used to generate their measured values. An antenna path is given in particular by the transmission from a first transmitting antenna to a first receiving antenna. Different antenna paths differ in particular in that they use different transmitting antennas and / or different receiving antennas for transmission.

[0014] A given order is understood in particular to mean that an order is or will be determined, and thus the vectors are in a certain order relative to each other, or this order is known and do not form an unsorted set of vectors. The order can be determined arbitrarily.

[0015] The measured value vectors, in particular row or column vectors, contain the measured values ​​of a radio signal or radio signal round trip as values, in particular as their coordinates. The number of values ​​or coordinates in a vector can, for example, correspond to the number of antenna paths. This is understood to mean, in particular, the number of different combinations of receiving and transmitting antennas used. The number of measured values ​​and / or coordinates in the frequency measured value vectors can also be one, but is in particular greater than or equal to two. The order can be given by the arrangement in a matrix, but can also be separated from this by a predetermined order and / or by numbering, indexing or other means of the measured value vectors.

[0016] The measured values ​​are usually complex. These measured values ​​are each given by a value (r) that depends on the received amplitude, such as a normalized amplitude, an energy or power, in particular as a magnitude, and a phase value (phi), which in particular represents the phase shift due to the signal transmission from the first to the second object or the signal round trip between the two objects. A measured value can then be represented, for example, as r * ej< * phi<. The measured values ​​can also be pre-processed; for example, the phase value can be calculated first or be an average of measurements on several signals at the same frequency. The phase value can also be a phase change calculated from the signal propagation time and caused by the distance between the first and second object. An equivalent phase change can be calculated based on the propagation time and the frequency.

[0017] Transmission is understood to mean, in particular, the transmission of a signal from a transmitting device, in particular an antenna, of the first object and the reception of the signal by a receiving device, in particular an antenna, of the second object, as well as, in particular, the transmission of a signal from a transmitting device, in particular an antenna, of the second object and the reception of the signal by a receiving device, in particular an antenna, of the first object. A transmitting device can also be used as a receiving device and, in particular, has and / or is provided by an antenna.

[0018] The transmission and reception of a plurality of radio signals means that radio signals are transmitted and at least a plurality of these radio signals are received. This does not preclude the possibility that more than a plurality of radio signals are transmitted but only the majority are received.

[0019] When forming the subspace matrices, only a portion of the measured value vectors, specifically either columns or rows of the measured value matrix, is selected and written into the subspace matrix. This reduces its size compared to the measured value matrix. The selection used to form the modified measured value vector set can, however, also include all measured value vectors; in particular, it does not include at least those that were used to form the subspace matrices of the first subset. When inverting the complex or the real part of all coordinates of the modified measured value vector set, it is important that only the complex or the real part is inverted, not both. In particular, the inversion is carried out identically for all selected measured value vectors.

[0020] The number of subspace matrices can be chosen based on the desired accuracy, the accuracy of the computational unit used, and the available computing time. It can be less than, equal to, or greater than the number of measured value vectors. The lower the number, the less computing power is required.

[0021] In particular, their size is chosen to be 10 to 50 times the number of antenna paths considered. It is also sufficient to select only one antenna path, and the antenna paths can be considered individually or separately, so that subspace matrices with a size of, for example, 10 to 50 times 1 are also possible.

[0022] In some applications, especially when working with CAPON's method or the inverse of the autocorrelation matrix, it is useful to choose the number of subspace matrices not significantly lower or not lower than the number of coordinates of the subspace matrix for each antenna path, in particular not to choose less than 75% of the number.

[0023] The summation of the subspace matrices can be weighted, in particular based on the quality of the reception of the measured value vectors, frequency measured value vectors and / or antenna measured value vectors contained therein. Thus, a quality metric can be used as a weighting factor. The quality or quality metric can, for example, be determined for each contained measured value vector and a metric of the subspace matrix can be derived from this, for example by aggregation, an average, minimum and / or maximum. The quality or quality metric of a measured value vector can, for example, be determined by taking several measurements on the same signal in close succession, which are then averaged, in particular to calculate the measured value. A value inversely proportional to the scatter, for example variance or standard deviation, of the measurements can be used as the quality metric.For example, the dispersion of the received amplitude, power, and / or phase shift due to signal transmission, particularly distance, can be used. This can improve the quality of the autocorrelation matrix.

[0024] The method can be used in particular within the framework of one or more of the following steps: transmitting a plurality of radio signals on different first frequencies, in particular with different first antennas, from a first object and receiving them at a second object, in particular with different second antennas, and optionally also transmitting a plurality of radio signals on different second frequencies, in particular identical or similar to the first frequencies, in particular with different, in particular the second, antennas, from the second object and receiving them at the first object, in particular with different, in particular the first, antennas. In this case, in particular the individual radio signals of the plurality have different frequencies and / or the plurality contains radio signals with different frequencies.It is therefore not necessary to repeatedly transmit a plurality of radio signals (e.g. with the same frequencies) on different frequencies.

[0025] Frequencies can be considered similar especially if their difference lies within the inaccuracy of the hardware used.

[0026] This can be carried out in particular by frequency hopping, in which, for example, signals with frequencies changed by a specified frequency interval are transmitted one after the other at a specified time interval.

[0027] Determining amplitude values ​​corresponding to the received amplitude, for example amplitude, or received power and phase values ​​which are due to the phase shift caused by the propagation from one object to another or the circular run, in particular the distance between the objects.

[0028] Determination of phase values ​​in each case for a frequency or frequency range, in particular from the first and / or second frequencies, indicating the phase shift of the signal transmission from the first to the second object or by the signal round trip, in particular due to the distance between the objects.

[0029] Creating a plurality of measured values ​​each from amplitude value and phase value, especially as a complex number.

[0030] Creating measured value vectors or a measured value matrix containing such as rows or columns. In the frequency measured value vectors, the components of the measured value vectors are in particular each given by a measured value of an antenna path. A frequency measured value vector is in particular formed from measurements on one or more signals of a first and / or second frequency. In particular, in the case of a signal path only from the first to the second object, it is formed from measurements on signals of a first frequency; in the case of a signal round trip, it is formed from measurements on signals from the first to the second object at a first frequency and on signals from the second to the first object at a second frequency, wherein the first and second frequencies in particular have a relative deviation of less than 500 kHz, in particular less than 100 kHz, and in particular are identical.In particular, the frequencies are chosen to be so similar that the product of the time inaccuracy of determining the measurement time of the measured value with the frequency difference is less than 0.05, which would correspond to a phase jitter of 18°.

[0031] Radio signals with a constant frequency, especially continuous wave, are particularly suitable. Data can also be modulated onto them. The measured value vectors can then be used to create the AKM.

[0032] The subspace matrices can be formed by selecting measured value vectors, in particular frequency measured value vectors, and incorporating them into the respective subspace matrix. For this purpose, a uniform scheme is generally used, which is identical for each selection in each subspace matrix, at least for one subset. When working with multiple, especially two, subsets of the subspace matrices, the selection rule in the two subsets is particularly similar, identical, or mirrored.

[0033] In particular, the selection of the measured value vectors for the subspace matrices is carried out according to the following scheme: Let v(p) be the measured value vectors, in particular frequency measured value vectors, of the set of measured value vectors, in particular frequency measured value vectors, with p from 0 to f-1 Let U(j) be the subspace matrices, each with k frequency measured value vectors, with k < f and u = 0 ... k -1 and U(j,u) the u-th frequency measured value vector of the subspace matrix U(j) U j u = v j * A + C + u * B , und / oder U j u = v * f − 1 − j * A + C + u * B and / or U j u = − v n − 1 − j * A + C + u * B where in particular B is not a divisor of A and / or in particular all j * A < > u * B for all j and u. j from the set of positive integers runs in particular from 1 to jmax with jmax chosen such that (j * A + C + u * B) is always < = (f-1).

[0034] Here v* is the complex conjugate of v.

[0035] It is preferred to form a first subset with j from 1 to jm according to U j u = v j * A + C + u * B and a second subset, in particular identical in number, with j from jm + 1 to jmax according to U j u = v * f − 1 − j * A + C + u * B oder U j u = − v f − 1 − j * A + C + u * bB , where − v = − Realteil v + i * Imaginärteil v

[0036] It is particularly advantageous for the U(j,u) to the U(j,u + 1) to have a fixed amount of frequency separation and / or amount of time separation of the underlying measurements on the received signal and / or the emission of the signal on which the measurement was made for all j, although this can be different for each u, for example Delta_t(u) and / or Delta_F(u). This is particularly useful for increasing accuracy in systems with high motion. With an approximately constant distance between the objects and / or an approximately constant radio environment, this becomes less important. For example, with identical time and frequency separations of the signals, this is even possible with constant Delta_t (= time separation) and Delta_F (= frequency step). This makes the selection of the measured value vectors while fulfilling the advantageous selection condition particularly easy.If subsets of the subspace vectors are used (first part ), the second subset can also be Delta_t(j | 1 ... jm, u) = - Delta_t(j|jm + 1 ... max, u) and / or Delta_F(j| 1 ... jm, u) = - Delta_F(j|jm+ 1 ... max, u), where, for example, j| 1 ...jm means that j lies in the range 1 to jm.

[0037] It is preferred if the measured value vectors of the subspace matrices are selected such that a time and / or frequency spacing pattern given in a subspace matrix between the measured value vectors is approximately identical, in particular identical, for all subspace matrices or all subspace matrices of the first subset, and in particular the same pattern, or the same pattern with the time and / or frequency spacing reversed, also applies to all subspace matrices of the second subset, or is inverted. In particular, frequencies with a spacing of less than 500 kHz, in particular less than 100 kHz, are considered approximately identical. In particular, the frequencies are made equal such that the product of the time inaccuracy of determining the measurement time and the frequency difference is less than 0.05, which would correspond to a phase jitter of 18°.

[0038] It is particularly advantageous to form the subspace matrices in such a way that the selections of the measured value vectors in the subspace matrices are different, in particular, that each measured value vector occurs in only one subspace matrix. This reduces the computational effort while still maintaining a relatively high level of accuracy.

[0039] Preferably, the complex measured values ​​of, in particular, a signal transmission or of, in particular, a signal round trip, in particular at a frequency, are recorded in the coordinates of the measured value vectors, in particular in the f rows or f columns.

[0040] Advantageously, the first and second subsets each have the same number of subspace matrices. This makes the calculation particularly accurate. In particular, they are not formed from the same frequency measurement vectors. Forming them from the same frequency measurement vectors also includes the formation of a specific frequency measurement vector in one subspace matrix and its complex conjugate in another, or a product of the specific frequency measurement vector and a scalar, even a negative one. This increases the accuracy relative to the computational effort.

[0041] Particularly advantageously, the subspace matrices of the first subset and the second subset are not formed from measured values ​​from measurements on the same received signal set. In particular, the first subset does not contain any frequency measurement value vectors, in particular, measured values ​​on received signals that the second subset contains. In particular, the frequency measurement value vectors, in particular rows or columns, from which the subspace matrices of the first subset are formed, are disjoint to the frequency measurement value vectors, in particular rows or columns, their complex conjugate or scalar-multiplied, even negative, measurement value vectors from which the subspace matrices of the second subset are formed. This increases the accuracy relative to the computational effort.

[0042] In some embodiments or environments, it can be highly advantageous if not all measurement value vectors, particularly rows or columns, are included in the subspace matrices. In particular, with regard to the time of measurement and / or emission of the signal at which the measurement was taken and / or with regard to its frequency, neighboring measurement value vectors to measurement value vectors included in the subspace matrices are not included. For example, every second measurement value vector can be omitted in an order based on time and / or frequency. Measurement value vectors taken from signals with noticeably different received energy, bandwidth, and / or fluctuation can also be omitted.This allows the computational effort to be significantly reduced and, in some cases, even improved without major losses in terms of accuracy, especially if the selection avoids the use of received signals that are particularly disturbed or dominated by long signal paths.

[0043] Advantageously, the first subspace matrix can be formed such that, starting with an A-th measured value vector, all B-th or a predetermined number of B-th measured value vectors are included in the subspace matrix and this is repeated for all subspace matrices or all subspace matrices of the first subset, wherein A is increased by a predetermined value, wherein B is in particular not equal to A and in particular B is not a divisor of A. A and B are integers, in particular positive.

[0044] Preferably, the frequency measurement value vectors, in particular rows or columns, are each formed from measured values ​​of a radio signal that was transmitted from a first to a second object at a frequency or are formed from measured values ​​of a signal round trip, wherein in particular the phase change resulting from the transmission, in particular the distance, between the objects is determined and / or a value dependent on the received amplitude is determined and in particular the measured values ​​are given by complex numbers, in particular each formed from the value dependent on the received amplitude and the phase change. In a signal round trip, the frequencies for the outward and return paths are in particular approximately identical. To determine frequency intervals, in particular a frequency value that corresponds to one of the two frequencies or a frequency that lies in between is then used.

[0045] To improve accuracy and reduce computational effort, the measured value vectors, in particular the measured values ​​and / or the measured value matrix, are subjected to filtering and / or smoothing, particularly before spatial smoothing. For example, an IIR filter, an FIR filter, and / or an FFT analysis and the removal of high frequency components are possible. This is particularly advantageous for avoiding negative effects due to rounding errors, especially with 32-bit floating-point numbers, when calculating eigenvectors and / or eigenvalues.

[0046] To increase the accuracy, different antenna paths are advantageously used between the two objects, in particular each frequency measurement value vector is formed from measured values ​​from reception at different receiving devices, in particular antennas, and / or from reception after transmission with different transmitting devices, in particular antennas, in particular of the same radio signal, and / or a first of rows and columns each has measurements on a received radio signal, in particular at one frequency, and the other of rows and columns has measured values ​​of the transmission with different transmitting and / or receiving antennas, and / or the values ​​in the measured value matrix are complex and in particular they each contain a statement on the received amplitude or power and on the received phase position and / or phase shift.

[0047] Preferably, the number of measured value vectors in each subspace matrix is ​​at least 30% less than f; in particular, the number of rows or columns of the subspace matrices is chosen to be at least 30% less than that of the measured value matrix. This allows the computational effort to be reduced with minimal loss, and in some cases even increases accuracy.

[0048] Eigenvectors and eigenvalues ​​can be calculated from the autocorrelation matrix. It is known that the eigenvalues ​​can be used to separate noise from signal. Further analyses of or using the AKM, for example, based on its inverse, are also known.

[0049] The autocorrelation matrix can also be used to separate signal components, for example to reduce the noise component in the autocorrelation matrix. A signal space can also be defined in the autocorrelation matrix based on at least one eigenvalue and / or vector calculation, in particular by considering the eigenvectors of the largest eigenvalues ​​as spanning the signal space. The number of eigenvectors used here can, for example, be based on an absolute or relative specification or be derived from the ratio of the eigenvalue values. For example, a certain predefined number of eigenvectors can be used, a relative number can be specified and / or a number can be determined based on the distribution of the eigenvalues. The specifications can also be minimum and / or maximum numbers.For example, with an absolute specified number of 3, the set of eigenvectors corresponding to the three largest eigenvalues ​​can be used. With a minimum number of 2 and a maximum of 10, and with a specification such that only eigenvectors of eigenvalues ​​that are no smaller than 50% of the value of the next largest eigenvalue are considered, the number can vary between 2 and 10, depending on the distribution of the size of the eigenvalues ​​of the second to tenth largest eigenvalues.

[0050] Test data or test vectors can be used to estimate distance and / or other properties of signal propagation.

[0051] It is possible to project text vectors into the signal space and / or an eigenvector space of the autocorrelation matrix and determine their length in the signal space. The eigenvector space is preferably formed from the eigenvectors of the autocorrelation matrix with the largest eigenvalues. The largest eigenvalues ​​can be selected, for example, based on a predetermined relative or absolute number or based on the ratios of the eigenvalues ​​to one another. The longest test vector in the projection can then be considered the one that best matches the actual signal propagation, and its properties, particularly distance, can be assumed to be those of the received signal. Averaging or interpolation of the properties of a plurality of largest projected test vectors can also be used.

[0052] The method preferably includes the calculation and / or estimation of at least one property of the signal propagation, in particular distance, based on a projection and / or multiplication of the autocorrelation matrix and / or its inverse, in particular with an array response and / or radiation characteristic. This makes it possible, for example, to determine the member(s) of the array response that are most similar to the autocorrelation matrix and that are assigned to a specific characteristic of properties, such as distance, orientation and / or direction, whereby the distance and / or relative orientation or the direction from the first to the second object can be determined. For this purpose, test value vectors or vectors (such as array response) can be used that describe the signal to be received under given propagation conditions. These can be determined as part of a calibration or calculated based on a model.For example, these test vectors can each be individually multiplied by the inverse of the autocorrelation matrix, and the shortest vector of results used to determine the property, in particular the one underlying the model. Test vectors for different distances can be used in this case. For example, these test vectors can each be individually multiplied by the signal space of the autocorrelation matrix, and the longest vector of results used to determine the property, in particular the one underlying the model. Test vectors for different distances can be used in this case. In particular, test vectors all have the same length, or an appropriate normalization is performed when considering the length after multiplication.

[0053] It is also possible to determine the phase shift difference between the signal component(s) with the largest eigenvalue(s) for the individual antenna paths or receiving antennas and use this to determine the signal's direction of arrival, particularly under the assumption that the order of the magnitudes of the eigenvalues ​​of the signal components is identical on all antenna paths or receiving antennas. Thus, the direction of arrival can be geometrically determined using the difference in the phase change and knowledge of the arrangement of the receiving antennas, particularly by assigning the signal components between the individual antenna paths based on the relative magnitude or order of the eigenvalues.

[0054] It is particularly advantageous to use a floating-point unit, in particular a digital signal processor having one, for the creation of the subspace matrices, their autocorrelation matrix and / or the summation and / or inversion and / or multiplication of the autocorrelation matrix or its inverse with a test vector from a plurality of test vectors. This can lead to significant speed gains.

[0055] Further advantages and possible embodiments of the invention will now be explained purely by way of example and not by way of limitation, using examples and schematic figures: For example, when transmitting 199 signals, each with a time interval of 10 ms and a frequency spacing of 500 Hz, over four antenna paths using two transmit and two receive antennas, a measurement matrix with 200 frequency measurement vectors and four complex coordinates each can be formed, from which subspace matrices are then formed. Four antenna measurement vectors, each with 200 coordinates, are then available / can be formed. With known spatial smoothing, the subspace matrices, for example, with a size of 24 measurement vectors each, would be formed as follows: U(1): Frequency measurement vectors 1-24 U(2): Frequency measurement vectors 2-25 etc. U(17): Frequency measurement vectors 175-199 According to the invention, the following could be formed: U(1): Frequency measurement vectors 1, 5, 9, 13, etc. 93 U(2): Frequency measurement vectors 3, 7, 11, 15, etc. 95 etc. U(54): Frequency measurement vectors 107, 111, 115, etc. 199 This shows that the computational effort can be significantly reduced. It has been shown that the accuracy of determining the property is reduced to a much lesser extent and can even increase depending on the computational accuracy and the number of subspace matrices.

[0056] Fig. 1 illustrates a possible procedure. After the measured values ​​have been acquired, the subspace matrices are formed by omitting the measured value vectors multiple times and / or inverting the order of the measured value vectors. These are correlated with each other, and the results are summed.

[0057] Fig. 2 a) illustrates a measured value matrix 1, whose complex coordinates are represented as boxes. It has four antenna measured value vectors 2 for four different antenna paths and fifteen frequency measured value vectors 3. The antenna measured value vectors 2 are row vectors and the frequency measured value vectors 3 are column vectors. However, this can also be chosen differently. The measured value matrix 1 was created by measuring the amplitude and phase shift of signals of fifteen different equidistant frequencies at equidistant times. Fig. 2b ) the frequency measurement value vectors 4 selected to form a first subspace matrix are marked by points. Fig. 2c ) shows the frequency measurement vectors 5 selected for the formation of a second subspace matrix. It can be seen that the pattern of the frequency and time intervals of their measurements is identical in both selections. Fig. 2 d) shows the selection of the frequency measurement vectors 6 from a modified, here complex conjugated matrix, to form a third subspace matrix, in which, in addition to the complex conjugation of the measured values ​​in the subspace matrix, the order of the frequency measurement vectors is reversed. This means that the order of the frequency measurement vectors 4 and 5 was selected from left to right, while the range sequence of the frequency measurement vectors 6 was selected from right to left. The Figuren 2 b, c und d The three subspace matrices formed are each individually correlated with themselves and then all summed to obtain the autocorrelation matrix.

Claims

1. A method for determining at least one distance, comprising providing an autocorrelation matrix of measured values, comprising the steps of a. Transmitting a first plurality of radio signals from a first object at different first frequencies, in particular with different first antennas of the first object, and receiving the first plurality of radio signals at a second object, in particular with different second antennas of the second object, and optionally also transmitting a second plurality of radio signals at different second frequencies, in particular on the different first frequencies or on frequencies similar to the first different frequencies, in particular with different, in particular the second, antennas of the second object, from the second object and receiving the second plurality of radio signals at the first object, in particular with different, in particular the first, antennas of the first object. b. Determining measured values on the first and / or second received radio signals to determine the distance travelled by the radio signals between the first and second objects c. Determine the autocorrelation matrix, i. wherein for this purpose a set of f, in particular complex, measured frequency value vectors (3) each having a coordinates with a > = 1 and with f > 1, in particular with f > 3, in particular f > 10, with a given sequence, in particular as a complex measured value matrix (1), in particular with a rows and f columns or a columns and f rows, based on the first and / or second measured values on the first and / or second radio signals, wherein the set of f measured frequency value vectors in particular spans a measured value space, wherein a measured frequency value vector is formed in each case from measurements on one or more signals of a first and / or second frequency, wherein the measured frequency value vector is formed by measurements on signals of a first frequency in the case of a signal run only from the first to the second object, and is formed by measurements on signals from the first to the second object at a first frequency and on signals from the second to the first object at a second, similar, frequency in the case of a signal round trip. ii. and wherein for this purpose the autocorrelation matrix with a first frequency vector number (4, 5, 6) lower than f, in particular with a lower number of columns and / or rows than that of the measured value matrix (1), is formed from the set of f measured frequency value vectors (3), in particular from the measured value matrix (1), by means of spatial smoothing, wherein a. for performing the spatial smoothing, a third plurality of subspace matrices of the set of measured frequency value vectors, in particular of the measured value matrix, is formed with in each case one, in particular the first, number of measured frequency value vectors (4, 5, 6), in particular number of column or row vectors, lower than f, in particular lower number of columns and / or rows than that of the measured value matrix, and wherein the subspace matrices are in each case correlated with themselves and the subspace matrices correlated with themselves are totalled, in particular weighted, wherein the method comprises determining said at least one distance on the basis of at least one projection and / or multiplication with the autocorrelation matrix and / or reducing the noise in the autocorrelation matrix and / or selecting a signal space in the autocorrelation matrix on the basis of at least one eigenvalue / vector calculation, characterised in that the subspace matrices are formed in such a way that b. in each case a selection with the same number for all subspace matrices, in particular one, in particular the first, number of measured frequency value vectors, forms a subspace matrix in the given sequence at least partially, in particular in each case, of non-adjacent measured frequency value vectors, in particular rows or columns of the measured value matrix and / or that a first subset of the subspace matrices is formed in such a way that a subspace matrix of the first subset is formed in each case by a selection with the same number of measured frequency value vectors (4, 5) for all subspace matrices, in particular one, in particular the first, number of frequency-measured value vectors, in particular rows or columns of the measured value matrix, the arrangement of the selected measured frequency value vectors in the subspace matrix being as in the given sequence, and in that a second subset of the subspace matrices is formed in such a way that a subspace matrix of the second subset is formed in each case by a selection with the same number of measured frequency value vectors, in particular one, in particular the first, for all subspace matrices, in particular the first, number of measured frequency value vectors, of modified measured frequency value vectors (6) from a modified measured frequency value vector set, in particular modified measured value matrix, and in that the modified measured frequency value vector set, in particular modified measured value matrix, is formed thereby, in that measured frequency value vectors are selected and their order is reversed with respect to the given order and the complex or the real component of all coordinates of the modified measured value vector set is inverted, the arrangement of the selected measured frequency value vectors in the subspace matrix of the second subset corresponding in each case to the reversed order,2. Method according to claim 1, wherein the selections of the measured frequency value vectors of the subspace matrices are different, in particular each measured frequency value vector only occurs in one subspace matrix.

3. Method according to one of the preceding claims, wherein in the coordinates of the measured frequency value vectors, in particular in the f rows or f columns, in each case the complex measured values of, in particular one, signal transmission or of, in particular one, signal round trip, in particular at one frequency, optionally via several antenna paths, are recorded.

4. Method according to one of the preceding claims, wherein the first and second subsets each have the same number of subspace matrices and in particular are not formed from the same measured value vectors, in particular are not formed from measured values of measurements on the same received signal set, in particular the first subset does not include any measured frequency value vectors, in particular, measured values on received signal frequencies, in which measured signals which the second subset contains, in particular the measured frequency value vectors, in particular rows or columns, from which the subspace matrices of the first subset are formed, are disjoint from the measured frequency value vectors, in particular rows or columns, from which the subspace matrices of the second subset are formed.

5. Method according to one of the preceding claims, wherein not all measured frequency value vectors, in particular rows or columns, are included in the subspace matrices.

6. Method according to one of the preceding claims, wherein the first subspace matrix is formed in that, starting with an A-th measured frequency value vector, all B-th (or a predetermined number B-th) measured frequency value vectors are included in the subspace matrix and this is repeated for all subspace matrices or all subspace matrices of the first subset, wherein A is increased by a predetermined value, wherein b is in particular not equal to A and in particular B is not a divisor of A.

7. Method according to one of the preceding claims, wherein the measured frequency value vectors of the subspace matrices are selected such that a time and / or frequency spacing pattern given in a subspace matrix between their measured frequency value vectors is approximately identical, in particular identical, for all subspace matrices or all subspace matrices of the first subset, and in particular the same pattern, or the same pattern with reversal of the time and / or frequency spacing, also applies to all subspace matrices of the second subset.

8. Method according to one of the preceding claims, wherein the measured frequency value vectors, in particular rows or columns, are each formed from measured values on a radio signal which was transmitted from a first to a second object at a frequency or are formed from measured values of a signal round trip, wherein in particular the phase change and / or signal propagation time resulting from the transmission between the objects and / or the phase change calculated from the signal propagation time due to the distance between the first and second object is determined and / or a value dependent on the received amplitude is determined and in particular the measured values are given by complex numbers, in particular formed in each case from the value dependent on the received amplitude and the phase change.

9. Method according to one of the preceding claims, wherein the measured value vectors, in particular measured frequency value vectors, antenna measured value vectors, measured values and / or measured value matrix are subjected to filtering and / or smoothing, in particular before the spatial smoothing.

10. Method according to one of the preceding claims, wherein each measured frequency value vector is formed from measured values from reception at different receiving devices and / or from reception after transmission with different transmitting devices, in particular of the same radio signal, and / or a first one of rows and columns in each case comprises measurements on a received radio signal, in particular at one frequency, and the other one of rows and columns comprises measured values of the transmission with different transmitting and / or receiving antennas, and / or the values in the measured value matrix, the measured frequency value vectors and / or antenna measured value vectors and / or antenna measured value in particular at a frequency, and the other of rows and columns has measured values of the transmission with different transmitting and / or receiving antennas, and / or the values in the measured value matrix, the measured frequency value vectors and / or antenna measured value vectors are complex and in particular each contain a statement on the received amplitude or power and on the received phase position.

11. Method according to one of the preceding claims, wherein the number of measured frequency value vectors in each subspace matrix is at least 30% less than f, in particular the number of rows or columns of the subspace matrices is at least 30% less than that of the measured value matrix.

12. Method according to any one of the preceding claims, wherein it comprises calculating at least one distance determined and / or estimated based on at least one projection and / or multiplication with the autocorrelation matrix and / or reducing noise in the autocorrelation matrix and / or selecting a signal space in the autocorrelation matrix based on at least one eigenvalue / vector calculation.

13. Method according to one of the preceding claims, wherein the creation of the subspace matrices, their autocorrelation matrix and / or the summation and / or the inversion and / or multiplication of the autocorrelation matrix or its inverse is carried out in each case with a test vector from a plurality of test vectors by means of a floating-point unit, in particular a digital signal processor having a floating-point unit.