Radar system for detecting surroundings using a model-based angle estimation by means of a beam scanning process

Abstract

The invention relates to a method for a radar system for detecting surroundings, having a plurality of individual antennas for transmitting and / or receiving radar signals. The method is characterized in that - a model-based angle formation process is carried out in which it is assumed that there are a plurality of different physical beam directions αk, where k = 1,…,K, for the relevant transmitted beams and / or received beams and the beam directions can be dependent on one another, - instead of the physical beam directions αk, the corresponding electrical beam directions φk can also be used, which can be formed in particular by the relationships φk = 2π∙sin(αk) and therefore the beam directions are generically referred to below as δ, which can represent physical as well as electrical beam directions, - instead of a parameter set which is defined in a multi-dimensional space (δ1,…,δK), a parameter set which is defined in a one-dimensional space (δt) and a parameter set which is defined in a maximally (K-1)-dimensional space (δo,1,…,δo,L) are used, wherein the angles δt and δo,1,…,δo,L are formed from the angles δ1,…,δK according to the breakdown δk = δt+gk,1∙δo,1+…+ gk,L∙δo,L where k = 1,…,K, - and this separation is preferably used in order to reduce the burden when calculating the model-based angle formation and / or storing parameter sets calculated a priori.

Description

[0001]202404901 1 Radar system for environmental sensing with model-based angle estimation with beam steering The invention relates to a radar system for environmental sensing for motor vehicle applications. According to the invention, the radar system has a model-based angle estimation with beam steering. Prior art Motor vehicles are increasingly equipped with driver assistance systems that use sensor systems to detect the environment and derive automatic reactions of the vehicle from the traffic situation thus detected and / or instruct the driver, in particular warn them. A distinction is made between comfort and safety functions. As a comfort function, FSRA (Full Speed ​​Range Adaptive Cruise Control) plays an important role in current development. The vehicle regulates its own speed to the desired speed specified by the driver, provided the traffic situation allows this.Otherwise, the vehicle's speed is automatically adjusted to the traffic situation. Safety functions now come in a wide variety of forms. One group consists of functions for reducing braking or stopping distances in emergency situations, up to and including autonomous emergency braking. Another group comprises lane-change functions: These warn the driver or intervene in the steering if the driver intends to make a dangerous lane change, i.e., if a vehicle in the adjacent lane is either in the blind spot (referred to as BSD – "Blind Spot Detection") or is approaching rapidly from behind (LCA – "Lane Change Assist"). In the foreseeable future, however, the driver will no longer just be assisted, but the driver's task will be increasingly performed autonomously by the vehicle; that is, the driver will be increasingly replaced; this is referred to as autonomous driving. Radar sensors are used for systems of the type described above.Radar sensors are often combined with sensors from other technologies, such as camera sensors. Radar sensors have the advantage, among others, of operating reliably even in adverse weather conditions and, in addition to measuring the distance to objects, can also directly measure their radial relative velocity via the Doppler effect. Transmission frequencies of 24 GHz, 77 GHz, and 79 GHz are typically used. Due to the increasing functional scope of such systems, the requirements are constantly rising, particularly with regard to angular resolution, i.e., resolution in the azimuth and elevation directions. Modern radar systems are characterized by the fact that they consist of many individual transmitting and receiving antennas, resulting in signals from spatially distinct antenna channels.which are used for angle estimation in the digital domain. A standard digital beamforming technique, e.g., a digital Fourier transform (DFT), is applied for this purpose. However, the separation capability of digital beamforming is limited, so that two targets with a small angular separation (and the same distance and relative velocity) cannot be correctly detected. Model-based angle estimation methods are used to solve this problem. However, these have the disadvantage of requiring high computational and storage resources, which increases the cost of the signal processing computers used. The object of the invention is to propose, starting from the prior art (e.g., DE 102012 105582 A1), an implementation of model-based angle estimators that require significantly reduced computational and storage resources.so that, on the one hand, more complex models with higher performance can be used and / or, on the other hand, simpler and therefore more cost-effective computing units can be used. This problem is fundamentally solved by a radar system according to claim 1. Advantageous embodiments of the invention are claimed in the dependent claims. The advantages of the invention result from the fact that a radar system with improved performance and / or a lower price can be realized. 202404901 3 The inventive method for a radar system for environmental detection, which has several individual antennas for transmitting and / or receiving radar signals, is characterized in that - a model-based angle formation is carried out, whereby it is assumed that there are several different physical beam directions αk with k = 1,…,K for the relevant transmitting beams and / or receiving beams, wherein these beam directions can be interdependent,- where, instead of the physical beam directions αk, the corresponding electrical beam directions φk can also be used, which can be formed in particular by the relationships φk = 2π∙sin(αk), and therefore, in the following, the beam directions are generically denoted by δ, which can mean both physical and electrical beam directions, - instead of a parameter set defined in multidimensional space (δ1,…,δK), a parameter set defined in one-dimensional space (δt) and a parameter set defined in at most (K-1)-dimensional space (δo,1,…,δo,L) are used, where the angles δt and δo,1,…,δo,L are derived from the angles δ1,…,δK by the decomposition δk = δt+gk,1∙δo,1+…+ gk,L∙δo,L with k = 1,…,K are formed, - and this separation is preferably used tothat the effort required to calculate model-based angle formation and / or to store a priori calculated parameter sets is reduced. Furthermore, the parameter set defined in space (δt) can effectively serve to emulate a beam swivel of the measured values ​​or values ​​derived from them by the angle δt, which can be understood or interpreted, at least approximately, as the emulation of a sensor rotated by the angle δt. Furthermore, the parameter set defined in L-dimensional space (δo,1,…,δo,L) can either be a projection matrix of a method for minimizing the squared error between the model and a measurement, or consist of parts of such a projection matrix, or be formed from values ​​derived from such a projection matrix.where this parameter set with reduced dimension L < K is preferably calculated a priori and used repeatedly for the model-based method. 202404901 4 Advantageously, the decomposition δk = δt+gk,1∙δo,1+…+gk,L∙δo,L with k = 1,…,K is formed such that one of the angles δt corresponds to one of the angles δk and the other angles δo,l with l = 1,…,L are the difference of the other angles δk to the angle δt. If there are K = 2 ray directions, the decomposition δk = δt+gk,1∙δo,1 can advantageously be formed from the angles δ1 and δ2 such that the angle δt is their central angle δt = (δ1+δ2) / 2 and the angle δo,1 is their distance δo,1 = δo = (δ1-δ2) / 2 from this central angle. Furthermore, the model can represent a target located at a height h above a road surface with the reflected rays created by the reflective properties of the road surface.so that the parameter set defined in space (δt) leads to a beam steering of the measured values ​​onto the road surface at a distance r of the target, where the angle δt can be calculated from the installation height of the sensor and the distance r, and the parameter set defined in space (δo) refers to the height h to be determined by the model-based approach. Furthermore, the model can represent a target located next to a reflective surface with the resulting mirror rays, so that the parameter set defined in space (δt) leads to a beam steering of the measured values ​​onto the reflective surface at a distance r of the target, and the parameter set defined in space (δo) refers to the distance of the target from the reflective surface. Furthermore, the model can refer to two targets with unknown angles δ1 and δ2, so that the parameter set defined in space (δt) effectively serves toto emulate a beam steering of the measured values ​​by the angle δt to the midpoint between the two targets. If the model represents two targets located at heights h1 and h2 above a road surface and at the same distance r with the mirror rays created by the reflective properties of the road surface, the parameter set defined in space (δt) can advantageously realize a beam steering of the measured values ​​to the road surface at the distance r of the targets, where the angle δt can be calculated from the installation height of the sensor and the distance r, and the parameter set defined in space (δo,1, δo,2) refers to the heights h1 and h2 to be determined by the model-based approach. 202404901 5 Furthermore, if one of the two heights can be assumed to be negligibly small, the parameter set defined in space (δo,1, δo,2) Reduce the defined parameter set to a parameter set defined in one-dimensional space (δo). If all elements or subgroups of the antenna array formed by transmitting and / or receiving antennas represent at least approximately a subset of an equidistant grid, and a method for minimizing the squared error is used, then, in an advantageous embodiment of the invention, for each angle combination in space (δo,1,…,δo,L), only one intermediate result from the projection matrix and measured values ​​or values ​​derived therefrom needs to be calculated. This intermediate result, representing a vector, can then be multiplied by beam steering vectors or vectors with rotation factors for different angles δt, thereby achieving a significant reduction in computational effort. Furthermore, the model-based method can refer not to the measured values ​​obtained directly from the antenna channels, but to measured values ​​derived from them.which result in particular after performing digital beamforming or filtering, possibly in combination with a sampling rate reduction, for which one or more discrete Fourier transforms can be used. Furthermore, in the presence of reflective surfaces, the model can also include so-called cross paths, i.e., transmitting at one angle δk1 and receiving at another angle δk2 and vice versa. Advantageously, the method can be applied in two dimensions, whereby in particular beam steering is carried out in the two-dimensional domain and the antenna array formed by the transmitting and / or receiving antennas extends over two dimensions.especially in the horizontal and vertical directions. Advantageously, the above methods are used for a radar system. Brief description of the drawings Fig. 1 shows an antenna arrangement with two transmitting and two receiving antennas. Fig. 2 shows a scenario with two targets at a relatively short distance. Fig. 3 shows a scenario with a target next to a reflective guardrail. Fig. 4 shows a scenario with a target above a road surface. Fig. 5 shows a scenario with two targets located at the same distance and at different heights above a road surface. Exemplary embodiments Today, radar systems for the detection of the surroundings of vehicles are implemented with antennas consisting of several spatially distributed individual antennas for transmitting and receiving; Fig. 1 shows an antenna with two transmitting antennas TX1 and TX2 spaced 2d∙λ apart and two receiving antennas RX1 and RX2 spaced d∙λ apart (λ denotes the radar wavelength).This results in the synthesis of N = 4 antenna channels: antenna channel n = 1 from the combination of TX1 and RX1, antenna channel n = 2 from the combination of TX1 and RX2, antenna channel n = 3 from the combination of TX2 and RX1, and antenna channel n = 4 from the combination of TX2 and RX2. This antenna array has an equidistant arrangement of the antenna channels with a grid spacing of d∙λ; it corresponds to an antenna array formed from one transmitting and four receiving antennas spaced d∙λ apart, provided the case of different beam directions for transmitting and receiving is disregarded. For determining the angle of targets, digital beamforming is typically performed, often by a discrete Fourier transform (DFT) in the form of an FFT (Fast Fourier Transform). From a signal-theoretical perspective, considering a maximum likelihood estimator, digital beamforming is based on the assumption thatthat there is only one point target in its input data. In principle, digital beamforming can still provide approximately correct results (especially if a suitable window function is used) even if there are multiple point targets with sufficient angular separation (i.e., if they are several digital beamwidths apart). However, if point targets are close together (e.g., at most one digital beamwidth), digital beamforming is no longer able to separate them or correctly determine their two angles – since the model underlying digital beamforming is a single target. Therefore, to separate two targets with a small distance and unknown angles (see Fig. 2), a signal model for two targets with the physical angles α1 and α2 is required.which is to be established for the corresponding electrical angles (often also referred to as phase angles) φ1 = 2π∙sin(α1) and φ2 = 2π∙sin(α2) (1); the measured values ​​expected by the model around,n of the four antenna channels n = 1,…,4 are then:, with the model matrix (often also called the control matrix) A = [a1 a2] with a1 = [1 exp(j∙d∙φ1) exp(j∙2d∙φ1) exp(j∙3d∙φ1)] T a2 = [1 exp(j∙d∙φ2) exp(j∙2d∙φ2) exp(j∙3d∙φ2)] T , (2b) where “exp” represents the exponential function, and with the two complex amplitudes c = [c1 c2] T , (2c) where the superscript “ T “which means transposition. For angle estimation, those electric angles φ1 and φ2 and those complex amplitudes c = [c1 c2] should now be used. T to determine which values ​​best match the four measured values ​​u = [u1 u2 u3 u4] T(3a) fits in the sense of least squares (which is equivalent to the maximum likelihood approach, i.e., yields the most probable solution). It is known from the literature (see, e.g., pages 1209-1210 in "Handbook for Digital Signal Processing" by SK Mitra and JF Kaiser from 1993) that this is possible for the two complex amplitudes c = [c1 c2] T a closed-form solution exists, since these appear linearly in the system of equations to be solved; the error E between measurement and the model (2) can then be expressed as follows: E = u H ∙{I4 - PA}∙u (3b) with the so-called projection matrix PA = A∙(A H ∙A) -1 ∙A H , (3c) 202404901 8 where the superscript “ H “The conjugated complex and transposed matrix means the superscript “ -1“The inverse and I4 the identity matrix of dimension 4x4. To determine the two angles φ1 and φ2, the error E must be minimized; that is, the combination of the two angles must be found for which relation (3) has its absolute minimum. Since relation (3) cannot be solved by closed-form analysis, a search procedure must be applied – in the simplest case by calculating the error E over all angle combinations φ1 and φ2 in order to then determine the absolute minimum. The computational effort required for this is high, especially because it takes place in two-dimensional space (φ1, φ2).To reduce the required computational effort, it is advantageous to calculate the projection matrix PA or values ​​derived from it a priori for a sufficiently dense network of angle combinations φ1 and φ2 and to store them as a constant field in a computer program (see also DE 102012105582 A1). A disadvantage of this approach is the high memory requirement, as these values ​​must be stored over two-dimensional space (φ1, φ2). The predetermined values ​​are then used many times during repeated application of the model-based angle calculation. An approach according to the invention will now be presented, which reduces the required computational and memory effort. For this purpose, the two electric angles φ1 and φ2 are expressed in terms of the central angle φc and their distance Δφ to the central angle: φ1 = φc + Δφ and φ2 = φc - Δφ (4a) with φc = (φ1 + φ2) / 2 and Δφ = (φ1 - φ2) / 2 .(4b) Using these two angles φc and Δφ, the model (i.e., by substituting (4a) into (2) and using the fact that the two elements of each row n of the model matrix A then have the same factor exp(j∙(n-1)∙d∙φc)): um = T∙Ã∙c (5a) with à = [ã1 ã2] with ã1 = [1 exp(j∙d∙Δφ) exp(j∙2d∙Δφ) exp(j∙3d∙Δφ)]. T 202404901 9 ã2 = [1 exp(-j∙d∙Δφ) exp(-j∙2d∙Δφ) exp(-j∙3d∙Δφ)] T , (5b) and T = [t1 t2 t3 t4] with t1 = [1 0 0 0] t2 = [0 exp(j∙d∙φc) 0 0] T t3 = [0 0 exp(j∙2d∙φc) 0] T t4 = [0 0 0 exp(j∙3d∙φc)] T ; (5c) This results in a separation of the two angles used, φc and Δφ, in the model; the modified model matrix à depends only on the midpoint angle Δφ, and the matrix T depends only on the midpoint angle φc. This separated model A = T∙à is now inserted into relation (3) of the model error E, where the relationship A H = (T∙Ã) H = à H ∙T Hused is: E = u H ∙{I4 - TÃ∙(à H T H ∙TÃ) -1 ∙à H T H}∙u ; with I4 = T∙I4∙T H and I4 = T H ∙T results in: E = u H T∙{I4 - Ã∙(à H ∙æ) -1 à H}∙T H u , which can be represented analogously to the original form (3): E = ũ H ∙{I4 - PÃ}∙ũ (6a) with the projection matrix Pà = Ã∙(Ã) relating to the modified model matrix à H ∙æ) -1 ∙à H (6b) and the modified measured values ​​ũ = T H u . (6c) The matrix T H , that is, the transpose of the complex conjugate matrix to T according to denotation (5c), represents a diagonal matrix with the principal axis elements exp(-j∙(n-1)∙d∙φc), n = 1,…,4, ; thus, the product T HThe original measured values ​​are rotated by the angle φc, thus generating the modified measured values ​​ũ – the measured values ​​are therefore controlled to the central angle φc, which corresponds at least approximately to a rotation of the sensor by the angle φc. The resulting relationship (6) with the modified model matrix à according to (5b) for the model error E is also intuitively plausible: if the sensor points towards the midpoint between the two targets, then the model is symmetrical, with the two model angles having half an angular distance Δφ with opposite signs. Thus, the pivoting, i.e., steering the measured values ​​to the midpoint of the angle φc, results in a projection matrix Pà which depends only on one angle Δφ (see Ref. (6b) and (5b)), whereas the original projection matrix PA depended on the two angles φ1 and φ2 (see Ref. (3c) and (2b)).This reduction by one dimension leads to a drastic reduction in the required storage space when determining the projection matrix or values ​​derived from it a priori. For controlling the measured values, i.e., ũ = T. H ∙u = tv○u , (7a) where “○” means element-wise multiplication, the control vectors tv = [1 exp(-j∙d∙φc) exp(-j∙2d∙φc) exp(-j∙3d∙φc)] T(7b) is required. These can be determined a priori for a sufficiently dense grid of the central angle φc and stored in memory; this also requires only a comparatively small amount of memory (since it is also only over one dimension φc). Even less memory is required if the rotation factors exp(-j∙x) are stored for a sufficiently dense grid over x = 0,…,2π in order to extract the required elements of the control vector tv from them. In contrast to the required memory, the calculation of the model error according to Eq. (6) does not lead to a reduction in the required computational effort; to determine the unknown angles φ1 and φ2, a matrix relationship must still be calculated over a two-dimensional space (φc, Δφ); strictly speaking, even slightly more computational effort is required because the rotation of the measured values ​​must also be carried out – but only in one dimension φc. In the following, it will be shown how the required computational effort can also be reduced.Starting from reference (6), the matrix difference B = {I4-PÃ} is used and the two multiplications with the swung measured values ​​ũ and their transposed conjugate complex ũ are performed. H are summarized as: E = sum(B○ṽ) , (8a) where “sum” means the sum over all elements, with B = {I4-PÃ} (8b) 202404901 11 and with the covariance ṽ representing a matrix of the modified measured values ​​ũ: ṽ = ũ*∙ũ T , (8c) where “*” represents the complex conjugate. With ũ = T H ∙u according to designation (6c), T H = T* (since T is a diagonal matrix), ũ* = T∙u* and ũ T = (T H ∙u) T = u T ∙T* results in ṽ = T∙{u*u T}∙T* = C○v (9a) with the matrix C = [c1 c2 c3 c4] resulting from the diagonal matrix T according to (5c), composed of rotation factors, with c1 = [1 exp(-j∙d∙φc) exp(-j∙2d∙φc) exp(-j∙3d∙φc)] T c2 = [exp(j∙d∙φc) 1 exp(-j∙d∙φc) exp(-j∙2d∙φc)] T c3 = [exp(j∙2d∙φc) exp(j∙d∙φc) 1 exp(-j∙d∙φc)]T c4 = [exp(j∙3d∙φc) exp(j∙2d∙φc) exp(-j∙d∙φc) 1] T ; (9b) and the covariance v of the original measured values ​​u: v = u*∙u T (9c) By reference (9a), the model error E according to reference (8a) is: E = sum(B○C○v). (10) Since the modified projection matrix Pà refers to a model for two targets with symmetric angles ±Δφ, it is real-valued and symmetric about the main diagonal, which also holds true for the matrix B = {I4-PÃ}. The matrix C and the covariance v are Hermitian (i.e., C H = C and v H= v). Using these relationships, the model error can be represented as follows: E = (b11v11 + b22v22 + b33v33 + b44v44) + real(2b12v12∙exp(-j∙d∙φc) + 2b23v23∙exp(-j∙d∙φc) + 2b34v34∙exp(-j∙d∙φc)) + real(2b13v13∙exp(-j∙2d∙φc) + 2b24v24∙exp(-j∙2d∙φc)) + real(2b14v14∙exp(-j∙3d∙φc)) , (11) where “real” represents the real part and bij and vij are the elements of matrices B and v are. In this representation, the same rotation factor exp(j∙(n-1)∙d∙φc) is contained in the elements of each row, so that it can be extracted; this then results in the scalar product of two vectors (symbolized by the sign “•”): 202404901 12 E = real(f•tv) (12a) with f = [f1 f2 f3 f4] T with f1 = b11v11 + b22v22 + b33v33 + b44v44 f2 = 2b12v12 + 2b23v23 + 2b34v34 f3 = 2b13v13 + 2b24v24 f4 = 2b14v14 (12b) and the control vector tv according to Ref. (7b): tv = [1 exp(-j∙d∙φc) exp(-j∙2d∙φc) exp(-j∙3d∙φc)] T(12c) The complex multiplication of the four products of the scalar product need not be fully executed, since only the real part is required. Therefore, it suffices to multiply the real part of one factor by the imaginary part of the other, and vice versa. To determine the unknown angles φ1 and φ2 in two-dimensional space (φc, Δφ), it is no longer necessary to calculate a matrix relation (as was required in Eq. (6)), but only the scalar product according to Eq. (12). For N antenna channels, a matrix relation entails a computational effort on the order of O(N). 2), while a scalar product only requires computational effort of O(N) – thus resulting in a reduction of computational effort by one dimension N. Since, in contrast to the simple example N = 4 used here, the number of channels N is significantly higher in radar sensors used today and in the future (in the range of 16 to >100), equation (12) results in a drastic reduction of the required computational effort. It should also be noted that the calculation of the vector f according to equation (12b) also requires a computational effort of dimension O(N). 2) but only needs to be performed in one-dimensional space (Δφ), and then the calculated vector f is applied to the many φc, so that the overall effort required is low and the above statement regarding the drastic reduction in computational effort, especially for large channel numbers N, remains valid. A further reduction in effort can be achieved for the calculation of the vector f and the storage of the real-valued coefficients 2bij if it is exploited that for an equidistant arrangement of the antenna channels, the matrix B is symmetric not only about the main diagonal but also about the off-diagonal (which is why 2b31 = 2b42 and 2b21 = 2b43). The calculation of the error E according to equation (12) is typically performed for an equidistant set of central angles φc. Then, the so-called chirped Z-transform can be used for parallelization and effort reduction.This reduction in computational effort according to the invention presupposes that the antenna channels are equidistant. With an arbitrary spacing of the antenna channels, the rotation factors exp(-j∙xji∙φc) within each line of reference (11) would not have had a constant factor xji = (n-1)∙d, but rather xji would have been the difference between the two antenna channels j and i that correspond to the indices in the factor 2bijvij before the rotation factor exp(-j∙xji∙φc) – i.e., in the example 2b13v13∙exp(-j∙x31∙φc), the distance from antenna channel 3 to antenna channel 1; thus, the separation into a scalar product according to reference (12) and the resulting drastic reduction in computational effort would not be possible. But the great advantage of Bez can also be applied to non-equidistant arrays.(12) can be used at least partially: - If the spacing of the antenna channels deviates only slightly from an equidistant arrangement, an equidistant arrangement can often be assumed for simplification, so that equation (12) can still be used. - Often, thinned antenna arrays are used, i.e., the individual antenna channels lie on an equidistant grid, but not all grid points are occupied. In equation (12), this leads to the control vector, and thus also the vector f, having more elements, i.e., the number of elements is greater than the number N of antenna channels. However, only a scalar product needs to be calculated instead of a matrix relation.- If the spacing of the antenna channels lies on an at least approximately equidistant grid only for subgroups, several different rotation factors may occur in the representation (11) of the error E per line, but in general they each occur multiple times (possibly also in different lines), so that they can also be extracted from several summands; this again results in a representation as a scalar product, where the length of the vectors used is above the number of channels N, but significantly below their square N. 2, resulting in a further significant reduction in the required computational effort. 202404901 14 Up to now, the two unknown electric angles φ1 and φ2 have been expressed in terms of the central angle φc and their distance Δφ from the central angle (see Ref. (4)). Alternatively, they can also be expressed in terms of one of the two angles and the distance of the other to it, e.g. φ1 = φt and φ2 = φt + φo (13a) with φt = φ1 and φo = φ2 - φ1 . (13b) With this decomposition of the angles φ1 and φ2, the properties and advantages derived above according to the invention also result, since, firstly, analogous to reference (5), a separation in the signal model also results (into a part dependent only on φt, which corresponds to a beam swivel by the angle φt, and another part dependent only on φo), and secondly, analogous to reference (11), a constant rotation factor exp(-j∙(n-1)∙d∙φt) can be extracted for the error E per line, which leads to a scalar product analogous to reference (11).(12) leads. The approach according to the invention can also be generalized: firstly, for situations and models where there are more than two different physical beam directions αk with electric angles φk with k = 1,…,K for the relevant transmitting beams and / or receiving beams, where these beam directions can be dependent on each other, and secondly, to arbitrary decompositions of the form φk = φt + gk,1∙φo,1 +…+ gk,L∙φo,L with k = 1,…,K , (14) where L ≤ (K-1) – an example in which dependencies of the angles result in L < (K-1) will be shown later. The decomposition (14) is characterized by the fact that it has an equal component φt for all angles φk, which corresponds to a beam steering, thereby generating the advantages for storage and computational effort shown above. The angle φt can correspond to one of the angles φk, but other decompositions are also possible. Now, let us consider some further examples.Figure 3 shows the example of a target at a distance sz from a guardrail, off which the rays are reflected. The transmitting and receiving rays then lie at the angles α1 and α2 shown, with so-called cross paths also occurring, i.e., transmitting at angle α1 and receiving at angle α2, and vice versa; for reasons of symmetry, the two cross paths have the same complex amplitude c3 and lead to an additional column a3 in the model matrix, so that instead of reference (2), the model now reads as follows: with the model matrix A = [a1 a2 a3] with a1 = [1 exp(j∙d∙φ1) exp(j∙2d∙φ1) exp(j∙3d∙φ1)] T a2 = [1 exp(j∙d∙φ2) exp(j∙2d∙φ2) exp(j∙3d∙φ2)] T a3 = [2 (exp(j∙d∙φ1) + exp(j∙d∙φ2)) (exp(j∙2d∙φ2) + exp(j∙2d∙φ1)) (exp(j∙d∙φ1+j∙2d∙φ2) + exp(j∙d∙φ2+j∙2d∙φ1))] T , (15b) and the three complex amplitudes c = [c1 c2 c3] T(15c) Column a3 also contains the factor exp(j∙(n-1)∙d∙φc) in the n-th element when angle decomposed according to (4), so that the separation of the model matrix A according to (5) remains valid: into the modified model matrix Ã, which depends only on the center-spacing angle Δφ, and the diagonal matrix T, which depends only on the center-spacing angle φc (in Fig. 3, the corresponding physical angles Δα and αc are shown, which, due to their small absolute values, are proportional to the electrical angles according to (1) – it should be noted that, for illustrative reasons, Fig. 3 shows the angles significantly larger than they actually are in the case of fusion during digital beamforming considered here). The diagonal matrix T implements a pivoting of the measured values ​​by the angle φc; As can easily be seen from geometric reasons, the measured values ​​are at least approximately swiveled to the point of the guardrail at distance r.If the distance ss of the guardrail to the sensor is known (especially if the position of the guardrail is determined from the radar image itself), then the rotation angle αc can be calculated directly from the distance ss and the measured target distance r: αc = arctan(ss / r) ; (16a) It should be noted that, due to the small target angle, the actually measured radial distance and the longitudinal distance r shown in Fig. 3 are approximately identical. For the electrical angle φc, using reference (1) and sin(φ) = φ for small phase angles φ: φc = 2π∙arctan(ss / r) , (16b) where the arctan function here gives the phase angle (whereas above it gives the physical angle).To determine the minimum error E and thus the target angle, only a search in one-dimensional space (Δφ) is now necessary; since Δφ corresponds to the distance sz of the target from the guardrail (at least approximately linearly), the search can also be considered to take place in one-dimensional space (sz). Fig. 4 shows a target at height hz above a road surface; for radar waves, the road surface represents an approximately ideal reflector (because its roughness is far below the radar wavelength). This results in identical conditions to those in the guardrail scenario according to Fig. 3, except that elevation angles are now used instead of azimuth angles. All results remain valid; the swivel angle φc is now calculated from the sensor's installation height hs and the target distance r: φc = 2π∙arctan(hs / r) .(17) By applying this rotation angle φc, the measured values ​​are swiveled, at least approximately, to the point on the road surface at the target distance r. To determine the target height hz, a search in one-dimensional space (Δφ) is necessary; since Δφ corresponds to the target height hz (at least approximately linearly), the search can also be seen as taking place in one-dimensional space (hz). Finally, the example according to Fig. 5 is considered with two targets at the same distance r with different heights hz1 and hz2 above a road surface. The beam swiveling of the measured values ​​by the angle φc is again performed on the road surface at the target distance (i.e., φc according to reference (17)). The four different beam directions φ1,1, φ1,2, φ2,1 and φ2,2 can be described in addition to φc with the two center-spacing angles Δφ1 and Δφ2: φ1,1 = φc + Δφ1 , φ1,2 = φc - Δφ1 , φ2,1 = φc + Δφ2 and φ2,2 = φc - Δφ2 .(18) The K = 4 different beam directions can thus be described by the rotation angle and L = 2 further angles; this is therefore an example of a decomposition according to 202404901 17 Ref. (14) with L < (K-1). To determine the two unknown target heights hz1 and hz2, a search in two-dimensional space (Δφ1, Δφ2) is necessary. It should also be noted that determining the two target heights with the originally considered antenna arrangement with 4 channels would not be possible, since there are now 6 unknown complex amplitudes and two unknown real-valued angles Δφ1 and Δφ2, which would lead to an underdetermined system of equations with only four complex measurements. Therefore, at least seven antenna channels are required. For the scenario of a stationary vehicle under a bridge, the height of the vehicle reflection can be considered negligible compared to the height of the bridge reflection, i.e.One of the two heights can be set to zero, so that the search is again only in one-dimensional space. So far, the determination of the unknown angles has been considered in the measurement domain, i.e., in the antenna channel domain. However, the calculation can also be shifted to the beamforming domain. In this case, the discrete Fourier transform (DFT) of the swept measurement values ​​ũ according to Equation (7) and a projection matrix resulting from a column-wise DFT of the modified model à according to Equation (5b) are used; however, not all frequency reference points of the DFT need to be used, but in the example of a beam swept around the center angle φc, only a few frequency reference points around 0 suffice; the number M of frequency reference points used is significantly less than the number of channels N, especially for large antenna arrays, resulting in reduced computational effort. However, a scalar product decomposition analogous to Equation (5b) is also possible.(12) is not possible in the beamforming range. To combine the advantages of a scalar product decomposition and a reduced size M of the vectors used compared to the number of channels N, the following procedure can be performed: First, digital beamforming is carried out, then the spectrum in the target region is extracted and transformed back into the measurement range using an inverse Fourier transform of reduced length; this can also be seen as filtering and sampling rate reduction in the measurement range. All formulas and approaches derived above can be applied to the alternative measurements thus obtained; because of the nature of the discrete Fourier transform, these measurements refer to an equidistant channel grid, so that the scalar product decomposition according to (12) is possible and valid.So far, we have considered a one-dimensional antenna array extending either horizontally for azimuth determination or vertically for elevation determination. For simultaneous azimuth and elevation measurements, two-dimensional antenna arrays are used. The methods described above can be easily extended to the two-dimensional domain; in particular, beam steering then takes place in two dimensions, i.e., the array is steered by an azimuth angle and an elevation angle. With a two-dimensional antenna array, digital beam shaping can also be performed in one direction, and the resulting values ​​can then be used to apply one of the methods derived above for the other direction.

Claims

202404901 19 Claims 1. A method for a radar system for environmental sensing with multiple individual antennas for transmitting and / or receiving radar signals, characterized in that: - a model-based angle calculation is performed, assuming that there are several different physical beam directions αk with k = 1,…,K for the relevant transmitting and / or receiving beams, wherein these beam directions can be dependent on each other; - wherein, instead of the physical beam directions αk, the corresponding electrical beam directions φk can also be used, which can be formed in particular by the relationships φk = 2π∙sin(αk), and therefore, in the following, the beam directions are generically designated by δ, which can mean both physical and electrical beam directions; - instead of a parameter set defined in multidimensional space (δ1,…,δK),a parameter set defined in a one-dimensional space (δt) and a parameter set defined in a space of at most (K-1)-dimensional space (δo,1,…,δo,L) are used, wherein the angles δt and δo,1,…,δo,L are formed from the angles δ1,…,δK by the decomposition δk = δt+gk,1∙δo,1+…+ gk,L∙δo,L with k = 1,…,K, - and this separation is preferably used to reduce the effort required to calculate the model-based angle formation and / or to store a priori calculated parameter sets.

2. The method of claim 1, wherein the parameter set defined in space (δt) effectively serves to emulate a beam swivel of the measured values ​​or values ​​derived from them by the angle δt, which can be interpreted at least approximately as an emulation of a sensor rotated by the angle δt.

3. The method of any one of the above claims, characterized in that the parameter set defined in L-dimensional space (δo,1,…,δo,L) defined parameter set is either a projection matrix of a procedure for minimizing the squared error between a model and a measurement, or consists of parts of such a projection, 202404901 20 matrix or is formed from values ​​derived from such a projection matrix, wherein this parameter set with reduced dimension L < K is preferably calculated a priori and is used repeatedly for a repeated application of the model-based method.

4. Method according to one of the preceding claims, wherein the decomposition δk = δt+gk,1∙δo,1+…+gk,L∙δo,L with k = 1,…,K is formed such that one of the angles δt corresponds to one of the angles δk and the other angles δo,l with l = 1,…,L are the difference of the other angles δk to the angle δt.

5. A method according to any one of claims 1-3, wherein there are K = 2 beam directions and the decomposition δk = δt+gk,1∙δo,1 is formed from the angles δ1 and δ2 such that the angle δt is their central angle δt = (δ1+δ2) / 2 and the angle δo,1 is their distance δo,1 = δo = (δ1-δ2) / 2 to this central angle. 6.The method of claim 5, wherein the model represents a target located at height h above a road surface with the mirror rays resulting from the reflective properties of the road surface, such that the parameter set defined in space (δt) leads to a beam swiveling of the measured values ​​onto the road surface at a distance r of the target, wherein the angle δt can be calculated from the installation height of the sensor and the distance r, and the parameter set defined in space (δo) refers to the height h to be determined by the model-based approach. 7.A method according to claim 5, characterized in that the model represents a target located next to a reflective surface with the resulting mirror rays, such that the parameter set defined in space (δt) leads to a beam steering of the measured values ​​onto the reflective surface at a distance r of the target, and the parameter set defined in space (δo) relates to the distance of the target from the reflective surface.

8. A method according to claim 5, characterized in that the model relates to two targets with unknown angles δ1 and δ2, such that the parameter set defined in space (δt). 202404901 21 The parameter set defined in claim 21 effectively serves to emulate a beam swivel of the measured values ​​by the angle δt to the midpoint between the two targets.

9. Method according to one of claims 1-3, wherein the model represents two targets located at heights h1 and h2 above a road surface and at the same distance r with the mirror rays resulting from the reflective property of the road surface, characterized in that the parameter set defined in space (δt) realizes a beam swivel of the measured values ​​onto the road surface at the distance r of the targets, wherein the angle δt can be calculated from the installation height of the sensor and the distance r, and the parameter set defined in space (δo,1, δo,2) refers to the heights h1 and h2 to be determined by the model-based approach. 10.A method according to claim 9, wherein one of the two heights can be assumed to be negligibly small, such that the parameter set defined in space (δo,1, δo,2) is reduced to a parameter set defined in one-dimensional space (δo).

11. A method according to any of the above claims, wherein all elements or subgroups of the antenna array formed by transmitting and / or receiving antennas represent at least approximately a subset of an equidistant grid, and a method for minimizing the squared error is used, characterized in that for each angle combination in space (δo,1,…,δo,L), an intermediate result from the projection matrix and measured values ​​or values ​​derived therefrom only needs to be calculated once, and then this intermediate result, representing a vector, is multiplied by beam steering vectors or vectors with rotation factors for different angles δt, thereby achieving a significant reduction in computational effort.

12. Method according to one of the above claims, characterized in that the model-based method does not refer to the measured values ​​obtained directly from the antenna channels, but to measured values ​​derived therefrom, which result in particular after performing digital beamforming or after filtering, optionally in combination with a sampling rate reduction. 202404901 22 for which one or more discrete Fourier transforms can be used.

13. Method according to one of the preceding claims, characterized in that, in the presence of reflective surfaces, the model also includes the so-called cross paths, i.e., transmitting at one angle δk1 and receiving at another angle δk2 and vice versa.

14. Method according to one of the preceding claims, which is applied in two dimensions, wherein, in particular, beam steering is performed in the two-dimensional domain and the antenna array formed by the transmitting and / or receiving antennas extends over two dimensions, in particular in the horizontal and vertical directions.

15. Radar system for environmental sensing with several individual antennas for transmitting and / or receiving radar signals, characterized in that a model-based angle formation is performed, wherein it is assumed thatthat for the relevant transmitting and / or receiving beams there are several different physical beam directions αk with k = 1,…,K, where these beam directions can be interdependent, - where instead of the physical beam directions αk the corresponding electrical beam directions φk can also be used, which can be formed in particular by the relationships φk = 2π∙sin(αk), and therefore the beam directions are generically denoted by δ in the following, which can mean both physical and electrical beam directions, - instead of a parameter set defined in multidimensional space (δ1,…,δK), a parameter set defined in one-dimensional space (δt) and a parameter set defined in at most (K-1)-dimensional space (δo,1,…,δo,L) are used, where the angles δt and δo,1,…,δo,L from the angles δ1,…,δK by the decomposition δk = δt+gk,1∙δo,1+…+ gk,L∙δo,L with k = 1,…,K ge- formed are 202404901 23 - and this separation is preferably used to reduce the effort required to calculate model-based angle formation and / or to store a priori calculated parameter sets.

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