METHOD FOR RADAR ANGLE ESTIMATION

Abstract

A method for angle estimation based on signals of a radar sensor with angular resolution in at least one dimension. The radar sensor includes a MIMO-enabled antenna array with at least three transmitting antennas and at least three receiving antennas. A cross-path model represented by a control matrix and models reflections of transmitted and/or received signals on a reflective surface is used to estimate a location angle of a radar target. The control matrix includes a Kronecker product A.sub.tx .Math.A.sub.rx of two submatrices, one, A.sub.tx, representing the arrangement of the transmitting antennas and the other, A.sub.rx, representing the arrangement of the receiving antennas. For calculating a DML estimation function, a matrix product Y=A.sup.H.sub.rx.Math.X.Math.A*.sub.tx is calculated approximately using an FFT from the submatrices and a reception matrix X that specifies the complex amplitudes of the signals received with different combinations of antennas.

Claims

1. A method for angle estimation based on signals, transmitted and received after reflection on an object, of a radar sensor with angular resolution in at least one dimension, the radar sensor including a MIMO-enabled antenna array with at least three transmitting antennas and at least three receiving antennas, the method comprising: estimating a location angle of a radar target using a cross-path model, in doing so, a necessary transmit-side and receive-side beamforming operation is approximately calculated using a fast Fourier transform.

2. The method according to claim 1, in which the cross-path model is represented by a control matrix A, the control matrix being broken down into a Kronecker product A.sub.tx .Math.A.sub.rx of two submatrices, a first one, A.sub.tx, of the two submatrices representing an arrangement of the transmitting antennas and the other one, A.sub.rx, of the two submatrices representing an arrangement of the receiving antennas, and the beamforming operation includes an approximate calculation of a matrix product Y=A.sup.H.sub.rx.Math.X.Math.A*.sup.tx from the submatrices and a reception matrix X that specifies complex amplitudes of signals received with different combinations of the transmitting and receiving antennas.

3. The method according to claim 1, wherein gaps in a grid of the transmitting and receiving antennas are filled in using zero insertion.

4. The method according to claim 1, in which a grid of the transmitting and receiving antennas is refined using zero padding, and the fast Fourier transform takes place on the refined grid.

5. The method according to claim 2, wherein a fine search based on a precise beamforming operation takes place after an angle estimation based on the approximately calculated beamforming operation.

6. A radar sensor, comprising: a transmitting and receiving device; and a digital evaluation device, wherein the digital evaluation devices is configured for angle estimation based on signals, transmitted and received after reflection on an object, of a radar sensor with angular resolution in at least one dimension, the radar sensor including a MIMO-enabled antenna array with at least three transmitting antennas and at least three receiving antennas, the digital evaluation device configured to: estimate a location angle of a radar target using a cross-path model, in doing so, a necessary transmit-side and receive-side beamforming operation is approximately calculated using a fast Fourier transform.

7. The radar sensor according to claim 6, wherein the radar sensor further comprises an internal evaluation stage and an external hardware accelerator in which at least portions of the estimation are implemented.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0016] FIG. 1 shows a schematic representation of the analog portion of a radar system, according to an example embodiment of the present invention.

[0017] FIG. 2 shows a diagram of an antenna array of the radar system, according to an example embodiment of the present invention.

[0018] FIG. 3 shows a diagram illustrating a scenario with multipath propagation, according to an example embodiment of the present invention.

[0019] FIG. 4 shows a block diagram for a method according to an example embodiment of the present invention.

[0020] FIG. 5 shows a flow chart for a method according to an example embodiment of the present invention.

DETAILED DESCRIPTION OF EXAMPLE EMBODIMENTS

[0021] An exemplary embodiment of a radar system with which the method according to the present invention is performed is explained with reference to FIGS. 1 and 2.

[0022] FIG. 1 shows, in a schematic and simplified manner, the structure of the analog portion of a radar sensor 8.

[0023] A frequency modulation device 10 controls an HF oscillator 12, which generates sequences of signals in the form of frequency ramps for multiple transmitting antennas 14. In each of the multiple transmission channels, an amplifier 16 is arranged, which either blocks the signals or forwards them, amplified, to the associated antenna. The oscillator 12 and the amplifiers 16 are controlled by a multiplexing device 18, for example according to a time and frequency multiplexing scheme, such that each of the transmitting antennas 14 transmits a frequency-modulated signal in a particular frequency subband within particular time slots.

[0024] The transmitted signal reflected on an object 24 is received by multiple receiving antennas 26 and, in each reception channel, is mixed by a mixer 28 with a portion of the signal of the HF oscillator 12 and brought into a low-frequency range. An A/D conversion then takes place in the usual manner by an A/D converter 30. The digitized signals are then further processed in a digital evaluation stage 32.

[0025] As FIG. 2 shows, the transmitting antennas 14 form a transmit array 34, and the receiving antennas 26 form a receive array 36. In the example shown, both arrays are two-dimensional so that MIMO angle measurements are possible in both azimuth and elevation.

[0026] In the receive array 36, the receiving antennas 26 are arranged at regular intervals in an angular resolution direction y, e.g., in the direction of the azimuth. The distances between the individual receiving antennas are so large that, even with a few antennas, a large aperture and a correspondingly high angular resolution is achieved. However, the distances from antenna to antenna are greater than half the wavelength of the radar radiation so that the Nyquist theorem is not fulfilled.

[0027] In the example shown here, the receiving antennas 26 are also arranged at regular intervals in elevation (in the angular resolution direction z), and the antenna distances in this direction are also so large that ambiguous subsampling takes place.

[0028] In this example, the transmitting antennas 14 of the transmit array 42 are only arranged at regular intervals in elevation, while the grid of the antennas has gaps in azimuth. The grid is so narrow in both dimensions that an unambiguous angle measurement is possible. In exchange, however, the aperture is smaller than in the receive array 44 so that the angular resolution is lower. Specifically, in this example, all antennas of the transmit array and of the receive array in both dimensions are arranged in a uniform grid with the grid dimension Dd, even if they do not completely fill this grid. In the receive array 36, only every second grid point is occupied.

[0029] The number of transmitting antennas 14 in each dimension matches the number of receiving antennas in the same dimension.

[0030] In the evaluation stage 32, a two-dimensional spectrum in the dimensions distance and relative velocity is first calculated in a conventional manner by means of a Fourier transform. This spectrum can then be used to identify individual objects and to determine their distances and relative velocities. In the case of a single target scenario, i.e., if there is only a single object in each distance/velocity cell, the MIMO model, which is briefly outlined below, can be used for the angle estimation in azimuth and elevation for each object. For simplicity, only the angle estimation in azimuth is considered, in which only the first row of the transmitting antennas 14 in the transmit array 34 and only the first row of the receiving antennas 26 in the receive array 36 have to be used.

[0031] X.sub.n denotes the three-component vector, the components of which (X.sub.n,1, X.sub.n,2, X.sub.n,3) specify the complex amplitudes of the signals that are transmitted by the nth transmitting antenna 14 and received by the three receiving antennas 26. If d is the distance from antenna element to antenna element, is the wavelength of the radar radiation, and s=X.sub.n,1 is the complex amplitude of the signal that is received by the first receiving antenna (for example, the receiving antenna to the farthest right of FIG. 2), the following relationship applies due to the run length differences between the signals that reach the different receiving antennas 14:

[00001]$x_n\left(\right)={s\left(1,e^{-2i\left(d/\right)\sin \left(\right)},e^{-2i\left(2d/\right)\sin \left(\right)}\right)}^T=s{\underset{\_}{a}}_{\mathrm{rx}}\left(\right)$

[0032] The superscript symbol T is to denote the transposition since vectors are written here as row vectors but are to be considered column vectors. The vector a.sub.rx is referred to as the receive control vector. This control vector specifies the geometric properties and wave propagation properties of the receive array.

[0033] Accordingly, for the transmit array 34, a control vector a.sub.rx can also be defined, which specifies the run length differences of the optical paths from the transmitting antennas to the object 24.

[0034] For the entire MIMO antenna array, the following control vector is obtained:

[00002]$\underset{}{a}\left(\right)={\underset{}{a}}_{tx}\left(\right).Math.{\underset{}{a}}_{rx}\left(\right)$

[0035] The symbol .Math. here means the Kronecker product.

[0036] The received signals form a vector x with N.sub.tx.Math.N.sub.rx components (9 components in this example since, in the direction y, the number N.sub.tx of the transmitting antennas is 3 and the number N.sub.rx of the receiving antennas is also 3), and the following applies:

[00003]$\underset{}{x}\left(\right)=s\underset{}{a}\left(\right)$

[0037] Knowing the control vector a() makes it possible to establish a relationship (which is unambiguous under suitable conditions) between the angle q of the object and the received signals x and to deduce the azimuth angle of the object from the amplitude and phase relationships of the received signals. However, since the receiving signals are more or less noisy in practice, the azimuth angle cannot be calculated exactly but can only be estimated, for example by means of a deterministic maximum likelihood estimation (DML).

[0038] If this principle is generalized to multitarget estimations, the single angle becomes a vector whose components specify the angles of the different targets, the control vector a becomes a control matrix A, the vector x becomes a reception matrix X (with a respective column for each target), and the following relationship applies:

[00004]$\begin{array}{cc}X=A\underset{}{}& \left(1\right)\end{array}$

[0039] Thus, in the case of two targets with the location angles .sub.1 and .sub.2:

[00005]$\begin{array}{cc}X=\left[{\underset{}{a}}_{\mathrm{tx}}\left({}_1\right).Math.{\underset{}{a}}_{\mathrm{cx}}\left({}_1\right){\underset{}{a}}_{\mathrm{tx}}\left({}_2\right).Math.{\underset{}{a}}_{\mathrm{rx}}\left({}_2\right)\right]& \left(2\right)\end{array}$

[0040] FIG. 3 outlines a scenario characterized by multipath propagation. The signal transmitted by the radar sensor 8 can propagate to the object 24 not only on a direct path 38 but also on an indirect path 40, which first leads to a reflective surface 42, e.g., a guard rail, and is then deflected to the object 24. Likewise, the signal reflected on the object 24 can propagate to the radar sensor 8 not only on a direct path 44 but also on an indirect path 46, on which the signal is also reflected on the surface 42 so that the radar sensor perceives a pseudo mirror object 24.

[0041] In the case of multipath propagation, the complete MIMO signal model is a cross-path model, which has the following form:

[00006]$\begin{array}{cc}X=\left[{\underset{}{a}}_{tx}\left({}_1\right).Math.{\underset{\_}{a}}_{\mathrm{rx}}\left({}_1\right){\underset{}{a}}_{tx}\left({}_2\right).Math.{\underset{}{a}}_{rx}\left({}_2\right){\underset{}{a}}_{tx}\left({}_2\right).Math.{\underset{}{a}}_{\mathrm{rx}}\left({}_1\right){\underset{}{a}}_{tx}\left({}_1\right).Math.{\underset{}{a}}_{\mathrm{rx}}\left({}_2\right)\right]& \left(3\right)\end{array}$

[0042] Although the last two terms can be combined into a single path due to the reciprocity of the cross-paths, i.e., the path combinations 38, 46 and 40, 44, the computational effort for calculating the reception matrix X is nevertheless greater than in the case of single path propagation.

[0043] In order to calculate a DML estimation function q2 (q1, q2), the control matrix A can be broken down into submatrices A.sub.tx and A.sub.rx as follows:

[00007]$\begin{array}{cc}A=A_{tx}\left({}_1,{}_2\right).Math.A_{rx}\left({}_1,{}_2\right)& \left(4\right)\end{array}$$A_{\mathrm{tx}}\left({}_1,{}_2\right)=\left[\begin{array}{cc}{A}_{tx}\left({}_1\right)& A_{tx}({}_2\end{array}\right]$$A_{\mathrm{rx}}\left({}_1,{}_2\right)=\left[\begin{array}{cc}{A}_{rx}\left({}_1\right)& X_{rx}\left({}_2\right)\end{array}\right]$

[0044] From the submatrices and the reception matrix X, a matrix product Y is then calculated.

[00008]$\begin{array}{cc}Y\left({}_1,{}_2\right)=A_{rx}^H\left({}_1,{}_2\right).Math.X.Math.A_{tx}^{}\left({}_1,{}_2\right)& \left(5\right)\end{array}$

[0045] A.sup.H.sub.rx is the Hermitian conjugate matrix to A.sub.rx, and A* .sub.tx is the complex conjugate matrix to A.sub.tx. If A.sub.tx is an N2 matrix, Y is an NN matrix, and A.sup.H.sub.rx is a 2N matrix, then Y is a 22 matrix. The four entries of this matrix Y correspond to the four combinations of transmit-side beamforming in the directions .sub.1,.sub.2 and receive-side beamforming in the directions .sub.1,.sub.2.

[0046] For the DML estimation function q.sup.2 (.sub.1, .sub.2), the following calculation rule now applies:

[00009]$\begin{array}{cc}{q}^2\left(q^1,q^2\right)=Re\left\{y^H.Math.z\right\}& \left(6\right)\end{array}$$y=\mathrm{vec}\left(Y\right)$$z=\mathrm{vec}\left(Z\right)$$Z=G_{\mathrm{rx}}^{-1}.Math.Y.Math.{\left(G_{\mathrm{tx}}^{-1}\right)}^{*}$$G_{\mathrm{rx}}^{-1}=\frac{1}{1-{.Math.a.Math.}^2}\left(\begin{array}{cc}1& -a\\ -a^{*}& 1\end{array}\right)$$G_{\mathrm{tx}}^{-1}=\frac{1}{1-{.Math.b.Math.}^2}\left(\begin{array}{cc}1& -b\\ -b^{*}& 1\end{array}\right)$$a={\underset{}{a}}_{rx}^H\left({}_1\right).Math.a_{rx}\left({}_2\right)$$b={\underset{}{b}}_{rx}^H\left({}_1\right).Math.{\underset{}{b}}_{rx}\left({}_2\right)$

[0047] vec (A) denotes the vectorization operator, which arranges the columns of an MN matrix A one above the other in an MN1 vector. The variables

[00010]$a,b,\frac{1}{1-{.Math.a.Math.}^2}\mathrm{and}\frac{1}{1-{.Math.b.Math.}^2}$

are functions of the angles .sub.1, .sub.2 and depend only on the control vectors a.sub.rx, a.sub.tx. They can therefore be calculated once and stored in flash memory before the radar sensor is put into operation.

[0048] The relatively complex calculation of the DML estimation function according to the rule (6) can be significantly simplified if the following conditions are at least approximately fulfilled: [0049] angle-independent ratios between the amplitude magnitudes of the receive signals; [0050] relative phases between antennas follow the ideal model according to the position of the antenna elements.

[0051] Under these conditions, the entries, needed for all angle combinations, of the matrix Y for an antenna array the antenna elements of which lie on a grid with the grid dimension d can be calculated by means of a FFT and zero insertion/zero padding. In doing so, the angle variable is expediently replaced by the variable u=sin (). The control vectors a.sup.H.sub.rx () and a.sup.+.sub.tx () then become vectors .sub.rx.sup.H(u) and .sub.tx*(u).

[0052] If the following is defined:

[00011]$\begin{array}{cc}{Y}_{rx}\left(u\right)={\underset{}{\stackrel{}{a}}}_{rx}^H\left(u\right).Math.X& \left(7\right)\end{array}$

the following applies to the matrix product Y in a good approximation:

[00012]$\begin{array}{cc}Y\left(u_1,u_2\right)\left[\begin{array}{c}{Y}_{rx}\left(u_1\right)\\ Y_{rx}\left(u_2\right)\end{array}\right].Math.\left[\begin{array}{cc}{\underset{\_}{\stackrel{}{a}}}_{\mathrm{tx}}^{*}\left(u_1\right)& {\underset{}{\stackrel{}{a}}}_{\mathrm{tx}}^{*}\left(u_2\right)\end{array}\right]=\left[\begin{array}{cc}{Y}_{11}& Y_{12}\\ Y_{21}& Y_{22}\end{array}\right]& \left(8\right)\end{array}$$Y_{11}=Y_{rx}\left(u_1\right).Math.{\underset{}{\stackrel{}{a}}}_{\mathrm{tx}}^{*}\left(u_1\right),Y_{12}=Y_{rx}\left(u_1\right).Math.{\underset{}{\stackrel{}{a}}}_{\mathrm{tx}}^{*}\left(u_2\right)$$Y_{21}=Y_{rx}\left(u_2\right).Math.{\underset{}{\stackrel{}{a}}}_{\mathrm{tx}}^{*}\left(u_1\right),Y_{22}=Y_{rx}\left(u_2\right).Math.{\underset{}{\stackrel{}{a}}}_{\mathrm{tx}}^{*}\left(u_2\right)$

[0053] Missing antenna elements in the grid d can be represented by inserting zeros in the reception matrix X. A sufficiently fine grid in u or in the angle , for example in order to bring the receive array 36 in FIG. 2 to the finer grid dimension d, can be achieved by means of zero padding. In this way, an equidistant 2D grid can be formed in u with N supporting points, and the vectors .sub.rx.sup.H(u) and .sub.tx*(u) can be replaced by a vector a.sub.FFT (u), the components of which have the shape e .sup.I 2n n d u, wherein the index n passes through the values n=0 to N1.

[0054] The matrix multiplication in (8) is then equivalent to a fast Fourier transform FFT. Overall, the required entries for Y can thus be approximated as follows:

[00013]$\begin{array}{cc}\stackrel{}{Y}=FF{T}_N\left({\left(FF{T}_N\left(\stackrel{}{X}\right)\right)}^T\right)& \left(9\right)\end{array}$

[0055] Here, {tilde over (Y)} is a complex N N matrix, {tilde over (X)} is the reception matrix filled in by zero insertion/zero padding, and FFTN is an operator acting row by row on a matrix and performing a Fourier transform on the discrete function defined by the matrix components in the relevant row. The two-time application of this operator in (9) thus represents a two-dimensional Fourier transform.

[0056] Due to the above two approximations, the values of the variables a and b now no longer depend on .sub.1,.sub.2 or u.sub.1, u.sub.2 but only on the difference |u.sub.1u.sub.2|. As a result, the required memory space for

[00014]$a,b,\frac{1}{1-{.Math.a.Math.}^2}\mathrm{and}\frac{1}{1-{.Math.b.Math.}^2}$

variables, only a 1D field instead of a 2D field needs to be stored. G.sub.rx.sup.1 and G.sub.tx.sup.1 likewise depend only on the difference |u.sub.1u.sub.2|.

[0057] Calculation rule (6) is thereby changed as follows:

[00015]$\begin{array}{cc}{q}^2\left(u_1,u_2\right)Re\left\{{\stackrel{}{y}}^H.Math.\stackrel{}{z}\right\}& \left(10\right)\end{array}$$\stackrel{}{Y}\left(u_1,u_2\right)=\left[\begin{array}{cc}{\stackrel{}{Y}}_{kk}& {\stackrel{}{Y}}_{kl}\\ {\stackrel{}{Y}}_{lk}& {\stackrel{}{Y}}_{ll}\end{array}\right]$$\stackrel{}{y}=\mathrm{vec}\left(\stackrel{}{Y}\left(u_1,u_2\right)\right)$$\stackrel{}{Z}=G_{rx}^{-1}\left(.Math.k-l.Math.\right).Math.\stackrel{}{Y}\left(u_1,u_2\right).Math.{\left(G_{\mathrm{tx}}^{-1}\left(.Math.k-l.Math.\right)\right)}^{*}$$\stackrel{}{z}=vec\left(\stackrel{}{Z}\right)$

[0058] Here, k and l are whole-number indices, each running from 0 to N1. If u=2/(N1) is the grid dimension in the space of the variables u, u.sub.1 and u.sub.2 can be expressed by k and l as follows:

[00016]$\begin{array}{cc}{u}_1=-1+ku{u}_2=-1+lu& \left(11\right)\end{array}$

[0059] The values of u.sub.1 and u.sub.2 then respectively run from 1 (corresponding to =90) to +1 (corresponding to =+90).

[0060] The calculation of the function q.sup.2 (u.sub.1, u.sub.2) according to (10) can be performed efficiently, whether in the evaluation stage 32 or in an external hardware accelerator.

[0061] For each index pair, the four complex values of the 2D FFT results Y (u.sub.1, u.sub.2) must be read from the memory. In addition, the two associated coefficients a,b must be read from a coefficient memory. In this case, a, b only depends on |kl|, i.e., can be kept constant for multiple index pairs if necessary. The scaling factors

[00017]$\frac{1}{1-{.Math.a.Math.}^2},\frac{1}{1-{.Math.b.Math.}^2}$

can either be read from a coefficient memory as well or calculated online. For the calculation of q.sup.2 (u.sub.1, u.sub.2) after the 2D FFT, two complex matrix multiplications (22) and the real part of a complex scalar product of length 4 are necessary. If the memory can provide the four complex values within one clock pulse and the matrix multiplication and scalar product operation are performed as a pipeline, one point of the function q.sup.2 (u.sub.1, u.sub.2) can be calculated per clock pulse.

[0062] In FIG. 4, the method sequence is shown in the form of a diagram. The method can, for example, be implemented in a hardware accelerator 48. In an FFT block 50, the matrix product Y (22 matrix) is calculated approximately according to equation (9). The result is passed to two multiplication blocks 52, 54, in which the matrix z is calculated by multiplying with the matrices G.sub.tx.sup.1 and G.sub.rx.sup.1. The precalculated coefficients a and b stored in memories 56, 58 are included here. The calculations take place sequentially for each index pair k, l.

[0063] In parallel thereto, the result of the FFT block 50 is passed to a further calculation block 60, in which the DML estimation function according to (10) is calculated by means of the matrices Y and Z. The function q.sup.2 (u.sub.1, u.sub.2) thus obtained is stored in a memory 62 in the form of a two-dimensional map. Finally, in a search block 64, the maximum of this function is sought. The coordinates u.sub.1 (=sin (.sub.1)) and u.sub.2 (=sin (.sub.2)) specify the location angles 1 and 2 of the located object 24 (FIG. 3) and of the mirror object 24.

[0064] In order to reduce the runtime, the method can be divided into a rough search and a fine search, as shown in FIG. 5. In step S1, the two-dimensional FFT with beamforming takes place. In a subsequent step S2, the DML estimation function is calculated approximately according to calculation rule (10).

[0065] For the maximum found in this manner with low resolution, a precise estimation function, which forms the basis for a fine search, is then calculated according to calculation rule (6) in step S3, limited to a smaller domain of location angles .sub.1 and .sub.2