JP5192463B2 - Signal processing device - Google Patents

Description

  The present invention relates to a signal processing apparatus that estimates the power of an incoming wave from a received signal of an antenna.

  Conventionally, it is an on-vehicle radar device that emits radar waves, receives the reflected waves, and analyzes the received signals, thereby analyzing the distance to the target (the vehicle ahead), the target and the own vehicle There are known radar devices that estimate the relative speed and target direction.

  In this type of radar apparatus, the distance to the target is estimated from the delay amount of the reflected wave with respect to the transmitted wave, and the relative speed between the target and the vehicle is estimated from the Doppler shift amount of the reflected wave with respect to the transmitted wave.

  The target direction is estimated by utilizing the fact that a phase difference corresponding to the direction of arrival is generated in the reflected wave received by each antenna element of the array antenna. As a method for estimating a target direction using an array antenna including a plurality of antenna elements, a MUSIC method and an ESPRIT method are known.

  Here, an outline of the MUSIC method will be described. It is assumed that the array antenna is a linear array antenna in which K antenna elements are arranged in parallel (see FIG. 1).

  First, a reception vector X shown in Expression (1) is formed from the reception signals of the respective antenna elements constituting the array antenna. Next, using this received vector X, an autocorrelation matrix Rxx of K rows and K columns for the received signal shown in Expression (2) is generated.

In the above equation, T represents a vector transpose and H represents a complex conjugate transpose. The element x _k (i) of the reception vector X (i) is a value at the time i of the reception signal of the k (where k = 1,..., K) -th antenna element. L is the number of samples. In this example, regarding the received signal of each antenna element, an expected value is taken using L samples, and an autocorrelation matrix Rxx is generated.

After generation of the auto-correlation matrix Rxx, the eigenvalues lambda ₁ of the autocorrelation matrix Rxx, ..., λ _{K (where, λ 1 ≧ λ 2 ≧ ...} λ K) and eigenvectors e _1, ..., calculates e _K, the thermal noise The number of incoming waves M is estimated from the number of eigenvalues larger than the threshold value λ _th corresponding to the power.

Then, the thermal noise power below (K-M) eigenvalues lambda _{M + 1,} ..., eigenvectors e _{M + 1} corresponding to the lambda _K, ..., and a noise subspace matrix E _N that was column e _K, From the complex response of the array antenna with respect to the azimuth θ, that is, the array response vector a (θ), a MUSIC spectrum expressed by the following evaluation function P _MU (θ) is obtained.

MUSIC spectrum represented by the evaluation function P _MU (θ), when the azimuth theta matches the incoming direction of the incoming wave, diverges next _{^{a H (θ) E N ≒}} 0, to stand sharp peaks, the incoming waves The azimuth θ ₁ ,..., Θ _M , that is, the azimuth of the target that generated the reflected wave can be obtained by extracting the peak (null point) of the MUSIC spectrum.

However, if only the peak is extracted by the MUSIC spectrum, the extracted peak may include a peak due to noise in addition to a peak due to the reflected wave.
For this reason, in estimating the azimuth of the target, the azimuths θ ₁ ,..., Θ _{M corresponding} to the number of incoming waves _M are extracted from the azimuth having the maximum peak value in the MUSIC spectrum, and these azimuths θ ₁ ,. _M is set to power estimation target, each orientation theta ₁ of the power estimation target, ..., power P of theta _M (theta _1), ..., determine the P (theta _M).

Then, among the azimuths θ ₁ ,..., Θ _M of the power estimation target, it is estimated that the azimuth whose power is the threshold value P _th or more is the azimuth of the target. The direction corresponding to the noise component is naturally low in power. Therefore, it is possible to suppress erroneous estimation of the target direction due to noise by estimating that the direction whose power is _{equal to} or greater than the threshold value P _th is the target direction.

The power (reception power) is estimated as follows. First, each orientation theta ₁ of the power estimation target, ..., array response vector a corresponding to _{θ M (θ 1), ...} , by a (theta _M), to produce an array response matrix V.

  Then, using this array response matrix V, a matrix S represented by the following equation is calculated (for example, see Patent Document 1).

Note that the matrix I in the above equation is a unit matrix, and σ ² is the thermal noise power. Since the true value of the thermal noise power σ ² is unknown, the threshold value λ _th is substituted, or the average of eigenvalues below the threshold value λ _th is substituted.

If the matrix S is calculated in this way, the power P (θ _m ) in the azimuth θ _m can be obtained from the m-th diagonal component of the matrix S (where m = 1,..., M).

Conventionally, the power for each azimuth is obtained in this way, and the azimuth whose power is greater than or _equal to the threshold P _th is estimated as the azimuth of the target.

JP 2007-147554 A

However, in the prior art, calculation (multiplication) of the order of K ² is required for calculating the matrix S, and if the number of antenna elements K is increased to improve the performance of the radar apparatus, the amount of calculation related to power estimation increases rapidly. There was a problem of increasing.

As described above, since the autocorrelation matrix Rxx is a matrix of K rows and K columns corresponding to the number K of antenna elements, the matrix {Rxx−σ ² I} is naturally a matrix of K rows and K columns. . On the other hand, since the array response matrix V is a matrix of K rows and M columns, the matrix {(V ^H V) ⁻¹ V ^H } is a matrix of M rows and K columns. Therefore, the calculation of the matrix (V ^H V) ⁻¹ V ^H (Rxx−σ ² I) requires K multiplications for each element, and a total of M × K ² times according to the number of elements M × K. The multiplication of is required.

As a technique for suppressing the amount of calculation, the inner product a (θ _p ) · a (θ _q ) between array response vectors increases as the azimuth difference decreases, and decreases as the azimuth difference increases. A device that suppresses the amount of calculation (see Patent Document 1) is conventionally known.

That is, the array response vector corresponding to the azimuth theta _m arriving waves to be estimated power a (θ _m), and the orientation theta orientation of the incoming waves close to _{m θ m1, θ m2, ...} , corresponding to theta _md Using the array response vectors a (θ _m1 ), a (θ _m2 ),..., A (θ _md ), the proximity azimuth array response matrix V _m is expressed as

By using this close azimuth array response matrix V _m , the power P (θ _m ) of the incoming wave arriving from the azimuth θ _{m is} expressed by the following equation.

Is estimated from the element value S _m [1, 1] of the first row and the first column of the matrix S _m represented by:
However, even if such a method is adopted, if the number K of antenna elements is increased, the amount of calculation related to power estimation increases on the K ² order.

  The present invention has been made in view of these problems, and an object of the present invention is to suppress an increase in calculation amount due to an increase in the number K of antenna elements by performing an efficient calculation when estimating power.

  The signal processing device of the present invention made to achieve the above object is a signal processing device for estimating the power of an incoming wave received by an array antenna based on the received signal of each antenna element constituting the array antenna, Correlation matrix generation means, expansion means, analysis means, and power estimation means are provided.

  The correlation matrix generating means generates an autocorrelation matrix Rxx for the received signal based on the received signal of each antenna element constituting the array antenna. On the other hand, the expansion means expands the autocorrelation matrix Rxx generated by the correlation matrix generation means, and calculates eigenvalues and eigenvectors of the autocorrelation matrix Rxx.

The analysis means, the eigenvalues lambda ₁ of the autocorrelation matrix Rxx, ..., lambda _K and eigenvectors e _1, ..., from e _K group, the eigenvalues lambda ₁ of the signal space, ..., lambda _M and eigenvectors e _1, ..., e extracting _M, power estimating means, and auto-correlation matrix Rxx, each arrival direction theta ₁ previously designated, ..., based on, an array response vectors theta _M, respective arrival direction theta _1, ..., theta _M the power of the incoming wave coming from the P (θ _1), ..., to estimate the P (θ _M).

Specifically, power estimating means, eigenvectors e _{M + 1} of the noise space, ..., e _K and the arrival direction θ _1, ..., θ _M of the array response vector _{a (θ 1), ...,} a (θ M) by using an orthogonal relationship, the eigenvalues lambda ₁ of the autocorrelation matrix Rxx, ..., lambda _K and eigenvectors e _1, ..., among the e _K eigenvalues lambda ₁ of the signal space, ..., lambda _M and eigenvectors e ₁ , ..., using e _M selectively, by approximating the autocorrelation matrix Rxx, the eigenvalues lambda ₁ of the signal space, ..., lambda _M and eigenvectors e _1, ..., approximation of the autocorrelation matrix Rxx consisting e _M matrix Rxx ', the arrival direction θ _1, ..., θ _M of the array response vector a (θ _1), ..., by the action of a (θ _M), the arrival direction θ _1, ..., coming from theta _M power P of the incoming wave (θ _1), ..., to estimate the P (θ _M).

If specifically, power estimating means, the arrival direction theta _1, ..., power P of the incoming wave coming from _{θ M (θ 1), ...} , upon estimating the P (theta _M), the orientation of the power estimation target An array response matrix V having array response vectors a (θ ₁ ),..., a (θ _M ) corresponding to θ ₁ ,..., θ _M as columns, and eigenvalues λ ₁ ,. lambda _K and eigenvectors e _1, ..., among the e _K, the eigenvalues lambda ₁ of the signal space with the exception of noise space, ..., λ _M and eigenvectors e _1, ..., using e _M, the autocorrelation matrix Rxx, matrix Rxx '

  Approximated by

By calculating the diagonal elements of the matrix S 'according to the orientation theta ₁ of the power estimation target, ..., theta power of the incoming wave coming from _{M P (θ 1), ...} , to estimate P (θ _M).
Where Λ _S is a diagonal matrix Λ _S = diag (λ ₁ ,..., Λ _M ) having eigenvalues λ ₁ ,..., Λ _M of the signal space as diagonal components, and E _S is an eigenvector of the signal space. e _1, ..., signal subspace matrix _{E S = [e 1, ...} , e M] to column e _M is superscript H is a complex conjugate transpose.

In addition, the power estimation means calculates a matrix {(V ^H V) ⁻¹ V ^H E _S } or [E _S ^H V (V ^H V) ⁻¹ } sandwiching the diagonal matrix Λ _S , Based on this calculation result, it is possible to adopt a configuration in which {(V ^H V) ⁻¹ V ^H (E _S Λ _S E _S ^H ) V (V ^H V) ⁻¹ } is calculated.

  That is, the power estimation means

  Calculate the values of the elements of the matrix W according to

Calculates the value of the diagonal elements of the matrix W _n in accordance with, by using these calculation results arrival to calculate the diagonal elements of the matrix S ', the orientation theta ₁ of the power estimation target, which ..., arriving from theta _M The wave power P (θ ₁ ),..., P (θ _M ) can be estimated.

When the array response matrix is V = [a (θ ₁ ),..., A (θ _M )] as shown in equation (5), the equation

Accordingly the arrival direction theta _1, ..., power P of the incoming wave coming from _{θ M (θ 1), ...} , can be estimated P (θ _M) (where, w [m, j] is the matrix The value of the element in the m-th row and the j-th column in W is represented, and w _n [m] represents the value of the element in the m-th row and the m-th column in the matrix W _n .)

According to the signal processing apparatus of the present invention configured as described above, the autocorrelation matrix Rxx is expanded (so-called spectrum expansion), and an array response vector is applied to the expanded autocorrelation matrix Rxx, so that each arrival Estimating the powers P (θ ₁ ),..., P (θ _M ) of the incoming waves coming from the directions θ ₁ ,..., Θ _M , and in this case, eigenvectors e _{M + 1} ,. By using the orthogonal relationship between _K and the array response vectors a (θ ₁ ),..., A (θ _M ) of the arrival directions θ ₁ ,..., Θ _M , each eigenvector e _{M + 1} ,. Since the calculation related to the multiplication of e _K and the array response vector is omitted, the amount of calculation related to the estimation of the powers P (θ ₁ ),..., P (θ _M ) can be suppressed.

  According to the signal processing apparatus of the present invention, it is necessary to calculate the eigenvalue and eigenvector by expanding the autocorrelation matrix Rxx. In a radar apparatus using this type of signal processing apparatus, the direction estimation of the incoming wave is performed. Therefore, since it is necessary to calculate eigenvalues and eigenvectors, there is no problem that the amount of calculation increases due to the expansion of the autocorrelation matrix Rxx.

Therefore, according to the present invention, it is possible to perform an efficient calculation when estimating the power, and it is possible to suppress an increase in the amount of calculation due to an increase in the number K of antenna elements, compared to the conventional case.
This point will be described in detail. When the autocorrelation matrix Rxx is expanded (spectrum expansion) by eigenvalues and eigenvectors, it can be expressed by the following equation.

However, lambda _N, like the diagonal matrix lambda _S, the eigenvalues lambda _{M + 1} of the noise space, ..., lambda _K pairs diagonal matrix with the diagonal elements _{Λ N = diag (λ M +} 1, ..., λ K ), and, E _N is the eigenvector e _{M +} 1 of the noise space, ..., the noise subspace matrix _{E N = [e M + 1} , ..., e K] to column e _K is.

On the other hand, power P (θ ₁ ),..., P (θ _M )

It can obtain | require by the diagonal component of the matrix S represented by these.
Here, when the orthogonal relationship is used, V ^H E _N is theoretically zero, and can be approximately regarded as zero even when an error due to observation is taken into consideration. Therefore, if the orthogonal relationship is used, the second term {(V ^H V) ⁻¹ V ^H (E _N Λ _N E _N ^H ) V (V ^H V) ⁻¹ } in the equation (17) is zero. Can be approximated. Therefore, by obtaining the diagonal component of the matrix S ′ according to the equation (12), the power can be obtained approximately, thereby omitting the calculation of the second term of the third equation in the equation (17). Thus, the amount of calculation related to power estimation can be suppressed.

Focusing on the fact that the matrix Λ _S is a diagonal matrix in which elements other than the diagonal component are zero, the above-described matrix W shown in Expression (13) is calculated, and the diagonal of the matrix (WΛ _S W ^H ) is calculated. For example, when the array response matrix V = [a (θ ₁ ),..., A (θ _M )], the component can be calculated by the arithmetic expression shown in the first term of Expression (15). Compared to the technique, the amount of calculation can be greatly reduced.

That is, as in the prior art, when the power is obtained without spectral expansion, the matrix Rxx is applied to the matrix {(V ^H V) ⁻¹ V ^H }, and the matrix {(V ^H V) ⁻¹ V ^{H is obtained.} When calculating Rxx}, M × K ^two multiplications are required, and the matrix {V (V ^H V) ⁻¹ } is applied to the matrix {(V ^H V) ⁻¹ V ^H Rxx} to obtain the matrix In calculating {(V ^H V) ⁻¹ V ^H RxxV (V ^H V) ⁻¹ }, K × M ² multiplications are required.

On the other hand, for the calculation of the matrix W, since the matrix {(V ^H V) ⁻¹ V ^H } is a matrix of M rows and K columns, and the matrix E _S is a matrix of K rows and M columns, K × M ² In the calculation of the first term of the equation (15) corresponding to the diagonal component of the matrix {(V ^H V) ⁻¹ V ^H RxxV (V ^H V) ⁻¹ }, the multiplication is 2 × M Only ² times.

Then, M corresponds to the number of incoming waves, and when the number of antenna elements K is increased to improve the device performance, no consideration is required, and the upper limit value is determined by the use environment.
Therefore, according to the signal processing apparatus of the present invention, when the number of antenna elements K is increased to improve the apparatus performance, the amount of calculation increases to the order of the power of the number of antenna elements K to the first power. In addition, the calculation amount does not increase in the order of the square of the number K of antenna elements, and more efficient calculation can be performed when calculating the power than the conventional technique, and the calculation amount due to the increase in the number K of antenna elements. It is possible to suppress the increase of.

Note that such a method of the present invention can also be applied to a signal processing apparatus that uses the proximity azimuth array response matrix V _m . Orientation theta _m arriving waves to be estimated power (m = 1, ..., M ) for each, to generate a proximity azimuth array response matrix V _m, this closest orientation array response matrix V _m, arriving from the direction theta _m The power P (θ _m ) of the incoming wave is

It is estimated from the element value S _m [1,1] of the first row and the first column of the matrix S _m represented by:
To use a proximity azimuth array response matrix V _m is in order to suppress the arithmetic quantity relating to the estimation of the power, the signal processing apparatus using near azimuth array response matrix V _m, by applying the technique of the present invention, The amount of calculation related to power estimation can be further suppressed.

  Also, the present invention estimates the power of the incoming wave received by the array antenna based on the received signal of each antenna element constituting the array antenna, and uses the direction of the incoming wave generated by the reflection of the radar wave on the target. The present invention can be applied to a signal processing device that estimates the azimuth of a certain target.

In this case, analysis means, the eigenvalues lambda ₁ of the autocorrelation matrix Rxx, ..., lambda _K and eigenvectors e _1, ..., a e _K group, the eigenvalues lambda ₁ of the signal space, ..., lambda _M and eigenvectors e _1, ..., and e _M, the eigenvalues λ _{M * 1} of the noise space, ..., λ _K and eigenvectors e _{M + 1,} ..., is separated into, and e _K, the eigenvalues λ ₁ of the signal space, ..., λ _M and eigenvectors e ₁ , ..., extracts the e _M, these eigenvectors e _1, ..., based on the e _K group, arrival direction theta ₁ of the incoming waves, ..., can be configured to estimate the theta _M.

Further, the power estimation means uses the above-described method based on the autocorrelation matrix Rxx and the array response vectors of the respective arrival directions θ ₁ ,..., Θ _M estimated by the analysis means. arrival direction θ _1, ..., θ power of the incoming wave coming from _{M P (θ 1), ...} , can be configured to estimate P (θ _M).

In addition, the signal processing device, the power P (θ ₁₎ which is estimated by the power estimator, ..., based on P (θ _M), the arrival direction theta _1, ..., among theta _M, the power is equal to or larger than the threshold It is possible to employ a configuration provided with target direction estimation means for estimating the direction as the direction of the target.

If the signal processing device is configured in this way, efficient calculation can be performed in estimating the power, and the target direction can be accurately estimated with a small amount of calculation.
The method of the present invention can be applied to a signal processing apparatus that estimates the arrival directions θ ₁ ,..., Θ _M of each incoming wave by the MUSIC method or ESPRIT method. That is, in the above-described signal processing apparatus, the analysis means can be configured to estimate the arrival directions θ ₁ ,..., Θ _M of each incoming wave by the MUSIC method or the ESPRIT method.

1 is a block diagram illustrating a configuration of a radar apparatus 1. FIG. It is the graph (upper stage) which showed the transmission signal Ss and the received signal Sr of the radar wave, and the graph (lower stage) which showed the beat signal BT. It is explanatory drawing which showed the correspondence of a target direction and a MUSIC spectrum. It is a flowchart showing the target azimuth | direction estimation process which the signal processing part 30 performs. 3 is a flowchart showing power estimation processing executed by a signal processing unit 30. It is a flowchart showing the power estimation process of a modification.

Embodiments of the present invention will be described below with reference to the drawings.
FIG. 1 is a block diagram showing the configuration of the on-vehicle radar device 1. FIG. 2 is a graph showing the transmission signal Ss and the reception signal Sr of the radar wave (upper stage) and a graph showing the beat signal BT (lower stage). It is.

  The radar apparatus 1 according to the present embodiment is a so-called FMCW radar apparatus. The oscillator 11 generates a high-frequency signal in the millimeter wave band whose frequency gradually increases and decreases linearly with respect to time, and the high-frequency signal generated by the oscillator 11. An amplifier 13, a distributor 15 that distributes the output of the amplifier 13 to the transmission signal Ss and the local signal L, and a transmission antenna 17 that radiates a radar wave corresponding to the transmission signal Ss (see the upper part of FIG. 2). And a receiving antenna 19 composed of K antenna elements that receive radar waves (reflected waves) reflected by a target (such as a vehicle ahead).

  The radar apparatus 1 sequentially selects one of the antenna elements constituting the reception antenna 19, and receives the reception signal Sr from the selected antenna element to the subsequent stage, and is supplied from the reception switch 21. Amplifier 23 for amplifying received signal Sr, mixer 25 for generating beat signal BT (see the lower part of FIG. 2) by mixing received signal Sr and local signal L amplified by amplifier 23, and generated by mixer 25 A filter 27 that removes unnecessary signal components from the beat signal BT, an A / D converter 29 that samples the output of the filter 27 and converts it into digital data, and a signal processing unit 30 that includes a microcomputer. .

  The signal processing unit 30 controls the start / stop of the oscillator 11 and the like, and performs signal processing using sampling data of the beat signal BT input from the A / D converter 29 by executing a program in the microcomputer, Processing for transmitting information such as the position, relative speed, and direction of the target obtained by signal processing to the inter-vehicle control ECU 40 is performed.

  The receiving antenna 19 is configured as a linear array antenna in which K antenna elements are arranged in a line. In the following, each of the K antenna elements is numbered and expressed as the i-th antenna element (i = 1, 2,..., K).

  In the radar apparatus 1 according to the present embodiment configured as described above, the oscillator 11 is started according to a command from the signal processing unit 30. Then, the high frequency signal generated by the oscillator 11 by the activation is amplified by the amplifier 13, input to the distributor 15, and power is distributed by the distributor 15. Thereby, in the radar apparatus 1, the transmission signal Ss and the local signal L are generated, and the transmission signal Ss is transmitted as a radar wave via the transmission antenna 17.

  On the other hand, the radar wave (reflected wave) transmitted from the transmission antenna 17 and reflected back to the target is received by each antenna element constituting the reception antenna 19. Each antenna element outputs a reception signal Sr toward the reception switch 21.

  Further, only the reception signal Sr of the i-th antenna element (i = 1,..., K) selected by the reception switch 21 is output from the reception switch 21 to the amplifier 23, and the reception signal amplified by the amplifier 23 is It is supplied to the mixer 25.

  In the mixer 25, the local signal L from the distributor 15 is mixed with the received signal Sr, and a beat signal BT that is a frequency component of the difference between the signals Sr and Ss is generated. The beat signal BT is sampled by the A / D converter 29 after unnecessary signal components are removed by the filter 27 and taken into the signal processing unit 30 as digital data.

  However, the reception switch 21 is switched so as to select all the antenna elements AN_1 to AN_K predetermined times during one modulation period of the radar wave. The A / D converter 29 performs sampling in synchronization with this switching timing.

  In addition, the signal processing unit 30 analyzes the sampling data of the beat signal by executing a program, thereby using a well-known method to measure the distance to the target (vehicle ahead) that is the source of the reflected wave of the radar wave. Also, the relative speed of the target with respect to the host vehicle is estimated.

  When the reception antenna 19 receives the reflected wave due to the transmission antenna 17 transmitting the radar wave based on the transmission signal Ss, the received signal Sr is not reflected by the radar wave as shown by the dotted line in the upper part of FIG. The time required for reciprocating between the target, that is, the time Tr corresponding to the distance to the target is delayed, and the Doppler shift is performed by the frequency fd corresponding to the relative speed with the target. The radar apparatus according to the present embodiment estimates the distance to the target and the relative speed with respect to the target from such information of the time Tr and the frequency fd included in the beat signal BT.

Further, the signal processing unit 30 estimates the azimuth of the target with reference to the traveling direction of the host vehicle (antenna direction) by executing the program. ESPRIT and MUSIC methods are known as azimuth estimation methods. For example, according to the MUSIC method, when a preceding vehicle is present in front of the host vehicle as shown in FIG. When the MUSIC spectrum is calculated based on the sampling data of the beat signal BT obtained from the D converter 29, a sharp peak appears in the direction corresponding to the preceding vehicle in the MUSIC spectrum, as shown in FIG. In the present embodiment, such a peak of the MUSIC spectrum is extracted, and the arrival directions θ ₁ ,..., Θ _M of the incoming waves that are considered to be the reflected waves of the radar waves are estimated.

However, due to noise, a peak may appear in the MUSIC spectrum even for an orientation without a target. For this reason, in this embodiment, by estimating the power of the incoming wave arriving from each of the directions θ ₁ ,..., Θ _M , the incoming wave having the power equal to or higher than the threshold P _th is regarded as a reflected wave of the radar wave. The direction corresponding to the reflected wave is estimated to be the target direction. FIG. 3 is an explanatory diagram showing the correspondence between the target orientation and the MUSIC spectrum.

  This point will be described in detail. In the present embodiment, the target direction is estimated by executing the target direction estimation process shown in FIG. FIG. 4 is a flowchart showing the target direction estimation process executed by the signal processing unit 30.

  When the target azimuth estimation process is started, the signal processing unit 30 calculates the autocorrelation matrix Rxx according to the equations (1) and (2) based on the beat signal BT (sampling data) sampled by the A / D converter 29. Generate (S110).

However, the value of the element x _k (i) (where k = 1,..., K) of the reception vector X (i) is the time i of the reception signal Sr of the k-th antenna element identified from the sampling data of the beat signal BT. The value at.

Then, after generation of the auto-correlation matrix Rxx, the eigenvalues lambda ₁ of the autocorrelation matrix Rxx, ..., lambda _{K (where, λ 1 ≧ λ 2 ≧ ...} λ K), and each eigenvalue lambda _1, ..., a lambda _K Corresponding eigenvectors e ₁ ,..., E _K are calculated (S120). However, eigenvectors e ₁ ,..., E _K are derived so as to satisfy e _i · e _j = δ _ij . Note that δ _ij is the Kronecker delta.

After calculation of the eigenvalues and eigenvectors in S120, estimating the number of incoming waves M from the number of predetermined threshold lambda _th larger eigenvalues corresponding to the thermal noise power (S130). That is, the arrival wave number M is estimated to be the number of eigenvalues larger than the threshold _λth .

Further, after finishing to estimate the number of incoming waves M, the threshold value lambda _th larger eigenvalues lambda _1, ..., eigenvectors e ₁ corresponding to lambda _M, ..., using e _M, the eigenvectors e _1, ..., a e _M to generate a signal subspace matrix E _s to the column, the threshold value lambda _th following eigenvalue lambda _{M + 1,} ..., eigenvectors e _{M + 1} corresponding to the lambda _K, ..., using e _K, the eigenvectors e A noise subspace matrix E _N having _{M + 1} ,..., E _K as columns is generated (S140).

Thereafter, based on the array response vector a (θ) determined from the configuration of the receiving antenna 19 and the noise subspace matrix E _N , a MUSIC spectrum is calculated according to the evaluation function P _MU (θ) shown in Expression (3) (S150). .

Then, based on the calculated MUSIC spectrum, the direction θ ₁ ,..., Θ _{M corresponding to the} number of incoming waves M in descending order of the peak value from the direction in which the peak value (value P _MU (θ)) is maximum in the MUSIC spectrum. , And the M azimuths θ ₁ ,..., Θ _M are estimated as arrival directions of incoming waves (hereinafter simply referred to as incoming wave directions) (S160).

After this, power estimation processing is executed (S170). FIG. 5 is a flowchart showing power estimation processing executed by the signal processing unit 30.
When the power estimation process shown in FIG. 5 is started, the signal processing unit 30 generates an array response matrix V = [a (θ ₁ ),..., A (θ _M )] according to the equation (5) (S171). A matrix (V ^H V) ⁻¹ is calculated using the array response matrix V (S173).

  Thereafter, a matrix W according to the following equation is calculated (S175).

Further, a matrix W _{n according} to the following equation is calculated (S177).

Where I is a unit matrix and σ ² is thermal noise power. Since the true value of σ ² is unknown, for example, the threshold value λ _th is used instead. Further, in S177, the value w _n diagonal elements of the matrix _{W n [i] (i =} 1, ..., M) enough be calculated, it is not necessary to calculate the values of all elements of the matrix W _n. In the following, the element value of the i-th row and i-th column of the matrix W _n is expressed as w _n [i], and the element value of the i-th row and j-th column of the matrix W is expressed as w [i, j]. .

  When the processing in S177 is finished, the signal processing unit 30 proceeds to S179, where

Accordingly, the power P (θ _m ) of each incoming wave azimuth θ _m (m = 1,..., M) is calculated (estimated). In this way, in the power estimation process, the estimated each incoming wave direction theta ₁ and, ..., theta _M power P (θ _1), ..., to estimate P (θ _M).

When the power estimation process is completed, the signal processing unit 30 proceeds to S180, and the threshold value P _th for the preset power and the powers P (θ ₁ ),..., P (θ _M ) of each incoming wave direction. compared bets, arrival wave azimuth theta _1, ..., from the theta _M, power over the azimuth threshold P _th, is estimated to be azimuth of the target. Then, information on the direction in which the power is greater than or equal to the threshold value P _th is transmitted to the vehicle control ECU 40 as information on the target direction along with information on the position and relative speed of the target. Thereafter, the target direction estimation process is terminated.

Here, the power calculation method in the conventional apparatus and the power calculation method in the radar apparatus 1 of the present embodiment will be summarized.
As is well known, the power (reception power) of the incoming wave received by the reception antenna 19 is expressed by the equation

It is possible to calculate from the diagonal component. That is, the power P (θ _m ) of each incoming wave azimuth θ _m (m = 1,..., M) can be estimated from the element values in the m-th row and m-th column of the matrix S.
However, when calculating the gracefully calculating the matrix S, the matrix ^{{(V H V) -1 V} H} by the action of matrix Rxx into the matrix ^{{(V H V) -1 V} H Rxx}, M × K ² multiplications are required, the matrix ^{{(V H V) -1 V} H Rxx}, by the action of the matrix ^{{V (V H V) -1} }, the matrix {(V ^H V) ^-1 In calculating V ^H RxxV (V ^H V) ⁻¹ }, K × M ² multiplications are required.

Therefore, if the number of antenna elements K is increased to improve the performance of the radar apparatus 1, the amount of calculation related to power estimation increases rapidly in the K ² order.
On the other hand, when estimating the arrival wave number M and the arrival wave direction, it is necessary to expand the autocorrelation matrix Rxx and calculate the eigenvalues and eigenvectors of the autocorrelation matrix Rxx. Further, eigenvectors e _{M + 1} of the noise space, ..., e _K and arrival wave azimuth θ _1, ..., θ _M of the array response vector a (θ _1), ..., between a (θ _M) is orthogonal There is a relationship. In this embodiment, these points are used to suppress the amount of calculation related to power estimation.

When the orthogonal relationship described above is used, V ^H E _N can be regarded as approximately zero even when an error due to observation is taken into consideration.
In addition, the autocorrelation matrix Rxx is expressed as

Can be expressed as Λ _S is a diagonal matrix Λ _S = diag (λ ₁ ,..., Λ _M ) having eigenvalues λ ₁ ,..., Λ _M of the signal space as diagonal components, and Λ _N is a diagonal matrix Λ as with _S, the eigenvalues lambda _{M + 1} of the noise space, ..., lambda diagonal matrix having _K a diagonal elements _{Λ N = diag (λ M +} 1, ..., λ K) is.

Here, the powers P (θ ₁ ),..., P (θ _M ) of the incoming waves arriving from the respective incoming wave azimuths θ ₁ ,..., Θ _M are calculated from the diagonal components of the matrix S shown in Expression (26). Therefore, if V ^H E _N is regarded as approximately zero, the autocorrelation matrix Rxx is given by

  The matrix S can be approximated by

Can be approximated to a matrix S ′.
Using this principle, in this embodiment, the autocorrelation matrix Rxx is approximated by the matrix Rxx ′, and the diagonal components of the matrix S ′ are calculated, so that each incoming wave azimuth θ ₁ ,. power P of the incoming wave coming from _{M (θ 1),} ..., with each other to such a P (θ _M), estimated with a small amount of calculation.

As described above, when the autocorrelation matrix Rxx and the matrix S are approximated to the matrix Rxx ′ and the matrix S ′, the operations related to the eigenvectors e _{M + 1} ,..., E _K in the noise space can be omitted. . Further, the approximate matrix Rxx ′ composed of the eigenvalues λ ₁ ,..., Λ _M and the eigenvectors e ₁ ,..., E _{M of} the signal space is left unfolded, and the diagonal matrix Λ _S is sandwiched as in this embodiment. If the matrix portion is calculated first, the amount of calculation of the matrix S ′ can be significantly suppressed by utilizing the fact that elements other than the diagonal component in the diagonal matrix Λ _S are zero, and the power P (θ ₁ ),..., P (θ _M ) can be reduced in the amount of computation.

The power P (θ _m ) derived by the equation (25) corresponds to the element value of the m-th row and the m-th column of the matrix S ′. For example, an operation necessary for calculating the first term of the equation (25) The amount is as follows.
That is, in the conventional apparatus, in order to calculate the values of the elements of the matrix {(V ^H V) ⁻¹ V ^H RxxV (V ^H V) ⁻¹ } corresponding to the first term of the equation (25), the matrix { and ^{(V H V) -1 V H} } by the action of matrix Rxx to, the operation of calculating the matrix ^{{(V H V) -1 V} H Rxx}, requires multiplication of M × K ² times, matrix { The matrix {V (V ^H V) ^-1 } is applied to (V ^H V) ⁻¹ V ^H Rxx}, and the matrix {(V ^H V) ⁻¹ V ^H RxxV (V ^H V) ⁻¹ } is obtained. When calculating, K × M ² multiplications are required.

On the other hand, in this embodiment, the number of multiplications for calculating the matrix W by applying the matrix E _s to the matrix {(V ^H V) ⁻¹ V ^H } is only K × M ² times. Further, when calculating the first term of the equation (25) using the element values of the matrix W, as can be understood from the equation (25), 2 × M times are required for each azimuth θ _m , Even if the multiplications of the orientations θ ₁ ,..., Θ _M are integrated, only 2 × M ² is required. Further, calculation of the K ² order is not necessary for calculating the matrix (V ^H V) ⁻¹ and the matrix {(V ^H V) ⁻¹ V ^H }.

  Since the upper limit value of M is determined depending on the use environment, when it is assumed that the number of antenna elements K is increased to improve the performance of the radar apparatus 1, M can be regarded as a fixed value.

Therefore, when the performance of the radar apparatus 1 is improved by increasing the number K of antenna elements, the calculation amount increases in the order of K ^{2 in} the conventional apparatus, whereas in this embodiment, the increase in the calculation amount is K ^1. As a result, according to the present embodiment, efficient calculation can be performed in the power estimation, and an increase in calculation amount due to an increase in the number K of antenna elements can be suppressed.

  Note that in azimuth estimation and power estimation using an array antenna with K antenna elements, since it is not possible to perform appropriate estimation unless the number of incoming waves is (K-1) or less, the number of incoming waves is assumed as a premise. M is (K-1) at the maximum.

Further, the amount of decrease Δ in the number of multiplications by the method of the present embodiment relative to the conventional method is Δ ^{2 because the} number of multiplications of the conventional method is K ² M + KM ² and the number of multiplications of the method of the present embodiment is KM ² + 2M ^2. = (K ² M + KM ² ) − (KM ² + 2M ² ) = K ² M−2M ² .

Therefore, when the number of incoming waves is M = 1, the amount of decrease Δ is Δ = K ² −2 and when the number of incoming waves is M = K−1, the amount of decrease Δ is Δ = (K−1) {(K -1) ² +1}.
In addition, the decrease amount delta, since the ^{Δ = K 2 M-2M 2} = -2 (M-K 2/4) 2 + K 4/8, on expression, the number of incoming waves M is in K ^2/4 Although the maximum one time, the K ≧ 2, for a ^{K 2/4 ≧ K-1} , substantially, when an incoming wave M = K-1, reduction Δ becomes maximum.

Therefore, according to the method of the present embodiment, the number of multiplications can be reduced by at least Δ = K ² −2 and the maximum can be reduced by Δ = (K−1) {(K−1) ² +1}. be able to.
By the way, the technique of the present embodiment uses the near azimuth array response matrix V _m shown in the equation (8) instead of the array response matrix V shown in the equation (5), and each incoming wave azimuth θ ₁ ,. _The present invention can also be applied to a radar apparatus that estimates _M power P (θ ₁ ),..., P (θ _M ).

Hereinafter, the above technique, an example applied to a radar apparatus using near azimuth array response matrix V _m, is described as a modification. However, since the radar apparatus according to the modified example is different from the radar apparatus 1 according to the above-described embodiment in the content of the power estimation process executed in S170, only the power estimation process according to the modified example will be selectively described below. .

FIG. 6 is a flowchart illustrating power estimation processing executed by the signal processing unit 30 of the radar apparatus according to the modification.
When the power estimation process of the modified example is started, the signal processing unit 30 uses any one of the incoming wave azimuths θ ₁ ,..., Θ _M estimated in S160 as the power estimation target direction θ _m (m = 1,. set M) (S210), generates a closest orientation array response matrix V _m corresponding to the power estimation target azimuth θ _m (S220).

Specifically, a matrix of array response vector a (θ _m) and a first column corresponding to the power estimation target orientation theta _m, arrival wave azimuth theta _1, ..., among theta _M, satisfy a predetermined condition to "orientation close to the power estimation target orientation theta _{m" θ m1, θ m2, ...,} θ md the array response vector a corresponding _{(θ m1), a (θ} m2), ..., a a a (theta _md) A near azimuth array response matrix V _m represented by Expression (8) arranged in the second and subsequent columns is generated.

Incidentally, "the orientation close to the power estimation target orientation theta _m" theta _m1 satisfying a predetermined condition, theta _{m @ 2,} ..., for the theta _md, as described in Patent Document 1, the power estimation target orientation theta _m It is also possible to determine a predetermined number d in order from the azimuth in the vicinity, or to determine the difference from the power estimation target azimuth θ _m within the upper limit Δθ.

When the processing in S220 is completed, the signal processing unit 30 calculates a matrix (V _m ^H V _m ) ⁻¹ using the proximity azimuth array response matrix V _m (S230), and uses the calculation result, A matrix W _{(m) according} to the following equation is calculated (S240).

Further, a matrix W _{n (m) according} to the following equation is calculated (S250).

Where I is a unit matrix and σ ² is thermal noise power. Since the true value of σ ² is unknown, for example, the threshold value λ _th is used instead. In S250, similar to the processing in S177, sufficient be calculated matrix W _n first row element value in the first row of _{(m) w n (m)} [1], of all the elements of the matrix W _{n (m)} There is no need to calculate a value. In the following, the element value of the i-th row and i-th column of the matrix W _{n (m)} is expressed as w _{n (m)} [i], and the element value of the i-th row and j-th column of the matrix W _(m) is expressed as Expressed as w _(m) [i, j].

  When this processing is finished, the signal processing unit 30 proceeds to S260, and the following equation

Accordingly, the power P (θ _m ) of the power estimation target direction θ _m is calculated (estimated).
After calculating the power P (θ _m ) in this way, the signal processing unit 30 proceeds to S270, sets all of the incoming wave azimuths θ ₁ ,..., Θ _M as the power estimation target azimuth θ _m , power P (θ _1), ..., and determines whether the calculated P (θ _M), if it is determined that not calculated (no in S270), the process proceeds to S210, arrival wave azimuth θ _1, ..., Of θ _M , an unprocessed incoming wave azimuth for which power is not calculated is set as a new power estimation target azimuth θ _m, and the processes after S220 are executed.

When all of the powers P (θ ₁ ),..., P (θ _M ) corresponding to the arriving wave azimuths θ ₁ ,..., Θ _M have been calculated (estimated), an affirmative determination is made in S270 and the power The estimation process ends.
In the modified radar apparatus for calculating the powers P (θ ₁ ),..., P (θ _M ) in this way, the calculation amount related to the power estimation is calculated based on the same principle as that of the radar apparatus 1 of the above-described embodiment. It can be suppressed to K ¹ order, and an increase in the amount of calculation related to power estimation due to an increase in the number K of antenna elements can be suppressed.

  As mentioned above, although the Example of this invention including a modification was described, the correspondence of these Examples and "Claims" is as follows. That is, the correlation matrix generating means is realized by the processing of S110 executed by the signal processing unit 30, the expanding means is realized by the processing of S120, the analyzing means is realized by the processing of S130 to S160, and the power estimating means is The target direction estimating means is realized by the processing of S180 executed by the signal processing unit 30.

Further, the present invention is not limited to the above-described embodiments, and can take various forms. For example, in the above embodiment, the arrival wave azimuths θ ₁ ,..., Θ _M are estimated using the MUSIC method, but the arrival wave azimuths θ ₁ ,..., Θ _M may be estimated by the ESPRIT method. Specifically, the processing at S150 and S160 may be replaced with the estimation processing of arrival wave azimuths θ ₁ ,..., Θ _M by the ESPRIT method. Even if it does in this way, the effect similar to the said Example can be acquired.

DESCRIPTION OF SYMBOLS 1 ... Radar apparatus, 11 ... Oscillator, 13, 23 ... Amplifier, 15 ... Distributor, 17 ... Transmitting antenna, 19 ... Receiving antenna, 21 ... Reception switch, 25 ... Mixer, 27 ... Filter, 29 ... A / D converter 30 ... Signal processing unit, 40 ... Vehicle distance control ECU

Claims (5)

A signal processing device that estimates the power of an incoming wave received by the array antenna, based on a reception signal of each antenna element constituting the array antenna,
Correlation matrix generating means for generating an autocorrelation matrix Rxx for the received signal based on the received signal of each antenna element constituting the array antenna;
Expansion means for expanding the autocorrelation matrix Rxx generated by the correlation matrix generation means and calculating eigenvalues and eigenvectors of the autocorrelation matrix Rxx;
Eigenvalues lambda ₁ of the autocorrelation matrix Rxx, ..., lambda _K and eigenvectors e _1, ..., from e _K group, the eigenvalues lambda ₁ of the signal space, ..., lambda _M and eigenvectors e _1, ..., analyzed to extract e _M Means,
The autocorrelation matrix Rxx, each arrival direction theta ₁ previously designated, ..., theta and the array response vector of _M, on the basis of said respective arrival direction theta _1, ..., the power of the incoming wave coming from theta _M P Power estimation means for estimating (θ ₁ ),..., P (θ _M );
With
Upon the power estimation means, wherein each arrival direction theta _1, ..., power P of the incoming wave coming from _{θ M (θ 1), ...} , to estimate P (theta _M),
Orientation theta ₁ of the power estimation target, ..., θ _M to the array response vector a corresponding (θ _1), ..., and generates an array response matrix V to columns a (θ _M),
Eigenvectors e _{M + 1} of the noise space, ..., e _K and the arrival direction θ _1, ..., θ _M of the array response vector a (θ _1), ..., by using the orthogonal relationship of a (θ _M), eigenvalues lambda ₁ of the autocorrelation matrix Rxx, ..., λ _K and eigenvectors e _1, ..., among the e _K, the eigenvalues lambda ₁ of the signal space with the exception of noise space extracted by said analyzing means, ..., λ _M and eigenvectors e _1, ..., by selectively using e _M, the autocorrelation matrix Rxx, the eigenvalues lambda ₁ of the signal space, ..., λ _M and eigenvectors e _1, ..., consisting of e _M matrix Rxx '

(Where Λ _S is a diagonal matrix Λ _S = diag (λ ₁ ,..., Λ _M ) having eigenvalues λ ₁ ,..., Λ _M of the signal space as diagonal components, and E _S is The signal subspace matrix E _S = [e ₁ ,..., E _M ] with the eigenvectors e ₁ ,..., E _M of the signal space as columns, and the superscript H is a complex conjugate transpose). Formula using matrix Rxx '

From the azimuth θ ₁ ,..., Θ _{M of the} power estimation target, by calculating the diagonal component of the matrix S ′ (where I is a unit matrix and σ ² is thermal noise power) A signal processing apparatus characterized by estimating powers P (θ ₁ ),..., P (θ _M ) of incoming waves. The power estimation means has the formula

Calculate the values of the elements of the matrix W according to

Calculate the value of the diagonal element of the matrix W _n according to
Using these calculation results, the matrix to calculate the diagonal elements of S ', the power estimation target azimuth theta _1, ..., the power of the incoming wave coming from _{θ M P (θ 1),} ..., P ( The signal processing apparatus according to claim 1, wherein θ _M ) is estimated. The power estimation means includes
_Assuming that the array response matrix V is V = [a (θ ₁ ),..., A (θ _M )], the equation

According, each arrival direction theta _1, ..., power P of the incoming wave coming from _{θ M (θ 1), ...} , to estimate P (θ _M) (where, w [m, j] is the matrix W Represents the value of the element in the m-th row and j-th column, and w _n [m] represents the value of the element in the m-th row and m-th column in the matrix W _n .)
The signal processing apparatus according to claim 2. Based on the received signal of each antenna element that constitutes the array antenna, the power of the incoming wave received by the array antenna is estimated, and the direction of the incoming wave that is the direction of the incoming wave that is generated when the radar wave is reflected on the target. The signal processing device according to any one of claims 1 to 3, wherein the direction is estimated.
The analyzing means uses eigenvalues λ ₁ ,..., Λ _K and eigenvectors e ₁ ,..., E _{K of the} autocorrelation matrix Rxx, eigenvalues λ ₁ ,..., Λ _M and eigenvectors e ₁ ,. and _M, the eigenvalues λ _{M * 1} of the noise space, ..., λ _K and eigenvectors e _{M + 1,} ..., is separated into, and e _K, the eigenvalues λ ₁ of the signal space, ..., λ _M and eigenvectors e _1, ... extracts the e _M, these eigenvectors e _1, ..., based on the e _K group, arrival direction theta ₁ of the incoming waves, ..., is in the configuration of estimating the theta _M,
The power estimation unit is configured to determine each arrival direction θ estimated by the analysis unit based on the autocorrelation matrix Rxx and the array response vector of each arrival direction θ ₁ ,..., Θ _M estimated by the analysis unit. _1, ..., power P of the incoming wave coming from theta _M (theta _1), ..., is in the configuration of estimating P (theta _M),
Furthermore, the signal processing device
Wherein said estimated by power estimating unit power P (θ _1), ..., based on P (θ _M), each arrival direction theta _1, ..., among theta _M, the power is equal to or larger than the threshold azimuth, the product A signal processing apparatus comprising target direction estimation means for estimating a target direction. 5. The signal processing apparatus according to claim 4, wherein the analysis unit estimates arrival directions θ ₁ ,..., Θ _M of the incoming wave by a MUSIC method or an ESPRIT method.

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