JP5311832B2 - Signal processing device - Google Patents

Description

  The present invention relates to a signal processing apparatus that estimates an unknown parameter of a signal observed by a sensor with high accuracy.

  As a signal processing apparatus that estimates an unknown parameter of a signal observed by a sensor with high accuracy, an apparatus adopting a method based on a maximum likelihood estimation method or a method based on a super-resolution method has been developed.

  However, in these signal processing apparatuses, it is necessary to accurately input the number of signals being observed. For this reason, an apparatus for estimating the number of observation signals is required.

  As a conventional method for estimating the number of signals included in observation data, a correlation matrix is calculated from observation data obtained by a plurality of sensors, and the number of signals is estimated from eigenvalues of the correlation matrix (see, for example, Non-Patent Document 1 and Non-Patent Document 2). ). Further, there is an unknown parameter estimation method based on ESPRIT or VESPA (see Non-Patent Documents 3 and 4).

  A signal processing apparatus including a signal number estimation process according to a conventional method calculates a correlation matrix of data observed by a plurality of sensors by a correlation matrix calculation means, and decomposes the correlation matrix into eigenvalues and eigenvectors by an eigenvalue eigenvector calculation means. In addition, the signal number estimation means performs signal number estimation processing by a conventional method using eigenvalues, the unknown parameter estimation means refers to the estimated number of signals, and uses the eigenvector (or correlation matrix) to estimate the maximum likelihood. The unknown parameters of the observed signal are estimated by the estimation process based on, and the estimation process based on the super-resolution method. Then, the estimated unknown parameter is output by the estimated value output means.

H. Krim, M. Viberg, “Two decades of array signal processing research: the parametric approach” IEEE Signal Processing Magazine, vol. 13, no. 4, pp. 67-94, Jul 1996 M. Wax, T. Kailath, “Detection of signals by information theoretic criteria” IEEE Trans. Acoustics Speech and Signal Processing, vol. 33, no. 2, pp. 387-392, Apr 1985 R. Roy and T. Kailath, “ESPRIT-Estimation of Signal Parameters via Rotational Invariance Techniques” IEEE Trans., Vol. ASSP-37, pp. 984-995, July 1989 M Dogan and J. Mendel, "Application of Cumulants to Array Processing-Part I: Aperture Extension and Array Calibration" IEEE Trans. Signal Processing, vol. 43, no. 5, pp. 1200-1216, May. 1995

  However, a problem with the conventional signal number estimation method that estimates the number of observation signals based on the size of the eigenvalue of the correlation matrix is a threshold value for discriminating between eigenvalues corresponding to signal components and noise components. It is necessary to determine the process. Further, in a signal processing apparatus using an estimation method based on the super-resolution method, the unknown parameter is estimated from the eigenvector, but the number of signals must be estimated from the eigenvalue.

  The present invention has been made in view of the above points, and estimates the number of observation signals with high accuracy without setting a threshold value for discriminating eigenvalues into those corresponding to signal components and those corresponding to noise components. An object of the present invention is to obtain a signal processing device capable of performing the above.

  The signal processing apparatus according to the present invention corresponds to an eigenvalue and an eigenvalue of a correlation matrix from a correlation matrix calculating unit that calculates a correlation matrix of data observed by a plurality of sensors, and a correlation matrix calculated by the correlation matrix calculating unit. Eigenvalue eigenvector calculation means for calculating eigenvectors, least square method calculation means for performing the least square method using eigenvector elements, and approximation error for calculating and evaluating the approximation error of the least square method from the calculation results of the least square method calculation means Determination means.

  According to the present invention, by using only the eigenvector of the correlation matrix, a signal number estimation method that does not require a threshold for discriminating the signal component and the noise component is adopted, and the signal number estimation process and the unknown parameter estimation process are performed using the eigenvector. It is possible to stabilize the arithmetic processing by carrying out only with this.

Embodiment 1 FIG.
When realizing a high-precision / high-resolution signal processing apparatus, a signal processing method based on a maximum likelihood estimation method or a method based on a super-resolution method is used. These methods can be operated with high accuracy / high resolution by inputting the exact number of signals included in the observation data. Therefore, it is necessary to separately provide a method for accurately estimating the number of signals included in the observation data.

  The signal processing apparatus according to the present invention employs a signal number estimation method that does not require a threshold for discriminating signal components and noise components by using only eigenvectors of a correlation matrix, and performs signal number estimation processing and unknown parameter estimation. By performing the processing using only eigenvectors, the arithmetic processing is stabilized.

  The signal number estimation method in this invention is based on ESPRIT shown in Non-Patent Document 3. In ESPRIT, the elements of eigenvectors are separated into two subsets, and a least square method between the subsets is implemented. In the principle of ESPRIT, this least square method uses the true value of the number of signals, so that the approximation error becomes zero. The conventional signal processing apparatus based on ESPRIT does not need to calculate the approximation error of the least square method, but the signal processing apparatus according to the present invention has a function of calculating the approximation error of the least square method.

  FIG. 1 is a block diagram showing a configuration of a signal processing apparatus according to Embodiment 1 of the present invention. The signal processing apparatus shown in FIG. 1 includes a plurality of sensors 11 to 1L, a correlation matrix calculation unit 2 that calculates a correlation matrix of data observed by these sensors 11 to 1L, and a correlation calculated by the correlation matrix calculation unit 2. Refer to the eigenvalue eigenvector calculation means 3 for decomposing the matrix into eigenvalues 4 and eigenvectors 5 corresponding to the eigenvalues, signal number estimation means 6 for performing signal number estimation processing by the conventional method using eigenvalues 4, and the estimated number of signals. Least square method computing means 9 for performing a least square method using elements of eigenvector 5, an approximation error judging means 101 for judging an approximation error of the least square method from a computation result of the least square method computing means 9, and an approximation error judgment A warning output means 111 for outputting a warning that the estimation process is not normal when the approximation error is large from the determination result of the means 101; and a least-square method of the least approximation error. Includes an unknown parameter estimation means 7 for estimating the unknown parameters using the calculation results, the estimated value outputting means 8 for outputting the estimated parameters.

  Since the approximation error of the least square method is defined as zero in the principle of ESPRIT, the approximation error determination unit 101 determines the least square method from the calculation result of the least square method calculation unit 9 as shown in the signal processing configuration diagram of FIG. By calculating / determining the approximate error, it is possible to output an alarm from the alarm output means 111 that the estimation process is not normal when the approximate error is large.

  In addition, the least square method is performed a plurality of times while changing the parameter k corresponding to the number of signals, the minimum approximation error is determined from the plurality of approximation errors, and the calculation result of the least square method resulting in the minimum approximation error It is a feature of the present invention to estimate unknown parameters using. With this feature, the signal processing apparatus according to the present invention eliminates the need to set a threshold, such as a threshold for the eigenvalue required by the conventional signal processing apparatus. Furthermore, by performing signal processing that minimizes the approximation error, calculation processing closest to the principle of ESPRIT is achieved, and highly accurate unknown parameter estimation processing is possible.

  The parameter k when the approximation error of the least squares method is minimized can be determined as an estimated value of the number of signals included in the observation data.

  The configuration diagrams of the signal processing apparatus shown in FIGS. 2 and 3 are configuration examples that implement only the least square method corresponding to the number of parameters k close to the number of signals estimated by the conventional signal number estimation method. By referring to the number of signals estimated by the conventional signal number estimation method, the calculation amount may be reduced in the entire signal processing.

  In the configuration example of FIG. 2, the least square method calculating means 9 shown in FIG. 1 has a plurality of least square method calculating means 91 that performs the least square method corresponding to the number of signals estimated from the elements of the eigenvector 5. .., 9M, and the approximation error determination unit 101 shown in FIG. 1 is a minimum approximation error determination unit 121 that determines the minimum approximation error from a plurality of approximation errors.

  3 includes signal number estimation means 6 for performing signal number estimation processing using the eigenvalue 4 calculated by the eigenvalue eigenvector calculation means 3 as in FIG. 1, and the least square method shown in FIG. The calculation means 9 is composed of a plurality of least squares calculation means 91,..., 9N for performing the least square method corresponding to the number of signals estimated by the signal number estimation means 6, and the approximate error determination shown in FIG. A case where the means 101 is composed of minimum approximation error determination means 121 for determining the minimum approximation error from a plurality of approximation errors is shown.

  As described above, the signal processing apparatus according to the present invention estimates the number of signals included in the observation data by having the function of calculating the approximation error of the least square method using the eigenvectors of the covariance matrix. This estimation method is characterized by not setting a threshold value used in the conventional estimation method.

Embodiment 2. FIG.
A specific example of performing unknown parameter estimation by ESPRIT in Non-Patent Document 3 in the signal processing device of the present invention will be shown. The specific example shown below is an example when ESPRIT is combined, and each calculation method is not limited to the exemplified method.

  A correlation matrix R averaged at a plurality of times is obtained for the data vector r observed by the sensors 11 to 1L.

Here, E [] is a time average operation, and ^H is a complex conjugate transpose operation of a vector. Spatial averaging can also be performed in the average calculation of equation (1). Eigenvalue lambda _l the correlation matrix R as Equation (2) is decomposed (l = 1, · · ·, L) and eigenvectors _{e l (l = 1, ···} , L) to, the eigenvalue lambda _l formula It is assumed that the relationship (3) is established.

Based on ESPRIT, the eigenvector e _l is divided into # 1 subset e _l ⁽¹⁾ and # 2 subset e _l ⁽²⁾ . The parameters k corresponding to the number of signals to define a matrix _E ^{k (2)} according to # 2 subsets and the matrix _E ^{k (1)} according to # 1 subset.

を最小二乗法で算出する。 Furthermore, the matrix E _k ⁽¹⁾ and the matrix E _k ⁽²⁾ are defined as the relationship of the expression (6) based on ESPRIT, and the matrix is an estimated value of the matrix Ψ _k.

Is calculated by the method of least squares.

を算出する最小二乗法には総合最小二乗法などを用いることができる。最小二乗法の近似誤差ε_ｋは式（７）のように得る。 matrix

As the least square method for calculating the total square method, an overall least square method or the like can be used. An approximation error ε _k of the least square method is obtained as shown in Equation (7).

Here, |||| _F is the Frobenius norm operation, and P is the number of elements of the vector e _l ⁽¹⁾ .

According to the principle of ESPRIT, the approximation error ε _k becomes zero with respect to the true value K of the number of signals.

As an actual problem, the approximation error ε _k rarely becomes zero. However, it is a characteristic according to the principle of ESPRIT that the approximation error ε _k is minimized when the parameter k is equal to the true value K. Therefore, the parameter k is scanned from 1 to P-1, and the minimum approximate error ε _k is searched. However, if the number of elements P is substituted for the parameter k, the approximation error ε _k becomes mathematically zero, so this processing is excluded.

を用いることで、ＥＳＰＲＩＴによる未知パラメータ推定処理が高精度に実施可能である。近似誤差ε_ｋが最小となる演算処理を実施することはＥＳＰＲＩＴの原理に対して最も妥当な信号処理方式である。このことから、固有値を用いる従来の信号数推定方式より、固有ベクトルを用いるこの発明の信号処理方式の方が最適解を得やすいことが分かる。また、最小の近似誤差ε_ｋを実現するパラメータｋを信号数の推定値

として、信号処理で使用可能である。 Matrix E _k ⁽¹⁾ , matrix E _k ⁽²⁾ and matrix corresponding to the smallest approximation error ε _k

By using, unknown parameter estimation processing by ESPRIT can be performed with high accuracy. It is the most appropriate signal processing method for the principle of ESPRIT to perform the arithmetic processing that minimizes the approximation error ε _k . From this, it can be seen that the signal solution method of the present invention using eigenvectors is easier to obtain the optimum solution than the conventional signal number estimation method using eigenvalues. In addition, the parameter k that realizes the minimum approximation error ε _k is an estimated value of the number of signals.

Can be used in signal processing.

Embodiment 3 FIG.
The signal processing apparatus of the present invention can also adopt VESPA (Virtual ESPRIT Algorithm) shown in Non-Patent Document 4 as a signal processing method. Specific examples are shown below. However, the calculation method shown below is only an example.

  VESPA is characterized by being estimated using a fourth-order cumulant shown in Equation (9).

When the #i sensor and the #j sensor are assumed to be guiding sensors, the following matrix C _{i, j} and matrix C _{j, i} are calculated using the fourth-order cumulant of Expression (8).

Here, x _i is an element of the data vector x corresponding to #i sensor, and ^* is a complex conjugate. As shown in the equation (12), the matrix C is divided into singular values σ _l (l = 1,..., L), left singular vectors u _l (l = 1,..., L), and right singular vectors v _l (l = 1,..., L).

Based on VESPA, the left singular vector is divided into # 1 subset v _l ⁽¹⁾ from # 1 elements to #L elements and # 2 subset v _l ⁽²⁾ from # L + 1 elements to # 2L elements. For parameter k corresponding to the number of signals to define a matrix _V ^{k (2)} according to # 2 subsets and the matrix _V ^{k (1)} according to # 1 subset.

を最小二乗法で算出する。 Further, the matrix V _k ⁽¹⁾ and the matrix V _k ⁽²⁾ are defined as the relationship of the expression (15) based on VESPA, and the matrix that is an estimated value of the matrix Ψ _k

Is calculated by the method of least squares.

を算出する最小二乗法には総合最小二乗法などを用いることができる。最小二乗法の近似誤差ε_ｋは式（１７）のように得る。 matrix

As the least square method for calculating the total square method, an overall least square method or the like can be used. An approximation error ε _k of the least square method is obtained as shown in Equation (17).

According to the VESPA principle, the approximation error ε _k becomes zero with respect to the true value K of the number of signals.

As an actual problem, the approximation error ε _k rarely becomes zero. However, the fact that the approximation error ε _k is minimized when the parameter k is equal to the true value K is a characteristic according to the VESPA principle. Therefore, the parameter k is scanned from 1 to L−1, and the minimum approximate error ε _k is searched. However, if the number of sensors L is substituted for the parameter k, the approximation error ε _k becomes mathematically zero, so this processing is excluded.

を用いることで、ＶＥＳＰＡによる未知パラメータ推定処理が高精度に実施可能である。近似誤差ε_ｋが最小となる演算処理を実施することはＶＥＳＰＡの原理に対して最も妥当な信号処理方式である。このことから、固有値を用いる従来の信号数推定方式より、固有ベクトルを用いるこの発明の信号処理方式の方が最適解を得やすいことが分かる。 Matrix V _k ⁽¹⁾ , matrix V _k ⁽²⁾ and matrix corresponding to the smallest approximation error ε _k

By using, unknown parameter estimation processing by VESPA can be performed with high accuracy. The approximation error epsilon _k is carried out smallest processing is the most appropriate signal processing scheme with respect to the principle of VESPA. From this, it can be seen that the signal solution method of the present invention using eigenvectors is easier to obtain the optimum solution than the conventional signal number estimation method using eigenvalues.

として、信号処理で使用可能である。 In addition, the parameter k that realizes the minimum approximation error ε _k is an estimated value of the number of signals.

Can be used in signal processing.

は、最尤推定法に基づく信号処理方式や超分解能法に基づく信号処理方式、独立成分分析などにおける信号数の入力値として使用可能である。 Embodiment 4 FIG.
Estimated number of signals estimated in Embodiment 2 and Embodiment 3

Can be used as an input value for the number of signals in a signal processing method based on the maximum likelihood estimation method, a signal processing method based on the super-resolution method, independent component analysis, and the like.

It is a block diagram which shows the structure of the signal processing apparatus which concerns on Embodiment 1 of this invention. It is a block diagram which shows the structure of the signal processing apparatus by the other modification of this invention. It is a block diagram which shows the structure of the signal processing apparatus by the further another modification of this invention.

Explanation of symbols

  11,..., 1L sensor, 2 correlation matrix computing means, 3 eigenvalue eigenvector computing means, 4 eigenvalues, 5 eigenvectors, 6 signal number estimating means, 7 unknown parameter estimating means, 8 estimated value output means, 9, 91,. .., 9M, 91,..., 9N least square method computing means, 101 approximate error determining means, 111 alarm output means, 121 minimum approximate error determining means.

Claims (9)

Correlation matrix calculation means for calculating a correlation matrix of data observed by a plurality of sensors;
Eigenvalue eigenvector calculation means for calculating the eigenvalue of the correlation matrix and the eigenvector corresponding to the eigenvalue from the correlation matrix calculated by the correlation matrix calculation means;
Least-squares arithmetic means for performing a least-squares method using eigenvector elements;
An approximation error determination unit that calculates and evaluates an approximation error of the least square method from the calculation result of the least square method calculation unit. The signal processing device according to claim 1,
A signal processing apparatus, further comprising: an alarm output unit that outputs an alarm that the estimation process is not normal when the approximate error is large from the determination result of the approximate error determination unit. The signal processing device according to claim 1 or 2,
Means for obtaining a first subarray of P sensors, a second subarray of the same shape as the first subarray, a matrix corresponding to the first subarray and a matrix corresponding to the second subarray from the signal space matrix; Further comprising
The eigenvalue eigenvector computing means calculates a signal space matrix obtained by arranging eigenvectors corresponding to k largest eigenvalues among eigenvalues of the correlation matrix,
The least square method computing means performs a least square method using a matrix corresponding to the first subarray and a matrix corresponding to the second subarray, performs a least square method in which the number of eigenvalues k is different, It consists of a plurality of least squares calculation means to obtain an approximation error,
The signal processing apparatus according to claim 1, wherein the approximation error determination unit is a minimum approximation error determination unit that determines a minimum approximation error from a plurality of approximation errors. In the signal processing device according to any one of claims 1 to 3,
Signal number estimating means for performing signal number estimation processing using the eigenvalue calculated by the eigenvalue eigenvector calculating means,
The least square method computing means comprises a plurality of least squares computing means for performing a least square method corresponding to the number of signals estimated by the signal number estimating means,
The signal processing apparatus according to claim 1, wherein the approximation error determination unit is a minimum approximation error determination unit that determines a minimum approximation error from a plurality of approximation errors. In the signal processing device according to any one of claims 1 to 4,
A signal processing apparatus, further comprising: an unknown parameter estimation unit that estimates an unknown parameter using a calculation result of a least square method that has a minimum approximation error based on an output of the approximation error determination unit. The signal processing device according to claim 5,
The signal processing apparatus according to claim 1, wherein the unknown parameter estimation means determines a parameter having a minimum approximation error of the least square method as an estimated value of the number of signals included in the observation data. In the signal processing device according to any one of claims 1 to 6,
An unknown parameter of a signal observed by the sensor is estimated by ESPRIT. In the signal processing device according to any one of claims 1 to 6,
An unknown parameter of a signal observed by the sensor is estimated by VESPA. The signal processing device according to claim 3 or 4,
The estimated number of signals is used for signal processing based on a maximum likelihood estimation method, signal processing based on a super-resolution method, or independent component analysis.

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