JP2011013031A - Arrival direction estimating apparatus - Google Patents

Abstract

PROBLEM TO BE SOLVED: To reduce calculation time, while maintaining the accuracy of estimating the direction of arrival.SOLUTION: The arrival direction estimating apparatus includes an angle calculation section 107 for updating an arrival angle initial value by the beam former method and obtaining the updated arrival angle; an angle correcting section 108 for adding a value obtained, by multiplying an updated amount which is the difference between the updated arrival angle and the initial value, by a correction coefficient greater than or equal to one to the initial value to obtain a corrected arrival angle; a repetition number determining section 110 for determining whether the arrival angle and corrected arrival angle have been obtained for all the number of a plurality of arrival waves; and a convergence determining section 111 for determining whether the update amount is a threshold or below. The corrected arrival angle is set to be the initial value, and the updated arrival angle and corrected arrival angle are obtained repeatedly, until the repetition number determining section 110 determines that the updated arrival angle and corrected arrival angle have been obtained for all the plurality of arrival waves and that the update amount is threshold or below. The angle correction section 108 sets the correction coefficient to be a value greater than or equal to one at least once out of the number of its repeated operations.

Description

  The present invention relates to a direction-of-arrival estimation technique, and more particularly to a calculation time reduction method.

  Conventionally, the SAGE method is known as an algorithm for estimating the direction of arrival of radio waves using an array antenna (see, for example, Non-Patent Document 1). The SAGE method has no limitation on the arrangement of array antennas and has high accuracy.

J.A.Fessler, and A.O.hero. “Space-alternating generalized expectation-maximization algorithm,” IEEE Trans. Signal Processing, vol. 42, no. 10, pp. 2664-2677, 1994.

However, since the SAGE algorithm is an algorithm that repeatedly obtains and updates a large number of unknown parameters, there is a problem that the calculation time until the updated result converges is long, and therefore reduction of the calculation time becomes a problem. .
The present invention has been made to solve the above-described problems, and an object of the present invention is to provide an arrival direction estimation device that reduces the calculation time while maintaining the arrival direction estimation accuracy.

  In order to solve the above-described problem, an arrival direction estimation apparatus according to the present invention updates an initial value of one arrival angle among a plurality of arrival waves by a beamformer method, and obtains an updated arrival angle; A value obtained by multiplying an update amount, which is a difference between the updated arrival angle and the initial value, by a correction coefficient of 1 or more is added to the initial value to obtain a corrected arrival angle; and the plurality of incoming waves A repetition number determination unit that determines whether or not the arrival angle and the corrected arrival angle have been obtained for all numbers, and a convergence determination unit that determines whether or not the update amount is equal to or less than a first threshold, The amount of update when the iteration number determination unit determines that the updated arrival angle and the corrected arrival angle have been obtained for all of the plurality of incoming waves, and the convergence determination unit sets the corrected arrival angle to the initial value Is the first threshold Until it is determined as follows, the angle calculation unit and the angle correction unit set the corrected arrival angle to the initial value, repeatedly obtain the updated arrival angle and the corrected arrival angle, the angle correction unit, The correction coefficient is set to a value larger than 1 for one or more times of repeated executions.

  According to the arrival direction estimation device of the present invention, it is possible to reduce the calculation time while maintaining the estimation accuracy of the arrival direction.

The block diagram which shows the arrival direction estimation apparatus which concerns on 1st Embodiment. The figure which shows the incoming wave which injects into an array antenna. The figure which shows the view of the SAGE method which concerns on this embodiment. The flowchart which shows operation | movement of an arrival direction estimation part. The figure which shows the arrival angle of the repetition frequency m times. The figure which shows the arrival angle of the frequency | count of repetition m + 1. The figure which shows correction | amendment of the arrival angle of the frequency | count of repetition m + 1. The figure which shows the structure of the array antenna of 4 rows 4 columns. The figure which shows the coordinate system which concerns on this embodiment. The figure which shows the change of the azimuth with respect to the repetition frequency using a conventional method. The figure which shows the change of the elevation angle with respect to the repetition frequency using the conventional method. The figure which shows the change of the azimuth with respect to the frequency | count of repetition using the method which concerns on this embodiment. The figure which shows the change of an elevation angle with respect to the repetition frequency using the method which concerns on this embodiment. The figure which shows an example of the correction coefficient (alpha) which concerns on 2nd Embodiment. The figure which shows an example of the correction coefficient (alpha) which concerns on 3rd Embodiment. The figure which shows another example of the correction coefficient (alpha) which concerns on 3rd Embodiment. The block diagram which shows the arrival direction estimation apparatus which concerns on 5th Embodiment. The flowchart which shows operation | movement of the arrival direction estimation part which concerns on 5th Embodiment. The figure which shows the hardware constitutions of an arrival direction estimation apparatus.

(First embodiment)
Hereinafter, an arrival direction estimation apparatus according to an embodiment of the present invention will be described in detail with reference to the drawings. In the following embodiments, the same reference numerals are assigned to the same numbered parts, and repeated description is omitted.
The configuration of the arrival direction estimation apparatus according to the present embodiment will be described in detail with reference to FIG.
The arrival direction estimation apparatus 100 according to the present embodiment includes an array antenna 101, a reception unit 102, and an arrival direction estimation unit 103. Furthermore, the arrival direction estimation unit 103 includes an initial value setting unit 104, an arrival signal calculation unit 105, a y _k (t) calculation unit 106, a θ _k calculation unit 107 (hereinafter also referred to as an angle calculation unit 107), A θ _k correction unit 108 (hereinafter also referred to as an angle correction unit 108), an s _k (t) calculation unit 109, a repeat count determination unit 110, and a convergence determination unit 111 are included. k is an index representing the number of incoming waves.

  The array antenna 101 is composed of a plurality of antennas (each antenna is also referred to as an antenna element) designed to receive incoming waves. An arbitrary antenna may be used as the antenna, and an antenna having a wide beam width, for example, a patch antenna may be used when receiving an incoming wave in a wide angle range. If it is desired to receive a narrow range of incoming waves, an antenna with a narrow beam width, for example, a horn antenna may be used. Furthermore, the arrangement of the array antenna 101 composed of a plurality of antennas may be an arbitrary arrangement. Some of the arrival direction estimation algorithms include a condition that all adjacent antenna element intervals are the same as an array condition, or a condition that a circular array is used. Arbitrary arrangement may be used without restricting various conditions.

  The receiving unit 102 generates a received signal x (t) from the incoming wave received by the array antenna 101. The received signal x (t) is a signal actually received by the array antenna 101, and is represented by a column vector having a component for each number of antenna elements. Further, the receiving unit 102 includes, for example, a frequency filter, a power amplifier, a frequency converter, and an analog-digital converter. If it is.

The arrival direction estimation unit 103 estimates the angle θ _k of the arrival direction of the incoming wave (hereinafter referred to as arrival angle θ _k ) from the received signal x (t) received from the reception unit 102, and uses the estimated arrival angle θ _k as an external Output to.

Furthermore, components included in the arrival direction estimation unit 103 will be described.
The initial value setting unit 104 sets the initial value of the arrival angle θ _k used for the arrival angle estimation algorithm by the number of arrival waves.
The arrival signal calculation unit 105 receives the reception signal x (t) from the reception unit 102 and the initial values of the plurality of arrival angles θ _k from the initial value setting unit 104, and receives the reception signal x (t) and the plurality of arrival angles θ. An incoming signal s _k ⁽⁰⁾ (t) for each incoming wave is calculated from the initial value of _k . The incoming signal s _k ⁽⁰⁾ (t) is a signal of the incoming wave k estimated from the known received signal x (t), and has an in-phase component and a quadrature component. That is, the signal from the direction defined by the initial values of the arrival angle theta _k is represented by a signal on the assumption that arrives. For example, the incoming signal s ₁ ⁽⁰⁾ (t) indicates a signal when the incoming wave 1 is assumed to arrive from a direction determined by the initial value of the incoming angle θ ₁ .
The y _k (t) calculation unit 106 receives the arrival signal s _k ⁽⁰⁾ (t) for each arrival wave, the reception signal x (t), and the initial values of the plurality of arrival angles θ _k from the arrival signal calculation unit 105. , Y _k (t) that is a received signal for each incoming wave is calculated. The received signal y _k (t) for each incoming wave is a signal received by each antenna element when the incoming signal s _k ⁽⁰⁾ (t) for the incoming wave k is received. It is represented by a column vector. For example, the received signal y ₁ (t) indicates a signal received by each antenna element when the incoming signal s ₁ ⁽⁰⁾ (t) for the incoming wave 1 is received. That is, when all the received signals y _k (t) for each incoming wave are added, the entire received signal x (t) received by the receiving unit 102 is obtained.
The θ _k calculation unit 107 receives the reception signal y _k (t) from the y _k (t) calculation unit 106, updates the arrival angle θ _k by the beamformer method based on the reception signal y _k (t), and updates it. An updated arrival angle that is the calculated arrival angle is calculated.
The θ _k correction unit 108 receives the reception signal y _k (t) and the updated arrival angle from the θ _k calculation unit 107, corrects the updated arrival angle, and calculates a corrected arrival angle that is the corrected arrival angle.
The s _k (t) calculation unit 109 receives the corrected arrival angle from the θ _k correction unit 108 and calculates a new arrival signal s _k (t) based on the corrected arrival angle.

The number-of-repetitions determination unit 110 determines whether the above-described processing from the y _k (t) calculation unit 106 to the s _k (t) calculation unit 109 has been performed for the number of incoming waves, and the processing is performed for the number of incoming waves. If not, the same processing from the y _k (t) calculation unit 106 to the s _k (t) calculation unit 109 is performed for the next incoming wave. When processing is performed for the number of incoming waves, the corrected arrival angle is sent to the convergence determination unit 111. Note that the repetition count determination unit 110 may receive the parameters calculated from the y _k (t) calculation unit 106 to the s _k (t) calculation unit 109 together. The parameters are, for example, the arrival angle θ _k , the incoming signal s _k (t), and the received signal y _k (t).

The convergence determination unit 111 determines whether the parameter received from the repetition count determination unit 110 has converged. When the convergence determination unit 111 determines that the convergence has not occurred, the new arrival signal s _k (t) among the received parameters is sent to the y _k (t) calculation unit 106. When the convergence determination unit 111 determines that the convergence has occurred, the parameter value is output to the outside. The determination of convergence is made based on whether or not the amount of change in the parameter value after update (hereinafter referred to as update amount) with respect to the parameter value before update is equal to or less than a threshold value. It should be noted that the parameters calculated from the y _k (t) calculation unit 106 to the s _k (t) calculation unit 109 may be received by the convergence determination unit 111 from the repetition count determination unit 110, or each unit may receive the parameter. At the time of calculation, parameters may be received from each unit. For _example, when _{the y} k (t) calculation unit 106 calculates a reception signal _y k (t), the convergence determination portion 111 the received signal _y k (t) may be received.

Here, the SAGE method used in the present embodiment will be described in detail with reference to FIGS.
In the following description, the number of incoming waves is two. FIG. 2 shows the relationship between the array antenna 201, the incoming wave 202, and its parameters. The incoming wave 1 is an incoming signal s ₁ (t) and an incoming angle θ ₁ . The incoming wave 2 is an incoming signal s ₂ (t) and an incoming angle θ ₂ . The received signal of the array antenna 201 at this time is x (t) = [x ₁ (t), x ₂ (t),..., X _p (t)] ^T. p is the number of antenna elements. T is a symbol representing transposition.

In the calculation of the SAGE method, a plurality of incoming waves are decomposed separately to obtain all parameters. FIG. 3 is a diagram showing a concept of calculation of the SAGE method. For the incoming wave 1, the incoming signal s ₁ (t), the incoming angle θ ₁ , and the received signal of the array antenna 201 are y ₁ (t) = [y ₁₁ (t), y ₁₂ (t),. _1p (t)] ^T. Here, the subscript of the vector component, for example, y ₁₂ (t) represents the received signal received by the antenna element of index 2 for the incoming wave 1. Similarly, for the incoming wave 2, the incoming signal s ₂ (t), the incoming angle θ ₂ , and the received signal of the array antenna are y ₂ (t) = [y ₂₁ (t), y ₂₂ (t),. y _2p (t)] ^T. That is, in this case, the reception signal x (t) can be expressed by the sum of the received signal y _{2 (t)} of the incoming wave 2 and the reception signal y ₁ of the incoming wave 1 _(t).

As described above, by giving the actual received signal x (t) and the initial values for θ ₁ and θ ₂ , other parameters are calculated in order and the values are updated, and the updated values converge. Repeat the calculation until As a result, six types of parameters s ₁ (t), θ ₁ , y ₁ (t), s ₂ (t), θ ₂ , y ₂ (t) are obtained by the SAGE method.

Next, an example of the operation of the arrival direction estimation unit 103 will be described in detail with reference to the flowchart of FIG. In the following description, the number of incoming waves is two as in the above-described calculation of the SAGA method. However, the number of incoming waves is not limited to two, and the same calculation can be performed even when there are a plurality of incoming waves.
First, in S401, the initial value setting unit 104 sets an initial value of the arrival angle theta _k of incoming waves by the number equal to the number of incoming waves. Here, initial values of θ ₁ and θ ₂ are set. The initial value setting method may be an arbitrary method, for example, a method of setting at random with respect to an assumed range of arrival angles. Alternatively, although the estimation accuracy is limited by the beam width, the direction of arrival may be estimated by the beam former method and the result may be used. The estimation accuracy of the beamformer method is limited because it is affected by the beam width, but the error is smaller than when the initial value is given randomly, and the number of iterations until the estimated arrival angle converges is reduced. In addition S401, the incoming signal calculation unit 105 receives from the initial value setting unit 104 and the arrival angle theta _k from the receiving unit 102 and the reception signal x (t), using the arrival angle theta _k and a reception signal x (t) Then, the incoming signal s _k (t) is calculated. The incoming signal s _k (t) can be obtained from the following equation.

Here, H is a symbol representing a complex conjugate transpose, and T is a symbol representing a transpose. Ns indicates the number of data sampling, but here, for simplicity, it is simply expressed as s ⁽⁰⁾ (t) without considering the number of sampling. m is the number of repetitions of the processing from S402 to S405 shown in FIG. 4, and the initial value is 0. X (t) is a column vector having elements corresponding to the number p of antenna elements. a (θ _k ^(m) ) is a mode vector having an angle θ, which is a column vector having elements corresponding to the number p of antenna elements, and the subscript K represents the number of incoming waves. The mode vector is a value determined from the coordinates (arrangement) of the antenna. That is, A ⁽⁰⁾ is a matrix of p rows and K columns. From s ⁽⁰⁾ (t) shown in Equation (1) and Equation (3), the incoming signal s ₁ ⁽⁰⁾ (t) of the incoming wave 1 and the incoming signal s ₂ ⁽⁰⁾ (t) of the incoming wave 2 are Each can be calculated. In the following steps, since processing is performed for each incoming wave, first, k = 1 is set and processing is performed for incoming wave 1.

Next, in S402, the y _k (t) calculation unit 106 receives the arrival signal s ⁽⁰⁾ (t), the reception signal x (t), and the arrival angle θ _k from the arrival signal calculation unit 105. The received signal y _k (t) is calculated. The received signal y _k (t) can be obtained by the following equation.

However, β _k is a non-negative coefficient. For example, β _k = 1 / K may be set. Further, y _k ^(m) (t), a (θ _k ^(m) ), and x (t) are column vectors having elements corresponding to the number p of antenna elements. Further, s ^(m) (t) is a column vector having elements corresponding to the number of incoming waves K. s _k ^(m) (t) represents an incoming signal of the k-th incoming wave, and is a scalar that is a value obtained from s ^(m) (t). A ^(m) is a matrix of p rows and K columns. From this equation (4), the received signal y ₁ (t) of the incoming wave 1 is calculated.

Next, in S403, the θ _k calculation unit 107 receives the reception signal y _k (t) from the y _k (t) calculation unit 106, and calculates the arrival angle θ _k ^{(m + 1)} . The arrival angle θ _k ^{(m + 1)} is calculated according to the beamformer method, and the value calculated in this step is used as the new arrival angle with respect to the arrival angle θ _k ^(m) used in the equations (2) and (4). Update as θ _k ^{(m + 1)} . In the beam former method, the arrival angle is obtained by calculating the following evaluation function. A new arrival angle resulting from this update is called an updated arrival angle.

y _k ^(m) (t) is a column vector having elements corresponding to the number p of antenna elements, and C _k ^(m) is a matrix of p rows and p columns. The updated arrival angle θ ₁ ^{(m + 1)} for the incoming wave 1 can be obtained from Equation (5). For example, when this step is the first processing for the incoming wave 1, since m = 0, the arrival angle set by the initial value setting unit 104 is θ ₁ ⁽⁰⁾ and is updated by Expression (5). The updated arrival angle can be expressed as θ ₁ ⁽¹⁾ .

Next, in S404, the θ _k correction unit 108 receives the received signal y _k (t) and the updated arrival angle θ _k ^{(m + 1)} from the θ _k calculation unit 107, and arrives according to the correction equation shown in the following equation (7). The corrected arrival angle is obtained by correcting the angle. This step is a calculation step specific to the present embodiment, which is performed in addition to the conventional SAGE method.
Θ _k ^{(m + 1)} after correction = θ _k ^(m) + α {θ _k ^{(m + 1)} −θ _k ^(m) } before correction (7)
Here, θ _k ^(m) is the arrival angle before being updated in S403, θ _k ^{(m + 1)} before correction is the updated arrival angle updated in S403, the arrival angle before correction, and θ after correction. _k ^{(m + 1)} is the arrival angle after being corrected in S404, that is, the corrected arrival angle. Thereby, θ ₁ ^{(m + 1)} (corrected arrival angle) after correction can be calculated from θ ₁ ^{(m + 1)} (update arrival angle) before correction for incoming wave 1. Α is a correction coefficient and is a constant of 1 or more. If α = 1, no correction is performed, so the conventional SAGE method is used. By this step, the number of repetitions required until the arrival angle value is stabilized is reduced, and the calculation time is reduced. S404 will be described in detail later with reference to FIG. 5, FIG. 6, and FIG.

Next, in S405, the s _k (t) calculation unit 109 receives the received signal y _k (t) and the corrected arrival angle θ _k ^{(m + 1)} from the θ _k correction unit 108, and this corrected arrival angle θ _k ^{(m + 1). )} To calculate a new incoming signal s _k ^{(m + 1)} (t). s _k ^{(m + 1)} (t) can be calculated by the following equation.

The incoming signal s ₁ ^{(m + 1)} (t) updated with respect to the incoming wave 1 can be calculated by the equation (8). That is, if the data of the first incoming signal s ₁ (t) already calculated in S401 is s ₁ ⁽⁰⁾ (t), the incoming signal s ₁ ⁽¹⁾ (t) is obtained by this calculation, and s ₁ ⁽¹⁾ Update s ₁ ⁽⁰⁾ (t) using (t).

Next, in S406, the repetition number determination unit 110 determines whether or not the steps from S402 to S405 are performed for the number of incoming waves. If it is determined that the processing is not performed for the number of incoming waves, k is incremented and the processing returns to S402, and the same processing as the steps S402 to S405 described above is performed for the number of other unprocessed incoming waves. Repeat. On the other hand, if it is determined that the processing is performed for the number of incoming waves, the process proceeds to the next S407.
The determination used in this step may be, for example, using the parameter received by the repetition count determination unit 110 to determine whether or not the number of incoming waves is being processed based on the parameter index. For example, when the processing for the incoming wave 1 is completed, the processing is still performed by referring to the number of initial values of the set arrival angle θ _k or the number of received signals y _k (t) for each incoming wave. Since there is no incoming wave, if there is an unprocessed incoming wave, the incoming wave 2 is also processed, and the received signal y ₂ (t), incoming signal s ₂ (t), incoming angle θ ₂ , correction The arrival angle θ ₂ and the new arrival signal s ₂ (t) are obtained using the same procedure and calculation formula, and the parameters are updated.
Finally, in S407, the convergence determination unit 111 determines whether or not the value of the parameter received from the s _k (t) calculation unit 109 has converged. In the determination of convergence, the update amount of the parameter after update with respect to the parameter before update is calculated, and when the update amount is equal to or less than the threshold, it is determined that the parameter has converged, and the entire process is terminated. The update amount is a change amount of the updated parameter value with respect to the pre-update parameter value represented by (θ _k ^{(m + 1)} −θ _k ^(m) ). Also, if it is determined that it has not converged, that is, if the update amount is larger than the threshold value, the value of m is incremented, and the convergence determining unit 111 sets parameters (s ₁ (t) and s that are new incoming signals). ₂ (t)) is sent to the y _k (t) calculation unit 106, and the processing from S402 to S406 is repeated until the value converges. Since all parameters related to the incoming wave are obtained as parameters used for this determination, if there are a plurality of parameters received from the repetition count determination unit 110, the convergence determination may be performed using any parameter. For example, when the purpose is arrival direction estimation, it can be determined that the arrival angle θ _k has converged if the update amount of the value of the arrival angle θ _k is less than or equal to the threshold, and it can be determined that it has not converged if it is greater than the threshold.

Here, the correction of the arrival angle in S403 and S404 will be described in more detail with reference to FIGS. As an example, let us consider correction for the arrival angle θ ₁ of the incoming wave 1.
First, FIG. 5 shows an example of the evaluation function in the beamformer method with the mth repetition in S403. The value of the evaluation function is calculated while changing the angle θ in Expression (5), and the angle at which the value of the evaluation function is maximum is defined as the arrival angle θ ₁ ^(m) . When θ ₁ is given as an initial value, that is, when θ ₁ ⁽⁰⁾ , it does not become a function as shown in FIG. 5 and shows a constant value.
Next, FIG. 6 shows an example of the evaluation function in the beamformer method with the number of repetitions m + 1 in S403. Compared with the m-th beamformer method, the value of the evaluation function changes. This is because the values of the received signals y ₁ (t) and y ₂ (t), the incoming signals s ₁ (t) and s ₂ (t), and the incoming angle θ ₂ are values when the m-th beamformer method is used. This is because it has changed.

Finally, FIG. 7 shows an example of m + 1 correction calculation of θ 1 in S404. 7 shows the mth arrival angle θ 1 (m) shown in FIG. 5, the m + 1th arrival angle θ 1 (m + 1) (update arrival angle) shown in FIG. 6, and the corrected arrival angle θ 1 (m + 1). ) (Corrected arrival angle) relationship. As shown in FIG. 7, with respect to changes in the m + 1 th arrival angle theta 1 (m + 1) arrival angle of m-th theta 1 with respect to (m), in the direction of arrival angle is changed, the arrival angle by the equation (6) By correcting the update amount with a value proportional to the coefficient α, the update amount is estimated to be large. That is, the correction is performed so that the value is further increased if the value of the arrival angle is increased, and is further decreased if the value of the arrival angle is decreased. As a result, the angle is updated to a different angle from the conventional optimum value, and the convergence of the parameters can be accelerated.

Next, the effect of reducing the amount of calculation compared to the conventional SAGE method will be described using specific numerical calculation results.
A model used for specific numerical calculation will be described. The array antenna is a 4-element × 4-element 16-element square array antenna as shown in FIG. The element interval 801 is a half wavelength.
Further, FIG. 9 shows a coordinate system for arranging the array antenna. The azimuth angle is φ and the elevation angle is θ. Assume that two incoming waves are incident on this array antenna. That is, the number of incoming waves is two. The two incoming waves have equal power and the correlation coefficient is 1. As for the arrival angle, the arrival wave 1 is (azimuth angle 1, elevation angle 1) = (90 °, 60 °), and the arrival wave 2 is (azimuth angle 2, elevation angle 2) = (120 °, 40 °).
The results calculated according to the conventional SAGE method under the above-described conditions will be described with reference to FIGS. 10 and 11 show changes in azimuth angle and elevation angle with respect to the number of processing repetitions. As the initial value, the incoming wave 1 has (initial value azimuth angle 1 = 60 °, initial value elevation angle 1 = 80 °), and the incoming wave 2 has (initial value azimuth angle 2 = 150 °, initial value elevation angle 2 = 20 °). Referring to FIGS. 10 and 11, it can be seen that the arrival angles of both the azimuth angle and the elevation angle converge gradually, and the arrival angles can be estimated with high accuracy in about 95 times. Here, the value of the arrival angle is a monotonically decreasing or monotonically increasing function with respect to the number of short-term repetitions.

Next, the results calculated according to the present embodiment will be described with reference to FIGS. 12 and 13 show changes in the azimuth angle and the elevation angle with respect to the number of processing repetitions, as in FIGS. 10 and 11. The same initial values as those of the conventional SAGE method are given to the two incoming waves. Since the arrival angle is two-dimensional, that is, an azimuth angle and an elevation angle, the correction calculation of Expression (6) is applied to each of the azimuth angle and the elevation angle. Specifically, it is calculated using the following formula.
Φ _k ^{(m + 1)} after correction = φ _k ^(m) + α {φ _k ^{(m + 1)} −φ _k ^(m) } before correction (9)
Θ _k ^{(m + 1)} after correction = θ _k ^(m) + α {θ _k ^{(m + 1)} −θ _k ^(m) } before correction (10)
Note that the calculation is performed with a coefficient α = 1.3. As shown in FIGS. 12 and 13, the arrival angles of both the azimuth and the elevation are converged earlier than the conventional method, and the arrival angles are estimated with high accuracy in about 50 times. In this way, by adding a correction calculation, the number of iterations can be halved while maintaining the estimation accuracy.

  According to the first embodiment described above, by performing correction that gives a larger value of the arrival angle to be updated than the conventional update amount, the parameter value converges earlier and the number of repetitions is reduced. Therefore, calculation time can be reduced.

(Second Embodiment)
The present embodiment is characterized in that the value of the correction coefficient α is set to be proportional to the magnitude of (θ _k ^{(m + 1)} −θ _k ^(m) ), that is, the update amount. In the first embodiment, the value of the correction coefficient α is a constant value, and constant correction is performed even if the update amount is large. In the present embodiment, the correction coefficient α is set in proportion to the size of the update amount. In other words, the correction is made larger when the update amount is large and is made small when the update amount is small. In some cases, convergence is accelerated and the number of repetitions can be reduced.

In the arrival direction estimation algorithm, when the update amount is large, the convergence may not be sufficiently advanced yet. In such a case, in some cases, it is effective to increase the correction amount so that the correction is made closer to the convergence value. In addition, when the update amount is small, it can be said that the convergence is approaching. Therefore, if the calculation is performed with the same correction coefficient α as when the update amount is large, the correction may be excessive and the convergence may be delayed. In such a case, the correction amount can be reduced to make the algorithm converge. Adjustment of the correction coefficient α is performed in the θ _k correction unit 108, and the update amount is calculated and then adjusted using this update amount. At this time, a table in which the proportional relationship between the update amount and the correction coefficient α is associated may be stored in advance, and this table may be referred to, or the calculated update amount is substituted into a calculation formula for calculating the correction coefficient α. The correction coefficient α may be calculated.
FIG. 14 shows the relationship between the update amount and the correction coefficient α. As shown in FIG. 14, when the update amount is large, the correction coefficient α is increased. When the update amount is small, the correction coefficient α is made small. In this way, the correction coefficient α is set so that the update amount is proportional. However, the minimum value of the correction coefficient α is 1. The correction coefficient α is not limited to be set in proportion to the update amount, but includes a case where a curve indicating the relationship between the update amount and the correction coefficient α is convex upward or downward. That is, in the present embodiment, the correction coefficient α only needs to be increased according to the update amount.

  According to the second embodiment described above, by setting the value of the correction coefficient α in proportion to the update amount, when the update amount is large, the correction amount is increased to accelerate the convergence, thereby Since the number of iterations required to converge is reduced, a reduction in calculation time can be achieved.

(Third embodiment)
The present embodiment is characterized in that the correction coefficient α is set to a value according to the number of repetitions of arrival direction estimation. In the arrival direction estimation algorithm, the value does not converge unless it is repeated to some extent, and in many cases, convergence does not proceed when the number of iterations is small, and tends to converge as the number of times increases. Therefore, in the initial stage where the number of iterations is small, the correction coefficient α is set to a large value to increase the speed of convergence, and as the number of iterations increases, the correction coefficient α is set to a small value so that convergence is not delayed by excessive correction. Like that. The adjustment of the correction coefficient α is performed by the _θk correction unit 108 as in the second embodiment, and the correction coefficient α is adjusted by referring to the index of the repetition count m included in each parameter. At this time, the θ _k correction unit 108 stores in advance a table in which the relationship between the number of repetitions m and the correction coefficient α is associated, and may refer to this table, or a calculation formula for calculating the correction coefficient α. The correction coefficient α may be calculated by substituting the number of repetitions to.

FIG. 15 shows the relationship between the number of algorithm iterations and the correction coefficient α. As shown in FIG. 15, when the number of repetitions is small, the correction coefficient α is set large to increase the effect of correction, and as the number of repetitions increases, the correction coefficient α is decreased to decrease the correction effect. Set. That is, the correction coefficient α is set to be inversely proportional to the number of algorithm iterations. By setting in this way, it is possible to reduce the number of repetitions while avoiding excessive correction.
Further, as an extreme case, the correction coefficient α may be set to α = 1 when the number of repetitions is equal to or greater than a certain threshold, and the correction coefficient α may be set larger than 1 when the number of repetitions is less than the threshold. An example in which the correction coefficient α is set in this way is shown in FIG. By setting in this way, when the number of iterations is large, the calculation is the same as that of the conventional SAGE method, so that it is possible to reduce the number of iterations until convergence while suppressing vibration.

  According to the third embodiment described above, the value of the correction coefficient α is inversely proportional to the number of iterations, so that when the number of iterations is small, the correction is made large and the convergence is stopped, and the number of iterations increases to approach convergence. Accordingly, it is possible to reduce the number of iterations until convergence is achieved by reducing the correction.

(Fourth embodiment)
In the second embodiment, the correction coefficient α is set to be large in proportion to the magnitude of the update amount. However, depending on the estimated arrival angle, when the update amount is large, the correction amount becomes too large. There is a possibility that the estimated value of the arrival angle after correction does not converge to a constant value, but increases and decreases repeatedly, and the parameter value vibrates and the number of convergence increases. Therefore, assuming such a case, the correction effect is reduced when the update amount is large, and the correction effect is increased when the update amount is small to reduce the number of repetitions. The same second embodiment, the adjustment of the correction coefficient α is carried out in the theta _k correcting unit 108.

  When the correction coefficient α is set according to the update amount, for example, the horizontal axis in FIGS. 15 and 16 may be replaced by “number of times” to “update amount”. In FIG. 15, when the update amount is large, the correction coefficient α is set small in order to reduce the correction effect. When the update amount is small, the correction coefficient α is set large in order to increase the correction effect. That is, the correction coefficient α is set to be inversely proportional to the update amount. In FIG. 16, the correction coefficient α is set to α = 1 when the magnitude of the update amount is equal to or greater than a predetermined threshold, and α is set to be greater than 1 when the magnitude of the update amount is smaller than the threshold.

  According to the fourth embodiment described above, for example, it is possible to suppress the vibration that may occur due to correction when the update amount is large and to reduce the number of repetitions until convergence.

  In addition, about how to give correction coefficient (alpha) according to the frequency | count and update amount in the above-mentioned 1st Embodiment to 4th Embodiment, you may implement not only the form of one Embodiment but combining multiple. . For example, for a single incoming wave, as in the first embodiment, when a constant value is given to the correction coefficient α, and it is determined that the algorithm has not converged after the algorithm has been repeated a certain number of times, the second implementation As in the embodiment, a correction coefficient α proportional to the update amount may be given. In addition, when the correction coefficient α is given in proportion to the update amount as in the second embodiment, and after the number of repetitions reaches a certain threshold, the correction is performed as in the third embodiment. The algorithm may be executed by giving the coefficient α inversely proportional to the number of repetitions.

(Fifth embodiment)
In the present embodiment, the correction coefficient α is set such that the corrected arrival angle is limited within a predetermined angle range. For example, consider the estimation of the direction of arrival of an incoming wave from a mobile phone terminal close to the ground, where a mobile phone base station is installed on the roof of a building. The incoming wave arrives from below the horizontal direction of the base station, and there is no need to consider the upper side from the horizontal direction. However, when the updated amount after correction is large, the arrival angle may be higher than the horizontal direction. In such a case, it is meaningless to calculate the arrival angle outside the assumed range, so when the arrival angle is larger than the horizontal direction, the convergence of the parameter can be accelerated by setting the upper limit value in the horizontal direction. it can.

Next, the calculation failure when the arrival angle is within the angle range will be described.
As described above, a mobile phone base station is installed on the roof of a building, and the direction of arrival of an incoming wave from a mobile phone terminal close to the ground is considered. The incoming wave arrives from below the horizontal direction of the base station, and there is no need to consider the upper side from the horizontal direction. Here, since it is not necessary to consider the upper side from the horizontal direction, the calculation for the upper side is unnecessary. By configuring the calculation algorithm and calculation hardware so as not to perform unnecessary calculation, the cost and size can be reduced. However, there is a problem that when such unnecessary calculation cannot be performed, if the data in that range is generated, the calculation is broken and an error occurs.
Therefore, in the present embodiment, the value of the correction coefficient α is set to be small so that the corrected arrival angle is limited within a predetermined angle range. In the case of this description, it is limited to be below the horizontal direction.

  According to the fifth embodiment described above, by setting the correction coefficient α so that the corrected arrival angle is limited within a predetermined angle range, a range in which calculation is meaningless, or It is possible to suppress the occurrence of arrival angles in a range that cannot be calculated, reduce the number of algorithm iterations, reduce the calculation time, and suppress calculation failures.

(Sixth embodiment)
In the first embodiment, it is determined whether or not the number-of-arrivals processing has been performed in the number-of-repetitions determination unit 110. If processing is not performed for the number of incoming waves, the processing from S402 to S405 shown in FIG. 4 is repeated. Is doing. In the present embodiment, the calculation time is effectively shortened by calculating the processes of S402 to S405 in parallel for each incoming wave according to the number of incoming waves, regardless of the number of repetitions determination unit 110. There is a special feature.
An arrival direction estimation apparatus 1700 according to this embodiment is shown in FIG. The difference from the arrival direction estimation apparatus 100 according to the first embodiment is that, in the arrival direction estimation unit 1701, the y _k (t) calculation unit 106, the θ _k calculation unit 107, the θ _k correction unit 108, and the s _k (t ) The calculation unit 109 is set as one set, 1701, 1702,... Are provided as many as the number of incoming waves, and the repetition number determination unit 110 is not provided.

  The operation of the arrival direction estimation unit 1701 according to this embodiment will be described with reference to the flowchart of FIG. First, the difference between the flowchart of FIG. 4 according to the first embodiment and FIG. 18 will be described. In the first embodiment, the process from S402 to S405 is calculated in order for each incoming wave, and it is determined whether or not the process has been performed for the number of incoming waves in S406. When the processing of the incoming wave 1 is completed, each parameter is calculated in series until the processing of the incoming wave 2, the processing of the incoming wave 3, and the processing of the incoming wave K.

On the other hand, in the flowchart of FIG. 18 according to the present embodiment, the processes from S402 to S405 are calculated in parallel for the number of incoming waves. For example, when there are two arriving waves, in S401 shown in FIG. 17, the initial value of the arrival angle θ _k is given by the number of arriving waves as in the process shown in FIG. 4, and s _k (t) is calculated. Next, a y _k (t) calculation unit 106, a θ _k calculation unit 107, a θ _k correction unit 108, and an s _k (t) calculation unit 109 are prepared for each of the incoming wave 1 and the incoming wave 2. The processes from S402 to S405 shown in S1801 and S1802 are performed in parallel. Thereafter, in S407, it is determined whether or not the parameter value has converged. If the parameter value has converged, the process ends. If the parameter value has not converged, m is incremented and the processing of S1801 and S1802 is repeated. The parallel calculation is to prepare arithmetic hardware such as a plurality of CPUs and perform different calculations at the same time. As a result, the overall calculation amount required for one iteration does not change, but a plurality of calculations can be performed at the same time, so that the effective calculation time can be shortened.

  According to the sixth embodiment described above, the effective calculation time can be shortened by calculating in parallel the number of incoming waves.

(Seventh embodiment)
In this embodiment, assuming two-dimensional arrival direction estimation of azimuth angle φ and elevation angle θ, in the first embodiment, the same correction coefficient α is used in the correction formula for the arrival angle of azimuth angle and elevation angle. In this embodiment, the correction formula for the azimuth angle is φ _k ^(m) + α_φ {φ _k ^{(m + 1)} −φ _k ^(m) }, and the correction formula for the elevation angle is θ _k ^(m) + α_θ {θ _k ^{(m + 1).} As -θ _k ^(m) }, a different value is used for the correction coefficient α depending on the azimuth angle and the elevation angle. As a result, it becomes possible to perform optimum correction for the azimuth angle and the elevation angle.
Depending on the arrangement of the array antenna, the estimation accuracy of the azimuth angle and the elevation angle may be different, and the error in the initial values of the azimuth angle and the elevation angle may be different. In such a case, since the optimum value of the correction value of the azimuth angle and the elevation angle is different, it is desirable that the value of the correction coefficient α is different between the azimuth angle and the elevation angle.

Specifically, if the azimuth angle is φ and the elevation angle is θ,
Φ _k ^{(m + 1)} after correction = φ _k ^(m) + α_φ {φ _k ^{(m + 1)} −φ _k ^(m) } before correction (11)
Θ _k ^{(m + 1)} after correction = θ _k ^(m) + α_θ {θ _k ^{(m + 1)} −θ _k ^(m) } before correction (12)
In this way, the correction equations are configured separately for the azimuth angle φ and the elevation angle θ, and are set separately for the correction coefficients α_φ and α_θ.

  According to the seventh embodiment described above, in the two-dimensional direction-of-arrival estimation, optimal correction can be performed by setting the correction coefficient α to a different value between the azimuth angle and the elevation angle. The number of repetitions is reduced, and the calculation time can be reduced.

When there are a plurality of incoming waves, a different correction coefficient α may be assigned to each incoming wave. In this case, since the optimum correction coefficient α according to the incoming wave can be set, the calculation time can be reduced. In addition, when there are a plurality of incoming waves and two-dimensional estimation of the azimuth angle φ and the elevation angle θ, a different correction coefficient α is assigned to each incoming wave, and a different correction coefficient α is assigned to the azimuth angle and the elevation angle. Good. In this case, since the optimum correction coefficient α can be set for the azimuth angle and elevation angle of each incoming wave, the calculation time can be reduced.
Furthermore, the correction coefficient α may be determined in advance for the number of repetitions m. In this case, it is not necessary to calculate the magnitude of the update amount. It is only necessary to determine a table of the number of repetitions m and the correction coefficient α in advance and refer to this table. This further reduces the amount of calculation. Alternatively, the value of the correction coefficient α may be a fixed value. In this case, since the procedure for setting the correction coefficient α is omitted, the calculation amount is further reduced.
Further, the value of the correction coefficient α may be obtained in advance. For example, there is a method of obtaining an optimum correction coefficient α from an analysis result using a received signal. Alternatively, an optimal correction coefficient α may be obtained using simulation.

Here, the hardware configuration of the arrival direction estimation apparatus 100 is shown in FIG. The arrival direction estimation apparatus 100 includes a ROM 1901 that stores an arrival direction estimation program for executing arrival direction estimation, a CPU 1902 that controls each part of the arrival direction estimation apparatus in accordance with a program in the ROM 1901, and control of the arrival direction estimation apparatus. A RAM 1903 that stores various necessary data, a communication I / F 1904 that communicates by connecting to a network, and a bus 1905 that connects each unit are provided.
The arrival direction estimation program may be provided by being stored in a computer-readable storage medium such as a CD-ROM, a flexible disk (FD), and a DVD as an installable or executable file.
In this case, the arrival direction estimation program is loaded onto the main storage device of the arrival direction estimation device 100 by being read from the storage medium and executed, and each part of the software configuration shown in FIG. 19 is formed on the main storage device. It has become so.
Further, the arrival direction estimation program of the present embodiment may be configured to be stored by being stored on a computer connected to a network such as the Internet and downloaded via the network or communication I / F 1904.

  The present embodiment is applied to an arrival direction estimation apparatus using an array antenna, but can also be applied to various technical fields in which an array antenna is used, such as radio wave monitoring, mobile communication, and a radar apparatus. In addition to estimating the arrival direction of radio waves, the present invention can also be applied to estimation of the arrival direction of sound waves. In addition to arrival direction estimation, the present invention can be applied to technical fields in which the same calculation procedure is used, such as radio wave and sound wave delay time estimation.

Although different from the present embodiment, in a general optimization problem, a parameter that maximizes or minimizes the evaluation function is searched under a fixed evaluation function. At this time, a method is known in which the parameter update amount is multiplied by a coefficient to increase the speed of optimization.
On the other hand, in this embodiment, a different evaluation function is calculated for each repetition count. Then, the evaluation function in the next iteration is prefetched to correct the parameter (arrival angle). That is, it is different from the method for improving the convergence speed in general optimization.

  Note that the present invention is not limited to the above-described embodiment as it is, and can be embodied by modifying the constituent elements without departing from the scope of the invention in the implementation stage. In addition, various inventions can be formed by appropriately combining a plurality of components disclosed in the embodiment. For example, some components may be deleted from all the components shown in the embodiment. Furthermore, constituent elements over different embodiments may be appropriately combined.

DESCRIPTION OF SYMBOLS 100 ... Arrival direction estimation apparatus, 101, 201 ... Array antenna, 102 ... Reception part, 103 ... Arrival direction estimation part, 104 ... Initial value setting part, 105 ... Arrival signal calculation , 106... Y _k (t) calculation unit, 107... Θ _k calculation unit, 108... Θ _k correction unit, 109... S _k (t) calculation unit, 110. Judgment unit 111 ... Convergence judgment unit 202 ... Arrival wave 801 ... Element spacing 1901 ... ROM 1902 ... CPU 1903 ... RAM 1904 ... Communication I / F, 1905 ... Bus.

Claims (5)

An angle calculation unit that updates an initial value of one arrival angle among a plurality of arrival waves by a beamformer method, and obtains an updated arrival angle;
An angle correction unit that obtains a corrected arrival angle by adding a value obtained by multiplying an update amount, which is a difference between the updated arrival angle and the initial value, by a correction coefficient of 1 or more to the initial value;
A repetition number determination unit that determines whether or not the arrival angle and the corrected arrival angle have been obtained for all of the plurality of arrival waves;
A convergence determination unit that determines whether or not the update amount is equal to or less than a first threshold,
Update amount when the repetition number determination unit determines that the updated arrival angle and the corrected arrival angle have been obtained for all of the plurality of incoming waves, and the convergence determination unit sets the corrected arrival angle to the initial value Until the angle is determined to be less than or equal to the first threshold, the angle calculation unit and the angle correction unit set the corrected arrival angle to the initial value, repeatedly obtaining the updated arrival angle and the corrected arrival angle,
The angle correction unit sets the correction coefficient to a value larger than 1 for one or more times of repeated executions. For a plurality of incoming waves, for each of the incoming waves, an initial value of the incoming angle of the incoming wave is updated in parallel by a beamformer method, and an angle calculating unit that obtains updated incoming angles by the number of the incoming waves;
For each incoming wave, a value obtained by multiplying the update amount, which is the difference between the updated arrival angle and the initial value, by a correction coefficient of 1 or more is added to the initial value to obtain the corrected arrival angle by the number of the incoming waves. An angle correction unit;
A convergence determination unit that determines whether or not the update amount is equal to or less than a first threshold,
The update when the iteration number determination unit determines that the updated arrival angle and the corrected arrival angle have been obtained for all of the plurality of incoming waves, and the convergence determination unit sets the corrected arrival angle to the initial value. Until it is determined that the amount is equal to or less than the first threshold, the angle calculation unit and the angle correction unit set the corrected arrival angle to the initial value, repeatedly obtaining the updated arrival angle and the corrected arrival angle,
The angle correction unit sets the correction coefficient to a value larger than 1 for one or more times of repeated executions.   The correction coefficient is set to 1 when the number of executions of the angle calculation unit and the angle correction unit is equal to or greater than a second threshold, and the correction is performed when the number of times is less than the second threshold. The arrival direction estimation apparatus according to claim 1 or 2, wherein the coefficient is set to a value larger than one.   The arrival direction estimation apparatus according to claim 1, wherein the correction coefficient is set so that the corrected arrival angle is limited within a predetermined angle range.   5. The direction-of-arrival estimation according to claim 1, wherein the angle correction unit uses different values of the correction coefficient in calculating the corrected arrival angle of an azimuth angle and an elevation angle. apparatus.

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