JP6663098B2 - Wave source position selection device, wave source position calculation device, wave source position selection method, wave source position calculation method, and program - Google Patents

Description

  The present invention relates to a wave source position selecting device for selecting a position of a wave source.

  In recent years, as one of the means for improving the frequency use efficiency to cope with a shortage of frequency resources and an explosive increase in mobile traffic, effective use of a frequency band (white space) that is not used spatially and temporally. Is mentioned. Thus, in order to efficiently use the vacant frequency band, it is necessary to appropriately grasp the spatial / temporal vacancy status for each frequency.

As a method of detecting such a white space, for example, there is a method of specifying an arrival range of a radio wave due to free space propagation loss from a position of a transmission wave source registered in advance, and setting a white space outside the range.
As a device for detecting an unused frequency spectrum, for example, a device described in Patent Document 1 is known.

JP 2012-529196 A

In the method of detecting a white space using the position of a pre-registered transmission wave source, there is a problem that a white space cannot be detected for a transmission wave source that has not been pre-registered. Therefore, there has been a demand to specify the position of a wave source that has not been registered in advance.
In addition to the purpose other than the detection of the white space, there has been a demand to specify the position of the transmission wave source for the purpose of specifying the transmission source of the illegal radio wave.

As a method of specifying the position of such a wave source, a calculation method using TDoA (Time Difference of Arrival) is known. In the calculation of the position of the wave source using the TDoA, the arrival time difference (TDoA) at which the same radio wave transmitted from the wave source arrives at each receiving device is used by using the cross-correlation of the data received by three or more receiving devices. ) Is calculated. As a method of specifying the position of the wave source, a calculation method using DoA (Direction of Arrival) is also known. In the calculation of the position of the wave source using the DoA, the position of the wave source is specified using the directions of the radio waves received by two or more receiving devices. For details of the method of calculating the position of the wave source using TDoA and DoA, refer to the following document, for example.
Literature (TDoA): K. Ho, Y. Chan, "Solution and performance analysis of geolocation by tdoa", IEEE Transactions on Aerospace and Electronic Systems, vol. 29, no. 4, p. 1311-1322, October 1993. Reference (DoA): SU Pillai, "Array Signal Processing", Springer-Verlag, 1989

  In the calculation of the position of such a wave source, since the cross-correlation of the received signal and the direction of the radio wave are used, the calculation may be affected by multipath. For example, when the cross-correlation is calculated for the received signal of the reflected wave (delayed wave) or when the direction of the reflected wave is determined to be the direction of the wave source, the calculation accuracy of the position of the wave source is reduced. In addition, when the accuracy of calculating the position of the wave source decreases, the accuracy of estimation of the range in which radio waves from the wave source reach and the accuracy of white space estimation also decrease.

  The present invention has been made in response to the above problems, and has a wave source capable of acquiring a position of a wave source more accurately even when there are temporal variations in characteristics of a propagation environment such as multipath. An object of the present invention is to provide a position selection device and the like.

In order to achieve the above object, a wave source position selecting device according to the present invention performs a process of calculating a wave source position, which is a position of a wave source, using radio waves from a wave source received by a plurality of receiving devices a plurality of times. A position calculating unit that obtains a wave source position, a receiving unit that receives received signal strengths at a plurality of receiving positions of radio waves from the wave source, a plurality of receiving positions, and a wave source position calculated by the position calculating unit. For each position, a distance calculation unit that calculates the distance and the azimuth from the wave source for a plurality of wave source positions, a plurality of signals including a reception signal strength at the reception position, and a distance and an azimuth from the wave source regarding the reception position. Regression that the attenuation characteristic function of the radio wave from the wave source for a specific azimuth from the source is smaller for observations that include an azimuth away from the specific azimuth. Estimating unit for estimating a plurality of azimuths from a wave source by analyzing a plurality of wave source positions, and a source position for selecting one wave source position from the plurality of wave source positions by using information on the estimation by the estimating unit. And a selection unit.
When the attenuation characteristic function is more appropriately estimated, the calculated position of the wave source is also considered to be accurate. Therefore, with such a configuration, a more accurate position of the wave source can be selected. . As a result, for example, by using the position of the wave source, more accurate white space estimation and the like can be performed.

Further, in the wave source position selection device according to the present invention, the wave source position selection unit determines whether or not the distance attenuation coefficient of the attenuation characteristic function estimated by the estimation unit is included in a predetermined range for each of a plurality of azimuth angles. This may be performed for each of the plurality of wave source positions, and the wave source position having the largest azimuth angle whose range attenuation coefficient is included in the range may be selected.
If the distance attenuation coefficient falls within an appropriate range, it can be considered that the attenuation characteristic function has been estimated appropriately, so that with such a configuration, an appropriate position of the wave source should be selected. Will be able to

Further, in the wave source position selecting device according to the present invention, the estimating unit includes a weighting function that is a function of a weight that becomes smaller as the distance from the specific azimuth angle increases, a received signal intensity received by the receiving unit, and an attenuation characteristic of the estimation target. The attenuation characteristic function is estimated such that the objective function including the difference from the received signal strength calculated by the function is minimized, and the wave source position selection unit determines the minimum of the objective function corresponding to the attenuation characteristic function estimated by the estimation unit. A total value, which is a value obtained by adding the values for each of a plurality of azimuth angles, may be acquired for each of a plurality of wave source positions, and the wave source position having the smallest total value may be selected.
When the minimum value of the objective function is small, it can be considered that the estimation of the attenuation characteristic function is appropriately performed, and thus, with such a configuration, an appropriate position of the wave source can be selected. .

Further, in the wave source position selecting device according to the present invention, a range estimating unit for estimating a range in which radio waves from the wave source reach using the attenuation characteristic function corresponding to the wave source position selected by the wave source position selecting unit, and a range estimating unit. And an output unit that outputs the range regarding the estimated range.
With such a configuration, for example, it is possible to estimate the reach of radio waves and the like.

Further, the wave source position calculating device according to the present invention is a receiving unit that receives a radio wave reception signal from a wave source received by three or more receiving devices from three or more receiving devices, and a plurality of pairs of receiving devices, By using the cross-correlation of the received signal, by performing a process of calculating the arrival time difference of the radio wave from the wave source for each different received signal, an arrival time difference calculation unit that obtains a plurality of arrival time differences for each pair, for each pair, The arrival time difference acquisition unit that acquires the arrival time difference that is a representative value from the plurality of arrival time differences, the position of the receiving device, and the arrival time difference acquired for each of the plurality of pairs acquired by the arrival time difference acquisition unit. And a wave source position calculator for calculating the wave source position.
If the wave source position fluctuates according to the fluctuation of the multipath and the like, and as a result, a plurality of arrival time differences also fluctuate, the representative value of the arrival time difference is a value close to the arrival time difference corresponding to the original wave source position. Since it can be considered, with such a configuration, a more accurate calculation of a wave source position can be realized by calculating a wave source position using the representative value of the arrival time difference.

Further, in the wave source position calculating device according to the present invention, the representative value may be a median value.
When the arrival time difference fluctuates due to the influence of multipath or the like, the intermediate value is considered to be a value close to the original arrival time difference, and thus such a configuration realizes more accurate calculation of the wave source position. be able to.

Further, in the wave source position calculating device according to the present invention, a receiving unit that receives received signal strengths at a plurality of receiving positions of radio waves from the wave source; a wave source position calculated by the wave source position calculating unit; Estimation unit that estimates the attenuation characteristic function of the radio wave from the wave source using the received signal strength at the reception position of, and estimates the range that the radio wave from the wave source can reach using the attenuation characteristic function estimated by the estimation unit A range estimating unit that performs the output, and an output unit that outputs the range estimated by the range estimating unit.
With such a configuration, for example, it is possible to estimate the reach of radio waves and the like.

  ADVANTAGE OF THE INVENTION According to the wave source position selection apparatus etc. by this invention, even when multipath etc. exist, it becomes possible to acquire the position of a wave source more accurately.

FIG. 1 is a diagram showing a configuration of an information communication system including a wave source position selection device according to a first embodiment of the present invention. FIG. 2 is a block diagram showing a configuration of a wave source position selecting device according to the embodiment. 4 is a flowchart showing the operation of the wave source position selecting device according to the embodiment. 4 is a flowchart showing the operation of the wave source position selecting device according to the embodiment. 4 is a flowchart showing the operation of the wave source position selecting device according to the embodiment. 4 is a flowchart showing the operation of the wave source position selecting device according to the embodiment. FIG. 4 is a diagram illustrating an example of a range and a white space according to the embodiment. FIG. 4 is a diagram illustrating an example of a range and a white space according to the embodiment. FIG. 4 is a block diagram illustrating a configuration of a wave source position calculation device according to a second embodiment of the present invention. 4 is a flowchart showing the operation of the wave source position calculation device according to the embodiment. 4 is a flowchart showing the operation of the wave source position calculation device according to the embodiment. FIG. 2 is a schematic diagram illustrating an example of an external appearance of a computer system according to each of the above embodiments. The figure which shows an example of a structure of the computer system in each said Embodiment.

  Hereinafter, a wave source position selection device and a wave source position calculation device according to the present invention will be described using embodiments. Note that, in the following embodiments, components and steps denoted by the same reference numerals are the same or equivalent, and repeated description may be omitted.

(Embodiment 1)
The wave source position selecting device according to the first embodiment of the present invention will be described with reference to the drawings. The wave source position selecting apparatus according to the present embodiment repeatedly obtains a wave source position, estimates attenuation characteristics for each azimuth angle in accordance with the obtained wave source position, and selects an appropriate wave source position using the estimation result and the like. It is.

  FIG. 1 is a diagram showing a configuration of an information communication system including a wave source position selecting device 10 according to the present embodiment. 1, the information communication system according to the present embodiment includes a plurality of first receiving devices 1, a plurality of second receiving devices 2, and a wave source position selecting device 10. The plurality of first receiving devices 1 and the plurality of second receiving devices 2 and the wave source position selecting device 10 are connected via a wired or wireless communication line 100. The communication line 100 may be, for example, the Internet, an intranet, a public telephone network, or the like. Note that the number of the first and second receiving devices 1 and 2 shown in FIG. 1 is an example, and the information communication system does not include the number of the first and second receiving devices 1 and 2 other than that shown in FIG. May be provided. As will be described later, the first receiving device 1 is used for specifying the position of the wave source 3, and the second receiving device 2 is used for acquiring an attenuation characteristic from the wave source 3.

  The first receiving device 1 receives a radio wave from the wave source 3. Normally, the first receiving device 1 acquires the reception signal from the wave source 3 in response to the reception of the radio wave, but this need not be the case. The received signal may be, for example, IQ data or a complex amplitude value of a baseband signal. If the received signal is not acquired, the first receiving device 1 may acquire the receiving direction of the radio wave from the wave source 3 (that is, the direction of the wave source 3). It is preferable that the first receiving device 1 can receive radio waves from the wave source 3 in a line-of-sight manner, but this is not necessary. As described later, when the position of the first receiving device 1 is also transmitted from the first receiving device 1 to the wave source position selecting device 10, the first receiving device 1 performs a process of acquiring the position. You may. When the first receiving device 1 is movable, it is preferable that the position of the first receiving device 1 is transmitted to the wave source position selecting device 10. Although the number of the first receiving devices 1 is not limited, for example, as described later, when the position detection is performed by TDoA, it is preferable that the number is three or more, and the position detection by DoA is performed. In this case, it is preferable that the number is two or more. When the position is detected by DoA, it is preferable that the first receiver 1 can change the directivity of radio wave reception. The directivity change may be made physically, such as, for example, rotating a directional antenna, or electronically, such as changing the directivity in a phased array antenna. Although FIG. 1 shows a case where the receiving antenna of the first receiving device 1 is a parabolic antenna, it goes without saying that this is not necessary.

The second receiving device 2 receives a radio wave from the wave source 3. The second receiving device 2 usually acquires the reception power of the radio wave from the wave source 3 according to the reception. Further, the second receiving device 2 may calculate the received signal strength from the received power. Here, the received signal strength is the strength (spatial power value) of the radio wave immediately before passing through the receiving antenna. Therefore, the received signal strength does not include the effect of the gain of the receiving antenna, and is represented by the following equation. In the following equation, the received power is the power of the signal received by the receiving device 1 via the receiving antenna.
Received signal strength = received power−received antenna gain The received signal strength may be transmitted to the wave source position selecting device 10. Note that the received signal strength may be calculated by the wave source position selecting device 10. In that case, the reception power and the reception antenna gain may be transmitted from the second reception device 2 to the wave source position selection device 10. In the present embodiment, a case where the received signal strength is transmitted from second receiving apparatus 2 to wave source position selecting apparatus 10 will be mainly described. Further, the second receiving device 2 may not necessarily be able to receive the radio wave from the wave source 3 in line of sight. That is, the second receiving device 2 may receive the radio wave from the wave source 3 out of line of sight. When the position of the second receiving device 2 is also transmitted from the second receiving device 2 to the wave source position selecting device 10, the second receiving device 2 may perform a process of acquiring the position. When the second receiving device 2 is movable, it is preferable that the position of the second receiving device 2 is transmitted to the wave source position selecting device 10. The second receiving device 2 may also transmit the frequency of the radio wave received from the wave source 3 to the wave source position selecting device 10.

  In addition, the number of the second receiving devices 2 may be larger than the number of the first receiving devices 1, but may not be. The number of the receiving devices may be, for example, the number per unit area. The first receiving device 1 can receive radio waves from the wave source 3 in a line of sight, for example, and may be provided for the information communication system according to the present embodiment. In such a case, it is usually difficult to arrange a large number of first receiving devices 1. On the other hand, the second receiving device 2 may receive the radio wave from the wave source 3 out of line of sight, and may be, for example, a receiving device such as a mobile phone. As such, the second receiving device 2 is usually simpler than the first receiving device 1. Therefore, even if the number of second receiving devices 2 is larger than the number of first receiving devices 1, it does not lead to a significant increase in cost of the information communication system according to the present embodiment.

  The acquisition of the position in the first receiving device 1 or the second receiving device 2 may be performed using, for example, a GPS (Global Positioning System) or may be performed using an autonomous navigation device such as a gyro. It may be performed by using a nearest base station such as a mobile phone or a wireless LAN, or may be performed by another method.

  The wave source 3 may be any one that transmits radio waves, and may be, for example, a wireless base station such as a mobile phone or a base station of a wireless system such as a taxi. , Or other radio waves. Further, in the present embodiment, for simplification of description, only the case where one wave source 3 exists will be described, but two or more wave sources 3 may exist. In that case, the calculation of the wave source position may be performed for each wave source 3.

  FIG. 2 is a block diagram showing a configuration of the wave source position selecting device 10 according to the present embodiment. Wave source position selecting device 10 according to the present embodiment includes receiving unit 11, position calculating unit 12, receiving unit 13, distance calculating unit 14, estimating unit 15, wave source position selecting unit 16, and range estimating unit 17. And an output unit 18.

  The receiving unit 11 receives the first observation information from the first receiving device 1. The first observation information is used for calculating the position of the wave source 3. One piece of first observation information is information on radio waves received by one first receiving device 1. The receiving unit 11 may receive a plurality of first observation information from each of the plurality of first receiving devices 1 or may transmit a plurality of first observation information from any one of the first receiving devices 1. You may receive it.

  When the position detection by TDoA is performed in the wave source position selection device 10, the first observation information may include a reception signal received by the first reception device 1 from the wave source 3. The received signal is used for calculating the position of the wave source 3 as described later, and may be, for example, IQ data or a complex amplitude value of a baseband signal. In this case, the receiving unit 11 receives three or more pieces of first observation information. Further, the received signals included in the three or more pieces of first observation information are used for calculating the arrival time difference of the radio wave, as described later, and therefore, are preferably synchronized. That is, it is preferable that a plurality of baseband signals corresponding to the radio wave of the same period are transmitted from three or more first receiving devices 1 to the wave source position selecting device 10. Therefore, for example, each first receiving device 1 may synchronize the timing using the GPS time, or may synchronize the timing using an optical fiber or the like that connects the plurality of first receiving devices 1. .

  When the position detection by DoA is performed in the wave source position selection device 10, the first observation information includes the direction of the wave source 3 acquired by the first receiving device 1 using the radio wave from the wave source 3. It may be. In this case, the receiving unit 11 receives two or more pieces of first observation information. The direction may indicate the direction of the wave source 3 from the first receiving device 1, for example. The direction may be indicated by, for example, an azimuth centered on the first receiving device 1 (for example, an azimuth that sets north to 0 degrees and east to 90 degrees). In addition, the direction of the wave source 3 may be acquired by, for example, changing the directivity regarding reception of radio waves in the first receiving device 1. Specifically, it may be determined that the direction in which the intensity of the radio wave is highest is the direction of the wave source 3.

  Further, the first observation information may include information from which the position of the first receiving device 1 can be obtained. The information whose position can be obtained may be, for example, the position itself or a first identifier that is an identifier of the first receiving device 1. If the information whose position can be acquired is the first identifier, the first identifier and the first receiving device 1 identified by the first identifier are recorded on a recording medium (not shown) of the wave source position selecting device 10. May be associated with the position. Then, the position corresponding to the first identifier may be acquired by the wave source position selecting device 10.

  The receiving unit 11 may receive a plurality of pieces of first observation information a plurality of times. That is, the plurality of first observation information items for different periods of the radio wave transmitted from the wave source 3 may be received by the receiving unit 11. The calculation of the wave source position is performed for each of the plurality of received first observation information. The different periods may be, for example, continuous periods or discontinuous periods (that is, there is a time interval greater than 0 between the periods). Also, some of the different periods may or may not overlap. Further, the receiving unit 11 may collectively receive, for example, a plurality of pieces of first observation information for the plurality of times. When the position is detected by TDoA, the receiving unit 11 may receive a plurality of first observation information including, for example, a continuous long reception signal. Then, in the wave source position selection device 10, a plurality of pieces of first observation information for different periods may be obtained by appropriately dividing the long received signal.

  Note that the receiving unit 11 may receive the first observation information directly from the first receiving device 1 or may receive the first observation information via another server or the like. In the latter case, for example, first observation information from a plurality of first receiving devices 1 is collected in a base station or the like, and the collected first observation information is collected from the base station or the like by a wave source position selecting device. 10 may be sent. The receiving unit 11 may or may not include a wired or wireless receiving device (for example, a modem or a network card) for performing reception. The receiving unit 11 may be realized by hardware, or may be realized by software such as a driver for driving a receiving device.

  The position calculation unit 12 calculates a wave source position that is the position of the wave source 3 using the radio waves from the wave sources 3 received by the plurality of first receiving devices 1. Further, the position calculation unit 12 acquires a plurality of wave source positions by performing the process of calculating the wave source position a plurality of times. The acquisition of the plurality of wave source positions may be performed, for example, on the plurality of pieces of first observation information received by the reception unit 11 for different periods. That is, the position calculation unit 12 calculates a certain wave source position using a plurality of first observation information corresponding to a certain period, and uses another plurality of first observation information corresponding to another period to obtain another wave source position. The calculation of the wave source position may be repeated. In the present embodiment, a description will be given of a calculation method using TDoA and a calculation method using DoA as a method for calculating the wave source position by the position calculation unit 12. However, the position calculation unit 12 determines the position of the wave source 3 by other methods. May be calculated. The position may be, for example, a latitude and a longitude, or a coordinate value with a certain position as a base point. The same applies to other positions.

[Calculation method by TDoA]
In this case, the receiving unit 11 receives the first observation information including the reception signal received from the wave source 3 by the first receiving device 1 from each of the three or more first receiving devices 1. And It is assumed that the received signals included in the plurality of first observation information are synchronized. Then, the position calculating unit 12 calculates the position of the wave source 3 using the received signals corresponding to the plurality of first receiving devices 1 and the positions of the plurality of first receiving devices 1. The position of the first receiving device 1 is, for example, a position acquired by using information from which the position transmitted from the first receiving device 1 can be acquired. Specifically, the position calculating unit 12 first calculates the arrival time difference of the radio wave from the wave source 3 using the cross-correlation of the received signal for the pair of the first receiving devices 1. The position calculator 12 calculates the arrival time difference for a plurality of pairs of the first receiver 1. Further, the position calculation unit 12 calculates the arrival time difference for the plurality of pairs for different received signals. As a result, a plurality of pairs of arrival time differences are obtained for each of the plurality of received signals (it can be considered that a plurality of arrival time differences are obtained for each of the plurality of pairs). Note that the arrival time difference is the difference between the propagation time of a radio wave from the wave source 3 to a certain first receiving device 1 and the propagation time of a radio wave from the wave source 3 to another first receiving device 1. Specifically, the position calculating unit 12 may calculate the arrival time difference as follows.

First, the position calculation unit 12 uses three or more synchronized reception signals to perform a cross-correlation C _ij ^(q regarding a pair of the i-th first reception device 1 and the j-th first reception device 1. ⁾ Calculate (τ). Incidentally, i, j is an integer from respectively 1 to _{N a,} a i ≠ j. Further, N _a is an integer of 3 or more of a first number of the receiving device 1. In addition, q is an integer from 1 to Q, and is an index for identifying a set of three or more synchronized received signals. The q can be considered as an index for calculating the wave source position or identifying the calculated wave source position. Q is an integer of 2 or more. That is, in the present embodiment, Q wave source positions are calculated using received signals corresponding to Q different periods. The cross-correlation between the reception signal r _i ^(q) (n) of the i-th first receiver 1 and the reception of the j-th first receiver 1 at a time shifted by τ as shown in the following equation: It is calculated for the combination with the signal r _j ^(q) (n−τ). Note that r _i ^(q) (n) is the value (IQ data or complex amplitude value) of the n-th sample in the q-th received signal acquired by the i-th first receiver 1. The sample is a sample when an analog reception signal is digitized.

Here, τ is an integer satisfying −L ₁ ≦ τ ≦ L ₁ . L ₁ is a predetermined positive integer. ^{_{Also, E [r i (q)}} (n) r j (q) * (n-τ)] is as follows.

In the above equation, _Nb is the number of samples for calculating the correlation. The position calculation unit 12 calculates the arrival time difference | τ _ij ^(max) (q) | using the above-described cross-correlation C _ij ^(q) (τ) as in the following equation. That is, the shift τ in the time direction at which the cross-correlation reaches a peak is defined as the arrival time difference. Strictly speaking, δ | τ _ij ^(max) (q) | obtained by multiplying | τ _ij ^(max) (q) | by the sampling period δ is the arrival time difference in units of time.

The position calculation unit 12 may calculate the arrival time difference for all pairs of three or more first receiving devices 1 used for calculating the position of the wave source 3, and at least two of the pairs may be calculated. The arrival time difference may be calculated for three pairs, preferably for three or more pairs. Further, the position calculation unit 12 calculates, for example, Q sets of arrival time differences corresponding to a plurality of pairs of the first receiving device 1 using Q sets of three or more synchronized reception signals. I do. That is, δ | τ _ij ^(max) (q) | is calculated for each of q = 1 to Q.

  The position calculation unit 12 calculates a wave source position that is the position of the wave source 3 using the position of the first receiving device 1 and the set of arrival time differences for each of the plurality of pairs acquired as described above. Is repeated for each set of arrival time differences. The position calculating unit 12 may calculate the Q wave source positions using, for example, a set of Q arrival time differences. Note that the position of the first receiving device 1 is the position of the first receiving device 1 forming a plurality of pairs of the receiving devices 1 whose arrival time differences have been calculated. The position of the first receiving device 1 may be, for example, latitude and longitude, or may be a coordinate value with a certain position as a reference point. Specifically, the position calculation unit 12 may calculate the position of the wave source 3 as follows.

First, for the q-th trial (the set of the q-th arrival time difference), the position calculation unit 12 uses the arrival time difference to determine the distance from the wave source 3 to the i-th first reception device 1 and the distance from the wave source 3 to j An arrival distance difference Δd _ij ^(q) , which is a difference from the distance to the first receiving device 1, is calculated. The arrival distance difference Δd _ij ^(q) is expressed by the following equation. In the following equation, χ is the speed of light. Further, the position calculation unit 12 performs a process of calculating the arrival distance difference Δd _ij ^(q) for each of q = 1 to Q.

It is already known that the position of the wave source 3 is specified by using the arrival distance difference regarding a plurality of pairs of the first receiving device 1. However, the position calculating unit 12 performs, for example, the wave source position S _q ^e as follows. May be calculated.

なお、Δｄ_m ^(q)は、上述のようにして算出された、ｍで識別されるペアに関するｑ番目の到来距離差である。また、Δｄ_m(Ｓ_q)は、次式で示されるように、位置座標から算出される到来距離差である。なお、Ｓ_iは、ｉ番目の第１の受信装置１の位置座標である。

Here, S _q ^e is the q-th estimated wave source position coordinates for this trial (wave source position), is it what is the calculation target of the position calculating unit 12. m is a combination of ij, that is, an index of the first receiving device 1 forming a pair of the first receiving devices 1, and M is a total number of pairs of the first receiving device 1. Further, S _q is the q th source locations _{of, | e m (S q)} | 2 is as follows.

Note that Δd _m ^(q) is the q-th arrival distance difference for the pair identified by m, calculated as described above. Further, Δd _m (S _q ) is an arrival distance difference calculated from position coordinates, as shown by the following equation. Note that S _i is the position coordinate of the i-th first receiver 1.

Position calculating section 12, the source locations S _q ^e, for example, may be calculated by non-linear least squares method, or may be calculated by other methods. The calculation may be performed using, for example, the Newton method or the Levenberg-Marquardt method. The position calculation unit 12, for each of the q = 1 to Q, and performs processing of calculating the wave source position S _q ^e. A method of calculating the wave source position when the set of the q-th arrival time difference includes only two arrival time differences will be briefly described. In that case, the arrival time difference is converted into an arrival distance difference. A set of points having a constant difference in arrival distance from two points is a hyperbola. Usually, there are two such hyperbolas, but one hyperbola can be specified according to the sign of τ _ij ^(max) (q). Therefore, the wave source position which is the intersection of the specified hyperbola can be calculated.

[Calculation method using DoA]
In this case, the receiving unit 11 receives the first observation information including the direction of the wave source 3 acquired by the first receiving device 1 from each of the two or more first receiving devices 1. And It is preferable that the plurality of first observation information items relate to radio waves received by two or more first reception devices 1 at the same time. Then, the position calculation unit 12 calculates the position of the wave source 3 using the directions of the wave sources 3 acquired by the plurality of first receiving devices 1 and the positions of the plurality of first receiving devices 1. . The position calculation unit 12 can obtain the position of the first receiving device 1 in the same manner as in the case of the calculation method using TDoA. If the position of a certain first receiving apparatus 1 and the direction of the wave source 3 therefrom are known, the wave source 3 will exist on a straight line passing through the position and extending in that direction. . Therefore, the position calculating unit 12 can identify two straight lines by knowing the positions of the two first receiving devices 1 and the direction of the wave source 3 from each first receiving device 1. , The position of the wave source 3 at the intersection of the straight lines can be calculated. In this case, it is preferable that the two first receiving devices 1 and the wave source 3 do not exist on the same straight line. Also in this case, three or more straight lines are specified, and the wave source position is calculated such that the sum of the distance between the wave source position and the three or more straight lines and the square of the distance is minimized. Good. Further, the position calculator 12 calculates the wave source position based on the DoA for different received signals. As a result, the wave source position is calculated for each of the plurality of received signals.

Here, the position calculation unit 12, the TDoA or DoA, and was calculated Q-number of source locations S _q ^e. As described above, q is an integer from 1 to Q, and Q is an integer of 2 or more. Also, source locations S _q ^e of the Q of the calculated may be stored in a recording medium (not shown).

The receiving unit 13 receives received signal strengths of the radio wave from the wave source 3 at a plurality of receiving positions. The reception of the received signal strength may be performed, for example, by receiving the received signal strength at a plurality of reception positions transmitted from the plurality of second receiving devices 2 or an input device (for example, a keyboard or a mouse, It may be performed by input from a touch panel or the like, or may be performed by reading from a predetermined recording medium (for example, an optical disk, a magnetic disk, a semiconductor memory, or the like). In the present embodiment, a case where receiving section 13 receives a plurality of received signal strengths from a plurality of second receiving apparatuses 2 will be mainly described. In addition, the receiving unit 13 may also receive the position of the second receiving device 2, that is, information from which the receiving position can be acquired. The information from which the reception position can be obtained may be, for example, the reception position itself, or a second identifier that is the identifier of the second reception device 2. The receiving unit 13 may receive information from which the reception position can be obtained from each of the plurality of second reception devices 2. When the information whose position can be acquired is the second identifier, the second identifier and the second receiving device 2 identified by the second identifier are recorded on the recording medium (not shown) of the wave source position selecting device 10. May be associated with the position. Then, the position corresponding to the second identifier may be acquired by the wave source position selecting device 10. The receiving unit 13 may also receive the frequency of the radio wave received at the receiving position. Let P _i be the received signal strength at the i-th reception position. The coordinates of the reception position are (X _i , Y _i ). Moreover, i-th received position received radio wave frequency (MHz) and f _i. Note that i is an integer from 1 to N, and N is an integer of 2 or more indicating the total number of reception positions. Receiving unit 13, by receiving a received signal strength at a plurality of receiving positions, for each i from 1 to N, and the received signal strength P _i, receiving position (X _i, Y _i) and to be able to know the Shall be Note that the frequency f _i may be further known. Here, f _i is any of the K frequencies. Here, K is a positive integer equal to or less than N. When K = 2, for example, f ₁ = f ₂ =..., F ₃ = f ₄ =.

  Note that the accepting unit 13 may or may not include a device (for example, a modem or a network card) for accepting. Further, the receiving unit 13 may be realized by hardware, or may be realized by software such as a driver for driving a predetermined device.

The distance calculation unit 14 calculates a distance from the wave source 3 and an azimuth angle for each reception position using the plurality of reception positions and the wave source position calculated by the position calculation unit 12. Further, the distance calculation unit 14 calculates the distance and the azimuth for each of the reception positions for a plurality of wave source positions. Specifically, the distance calculation unit 14 uses the N reception positions (X _i , Y _i ) and the Q wave source positions S _q ^e to calculate the distance from each wave source position to the reception position, the wave source The azimuth of the direction of the receiving position centered on the position is calculated. The distance from the wave source position to the receiving position is usually a linear distance between the wave source position and the receiving position. The azimuth from the wave source position to the reception position may be, for example, 0 degree in the north and 90 degrees in the east with respect to the wave source position, and may be based on other directions. You may. In addition, information including the distance and the azimuth angle from the q-th source position with respect to the i-th receiving position and the received signal strength of the radio wave received at the i-th receiving position correspond to the q-th source position. It is referred to as i-th second observation information. That is,
i-th second observation information corresponding to the q-th source position = (x _i ^(q) , θ _i ^(q) , P _i )
It may be. Here, q th source locations S _q ^e and the receiving position of (X _i, Y _i) the distance between the (km) and x _i ^(q), receives a position around the q-th source locations S _q ^e ( The azimuth (deg) in the direction of X _i , Y _i ) is defined as θ _i ^(q) . P _i is the received signal strength (dBm) of the radio wave received at the receiving position of x _i ^(q) and θ _i ^(q) . As can be seen from the above equation, there are Q i-th pieces of second observation information for each wave source position. In addition, since i is an integer from 1 to N, there are Q × N pieces of second observation information. Further, the second observation information may include a frequency. In that case,
i-th second observation information corresponding to the q-th source position = (x _i ^(q) , θ _i ^(q) , P _i , f _i )
Becomes

The estimating unit 15 uses the plurality of pieces of second observation information including the received signal strength at the reception position and the distance and azimuth from the wave source 3 regarding the reception position, and uses the attenuation characteristics for a specific azimuth from the wave source 3. The function is estimated by regression analysis in which observation information including an azimuth away from a specific azimuth has a smaller effect. Further, the estimation unit 15 estimates the attenuation characteristic function in the direction of the specific azimuth angle for a plurality of azimuth angles from the wave source 3. For the method of estimating such a damping characteristic function, refer to the following document, for example.
References: Kenshi Horibata, Kazuo Sugano, Akihiro Hasegawa, Toshiyuki Maeyama, Yoshio Takeuchi, "A Method for Estimating Propagation Loss Using Azimuth Variables Using Weighted Least Squares", Proc. Of IEICE Society Conference, p. 403, September 2014

  Further, the estimating unit 15 estimates the attenuation characteristic function for each of the plurality of specific azimuths for the plurality of wave source positions. As a result, for a plurality of wave source positions, attenuation characteristic functions for each of a plurality of azimuth angles are estimated. Note that the attenuation characteristic function is a function related to the attenuation characteristic of the radio wave from the wave source 3 and is a function that depends on the distance from the wave source 3. The attenuation characteristic function may indicate, for example, a propagation loss (path loss) of a radio wave, or may indicate a received signal strength or the like. Note that, as described later, the sum of the path loss and the received signal strength is usually a transmission power that is a constant value, and thus the two values are related to each other. Note that the plurality of azimuth angles may be, for example, all azimuth angles (360 degrees) at predetermined angle intervals (for example, 5 degrees or 10 degrees), or some of the azimuth angles may be provided at each angle interval. The range of the azimuth angle (for example, from 90 degrees to 270 degrees) may be used. Note that the angular intervals need not be uniform. In the present embodiment, a case will be mainly described in which the estimation unit 15 estimates the attenuation coefficient for all azimuths at predetermined angular intervals. The specific azimuth angle θ over all azimuth angles for each predetermined angle interval may be, for example, θ = 0 °, ε, 2 × ε, 3 × ε,..., B × ε. Here, ε is an interval (deg) between specific azimuth angles, and B is a minimum integer satisfying ε × (B + 1) ≧ 360 °. Note that ε may or may not be a divisor of 360 degrees. The estimation of the attenuation characteristic function by the regression analysis may be performed using, for example, the least square method, or may be performed using the minimum absolute value method. That is, the estimation unit 15 may calculate the attenuation characteristic function by a weighted least squares method or a minimum absolute value method using a weight that becomes smaller as the distance from the direction of the specific azimuth angle increases. In that case, the attenuation characteristic function to be fitted to the observation information is specified in consideration of the weight. Therefore, the estimating unit 15 estimates the attenuation characteristic function related to the specific azimuth using a weight function that is a function of weight that decreases as the distance from the specific azimuth increases and includes one or more parameters related to the decrease. Will do. The number of parameters included in the weight function may be one, or may be two or more. The weighting function is, for example, a function having a larger value as the absolute value of the difference between the azimuth included in the observation information and the specific azimuth is smaller, and a smaller value as the absolute value of the difference is larger. Good. A specific example of the function will be described later. Note that, for example, the maximum value of the weight may be 1, and the minimum value may be 0, or another value. The estimating unit 15 may perform a regression analysis using observation information having different frequencies. In that case, the attenuation characteristic function is a function that also depends on the frequency of the radio wave. Further, the regression analysis performed by the estimation unit 15 may be a linear regression analysis such as a least square method or a minimum absolute value method, or may be a non-linear regression analysis. In the latter case, the attenuation characteristic function may be estimated by improving the approximate solution by iterative calculation, for example, by an iterative least square estimation method.

Here, the relationship between the received signal strength and the transmission power is
Received signal strength = transmission power−path loss. As described above, the attenuation characteristic function estimated by the estimating unit 15 may indicate “path loss” in the above equation, or may indicate “transmission power−path loss” (= received signal strength). Good. This is because both can be considered to be at least related to the attenuation characteristics of radio waves. In the present embodiment, a case where the attenuation characteristic function indicates "transmission power-path loss", that is, a case where the attenuation characteristic function is a function indicating the received signal strength according to the distance from the wave source 3 will be mainly described. Strictly speaking, “transmission power” in the above equation is antenna power including the influence of the gain of the transmission antenna. Here, it is considered that the transmission power does not usually change. Next, estimation of the attenuation characteristic function will be described separately for a case where no frequency is used and a case where a frequency is used.

[Estimation of attenuation characteristic function without using frequency]
In this case, the plurality of pieces of second observation information corresponding to the q-th wave source position are as follows.
A set of second observation information corresponding to the q-th source position = ｛(x ₁ ^(q) , θ ₁ ^(q) , P ₁ ), (x ₂ ^(q) , θ ₂ ^(q) , P ₂ ) ^{_{, ..., (x N (q}} ), θ N (q), P N)}

Next, a specific azimuth that is an azimuth corresponding to a specific direction is defined as θ. Then, the attenuation characteristic function P _θ ^(q) (dBm) of the specific azimuth angle θ when the q-th wave source position is adopted is defined as the following equation. Note that x _θ ^(q) is a distance (km) from the q-th source position in the direction of the specific azimuth angle θ centered on the q-th source position. It is assumed that the attenuation characteristic function indicates the received signal strength.
P _θ ^(q) = g _θ ^(q) (x _θ ^(q) , θ)
Here, for the received signal strength P _i of the i-th second observation information (x _i ^(q) , θ _i ^(q) , P _i ) corresponding to the q-th source position, P _θ ^(q) Δ _i ^(q) .
δ _i ^(q) = P _i −g _θ ^(q) (x _i ^(q) , θ)

Then, the estimating unit 15 is the optimal solution g that optimizes the objective function E _θ ^(q) corresponding to the next q-th source position for all the second observation information corresponding to the q-th source position. Calculate _θ ^(q) . Note that the optimization is to minimize the objective function. The calculation of g _θ ^(q) that minimizes the objective function may be performed using, for example, the steepest descent method, or may be performed using another method. ^{_{Incidentally, F (θ i (q)}} ) becomes smaller as θ _i ^(q) is separated from a specific azimuth angle theta, a larger weight as θ _i ^(q) is closer to a particular azimuth angle theta. N is the total number of pieces of second observation information corresponding to the q-th source position, as described above.

Next, g _θ ^(q) (x _θ ^(q) , θ) will be described. g _θ ^(q) (x _θ ^(q) , θ) may be, for example, represented by the following equation. Note that a ^(q) (θ) and c ^(q) (θ) are attenuation coefficients. a ^(q) (θ) may be called a distance attenuation coefficient, and c ^(q) (θ) may be called a constant term. The damping coefficients a ^(q) (θ) and c ^(q) (θ) are both functions of θ determined by θ.
^{_{P θ (q) = g θ}} (q) (x θ (q), θ) = a (q) (θ) × logx θ (q) + c (q) (θ)

In this case, the calculation of the optimal solution for optimizing the objective function described above is the calculation of the attenuation coefficients a ^(q) (θ) and c ^(q) (θ). If the transmission power is included in the attenuation coefficient c ^(q) (θ), P _θ ^(q) indicates the received signal strength, and if the transmission power is not included in the attenuation coefficient c ^(q) (θ), P _θ ^(q) indicates a path loss. When P _θ ^(q) is represented by the above equation, δ _i ^(q) and E _θ ^(q) are represented by the following equations.
δ _i ^(q) = P _i −a ^(q) (θ) × logx _i ^(q) −c ^(q) (θ)

Incidentally, the attenuation coefficient to minimize such E _theta and ^{(q) a (q) (} θ), c (q) (θ) by calculating the damping coefficient of the function ^{_{g θ (q) a (q}} ) (θ), c ^(q) (θ) is estimated by the weighted least squares method. Therefore, the estimating unit 15 calculates the optimal solution for optimizing the objective function including the weight F (θ _i ^(q) ) that becomes smaller as the distance from the specific azimuth angle θ increases, thereby obtaining the weighted least squares method, A ^(q) (θ) and c ^(q) (θ) may be calculated using regression analysis such as the minimum absolute value method. By calculating those attenuation coefficients, the attenuation characteristic function P _θ ^(q) is calculated. That is, the estimating unit 15 estimates the weighting function F (θ _i ^(q) ), which is a function of the weight that decreases as the distance from the specific azimuth angle θ increases, the received signal strength P _i received by the receiving unit 13, An objective function E _θ ^{(q )} including a difference δ _i ^(q) from the received signal strength “a ^(q) (θ) × log x _i ^(q) + c ^(q) (θ)” calculated by the target attenuation characteristic function. ⁾ Is estimated to be the minimum.

Next, the weight function F (θ _i ^(q) ) will be described. As described above, the weighting function may be any as long as it becomes smaller as the distance from the specific azimuth angle θ increases. For example, F ₁ (θ _i ^(q) ) or F ₂ (θ _i ^(q) ) may be used. The weight function is a function including one or more parameters related to the decrease, as described above. The parameter related to the decrease is a parameter that defines the degree of the decrease. For example, when moving away from the direction of the specific azimuth angle θ, whether to decrease rapidly or gradually is determined by a parameter. In ^{_{F 1 (θ i (q)}} ), α, β , when θ _i ^(q) is separated from the particular azimuth angle theta, characterizing or ^{_{F 1 (θ i (q)}} ) is reduced how much parameters It is. The parameters α and β are values in the range of 0 <α <1, β> 0. Further, as the value of the parameter β increases, observation information of an azimuth angle further away from the specific azimuth angle θ is used, and therefore, for example, an upper limit such as β ≦ 180 (degrees) may be set. F ₂ (θ _i ^(q) ) is a weight based on the pass characteristic of the Butterworth filter, parameter η is the cutoff angle, parameter γ is a coefficient related to the cutoff rate, and parameter M is the order. is there. The parameters η, γ, and M are values in the range of η> 0, γ> 0, and M> 0. Further, η ≦ 180 (degrees) may be satisfied, and M ≧ 1 may be satisfied. | Θ−θ _i ^(q) | may be, for example, 0 ≦ | θ−θ _i ^(q) | ≦ 180 (degrees).

Adjusting the values of the parameters α and β of F ₁ (θ _i ^(q) ) and the values of the parameters η, γ and M of F ₂ (θ _i ^(q) ) affect the estimation of the attenuation characteristic function. Is changed, and as a result, the estimation result of the attenuation characteristic function differs. Therefore, it is required to set parameter values so that the attenuation characteristic function can be appropriately estimated. It should be noted that since F ₂ (θ _i ^(q) ) can set the cutoff rate and the like more finely, it is possible to set a weight with a higher degree of freedom.

Further, the attenuation characteristic function P _θ ^(q) of the specific azimuth θ is fitted with the received signal strength included in the observation information having the azimuth close to the specific azimuth θ. On the other hand, the attenuation characteristic function P _θ ^(q) is also affected by the received signal strength included in the observation information having an azimuth angle away from the specific azimuth angle θ. Even if there is only a small amount of information, it can be avoided that an inappropriate attenuation characteristic function is estimated.

As described above, when the ^{_{g θ (q) (x θ}} (q), θ) = a (q) (θ) × logx θ (q) + c (q) (θ) is linear regression It becomes a model, and the optimal solution can be calculated using the analytical least squares method or the minimum absolute value method.However, in the case of a non-linear regression model, for example, by improving the approximate solution by iterative calculation, , A damping characteristic function may be estimated.

[Estimation of attenuation characteristic function using frequency]
In this case, the plurality of pieces of second observation information corresponding to the q-th wave source position are as follows.
A set of second observation information corresponding to the q-th source position = ｛(x ₁ ^(q) , θ ₁ ^(q) , P ₁ , f ₁ ), (x ₂ ^(q) , θ ₂ ^(q) , P ₂ , f ₂ ),..., (X _N ^(q) , θ _N ^(q) , P _N , f _N )｝

When the specific azimuth angle θ is set in the same manner as when no frequency is used, the attenuation characteristic function P _θ ^(q) (dBm) of the specific azimuth angle θ when the q-th wave source position is adopted is as follows. . Note that f is the frequency (MHz) of the radio wave from the wave source 3.
P _θ ^(q) = g _θ ^(q) (x _θ ^(q) , f, θ)

Therefore, P _θ ^(q) for the received signal strength P _i of the i-th second observation information (x _i ^(q) , θ _i ^(q) , P _i , f _i ) corresponding to the q-th source position is residual [delta] _i of ^(q) is as follows.
δ _i ^(q) = P _i −g _θ ^(q) (x _i ^(q) , f _i , θ)

Note that the estimation unit 15 is an optimal solution g _θ ^{( q} _θ ^(q) that optimizes the objective function E _θ ^(q) corresponding to the q-th source position for all the second observation information corresponding to the q-th source position. Calculating ^q) is the same as when no frequency is used. When using a frequency, g _θ ^(q) (x _θ ^(q) , f, θ) is represented by, for example, the following equation.
^{_{P θ (q) = g θ}} (q) (x θ (q), f, θ) = a (q) (θ) × logx θ (q) + b × logf + c (q) (θ)

Here, the attenuation coefficient b is a frequency coefficient. For example, when a propagation model of a radio wave from the wave source 3 to the receiving device 1 is a free space model, b may be set to 20 and from the wave source 3 to the receiving device 1 of radio wave propagation model Okumura - when the Hata model (urban model) may be b = 26.16-1.1 × h _m +1.56. However, this model can be applied only when the following conditions are satisfied.
30 <h _b <200
1 <h _m <10
150 <f <2200
1 <x _i ^(q) <20

Note that h _b is the height of the transmitting antenna (m), _hm is the height of the receiving antenna (m), f is the frequency of the radio wave (MHz), and x _i ^(q) is This is the distance (km) to the receiving device 1. In this case, it is necessary to obtain the receive antenna height h _m. The reception antenna height h _m, for example, may be included in the observation information, or, at the source locations selector 10, a receiver identifier, the height of the antenna receiving apparatus 1 identified by the receiver identifier May be stored in a recording medium (not shown) in association with the data. Note that the receiving antenna height and the transmitting antenna height may be reversed. That is, h _b may be the height of the receiving antenna (m), and h _m may be the height of the transmitting antenna (m). In addition, since the height of the transmitting antenna is generally unknown, the Okumura-Hata model may be applied on the assumption that the condition regarding the transmitting antenna height is satisfied.

Therefore, also in this case, the calculation of the optimal solution for optimizing the objective function is the calculation of the attenuation coefficients a ^(q) (θ) and c ^(q) (θ). When P _θ ^(q) is represented by the above equation, δ _i ^(q) and E _θ ^(q) are represented by the following equations.
δ _i ^(q) = P _i −a ^(q) (θ) × logx _i ^(q) −b × logf _i −c ^(q) (θ)

The weight F (θ _i ^(q) ) is the same as the case where no frequency is used, and for example, F ₁ (θ _i ^(q) ) or F ₂ (θ _i ^(q) ) may be used. In this way, even when the frequency is used, the attenuation characteristic function is calculated by calculating the attenuation coefficients a ^(q) (θ) and c ^(q) (θ) that optimize the objective function E _θ ^(q). Can be estimated. In the case where frequencies are also used, the function fitting can be performed using radio waves of different frequencies, so that the number of samples increases. Therefore, for example, even if the number of receiving devices 1 is small, it is possible to estimate a more accurate attenuation characteristic function.

Further, in the above description, the frequency coefficient b is given from the model, but this need not be the case. When the frequency coefficient b is not given from the model, the attenuation characteristic function P _θ ^(q) and the residual δ _i ^(q) may be represented by the following equations.
^{_{P θ (q) = g θ}} (q) (x θ (q), f, θ) = a (q) (θ) × logx θ (q) + b (q) (θ) × logf + c (q) (θ )
δ _i ^(q) = P _i −a ^(q) (θ) × log x _i ^(q) −b ^(q) (θ) × log f _i −c ^(q) (θ)
Then, the attenuation coefficients a ^(q) (θ), b ^(q) (θ), and c ^(q) (θ), which are the optimal solutions for minimizing the objective function E _θ ^(q) , may be calculated. . That is, the attenuation coefficient b ^(q) (θ), which is a frequency coefficient, may also be calculated. Thus, estimating the attenuation coefficient of the attenuation characteristic function means estimating all the attenuation coefficients a ^(q) (θ), b ^(q) (θ), and c ^(q) (θ). Alternatively, it may be to estimate some of the attenuation coefficients a ^(q) (θ) and c ^(q) (θ). In the following description, a case will be mainly described in which the attenuation characteristic function is estimated without using the frequency.

In the above description, the case where the attenuation characteristic function is the received signal strength has been described. However, if the transmission power of the wave source 3 can be known, the attenuation characteristic function indicating the path loss is calculated using the transmission power. Needless to say, it can be estimated. In that case, the attenuation characteristic function is a path loss, a "transmission power -P _theta ^(q)". In the estimation method using the frequency, the same wave source 3 transmits radio waves of different frequencies with the same transmission power, or a plurality of different wave sources 3 located in close positions transmit radio waves of different frequencies with the same transmission power. When transmission is performed via transmission antennas having the same antenna gain, the attenuation characteristic function indicating the received signal strength can be calculated as described above. On the other hand, if not, the estimation unit 15 estimates the attenuation characteristic function indicating the path loss using the transmission power. In such a case, when transmission power is required for estimating the attenuation characteristic function, the transmission power may be estimated from, for example, received power or received signal strength, and may be registered in advance from the wave source 3 or another device. Value may be obtained. When estimating the transmission power, the estimating unit 15 estimates the transmission power using all the reception powers of the plurality of second reception devices 2 or reception powers equal to or higher than a predetermined threshold. Good. Then, the estimation unit 15 may estimate an attenuation characteristic function indicating a path loss using the estimated transmission power and the received signal strength of the second reception device 2. When estimating the transmission power, a model (for example, a free space model, a two-wave model of ground reflection, an Okumura-Hata model, or the like) corresponding to the propagation path between the wave source 3 and the second receiving device 2 is used. ), A function G (x, f) of path loss using the coefficients a, b, c = a × log (x) + b × log (f) + c may be used. Here, x is the distance from the wave source 3 to the second receiving device 2, and f is the frequency. In addition, the selection of the model may be performed using, for example, a delay profile acquired by the second receiving device 2. For example, when the delay profile indicates that it is line of sight, a free space model or a two-wave model of ground reflection is selected. When the delay profile indicates that it is not line of sight, the Okumura-Hata model is selected. You may. Further, among the plurality of transmission powers calculated in this way, the maximum value may be set as the transmission power of the wave source 3 or the average + 3 × (standard deviation) may be set as the transmission power of the wave source 3. Note that the standard deviation is the standard deviation of the calculated transmission power. The former considers the maximum transmission power to be the actual transmission power because the transmission power calculated from the reception power received via the propagation path that is an ideal prospect is considered to be the maximum value. is there. In the latter case, the average + 3.times. (Standard deviation) becomes a value close to the maximum value in consideration of the statistical variation, so that the value is regarded as the actual transmission power. If the received power is also acquired by the first receiving device 1, the transmission power may be estimated using the received power acquired by the first receiving device 1.

The estimation unit 15 estimates the attenuation characteristic function for each of the plurality of specific azimuth angles θ as described above for each of the wave source positions S _q ^e of q = 1 to Q. The estimated attenuation characteristic function, that is, the attenuation coefficient a ^(q) (θ), c ^(q) (θ), etc., may be stored in a recording medium (not shown) for each wave source position. Further, in the case where the minimum value of the objective function for each specific azimuth angle θ is also used in the selection of the wave source position described later, for a plurality of wave source positions, the objective function E _θ ^(q) The minimum value may be stored in a recording medium (not shown).

  The source position selection unit 16 selects one source position from a plurality of source positions by using information about the estimation by the estimation unit 15. The information on the estimation may be, for example, the estimated distance attenuation coefficient, the value (minimum value) of the objective function minimized at the time of the estimation, or other information. The wave source position selecting unit 16 may select the wave source position using, for example, the estimated distance attenuation coefficient, or may select the wave source position using the minimum value of the objective function. Next, the selection of the wave source position will be described separately for a case where the estimated distance attenuation coefficient is used and a case where the minimum value of the objective function is used.

[Selection of wave source position using distance attenuation coefficient]
The wave source position selector 16 includes the distance attenuation coefficient a ^(q) (θ) of the attenuation characteristic function P _θ ^(q) corresponding to the q-th wave source position, which is estimated by the estimator 15, in a predetermined range. Is determined for each of a plurality of azimuth angles. The range includes at least the upper limit. Also, the range may or may not include the lower limit. For example, the range is
a ^(q) (θ) ≦ A _UB
Or
A _LB ≤ a ^(q) (θ) ≤ A _UB
It may be. In the present embodiment, a case where the range includes only the upper limit will be mainly described. The range is preferably a range of an appropriate value of the distance attenuation coefficient. The upper limit _AUB is not particularly limited, but may be, for example, "-20". In free space, the power of the radio wave is inversely proportional to the square of the distance from the wave source, so that the distance attenuation coefficient is -20. Since attenuation is considered to be greater outside of free space, a ^(q) (θ) is usually considered to be -20 or less, so the upper limit A _UB may be set as described above. The lower limit A _LB is not particularly limited, but may be, for example, −60 or −70. Usually, it is difficult to imagine that the distance attenuation coefficient becomes a value smaller than the lower limit _ALB . Moreover, the wave source position selecting unit 16, the determination is performed for each of a plurality of source locations S _q ^e. Note that the wave source position selecting unit 16 calculates, for each wave source position, a range azimuth number N ^{(q) in} which a ^(q) (θ) is the number of specific azimuth angles θ included in a predetermined range, for example. You may count. Then, the wave source position selection unit 16 selects a wave source position having the largest azimuth angle in which the distance attenuation coefficient a ^(q) (θ) is included in the range. Incidentally, when the range azimuth number N ^(q) is the q is a maximum and qb, so that the wave source position S _qb ^e is selected. It is considered that the distance attenuation coefficient calculated using the accurate wave source position is included in an appropriate range. Therefore, it is considered that a more appropriate wave source position can be selected by selecting a wave source position having a large in-range azimuth number N ^(q) .

[Selection of wave source position using minimum value of objective function]
The wave source position selector 16 adds the minimum value of the objective function E _θ ^(q) corresponding to the attenuation characteristic function P _θ ^(q) of the q-th wave source position estimated by the estimator 15 for each of a plurality of azimuth angles. A total value E _sum ^(q) is obtained for each of the plurality of wave source positions. Note that the sum E _sum ^(q) may be the _sum of the minimum value of the objective function E _θ ^(q) for each specific azimuth angle θ. Then, the wave source position selector 16 may select the wave source position having the minimum _sum E _sum ^(q) . Note that the minimum value of the objective function E _θ ^(q) is the value of the objective function into which the optimal solution (attenuation coefficient) estimated by the estimating unit 15 is substituted. It can be considered that the smaller the minimum value of the objective function is, the smaller the error is in the fitting. Therefore, when the total value E _sum ^(q) is the smallest, the fitting with the smallest error, that is, an appropriate fitting is performed. The fitting is performed, and the corresponding source position can be considered to be the more accurate source position. Incidentally, when the sum E _sum ^(q) is the q is the smallest and qb, so that the wave source position S _qb ^e is selected.

  Since the estimating unit 15 estimates the attenuation characteristic function for each wave source position, selecting the wave source position results in selecting the attenuation characteristic function corresponding to the selected wave source position. . Therefore, it may be considered that the wave source position selection unit 16 has selected the attenuation characteristic function corresponding to the appropriate wave source position as a result.

The range estimating unit 17 estimates a range in which radio waves from the wave source 3 reach using the attenuation characteristic function corresponding to the wave source position selected by the wave source position selecting unit 16. For example, the range if the source locations S _qb ^e is selected, the range estimation unit 17, by using the estimated by the estimation unit 15 damping characteristic function P _theta ^(qb), reached by radio waves from a wave source 3 It may be estimated. The attenuation characteristic function P _θ ^(qb) is an attenuation characteristic function for each of a plurality of specific azimuths. The range may be, for example, a range in which radio waves from the wave source 3 can be used, or a range in which radio waves from the wave source 3 are affected. When the wave source 3 is a base station of a mobile phone, for example, the former range is a range in which a mobile phone call can be made, and the latter range may not be a mobile phone call, Radio waves of the same frequency may be in a range that cannot be used for other purposes. If an area other than this range can be considered as a white space, the range estimating unit 17 can be considered to be substantially estimating the white space. The white space is a regional area where radio waves from the wave source 3 do not reach. The range estimating unit 17 uses the attenuation characteristic function estimated by the estimating unit 15 to calculate, for each specific azimuth in which the attenuation characteristic function is estimated, the distance from the wave source 3 at which the received signal power becomes a predetermined threshold. May be calculated, and an area connecting the radio wave arrival ends, which is a point corresponding to the distance, may be set as the radio wave reach range. Specifically, when the attenuation characteristic function for the specific azimuth angle θ is estimated, the position of the distance d at which the received signal strength becomes the threshold value P ^TH may be used as the radio wave arrival end. In this manner, a plurality of sets of the specific azimuth angle θ and the distance d to the radio wave arrival end can be obtained. If the attenuation characteristic function does not indicate the received signal power, the range estimating unit 17 may estimate the range using the transmission power of the wave source 3 as well.

  FIG. 5A and FIG. 5B are diagrams illustrating an example of the reach of radio waves. The boundary of the reach of the radio wave may pass through each of the arrival ends of the radio wave as shown in FIG. 5A, or may not be as shown in FIG. 5B. In the latter case, for example, the range estimation unit 17 sets the acquired specific azimuth angle θ and the distance d in a coordinate system in which the horizontal axis is the azimuth and the vertical axis is the radio wave arrival distance (θ, d) is plotted. Then, the one corresponding to the curve specified so that the distance between the plotted point and the curve is the shortest may be the boundary of the reach of the radio wave. Note that the radio wave arrival distance is a distance from the wave source 3 to the radio wave arrival end. When the wave source 3 transmits radio waves of a plurality of frequencies, the range estimating unit 17 may estimate the reach of radio waves for each of the frequencies. Further, the range estimating unit 17 may separately perform a process of specifying a white space. When the number of the wave sources 3 is one, the white space can be specified as a result by specifying the reach of the radio wave as described above. A range in which radio waves from any of the wave sources 3 do not reach is a white space. Therefore, the range estimating unit 17 may specify a white space that is an area that is not included in any radio wave reach. As a result, there is no limitation on the method of specifying the range or white space of the radio wave as long as the range or the white space of the radio wave can be distinguished from the rest. The range estimating unit 17 may acquire, for example, information indicating an outline of a region such as a radio wave arrival range.

  The output unit 18 outputs the range estimated by the range estimating unit 17. The output may be, for example, outputting information indicating a radio wave coverage or white space, or outputting a determination result as to whether a certain position is included in the radio coverage or white space. It may be. When outputting the determination result, for example, the output unit 18 may make a determination using the estimation result by the range estimating unit 17, or another component may make the determination. The position to be determined may be received by the receiving unit 13, for example.

  Here, the output may be, for example, a display on a display device (for example, a CRT or a liquid crystal display), transmission via a communication line to a predetermined device, printing by a printer, or printing on a recording medium. It may be stored or delivered to other components. Note that the output unit 18 may or may not include a device that performs output (for example, a display device or a transmission device). Further, the output unit 18 may be realized by hardware, or may be realized by software such as a driver for driving those devices.

Next, the operation of the wave source position selecting device 10 will be described with reference to the flowchart of FIG.
(Step S101) The receiving unit 11 receives the first observation information from the plurality of first receiving devices 1, respectively. Note that the transmission of the first observation information may be performed, for example, by transmitting a transmission request to transmit the first observation information from the wave source position selection device 10 to each of the first reception devices 1. Good. The received plurality of first observation information may be stored in a recording medium (not shown).

  (Step S102) The position calculation unit 12 acquires a wave source position using the plurality of pieces of first observation information received in step S101. The wave source position may be stored in a recording medium (not shown).

  (Step S103) The position calculation unit 12 determines whether or not the wave source position has been obtained in step S102 at least Q times. If the wave source position has been acquired at least Q times, the process proceeds to step S104, otherwise, the process returns to step S101.

  (Step S104) The receiving unit 13 receives received signal strengths at a plurality of reception positions. Further, the receiving unit 13 may receive the receiving position and the frequency together with the received signal strength. Further, the receiving unit 13 may receive the received signal strength and the like from the second receiving device 2. The received plurality of received signal strengths and the like may be stored in a recording medium (not shown).

  (Step S105) The distance calculation unit 14 calculates the distance and the azimuth from the wave source 3 for each reception position corresponding to each received signal strength received in step S104. Further, the distance calculation unit 14 performs the calculation for each of a plurality of wave source positions. The distance and azimuth corresponding to each reception position calculated for each wave source position may be stored in a recording medium (not shown).

  (Step S106) The estimating unit 15 uses a plurality of pieces of second observation information including the received signal strength at the reception position and the distance and azimuth of the reception position from the wave source 3 for each of a plurality of specific azimuths. Get the attenuation characteristic function. The obtained attenuation characteristic function may be stored in a recording medium (not shown). Further, the estimation unit 15 acquires the attenuation characteristic function for each of the plurality of specific azimuths for each wave source position. The details of this process will be described later with reference to the flowchart of FIG. 4A.

  (Step S107) The wave source position selecting unit 16 selects one wave source position from a plurality of wave source positions using the information on the estimation of the attenuation characteristic function in step S106. The details of this process will be described later with reference to the flowcharts in FIGS. 4B and 4C.

  (Step S108) The range estimating unit 17 estimates the reach of the radio wave using the attenuation characteristic function for each of a plurality of azimuth angles corresponding to the wave source position selected by the wave source position selecting unit 16. The range of the radio wave as the estimation result may be stored in a recording medium (not shown).

  (Step S109) The output unit 18 outputs the result of the range estimation by the range estimation unit 17. Then, a series of processes regarding the estimation of the arrival range of the radio wave ends.

  Note that the white space may be detected in step S108 of the flowchart in FIG. In addition, by repeatedly executing the processing of the flowchart in FIG. 3, it is possible to detect the reach of radio waves and the white space in the time direction. In that case, the process including the process of selecting the wave source position may be repeated, or the process of selecting the wave source position is not repeated, and only the estimation of the attenuation characteristic function, and the estimation and output of the radio wave arrival range are repeated. Is also good.

FIG. 4A is a flowchart showing details of the process of estimating the attenuation characteristic function (step S106) in the flowchart of FIG.
(Step S201) The estimation unit 15 sets the counter q to 1.

  (Step S202) The estimating unit 15 sets a specific azimuth θ, which is an azimuth indicating a specific direction, to 0 degrees.

  (Step S203) The estimation unit 15 estimates the attenuation characteristic function related to the specific azimuth angle θ using the plurality of pieces of second observation information. This estimation may or may not be based on frequency.

  (Step S204) The estimating unit 15 increments the specific azimuth angle θ by ε. Note that ε may or may not be a divisor of 360 degrees.

  (Step S205) The estimation unit 15 determines whether the specific azimuth angle θ is equal to or greater than 360 degrees. If the angle is 360 degrees or more, the process proceeds to step S206. Otherwise, the process returns to step S203.

  (Step S206) The estimation unit 15 determines whether or not the counter q is equal to or larger than a preset Q. Then, when the counter q is equal to or larger than Q, the process returns to the flowchart of FIG. 3, and otherwise, the process proceeds to step S207.

  (Step S207) The estimation unit 15 increments the counter q by one. Then, the process returns to step S202.

FIG. 4B is a flowchart showing details of the process of selecting a wave source position (step S107) in the flowchart of FIG. In the flowchart of FIG. 4B, a case will be described in which selection is performed using a distance attenuation coefficient.
(Step S301) The wave source position selector 16 sets the counter q to 1.

(Step S302) The wave source position selecting unit 16 counts the number of azimuth angles N ^(q) within the range where a ^(q) (θ) ≦ A _UB . The wave source position selection unit 16 sets, for example, N ^(q) to an initial value of 0, and thereafter, for each of the specific azimuth angles θ = 0 °, ε, 2 × ε, 3 × ε,. , A ^(q) (θ) ≦ A _UB , N ^(q) may be counted up by one.

  (Step S303) The wave source position selection unit 16 determines whether or not the counter q is equal to or larger than a preset Q. If the counter q is equal to or larger than Q, the process proceeds to step S304; otherwise, the process proceeds to step S305.

(Step S304) The wave source position selecting unit 16 selects a wave source position corresponding to q having the maximum in-range azimuth number N ^(q) . When there are a plurality of such qs, the wave source position selection unit 16 may, for example, randomly select one q from such a plurality of qs, or the minimum value of the sum E _sum ^(q) may be selected wave source position corresponding to q is the minimum of the objective function E _theta corresponding ^(q) to. Then, the process returns to the flowchart of FIG.

  (Step S305) The wave source position selector 16 increments the counter q by one. Then, the process returns to step S302.

FIG. 4C is a flowchart showing details of the process of selecting a wave source position (step S107) in the flowchart of FIG. In the flowchart of FIG. 4C, a case will be described in which selection is performed using the minimum value of the objective function.
(Step S401) The wave source position selector 16 sets the counter q to 1.

(Step S402) The wave source position selection unit 16 calculates the total value E _sum ^(q) of the minimum values of the objective function E _θ ^(q) . The wave source position selector 16 adds, for example, the minimum value of the objective function E _θ ^{(q) to} each of the specific azimuth angles θ = 0 °, ε, 2 × ε, 3 × ε,. _May be used to calculate the total value E _sum ^(q) .

  (Step S403) The wave source position selector 16 determines whether or not the counter q is equal to or larger than a preset Q. If the counter q is equal to or larger than Q, the process proceeds to step S404; otherwise, the process proceeds to step S405.

(Step S404) The wave source position selector 16 selects a wave source position corresponding to q having the minimum total value E _sum ^(q) . When there are a plurality of such qs, the wave source position selection unit 16 may, for example, randomly select one q from such a plurality of qs, or May be selected as the wave source position corresponding to q at which the in-range azimuth angle number N ^(q) corresponding to the maximum is q. Then, the process returns to the flowchart of FIG.

  As described above, according to the wave source position selecting apparatus 10 of the present embodiment, a more accurate wave source position can be selected even when there is a temporal variation in the characteristics of the propagation environment such as multipath. In addition, by estimating the reach of the radio wave using the wave source position selected in this way, the reach of the radio wave, the white space, and the like can be estimated with higher accuracy.

  In the present embodiment, a case has been described in which the wave source position selecting device 10 also estimates the reach of radio waves, but this is not essential. When the arrival range of the radio wave is not estimated, the wave source position selection device 10 may not include the range estimation unit 17. The output unit 18 may output, for example, a selected wave source position or an attenuation characteristic function corresponding to the selected wave source position.

(Embodiment 2)
A wave source position calculating device according to a second embodiment of the present invention will be described with reference to the drawings. The wave source position calculation device according to the present embodiment repeatedly calculates the arrival time difference in the calculation of the wave source position by TDoA, acquires an appropriate value from the plurality of calculated arrival time differences, and uses the acquired arrival time difference. Is used to calculate the wave source position.

  The configuration of the information communication system including the wave source position calculation device 20 according to the present embodiment is the same as that of the first embodiment except that the wave source position selection device 10 is replaced with the wave source position calculation device 20 in FIG. Yes, the detailed description is omitted. In the present embodiment, since the wave source position calculating device 20 calculates the wave source position by TDoA, it is assumed that three or more first receiving devices 1 exist. Further, it is assumed that the first observation information includes a reception signal corresponding to a radio wave from the wave source 3 received by the first receiver 1.

  FIG. 6 is a block diagram illustrating a configuration of the wave source position calculation device 20 according to the present embodiment. The wave source position calculating device 20 according to the present embodiment includes a receiving unit 21, an arrival time difference calculating unit 22, an arrival time difference obtaining unit 23, a wave source position calculating unit 24, a receiving unit 25, a distance calculating unit 26, A section 27, a range estimating section 17, and an output section 18 are provided. Note that the configuration and operation of the range estimating unit 17 and the output unit 18 are such that the range estimating unit 17 uses the attenuation characteristic function estimated by the estimating unit 27 instead of the estimating unit 15 to reach the range of the radio wave from the wave source 3. Is the same as in the first embodiment, except for estimating.

  The receiving unit 21 receives the first observation information from three or more first receiving devices 1. It is assumed that the first observation information includes a reception signal of a radio wave from the wave source 3 received by the first receiver 1. The received signal is used for calculating the position of the wave source 3, and may be, for example, IQ data or a complex amplitude value of a baseband signal. Further, the received signals included in the three or more pieces of first observation information are used for calculating the arrival time difference of the radio wave, as described later, and therefore, are preferably synchronized. Further, the first observation information may include information from which the position of the first receiving device 1 can be obtained. Note that the receiving unit 21 is the same as the receiving unit 11 that receives a plurality of pieces of first observation information for calculating a wave source position by TDoA.

  Further, the receiving unit 21 may receive a plurality of first observation information a plurality of times. That is, a plurality of pieces of first observation information for different periods of the radio wave transmitted from the wave source 3 may be received by the receiving unit 21. The arrival time difference is calculated for each of the received plurality of first observation information. The different periods may be, for example, continuous periods or discontinuous periods. Also, some of the different periods may or may not overlap. Further, the receiving unit 21 may, for example, collectively receive a plurality of pieces of first observation information for the plurality of times. In addition, the receiving unit 21 may receive a plurality of pieces of first observation information including a continuous long received signal, for example. Then, in the wave source position calculation device 20, a plurality of first observation information items for different periods may be obtained by appropriately dividing the long received signal.

  The receiving unit 21 may receive the first observation information directly from the first receiving device 1 or may receive the first observation information via another server or the like. Further, the receiving unit 21 may or may not include a wired or wireless receiving device (for example, a modem or a network card) for performing reception. Further, the receiving unit 21 may be realized by hardware, or may be realized by software such as a driver for driving the receiving device.

  The arrival time difference calculator 22 calculates the arrival time difference of the radio wave from the wave source 3 using the cross-correlation of the received signal for the pair of the first receiving devices 1. Further, the arrival time difference calculation unit 22 calculates the arrival time difference for a plurality of pairs of the first receiving device 1. The arrival time difference calculation unit 22 calculates arrival time differences for the plurality of pairs for different received signals. As a result, a plurality of arrival time differences are obtained for each of the plurality of pairs. Note that the arrival time difference is the difference between the propagation time of a radio wave from the wave source 3 to a certain first receiving device 1 and the propagation time of a radio wave from the wave source 3 to another first receiving device 1. Specifically, the arrival time difference calculator 22 may calculate the arrival time difference as follows.

First, the arrival time difference calculation unit 22 uses three or more synchronized reception signals to obtain a cross-correlation C _ij ⁽ _i.e. , a pair of the i-th first reception device 1 and the j-th first reception device 1 ^{). q)} Calculate (τ). The method for calculating the cross-correlation is the same as that described in the first embodiment, and a detailed description thereof will be omitted. The arrival time difference calculation unit 22 calculates an arrival time difference | τ _ij ^(max) (q) | using the calculated cross correlation C _ij ^(q) (τ). Strictly speaking, δ | τ _ij ^(max) (q) | obtained by multiplying | τ _ij ^(max) (q) | by the sampling period δ is the arrival time difference in units of time. The method of calculating the arrival time difference is the same as that described in the first embodiment, and a detailed description thereof will be omitted.

  In addition, the arrival time difference calculation unit 22 may calculate the arrival time difference for all pairs of three or more first receiving devices 1 used for calculating the position of the wave source 3, and at least one of the pairs The arrival time difference may be calculated for two pairs, preferably for three or more pairs. Further, the arrival time difference calculation unit 22 calculates Q sets of arrival time differences corresponding to a plurality of pairs of the first receiving device 1 using Q sets of three or more synchronized reception signals. . As a result, Q arrival time differences are obtained for each of the plurality of pairs.

The arrival time difference acquisition unit 23 acquires a arrival time difference that is a representative value from a plurality of arrival time differences for each pair of the first receiving devices 1. For example, for the pair of the i-th first receiving device 1 and the j-th first receiving device 1, the Q arrival time differences are calculated by the arrival time difference calculation unit 22, so that the arrival time difference acquisition unit 23 Acquires the arrival time difference that is a representative value from the Q arrival time differences. The representative value may be, for example, a median value or an average value. For example, the median of δ | τ _ij ^(max) (q) | corresponding to 1 ≦ q ≦ Q may be selected by the arrival time difference acquisition unit 23, and δ | τ _ij corresponding to 1 ≦ q ≦ Q. The average value of ^(max) (q) | may be calculated by the arrival time difference acquisition unit 23. In the present embodiment, a case where the representative value is the median value will be mainly described. The arrival time difference acquisition unit 23 performs a process of acquiring a representative value of the arrival time difference for all the sets of ij for which the arrival time differences have been calculated. For example, assuming that q corresponding to the median of δ | τ _ij ^(max) (q) | is qb (ij), the arrival time difference acquisition unit 23 sets the i-th first receiving device 1 and the j-th The arrival time difference δ | τ _ij ^(max) (qb (ij)) | is selected for one pair with the receiving device 1.

  As described above, the arrival distance difference is obtained by multiplying the arrival time difference by the light speed χ. Therefore, the arrival time difference calculation unit 22 has substantially calculated the arrival distance difference, and the arrival time difference acquisition unit 23 has substantially obtained the arrival distance difference that is a representative value from a plurality of arrival distance differences. You can also think.

  The wave source position calculation unit 24 calculates a wave source position, which is the position of the wave source 3, using the position of the first receiving device 1 and the arrival time differences of a plurality of pairs acquired by the arrival time difference acquisition unit 23. . Note that the position of the first receiving device 1 is the position of the first receiving device 1 forming a plurality of pairs of the receiving devices 1 whose arrival time differences have been calculated. Specifically, the wave source position calculation unit 24 may calculate the position of the wave source 3 as follows.

First, the wave source position calculation unit 24 calculates the difference between the distance from the wave source 3 to the i-th first receiving device 1 and the distance from the wave source 3 to the j-th first receiving device 1 using the arrival time difference. The arrival distance difference Δd _ij ^{(qb (ij))} is calculated. The arrival distance difference Δd _ij ^{(qb (ij))} is expressed by the following equation. In the following equation, χ is the speed of light.

It is already known that the position of the wave source 3 is specified by using the arrival distance difference regarding the plurality of pairs of the first receiving device 1. However, the wave source position calculating unit 24 calculates the wave source position S _qb as follows, for example. ^e may be calculated.

Here, S _qb ^e is the estimated wave source position coordinates (wave source position), is it what is the calculation target wave source position calculation section 24. m is a combination of ij, that is, an index of the first receiving device 1 forming a pair of the first receiving devices 1, and M is a total number of pairs of the first receiving device 1. Further, S _qb ^e is a wave source ^{_{position, | e m (S qb e}} ) | 2 is as follows.

Here, Δd _m ^{(qb (m))} is the arrival distance difference selected as described above. Δd _m (S _qb ) is the arrival distance difference calculated from the position coordinates, as shown by the following equation. Note that S _i is the position coordinate of the i-th first receiver 1.

Wave source position calculation section 24, the estimated wave source coordinates S _qb ^e, for example, may be calculated by non-linear least squares method, or may be calculated by other methods. The calculation may be performed using, for example, the Newton method or the Levenberg-Marquardt method. When the representative value is an average value, the arrival distance difference obtained by multiplying the arrival time difference of the average value by the speed of light ^{代 え} instead of the arrival distance difference Δd _ij ^{(qb (ij))} of the intermediate value in the above equation is obtained. Shall be used.

  The receiving unit 25 receives received signal strengths of the radio wave from the wave source 3 at a plurality of receiving positions. The receiving unit 25 is the same as the receiving unit 13 of the first embodiment, and a detailed description thereof will be omitted.

The distance calculation unit 26 calculates the distance and the azimuth from the wave source 3 for each reception position using the plurality of reception positions and the wave source position calculated by the wave source position calculation unit 24. Specifically, the distance calculation unit 26 receives the position (X _i, Y _i) and, by using the wave source position S _qb ^e, receiving position around the distance from the wave source position to the receiving position, the source locations Is calculated. The distance from the wave source 3 to the receiving position is usually a linear distance between the wave source 3 and the receiving position. Further, the azimuth from the wave source 3 to the reception position may be, for example, 0 degree in the north and 90 degrees in the east with respect to the wave source 3, and may be based on another direction. You may. The information including the distance and azimuth from the wave source 3 with respect to the i-th reception position and the received signal strength of the radio wave received at the i-th reception position is referred to as the i-th second observation information. To That is,
i-th second observation information = (x _i , θ _i , P _i )
It may be. Here, the wave source position S _qb ^e and the receiving position (X _i, Y _i) the distance between the (km) and x _i, received position (X _i, Y _i) centered on the source locations S _qb ^e direction The azimuth (deg) is defined as θ _i . P _i is the reception signal strength (dBm) of the radio wave received at the reception position of x _i , θ _i . Since i is an integer from 1 to N, there are N pieces of second observation information in the present embodiment. Further, the second observation information may include a frequency. In that case,
i-th second observation information = (x _i , θ _i , P _i , f _i )
Becomes The frequency f _i is the same as in the first embodiment.

  The estimating unit 27 estimates the attenuation characteristic function of the radio wave from the wave source 3 using the wave source position calculated by the wave source position calculating unit 24 and the received signal strengths at the plurality of receiving positions received by the receiving unit 25. . The estimation may be performed using the distance from the wave source 3 and the azimuth angle for each reception position calculated by the distance calculation unit 26. In this embodiment, such a case will be mainly described. In the process of estimating the attenuation characteristic function by the estimating unit 27, instead of performing the estimation of the attenuation characteristic function for each of the plurality of specific azimuths with respect to the Q source positions, the attenuation characteristic for each of the plurality of specific azimuth angles is used. The process of estimating the attenuation characteristic function by the estimating unit 15 of the first embodiment may be the same as that of estimating the function except for the one source position calculated by the source position calculating unit 24. In the present embodiment, such a case will be mainly described, and detailed description thereof will be omitted.

Next, the operation of the wave source position calculation device 20 will be described with reference to the flowchart of FIG.
(Step S501) The receiving unit 21 receives the first observation information from three or more first receiving devices 1, respectively. Note that the transmission of the first observation information may be performed, for example, by transmitting a transmission request to transmit the first observation information from the wave source position calculation device 20 to each of the first reception devices 1. Good. The received plurality of first observation information may be stored in a recording medium (not shown). Note that the first observation information includes a reception signal synchronized between the plurality of first reception devices 1.

  (Step S502) The arrival time difference acquisition unit 23 calculates arrival time differences for a plurality of pairs of the first receiving devices 1 that have transmitted the first observation information. The arrival time difference may be stored in a recording medium (not shown).

  (Step S503) The arrival time difference acquisition unit 23 determines whether or not the arrival time difference has been calculated for a plurality of pairs in step S502 at least Q times. Then, if the arrival time difference for a plurality of pairs has been calculated Q times or more, the process proceeds to step S504; otherwise, the process returns to step S501.

  (Step S504) The arrival time difference acquisition unit 23 acquires a plurality of representative values of arrival time differences for each pair. The acquisition of the representative value is performed independently for each pair.

  (Step S505) The wave source position calculation unit 24 calculates the wave source position using the representative value of the arrival time difference acquired in step S504 for each pair. The wave source position may be stored in a recording medium (not shown).

  (Step S506) The receiving unit 25 receives received signal strengths at a plurality of receiving positions. The receiving unit 25 may receive the receiving position and the frequency together with the received signal strength. Further, the receiving unit 25 may receive the received signal strength and the like from the second receiving device 2. The received plurality of received signal strengths and the like may be stored in a recording medium (not shown).

  (Step S507) The distance calculation unit 26 calculates the distance and the azimuth from the wave source 3 for each reception position corresponding to each reception signal strength received in step S506. The distance and azimuth corresponding to each reception position may be stored in a recording medium (not shown).

  (Step S508) The estimation unit 27 uses, for each of the plurality of specific azimuths, the received signal strength at the reception position and the plurality of pieces of second observation information including the distance and the azimuth from the wave source 3 regarding the reception position. Get the attenuation characteristic function. The obtained attenuation characteristic function may be stored in a recording medium (not shown). The details of this process will be described later with reference to the flowchart of FIG.

  (Step S509) The range estimating unit 17 estimates the arrival range of the radio wave using the attenuation characteristic function for each of the plurality of azimuth angles estimated by the estimating unit 27. The range of the radio wave as the estimation result may be stored in a recording medium (not shown).

  (Step S510) The output unit 18 outputs the result of the range estimation by the range estimation unit 17. Then, a series of processes regarding the estimation of the arrival range of the radio wave ends.

  In step S509 of the flowchart in FIG. 7, a white space may be detected. In addition, by repeatedly executing the processing of the flowchart in FIG. 7, it is possible to detect the reach of radio waves and the white space in the time direction. In that case, the process of calculating the wave source position may be repeated, or the process of calculating the wave source position may not be repeated, but only the estimation of the attenuation characteristic function, and the estimation and output of the radio wave arrival range may be repeated. Is also good.

FIG. 8 is a flowchart showing details of the process (step S508) of estimating the attenuation characteristic function in the flowchart of FIG.
(Step S601) The estimating unit 27 sets a specific azimuth θ which is an azimuth indicating a specific direction to 0 degree.

  (Step S602) The estimation unit 27 estimates the attenuation characteristic function for the specific azimuth angle θ using the plurality of pieces of second observation information. This estimation may or may not be based on frequency.

  (Step S603) The estimating unit 27 increments the specific azimuth angle θ by ε. Note that ε may or may not be a divisor of 360 degrees.

  (Step S604) The estimation unit 27 determines whether or not the specific azimuth angle θ is equal to or greater than 360 degrees. If the angle is 360 degrees or more, the process returns to the flowchart of FIG. 7, and if not, the process returns to step S602.

  As described above, according to the wave source position calculation device 20 according to the present embodiment, the wave source position is calculated using the representative values of the plurality of arrival time differences. Therefore, even when there is a temporal variation in the characteristics of the propagation environment such as multipath, the wave source position can be calculated using the arrival time difference that is less affected by multipath or the like. As a result, the calculation accuracy of the wave source position can be improved. In addition, by using such a highly accurate wave source position, it is possible to more accurately estimate a radio wave reach range, a white space, and the like.

  In the present embodiment, a case has been described in which the wave source position calculation device 20 also estimates the reach of radio waves, but this is not essential. When the arrival range of the radio wave is not estimated, the wave source position calculation device 20 may not include the range estimation unit 17. The output unit 18 may output, for example, the estimated attenuation characteristic function.

  Further, in the present embodiment, a case has been described in which the wave source position calculation device 20 also estimates the attenuation characteristic function, but this is not essential. When the attenuation characteristic function is not estimated, the wave source position calculation device 20 may not include the reception unit 25, the distance calculation unit 26, the estimation unit 27, and the range estimation unit 17. The output unit 18 may output, for example, the calculated wave source position.

  Further, in the present embodiment, a case has been described where the attenuation characteristic function relating to a specific azimuth from the wave source 3 is estimated by regression analysis in which the second observation information at an azimuth away from the specific azimuth has a smaller effect. , But not necessarily. When such estimation is not performed, the estimating unit 27 may perform, for each reception position, a process of calculating an attenuation characteristic function in a direction of a straight line passing through the wave source 3 and the reception position, for example. In that case, the estimation unit 27 estimates only one coefficient included in the attenuation characteristic function using the received signal strength corresponding to the reception position. Therefore, for example, the estimation unit 27 may estimate only the distance attenuation coefficient (a), and use the values given from the model for the other coefficients (b, c). In such a case, it is not appropriate that the influence of the transmission power is included in the constant term c, so that the transmission power of the radio wave transmitted from the wave source 3 is preferably acquired separately. That is, it is preferable that the above-described attenuation characteristic function indicates a path loss. The transmission power may be known in advance, for example, or may be calculated from the reception power of the received radio wave. Here, a method of determining the frequency coefficient b and the constant term c will be briefly described. For example, the estimation unit 27 may use the coefficients b and c of the free space model by setting that everything from the wave source 3 to each of the second receiving devices 2 is a free space model. On the other hand, the estimating unit 27 determines whether or not the distance from the wave source 3 to the second receiving device 2 is line-of-sight using the time variation of the received signal strength and the delay profile. The coefficients b and c of the two-wave model of reflection may be used, and the coefficients b and c of the Okumura-Hata model may be used when it is not line of sight. The delay profile used in the determination may be transmitted from the second receiving device 2 to the wave source position calculating device 20. A brief description will be given as to which of the free space model and the two-wave model of ground reflection is selected. When the height of the receiving antenna of the second receiving device 2 is sufficiently high and the frequency is high, the distance to the break point at which the first Fresnel zone starts to be blocked by the ground is large, so that there is no problem even if the free space model is used. Otherwise, the effect of shielding the first Fresnel zone cannot be ignored, so it is preferable to use a two-wave model of ground reflection. Therefore, for example, the estimating unit 27 adopts the free space model when the reception antenna height of the second receiving device 2 is equal to or more than the threshold value related to the antenna height and the frequency f is equal to or larger than the threshold value related to the frequency. If not, a two-wave model of ground reflection may be adopted. Note that the determination of the coefficients b and c is usually performed for each second receiving device 2. In this way, by determining the coefficients b and c and calculating the distance attenuation coefficient a, the attenuation characteristic function, which is the path loss, can be estimated for each of the second receivers 2. As described above, when the calculation of the attenuation characteristic function for each specific azimuth is not performed, the distance calculation unit 26 may calculate the distance between the position of the wave source 3 and the reception position, for example. Good. In the present embodiment, two methods for estimating the attenuation characteristic function using the calculated wave source position and the received signal strength at each reception position have been described. Needless to say, the damping characteristic function may be estimated by the following.

  Further, in each of the above-described embodiments, the case where the wave source position selecting device 10 and the wave source position calculating device 20 receive the received signal strength and the like via the communication line 100 has been described. For example, when the wave source position selecting device 10 or the wave source position calculating device 20 receives the received signal strength or the like via a recording medium or the like, the second receiving device 2 may not be connected to the communication line 100. .

  Further, in each of the above embodiments, each process or each function may be realized by centralized processing by a single device or a single system, or may be realized by distributed processing by a plurality of devices or a plurality of systems. It may be realized by doing.

  In each of the above-described embodiments, the information exchange performed between the components may be performed, for example, when two components performing the information exchange are physically different from each other. Output of information and reception of information by the other component, or if the two components that deliver the information are physically the same, one configuration It may be performed by shifting from the processing phase corresponding to the element to the processing phase corresponding to the other component.

  Further, in each of the above embodiments, information relating to the processing executed by each component, for example, each component received, obtained, selected, generated, transmitted, received, etc. Information, information such as thresholds, formulas, addresses, and the like used by each component in processing may not be specified in the above description, and may be temporarily or long-term retained in a recording medium (not shown). . The storage of information on the recording medium (not shown) may be performed by each component or a storage unit (not shown). The reading of information from the recording medium (not shown) may be performed by each component or a reading unit (not shown).

  Further, in each of the above embodiments, when information used by each component or the like, for example, information such as a threshold or an address used by each component in processing or various set values may be changed by a user, Even if it is not specified in the above description, the user may or may not be able to change such information as appropriate. When the information can be changed by the user, the change is realized by, for example, a receiving unit (not shown) that receives a change instruction from the user and a changing unit (not shown) that changes the information according to the change instruction. You may. The reception of the change instruction by the receiving unit (not shown) may be, for example, reception from an input device, reception of information transmitted via a communication line, or reception of information read from a predetermined recording medium. .

  In each of the above embodiments, when two or more components included in the wave source position selection device 10 and the wave source position calculation device 20 include a communication device, an input device, and the like, the two or more components are physically unitary. It may have one device or may have separate devices.

  Further, in each of the above embodiments, each component may be configured by dedicated hardware, or a component that can be realized by software may be realized by executing a program. For example, each component can be realized by a program execution unit such as a CPU reading and executing a software program recorded on a recording medium such as a hard disk or a semiconductor memory. At the time of execution, the program execution unit may execute the program while accessing the storage unit and the recording medium. In addition, the software which implement | achieves the wave source position selection apparatus 10 in the said embodiment is the following programs. In other words, this program performs position calculation for acquiring a plurality of wave source positions by performing a plurality of times of processing for calculating a wave source position, which is the position of a wave source, using radio waves from wave sources received by a plurality of receiving devices. Unit, a receiving unit that receives the received signal strength at a plurality of receiving positions of radio waves from the wave source, a plurality of receiving positions, and the wave source position calculated by the position calculating unit, for each receiving position, the distance from the wave source and To calculate the azimuth, the distance calculator performing a plurality of wave source positions, the received signal strength of the receiving position, and a plurality of observation information including the distance and the azimuth from the wave source with respect to the receiving position, from the wave source, The regression analysis of the attenuation characteristic function of the radio wave from the source with respect to a specific azimuth angle is performed by regression analysis so that the observation information including the azimuth angle away from the specific azimuth has a smaller effect Estimating for a plurality of azimuth angles, using an estimating unit that performs a plurality of wave source positions, and information about estimation performed by the estimating unit, to function as a wave source position selecting unit that selects one wave source position from the plurality of wave source positions. Program.

  The software that implements the wave source position calculation device 20 in the above embodiment is a program as described below. In other words, this program causes the computer to transmit a received signal of a radio wave from a wave source received by three or more receiving devices from a plurality of pairs of receiving units and receiving devices from three or more receiving devices. By using the cross-correlation to perform a process of calculating the arrival time difference of the radio wave from the wave source for each of the different received signals, an arrival time difference calculation unit that obtains a plurality of arrival time differences for each pair, a plurality of arrival time differences for each pair From the arrival time difference acquisition unit that acquires the arrival time difference that is a representative value, the position of the receiving device, and the arrival time difference acquired for each of the plurality of pairs acquired by the arrival time difference acquisition unit, the wave source position that is the position of the wave source. This is a program for functioning as a wave source position calculation unit for calculation.

  Note that, in the above-described program, functions realized by the program do not include functions that can be realized only by hardware. For example, functions that can be realized only with hardware such as a modem or an interface card in a reception unit that receives information, a reception unit that receives information, an output unit that outputs information, and the like are at least not included in the functions realized by the program. .

  Further, the program may be executed by being downloaded from a server or the like, and the program recorded on a predetermined recording medium (for example, an optical disk such as a CD-ROM, a magnetic disk, a semiconductor memory, or the like) may be read. May be performed by Further, this program may be used as a program constituting a program product.

  The computer that executes this program may be a single computer or a plurality of computers. That is, centralized processing or distributed processing may be performed.

  FIG. 9 is a schematic diagram illustrating an example of the external appearance of a computer that executes the program and realizes the wave source position selection device 10 and the wave source position calculation device 20 according to each of the above embodiments. Each of the above embodiments can be realized by computer hardware and a computer program executed thereon.

  9, the computer system 900 includes a computer 901 including a CD-ROM drive 905, a keyboard 902, a mouse 903, and a monitor 904.

  FIG. 10 is a diagram showing the internal configuration of the computer system 900. 10, a computer 901 is connected to an MPU (Micro Processing Unit) 911, a ROM 912 for storing a program such as a boot-up program, and a MPU 911 in addition to a CD-ROM drive 905, and is connected to the MPU 911. A RAM 913 for temporarily storing and providing a temporary storage space, a hard disk 914 for storing application programs, system programs, and data, and a bus 915 for mutually connecting the MPU 911, the ROM 912, and the like are provided. Note that the computer 901 may include a network card (not shown) that provides a connection to a LAN, a WAN, or the like.

  A program that causes the computer system 900 to execute the functions of the wave source position selecting device 10 and the wave source position calculating device 20 according to the above embodiments is stored in the CD-ROM 921, inserted into the CD-ROM drive 905, and stored in the hard disk 914. It may be forwarded. Alternatively, the program may be transmitted to the computer 901 via a network (not shown) and stored in the hard disk 914. The program is loaded into the RAM 913 at the time of execution. Note that the program may be loaded directly from the CD-ROM 921 or a network. Further, the program may be read into the computer system 900 via another recording medium (for example, a DVD or the like) instead of the CD-ROM 921.

  The program may not necessarily include an operating system (OS) that causes the computer 901 to execute the functions of the wave source position selection device 10 and the wave source position calculation device 20 according to each of the above embodiments, or a third-party program. The program may include only a part of an instruction that calls an appropriate function or module in a controlled manner to obtain a desired result. It is well known how the computer system 900 operates, and a detailed description thereof will be omitted.

  In addition, the present invention is not limited to the above-described embodiments, and various changes can be made, and it goes without saying that these are also included in the scope of the present invention.

  As described above, according to the wave source position selection device and the like of the present invention, the effect that the position of the wave source can be obtained more accurately even when there is a temporal variation in the characteristics of the propagation environment such as multipath is obtained. This is useful as a device or the like for specifying a wave source position.

REFERENCE SIGNS LIST 1 first receiving device 2 second receiving device 3 wave source 10 wave source position selecting device 11, 21 receiving unit 13, 25 receiving unit 12 position calculating unit 14, 26 distance calculating unit 15, 27 estimating unit 16 wave source position selecting unit 17 Range estimation unit 18 Output unit 20 Wave source position calculation device 22 Arrival time difference calculation unit 23 Arrival time difference acquisition unit 24 Wave source position calculation unit

Claims (10)

A position calculating unit that obtains a plurality of wave source positions by performing a process of calculating a wave source position that is the position of the wave source a plurality of times using radio waves from the wave sources received by the plurality of receiving devices,
A receiving unit that receives received signal strengths at a plurality of reception positions of radio waves from the wave source,
Using the plurality of reception positions and the wave source position calculated by the position calculation unit, for each of the reception positions, calculating a distance and an azimuth from the wave source for the plurality of wave source positions. A calculating unit;
Using a plurality of pieces of observation information including the reception signal strength at the reception position and the distance and azimuth from the wave source with respect to the reception position, for a specific azimuth from the wave source, the attenuation characteristic function of radio waves from the wave source An estimation unit that performs estimation for a plurality of azimuths from the wave source, by regression analysis having a smaller influence as the observation information including an azimuth angle away from the specific azimuth angle, for the plurality of wave source positions,
A wave source position selecting device, comprising: a wave source position selecting unit that selects one of the wave source positions from the plurality of wave source positions using information on the estimation by the estimating unit. The wave source position selection unit, for each of the plurality of azimuth angles to determine whether the distance attenuation coefficient of the attenuation characteristic function estimated by the estimation unit is included in a predetermined range for each of the plurality of wave source positions. The wave source position selecting device according to claim 1, wherein the wave source position having the largest azimuth angle whose distance attenuation coefficient is included in the range is selected. The estimating unit includes a weighting function that is a function of a weight that decreases as the distance from the specific azimuth angle increases, a received signal strength received by the receiving unit, and a received signal strength calculated by an attenuation characteristic function to be estimated. Estimate the damping characteristic function so that the objective function including the difference with
The wave source position selection unit obtains a total value that is a value obtained by adding the minimum value of the objective function corresponding to the attenuation characteristic function estimated by the estimation unit for each of the plurality of azimuths, for each of the plurality of wave source positions, The source position selecting device according to claim 1, wherein the source position having the minimum sum is selected. Using an attenuation characteristic function corresponding to the wave source position selected by the wave source position selecting unit, a range estimating unit that estimates a range in which radio waves from the wave source reach,
The wave source position selecting device according to any one of claims 1 to 3, further comprising: an output unit configured to output the range estimated by the range estimating unit. A receiving unit that receives a reception signal for each different period of a radio wave from a wave source received by a reception device from three or more reception devices,
By using the cross-correlation of the received signals for the pair of receiving devices, by performing a process of calculating the arrival time difference of the radio wave from the wave source for each of the received signals for different periods, to obtain a plurality of arrival time differences for the pair The arrival time difference calculating unit for performing at least two pairs of the receiving device,
For each pair, an arrival time difference acquisition unit that acquires an arrival time difference that is a representative value from the plurality of arrival time differences,
The position of the receiving device, acquired by the arrival time difference acquisition unit, using the arrival time difference for each of a plurality of pairs, a wave source position calculation unit that calculates a wave source position that is the position of the wave source,
A receiving unit that receives received signal strengths at a plurality of reception positions of radio waves from the wave source,
An estimating unit that estimates the attenuation characteristic function of the radio wave from the wave source using the wave source position calculated by the wave source position calculating unit and the received signal strength at the plurality of receiving positions received by the receiving unit.
Using the attenuation characteristic function estimated by the estimating unit, a range estimating unit that estimates a range in which radio waves from the wave source reach,
An output unit configured to output the range estimated by the range estimating unit; The wave source position calculating device according to claim 5, wherein the representative value is a median. A position calculation step of obtaining a plurality of wave source positions by performing a process of calculating a wave source position that is the position of the wave source a plurality of times using radio waves from the wave sources received by the plurality of receiving devices,
A receiving step of receiving received signal strengths at a plurality of receiving positions of radio waves from the wave source,
Using the plurality of reception positions and the wave source position calculated in the position calculation step, for each of the reception positions, calculating a distance and an azimuth from the wave source for the plurality of wave source positions. A calculating step;
Using a plurality of pieces of observation information including the reception signal strength at the reception position and the distance and azimuth from the wave source with respect to the reception position, for a specific azimuth from the wave source, the attenuation characteristic function of radio waves from the wave source An estimation step for the plurality of wave source positions, by estimating a plurality of azimuths from the wave source, by regression analysis having a smaller effect as the observation information including the azimuth angle away from the specific azimuth angle,
A source position selecting step of selecting one source position from the plurality of source positions using information about the estimation in the estimating step. A receiving step of receiving, from three or more receiving devices, received signals for different periods of radio waves from a wave source received by the receiving device,
By using the cross-correlation of the received signals for the pair of receiving devices, by performing a process of calculating the arrival time difference of the radio wave from the wave source for each of the received signals for different periods, to obtain a plurality of arrival time differences for the pair Calculating the arrival time difference for at least two pairs of the receiving device;
For each pair, an arrival time difference acquisition step of acquiring an arrival time difference that is a representative value from the plurality of arrival time differences,
The position of the receiving device, acquired in the arrival time difference acquisition step, using the arrival time difference for each of a plurality of pairs, a wave source position calculation step of calculating a wave source position that is the position of the wave source,
A receiving step of receiving received signal strengths at a plurality of receiving positions of radio waves from the wave source,
An estimation step of estimating an attenuation characteristic function of a radio wave from the wave source, using the wave source position calculated in the wave source position calculation step and received signal strengths at a plurality of reception positions received in the reception step,
Using the attenuation characteristic function estimated in the estimation step, a range estimation step of estimating a range in which radio waves from the wave source reach,
An output step of outputting an output relating to the range estimated in the range estimation step . Computer
A position calculating unit that obtains a plurality of wave source positions by performing a plurality of times of calculating a wave source position that is the position of the wave source using radio waves from the wave sources received by the plurality of receiving devices,
A receiving unit that receives received signal strength at a plurality of reception positions of radio waves from the wave source,
Using the plurality of reception positions and the wave source position calculated by the position calculation unit, for each of the reception positions, calculating a distance and an azimuth from the wave source for the plurality of wave source positions. Calculator,
Using a plurality of pieces of observation information including the reception signal strength at the reception position and the distance and azimuth from the wave source with respect to the reception position, for a specific azimuth from the wave source, the attenuation characteristic function of radio waves from the wave source An estimation unit that performs estimation for the plurality of azimuths from the wave source by regression analysis having a smaller influence as the observation information including the azimuth away from the specific azimuth, and for the plurality of wave source positions,
A program for functioning as a wave source position selection unit that selects one wave source position from the plurality of wave source positions by using information about the estimation by the estimation unit. Computer
A receiving unit that receives a reception signal for each different period of a radio wave from a wave source received by the reception device from three or more reception devices,
By using the cross-correlation of the received signals for the pair of receiving devices, by performing a process of calculating the arrival time difference of the radio wave from the wave source for each of the received signals for different periods, to obtain a plurality of arrival time differences for the pair Time difference arriving unit for performing at least two pairs of the receiving device,
For each pair, an arrival time difference acquisition unit that acquires an arrival time difference that is a representative value from the plurality of arrival time differences,
The position of the receiving device, acquired by the arrival time difference acquisition unit, using the arrival time difference for each of a plurality of pairs, a wave source position calculation unit that calculates a wave source position that is the position of the wave source ,
A receiving unit that receives received signal strength at a plurality of reception positions of radio waves from the wave source,
An estimating unit that estimates an attenuation characteristic function of a radio wave from the wave source using the wave source position calculated by the wave source position calculating unit and received signal strengths at a plurality of receiving positions received by the receiving unit.
A range estimating unit that estimates a range in which radio waves from the wave source reach using the attenuation characteristic function estimated by the estimating unit;
A program for functioning as an output unit that outputs the range estimated by the range estimation unit .

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