JP7007023B2 - Radio wave monitoring device, radio wave monitoring system, radio wave monitoring method and program - Google Patents

Description

The present invention relates to a radio wave monitoring device, a radio wave monitoring system, a radio wave monitoring method and a program.

Radio wave monitoring is performed using sensors to estimate the position of an illegal radio station that emits illegal radio waves. Further, as a method of radio wave monitoring, a spatial power distribution is generated by spatial interpolation. In connection with this technique, Patent Document 1 discloses a radio search device that searches for a radio based on the strength of a radio signal received from one or more radios. The wireless search device according to Patent Document 1 has a position estimation unit that estimates the direction in which the wireless device is located, and detects a change in the direction of the wireless search device when the user holding the wireless search device changes its direction. It is equipped with a sensor. Further, the wireless search device according to Patent Document 1 includes a wireless communication unit that receives a wireless signal from a wireless device and measures the strength of the wireless signal.

Further, Patent Document 2 discloses a simulation device that performs high-resolution and high-precision simulation over a wide area in consideration of observation data having non-ideal, discontinuous or specificity. The simulation apparatus according to Patent Document 2 uses a kriging method, which is a kind of spatial interpolation, to generate a posterior distribution.

Japanese Unexamined Patent Publication No. 2017-142255 International Publication No. 2016/031174

For example, when radio wave monitoring is performed in an urban area, it is difficult to perform radio wave monitoring by a method of detecting the direction of arrival of radio waves (AOA; Angle of Arrival) by a multipath or the like generated by the reflection of radio waves on a building or the like. be. Therefore, it is difficult to accurately estimate the emission source of radio waves by the technique according to Patent Document 1. In addition, depending on the radio wave monitoring environment, it may not be possible to arrange many sensors. If many sensors cannot be placed, accurate estimation may not be possible even if the Kriging method is used. Therefore, in the technique according to Patent Document 2, when the number of sensors is small, there is a possibility that the emission source of radio waves cannot be estimated accurately. Therefore, in the technique according to the above patent document, there is a possibility that the emission source of the radio wave cannot be estimated accurately due to the environmental conditions.

The object of the present disclosure is to solve such a problem, and a radio wave monitoring device, a radio wave monitoring visual system, which can accurately estimate the emission source of radio waves regardless of environmental conditions. The purpose is to provide radio wave monitoring methods and programs.

The radio wave monitoring device according to the present disclosure is a measurement value acquisition means for acquiring the measurement value of the reception intensity of the radio wave measured by each of the plurality of sensors arranged at each of the plurality of first positions from each of the plurality of sensors. , The first error indicating the error between the first estimated value and the measured value of the reception intensity of the radio wave at the first position when it is assumed that the radio wave is emitted from each of a plurality of arbitrary second positions. It has an error calculating means for calculating, and a emitting source estimating means for estimating the position of the second position where the first error is minimized as the position of the emitting source of the radio wave.

Further, the radio wave monitoring system according to the present disclosure includes a plurality of sensors arranged at each of a plurality of first positions and a radio wave monitoring device for monitoring radio waves, and the radio wave monitoring device is based on the plurality of sensors. The first, assuming that the measured value of the received radio wave received from each of the measured values is acquired from each of the plurality of sensors, and the radio wave is emitted from each of the plurality of arbitrary second positions. An error calculating means for calculating a first error indicating an error between a first estimated value of radio wave reception intensity at a position and the measured value, and the second position where the first error is minimized are used for radio waves. It has a source estimation means for estimating the position of the source of the radio wave.

Further, in the radio wave monitoring method according to the present disclosure, the measured value of the reception intensity of the radio wave measured by each of the plurality of sensors arranged at each of the plurality of first positions is acquired from each of the plurality of sensors, and is arbitrary. A first error indicating an error between the first estimated value and the measured value of the reception intensity of the radio wave at the first position when it is assumed that the radio wave is emitted from each of the plurality of second positions is calculated. The second position where the first error is minimized is estimated as the position of the radio wave emission source.

Further, the program according to the present disclosure includes a step of acquiring the measured value of the reception intensity of the radio wave measured by each of the plurality of sensors arranged at each of the plurality of first positions from each of the plurality of sensors, and an arbitrary step. A step of calculating a first error indicating an error between the first estimated value and the measured value of the reception intensity of the radio wave at the first position when it is assumed that the radio wave is emitted from each of the plurality of second positions. Then, the computer is made to perform a step of estimating the position of the emission source of the radio wave at the second position where the first error is minimized.

According to the present disclosure, it is possible to provide a radio wave monitoring device, a radio wave monitoring visual system, a radio wave monitoring method and a program capable of accurately estimating a radio wave emission source regardless of environmental conditions.

It is a figure which shows the outline of the radio wave monitoring apparatus which concerns on embodiment of this disclosure. It is a figure which shows the radio wave monitoring system which concerns on Embodiment 1. FIG. It is a figure which illustrates the space where the sensor which concerns on Embodiment 1 are arranged. It is a figure which shows the structure of the radio wave monitoring apparatus which concerns on Embodiment 1. FIG. It is a flowchart which shows the radio wave monitoring method performed by the radio wave monitoring apparatus which concerns on Embodiment 1. FIG. It is a figure which illustrates the sensor information which concerns on Embodiment 1. FIG. It is a flowchart which shows the process performed by the maximum likelihood estimation part which concerns on Embodiment 1. It is a figure which illustrates the state which the space is divided into N * M pieces. It is a figure which illustrates the heat map which shows the minimum value of the sum-of-squares error at each position. It is a flowchart which shows the process performed by the electric power distribution estimation part which concerns on Embodiment 1. FIG. It is a figure which illustrates the electric power distribution generated by the electric power distribution estimation part which concerns on Embodiment 1. FIG. It is a flowchart which shows the process performed by the error distribution calculation part which concerns on Embodiment 1. It is a figure which illustrates the combination of a sensor, and the difference of a distance and an error between these. It is a figure which illustrates the electric power distribution corrected by the electric power distribution correction part which concerns on Embodiment 1. FIG.

(Summary of Embodiments of the present disclosure)
Prior to the description of the embodiments of the present disclosure, an outline of the embodiments according to the present disclosure will be described. FIG. 1 is a diagram showing an outline of the radio wave monitoring device 1 according to the embodiment of the present disclosure. The radio wave monitoring device 1 has a measured value acquisition unit 2 that functions as a measured value acquisition means, an error calculation unit 4 that functions as an error calculation means, and a emission source estimation unit 6 that functions as a emission source estimation means.

The measured value acquisition unit 2 acquires the measured value of the reception intensity of the radio wave measured by each of the plurality of sensors arranged at each of the plurality of first positions from each of the plurality of sensors. The error calculation unit 4 shows an error between the first estimated value and the measured value of the reception intensity of the radio wave at the first position when it is assumed that the radio wave is emitted from each of a plurality of arbitrary second positions. Calculate the error of. The emission source estimation unit 6 estimates the second position where the first error is minimized as the position of the emission source of the radio wave.

As described above, the radio wave monitoring device 1 according to the present embodiment is configured to estimate the position where the error between the estimated value of the reception intensity and the measured value is minimized as the position of the radio wave emission source. There is. Therefore, the radio wave monitoring device 1 according to the present embodiment can accurately estimate the emission source of the radio wave even if the sensor does not detect the arrival direction of the radio wave. Further, since the radio wave monitoring device 1 according to the present embodiment is configured in this way, it is possible to accurately estimate the emission source of the radio wave even if the number of sensors is small. Therefore, the radio wave monitoring device 1 according to the present embodiment can accurately estimate the emission source of the radio wave regardless of the environmental conditions.

Even if a radio wave monitoring system composed of the radio wave monitoring device 1 and a plurality of sensors is used, it is possible to accurately estimate the emission source of the radio wave regardless of the environmental conditions. Further, even by using the radio wave monitoring method executed by the radio wave monitoring device 1 and the program for executing the radio wave monitoring method, it is possible to accurately estimate the emission source of the radio wave regardless of the environmental conditions.

(Embodiment 1)
Hereinafter, embodiments will be described with reference to the drawings. In order to clarify the explanation, the following description and drawings are omitted or simplified as appropriate. Further, in each drawing, the same elements are designated by the same reference numerals, and duplicate explanations are omitted as necessary.

FIG. 2 is a diagram showing a radio wave monitoring system 10 according to the first embodiment. The radio wave monitoring system 10 includes a plurality of sensors 20 and a radio wave monitoring device 100. The radio wave monitoring device 100 corresponds to the radio wave monitoring device 1 shown in FIG. The plurality of sensors 20 and the radio wave monitoring device 100 may be communicably connected via a wired or wireless network 12. The sensor 20 receives a radio wave emitted from a certain emission source and measures the reception power (reception intensity) of the radio wave. The sensor 20 does not have to measure the received power as the reception strength, and may measure, for example, RSSI (Received Signal Strength Indicator).

FIG. 3 is a diagram illustrating a space 30 in which the sensor 20 according to the first embodiment is arranged. Six sensors 20-1 to 20-6 are arranged in the space 30. Further, when a plurality of sensors 20-1 to 20-6 are not distinguished, they may be referred to as a sensor 20. Further, sensors 20-1 to 20-6 may be referred to as sensors # 1 to # 6, respectively, and when sensors # 1 to # 6 are not distinguished, sensor # n (where n is an integer of 1 to 6). ) May be called.

The sensors 20-1 to _20-6 are arranged at the sensor positions ( _first position) r1 to r6, respectively. Further, in the space 30, there is a radio wave emitting source 90 that emits radio waves. The radio wave emission source 90 is arranged at the emission source actual position Rs. The radio wave emission source 90 emits radio waves with a certain transmission power (transmission output).

The radio wave monitoring device 100 is, for example, a server installed in a radio wave monitoring center or the like. The radio wave monitoring device 100 monitors radio waves using the measured values of the received power measured by the plurality of sensors 20. The radio wave monitoring device 100 estimates the position of the radio wave emission source 90 and the transmission power (transmission output) of the radio wave emission source 90. Further, the radio wave monitoring device 100 estimates the power distribution (intensity distribution) of the radio wave in the space 30. Details will be described later.

FIG. 4 is a diagram showing the configuration of the radio wave monitoring device 100 according to the first embodiment. The radio wave monitoring device 100 has a control unit 102, a storage unit 104, a communication unit 106, and an interface unit 108 (IF; Interface) as a main hardware configuration. The control unit 102, the storage unit 104, the communication unit 106, and the interface unit 108 are connected to each other via a data bus or the like.

The control unit 102 is, for example, a processor such as a CPU (Central Processing Unit). The control unit 102 has a function as an arithmetic unit that performs control processing, arithmetic processing, and the like. The storage unit 104 is a storage device such as a memory or a hard disk. The storage unit 104 is, for example, a ROM (Read Only Memory), a RAM (Random Access Memory), or the like. The storage unit 104 has a function for storing a control program, an arithmetic program, and the like executed by the control unit 102. In addition, the storage unit 104 has a function for temporarily storing processed data and the like. The storage unit 104 may include a database.

The communication unit 106 performs processing necessary for communicating with the sensor 20 (and other devices) via the network 12. The communication unit 106 may include a communication port, a router, a firewall, and the like. The interface unit 108 is, for example, a user interface (UI; User Interface). The interface unit 108 has an input device such as a keyboard, a touch panel or a mouse, and an output device such as a display or a speaker. The interface unit 108 accepts a data input operation by a user (operator) and outputs information to the user. The interface unit 108 may display a measured value received from the sensor 20 (sensor information or the like described later), a diagram showing the processing result performed by the radio wave monitoring device 100 (power distribution map or the like described later), or the like.

Further, the radio wave monitoring device 100 includes a maximum likelihood estimation unit 110, a power distribution estimation unit 120, an error distribution calculation unit 130, and a power distribution correction unit 140 (hereinafter referred to as “each component”). Further, the maximum likelihood estimation unit 110 includes a measured value acquisition unit 112, an error calculation unit 114, and a emission source estimation unit 116 (hereinafter referred to as “each component”). The maximum likelihood estimation unit 110, the power distribution estimation unit 120, the error distribution calculation unit 130, and the power distribution correction unit 140 are the maximum likelihood estimation means, the power distribution estimation means (intensity distribution estimation means), the error distribution calculation means, and the error distribution calculation means, respectively. It functions as a power distribution correction means (intensity distribution correction means). Further, the measured value acquisition unit 112, the error calculation unit 114, and the emission source estimation unit 116 function as the measurement value acquisition means, the error calculation means, and the emission source estimation means, respectively.

It should be noted that each component can be realized, for example, by executing a program under the control of the control unit 102. More specifically, each component can be realized by the control unit 102 executing the program stored in the storage unit 104. Further, each component may be realized by recording a necessary program on an arbitrary non-volatile recording medium and installing it as needed. Further, each component is not limited to being realized by software by a program, and may be realized by any combination of hardware, firmware, and software. Further, each component may be realized by using a user-programmable integrated circuit such as an FPGA (field-programmable gate array) or a microcomputer. In this case, this integrated circuit may be used to realize a program composed of each of the above components. The specific functions of each component will be described later.

The maximum likelihood estimation unit 110 estimates the position of the radio wave emission source 90 and the transmission power of the radio wave in the radio wave emission source 90 by the maximum likelihood estimation. The measured value acquisition unit 112 corresponds to the measured value acquisition unit 2 shown in FIG. The measured value acquisition unit 112 acquires the measured value of the received power of the radio wave measured by the sensors 20-1 to 20-6 from each of the sensors 20-1 to 20-6.

The error calculation unit 114 corresponds to the error calculation unit 4 shown in FIG. The error calculation unit 114 estimates the received power of the radio waves at the sensor positions _r1 to _r6 when it is assumed that the radio waves are emitted from each of a plurality of arbitrary assumed positions (second positions) in the space 30 (first position). Estimated value) is calculated. Further, the error calculation unit 114 calculates an error (first error) between the estimated value of the received power (first estimated value) and the measured value acquired by the measured value acquisition unit 112. Here, the error calculation unit 114 calculates an estimated value based on the propagation loss of the radio wave between the sensor position and the assumed position. Details will be described later.

The emission source estimation unit 116 corresponds to the emission source estimation unit 6 shown in FIG. The emission source estimation unit 116 estimates the position of the radio wave emission source 90 as the assumed position where the error (first error) between the estimated value (first estimated value) and the measured value is minimized. Further, the emission source estimation unit 116 transmits the assumed transmission power (assumed transmission output), which is the transmission power of the radio wave assumed to have been emitted at the assumed position estimated to be the position of the radio wave emission source 90, at the radio wave emission source 90. Estimated as electric power. Details will be described later. Here, the hypothesized position estimated to be the position of the radio wave emission source 90 is referred to as an estimated emission source position. Further, the assumed transmission power estimated to be the transmission power is referred to as an estimated transmission power.

The power distribution estimation unit 120 estimates the power distribution (intensity distribution) of the received power in the space 30 when the radio wave is emitted from the estimated emission source position with the estimated transmission power. Details will be described later. The error distribution calculation unit 130 uses the error (second error) between the estimated value (second estimated value) and the measured value at the sensor position in the power distribution estimated by the power distribution estimation unit 120 by spatial interpolation. , The error distribution in which the error in the space 30 is interpolated is calculated. Details will be described later. The power distribution correction unit 140 corrects the power distribution (intensity distribution) estimated by the power distribution estimation unit 120 by using the error distribution calculated by the error distribution calculation unit 130. Details will be described later.

FIG. 5 is a flowchart showing a radio wave monitoring method performed by the radio wave monitoring device 100 according to the first embodiment. First, the measured value acquisition unit 112 of the maximum likelihood estimation unit 110 acquires the measured values P ₁ to P ₆ (measured value P _n ) of the received power from the sensors 20-1 to 20-6 (sensor # n), respectively. (Step S102). Here, the measured value P _n is a measured value of the received power in the sensor # n. At this time, the measured value acquisition unit 112 may receive the measured value from the sensor 20 via the network 12. Here, the measured value acquisition unit 112 may acquire position information indicating the sensor position rn of the sensor 20 (sensor # _n ) when acquiring the measured value P _n . As a result, the measured value acquisition unit 112 may acquire (generate) sensor information as illustrated in FIG.

FIG. 6 is a diagram illustrating the sensor information according to the first embodiment. The sensor information is associated with the sensor position r _n of the sensor # n and the measured value P _n of the sensor # n for each sensor # n. The sensor position r _n may be a coordinate value of the sensor # n or a position vector of the sensor # n.

Next, the maximum likelihood estimation unit 110 estimates the position and transmission power of the radio wave emission source 90 by maximum likelihood estimation (step S110). Specifically, the maximum likelihood estimation unit 110 estimates the received power at _each sensor position r1 to r6 when it is assumed that the radio wave is emitted from an arbitrary position, and the measured value at the sensors # 1 to # ₆ . From the error with, the above maximum likelihood estimation process is performed. The specific processing of S110 will be described later with reference to FIG. 7.

Here, the mathematical formula used in the above maximum likelihood estimation process will be described. Let r be the position vector at the assumed position of the radio wave emission source 90 in the two-dimensional plane of the space 30. Further, r ₁ to r ₆ are set as the position vectors of the sensors # 1 to # 6. Further, it is assumed that the transmission power (assumed transmission power) of the radio wave emission source 90 is _PT . Here, _PT is a variable. At this time, the received power PR, _n estimated at the position (rn) of the sensor # _n is expressed by the following equation 1.

Here, L (l) is a function indicating the propagation loss and is expressed by the following equation 2. Here, in Equation 2, l indicates the distance from the radio wave emission source 90 to the sensor position. Further, it is a constant of a = 2 to 5, preferably a = 2 to 4. Further, in Equation 2, λ is the wavelength of the radio wave.

Further, the error _en between the received power PR _{, n} estimated using the equation 1 and the actual measured value is expressed by the following equation 3. Note that P _n is a measured value of the sensor # n.

Then, in order to evaluate the error en by the least squares method, the sum of _squares error E represented by the following equation 4 is obtained. In this embodiment, Equation 4 is referred to as an error function.

The sum of squares error E (error function) represented by this equation 4 is the likelihood function of maximum likelihood estimation. E indicates an error between the measured value and the estimated value in the sensor 20 when it is assumed that the radio wave of the assumed transmission power _PT is emitted from the position of the position vector r. Here, E is a function of _PT from Equations 1 and 3. The maximum likelihood estimation unit 110 calculates the _PT that minimizes E by changing the assumed transmission power _PT . For example, as shown in the following equation 5, the _{PT when the value obtained by partially differentiating E with respect to the PT becomes} 0 is obtained.

FIG. 7 is a flowchart showing a process (S110) performed by the maximum likelihood estimation unit 110 according to the first embodiment. First, the maximum likelihood estimation unit 110 divides the space 30 into N spaces horizontally and M spaces vertically (step S112). FIG. 8 is a diagram illustrating a state in which the space 30 is divided into N * M pieces.

Next, the error calculation unit 114 of the maximum likelihood estimation unit 110 calculates the estimated values PR, _{n , NM} at the sensor position rn when the radio wave is emitted from the position r _NM with the assumed transmission power _{PT, NM} . (Step S114). Here, the position r _NM indicates a position where the space 30 is divided by the processing of S112, that is, each of the divisions exemplified in FIG. That is, there are N * M positions r _NM . The estimated values _{PR, n, and NM} are calculated for each sensor 20 (that is, for each of the sensors # 1 to # 6).

Further, from the above equation 1 _{, PR, n, and NM} are represented by the following equation 6. In the following equation 5, r _NM indicates the position vector of the position r _NM . Here, _{PT and NM} are variables. In this way, by calculating the estimated value using the propagation loss, it becomes possible to calculate the estimated value more easily and accurately.

Next, the error calculation unit 114 calculates the error en, NM between the estimated value PR, _{n , NM} and the measured value P _n (step S116). Specifically, the error calculation unit 114 calculates the error from the above formula 3 by the following formula 7. The errors _{en and NM} are calculated for each sensor 20 (that is, sensors # 1 to # 6 respectively). That is, the error calculation unit 114 sets the error e _{1, NM} , the error e _{2, NM} , the error e _{3, NM} , the error e _{4, NM} , the error e _{5, NM,} and the error e _{6, NM} for each position r _NM . calculate.

Next, the error calculation unit 114 calculates the squared sum error _ENM of the errors en _{and NM} of the six sensors 20 (step S118). This sum of squares error _ENM is an error function. Further, as described above, this square sum error _ENM is a likelihood function in maximum likelihood estimation. The sum of squares error _ENM is expressed by the following equation 8 from the above equation 4. As described above, ENM is a function (error function) of the variables _{PT and NM .} By calculating the error function in this way, the radio wave emission source 90 can be estimated more accurately.

Next, the error calculation unit 114 calculates the minimum value _{ENM, min} of the sum of squares error _ENM at the position r _NM and the assumed transmission power _{PT, NM, min} at that time (step S120). Specifically, the error calculation unit 114 partially differentiates the ENM from the above equation 5 with respect to _{PT and NM as} shown in the following equation 9, and the assumed transmission power P when the value becomes 0. _{Let T and NM} be the assumed transmission powers _{PT, NM and min} . Further, the error calculation unit 114 sets the value when the assumed transmission powers _{PT, NM, and min are} substituted into the squared sum error ENM shown in Equation 8 as the minimum value _{ENM, min} of the squared sum error _ENM . ..

Further, the error calculation unit 114 determines whether or not the _{ENM, min} and the assumed transmission power _{PT, NM, min} have been calculated for all the positions r _NM (that is, for all N * M positions) (step). S122). If the calculation has not been completed for all positions r _NM (NO in S122), the process returns to S114.

On the other hand, when the calculation is completed for all the positions r _NM (YES in S122), the emission source estimation unit 116 of the maximum likelihood estimation unit 110 is the position r where the minimum value _{ENM, min} of the square sum error _ENM is the minimum. The _NM is estimated to be the position of the radio wave emission source 90 (estimated emission source position) (step S124). In this way, the position of the radio wave emission source 90 is estimated more accurately by estimating the position r _NM where the minimum value E _{NM, min} of the sum of squares error E _NM is the minimum as the position of the radio wave emission source 90. It becomes possible. The emission source estimation unit 116 may generate the heat map illustrated in FIG. Then, the emission source estimation unit 116 may use this heat map to estimate the position r _NM at which the minimum values _{ENM and min} are minimized.

FIG. 9 is a diagram illustrating a heat map showing the minimum values _{ENM and min} of the sum of squares errors at each position r _NM . The upward axis (−Eσ) is the square root of the minimum sum of squares errors ENM _{, min} at each position r _NM multiplied by -1. That is, −Eσ = −√ (ENM _{, min} ). Here, since Eσ is a positive number, in the heat map illustrated in FIG. 9, the minimum point of Eσ, that is, the minimum value ENM _{, min} is represented by an upwardly convex vertex. Therefore, the position re indicated by the _arrow is the estimated emission source position.

Further, the emission source estimation unit 116 estimates the assumed transmission powers _{PT and NM} at the estimated emission source position (estimated emission source position) as the transmission power (estimated transmission power _PT ) of the radio wave emission source 90 (step). S126). With such a configuration, the emission source estimation unit 116 can calculate the estimated transmission power P _Te together with the estimated emission source position _re . Therefore, it is possible to estimate the transmission power of the radio wave emission source 90 efficiently and accurately.

In the above description, the error calculation unit 114 calculates the minimum value _{ENM, min} by partially differentiating the squared sum error ENM with the assumed transmission power _{PT, NM .} Not limited to. For example, the error calculation unit 114 may change the assumed transmission powers _{PT and NM} from Pmin to Pmax in a step of ΔP to calculate the squared sum error ENM in each of the assumed transmission powers _{PT and NM .} good. Here, Pmin, Pmax and ΔP are predetermined constants. Then, the error calculation unit 114 sets the minimum squared sum error ENM as the minimum value _{ENM, min} , and assumes the assumed transmission power _{PT, NM} when the minimum value E _{NM , min} is taken, and assumes the transmission power _{PT, NM. , Min} may be used. With such a configuration, it is not necessary to partially differentiate the square sum error ENM with the assumed transmission powers _{PT and NM .}

Next, the power distribution estimation unit 120 estimates the power distribution (intensity distribution) due to the propagation loss (step S130 in FIG. 5). Hereinafter, it will be described in detail with reference to FIG.
FIG. 10 is a flowchart showing a process (S130) performed by the power distribution estimation unit 120 according to the first embodiment. The power distribution estimation unit 120 calculates the power distribution of the received power in the space 30 when the radio wave is emitted from the estimated emission source position re with the estimated transmission power P _Te (step _S132 ). Specifically, the power distribution estimation unit 120 estimates the received power PR at an arbitrary position _r using the propagation loss using the following equation 10. In Equation 10, r is a position vector at an arbitrary position.

FIG. 11 is a diagram illustrating the power distribution generated by the power distribution estimation unit 120 according to the first embodiment. The power distribution is a contour line with the estimated emission source position re as the _apex . Here, in the power distribution shown in FIG. 11, it is assumed that the space 30 is homogeneous without considering the reflection and fading of radio waves to the building, so that the received power _PR is from the estimated _emission source position re. Depends only on distance. Therefore, the power distribution shown in FIG. 11 is a concentric _circle centered on the estimated emission source position re. In this way, by estimating the power distribution using the propagation loss, it becomes possible to estimate the power distribution more easily.

Next, the power distribution estimation unit 120 calculates the estimated values PR _{and n} at each sensor position r _n (n = 1 to 6) (step S134). Specifically, the power distribution estimation unit 120 calculates the estimated values _{PR and n} (second estimated value) of the received power at _each of the sensor positions r1 to r6 shown in FIG. ₁₁ by the following equation 11. do. That is, the power distribution estimation unit 120 calculates the estimated values _{PR and n} (second estimated value) at the sensor position (first position) in the power distribution (intensity distribution) estimated by the process of S132.

Next, the power distribution estimation unit 120 calculates an error e ( _rn ) between the estimated values PR _{and n} and the measured value (step S136). Specifically, the power distribution estimation unit 120 calculates the error from the above equation 3 by the following equation 12. The error e ( _rn ) is calculated for each sensor 20 (that is, for each of the sensors # 1 to # 6). That is, the power distribution estimation unit 120 has an error e (r ₁ ), an error e (r ₂ ), an error e (r ₃ ), an error e (r ₄ ), an error e (r ₅ ), and an error e (r ₆ ). ) Is calculated.

Next, the error distribution calculation unit 130 calculates the error distribution by spatial interpolation (step S140 in FIG. 5). Hereinafter, it will be described in detail with reference to FIG. Here, in the first embodiment, the error distribution calculation unit 130 calculates the error distribution by using the kriging method. However, the error distribution may be calculated by spatial interpolation other than the Kriging method.

FIG. 12 is a flowchart showing a process (S140) performed by the error distribution calculation unit 130 according to the first embodiment. The error distribution calculation unit 130 calculates the difference between the distance between any two sensors 20 and the error e ( _rn ) (step S142). Then, the error distribution calculation unit 130 determines whether or not the processing of S142 has been performed for all the combinations of the sensors 20 (step S144). When the processing of S142 is not performed for all the combinations of the sensors 20 (NO of S144), the processing of S142 is performed.

FIG. 13 is a diagram illustrating the combination of the sensors 20 and the difference in the distance and the error e ( _rn ) between them. Note that z ( _n ) is a variable at the position rn (error e ( _rn ) in this example). In the figure illustrated in FIG. 13, the combinations showing the shortest distances between the sensors 20 are shown in order. That is, the distance between the sensor # 4 and the sensor # 5 is the shortest among all the combinations of the sensors 20 ( ₆ C ₂ = 15 combinations). The difference in error at this time is | e (r ₄ ) -e (r ₅ ) |.

Next, the error distribution calculation unit 130 performs variogram analysis on the difference between the distance between the sensors 20 and the error, and calculates the covariance function (step S146). Specifically, the error distribution calculation unit 130 performs a semivariogram (quasi-variance) analysis on the relationship between the distance shown in FIG. 13 and the difference in error. Then, the error distribution calculation unit 130 uses a model function (linear model function, exponential model function, sphere model function, etc.) to show the relationship between the distance and the error difference shown in FIG. 13, and the semivariogram function γ (h). ) Is calculated. Then, the error distribution calculation unit 130 calculates the covariance function C (h) from the semivariogram function γ (h). Here, h indicates the distance between two points. Further, since C (h) = C (0) -γ (h), the covariance function C (h) can be calculated from the semivariogram function γ (h).

Next, the error distribution calculation unit 130 calculates the weighting coefficient λ used in the kriging interpolation using the covariance function C (h) calculated in S146 (step S148). The equation showing the kriging interpolation at an arbitrary position r is expressed by the following equation 13. The error distribution calculation unit 130 calculates the weighting coefficient λ represented by this equation 13. Further, e ^* (r) indicates an error distribution.

In the Kriging method, the estimated value is obtained when the covariance value between the measurement points is multiplied by the weighting coefficient and the covariance value between the measurement point and the estimation point (point to be interpolated) becomes equal. The error between and the true value is minimized. Therefore, the weighting coefficient λ that satisfies the following equation 14 may be obtained. Here, the weighting coefficient λ _β is a coefficient indicating how much the measured value of the measurement point β (sensor # β) affects the estimation point (position r).

Here, since β and n are both integers of 1 to 6, Equation 14 is a simultaneous equation of 6 elements. Therefore, if the determinant of the covariance between the measurement points is K, the determinant of the covariance between the measurement points and the estimation points is k, and the equation 14 is rewritten into the matrix format, it is expressed by the following equation 15. .. Here, λ (r) is a 6 × 1 matrix.

Here, K is a 6 × 6 matrix represented by the following equation 16.

Further, k is a 6 × 1 matrix represented by the following equation 17.

From the above equation 15, the error distribution calculation unit 130 calculates the weighting coefficient λ using the following equation 18.

Next, the error distribution calculation unit 130 calculates the error distribution e ^* (r) by kriging interpolation of the error at the position r which is the estimation point (step S150). Specifically, the error distribution calculation unit 130 calculates the error distribution e ^* (r) from the above equation 13 by using the weighting coefficient λ calculated by the above equation 18.

Next, the power distribution correction unit 140 corrects the power distribution estimated in the process of S130 (step S160 in FIG. 5). Specifically, the power distribution correction unit 140 calculates the power distribution (received power PR) at an arbitrary position _r using the following equation 19. That is, the power distribution correction unit 140 can correct the power distribution by dividing the error distribution calculated using the equation 13 from the power distribution estimated using the equation 10.

FIG. 14 is a diagram illustrating a power distribution corrected by the power distribution correction unit 140 according to the first embodiment. While the power distribution shown in FIG. 11 was concentric circles, the power distribution shown in FIG. 14 is not concentric circles, and the difference in the influence of the radio wave environment at each position is accurately represented. Therefore, the power distribution correction unit 140 according to the first embodiment can accurately simulate the power distribution in the space 30. That is, the radio wave monitoring device 100 according to the first embodiment uses the error distribution calculated by the error distribution calculation unit 130 to correct the power distribution estimated by the power distribution estimation unit 120, so that the power distribution is accurately corrected. It is possible to simulate the power distribution.

As described above, the radio wave monitoring device 100 according to the first embodiment estimates the position of the radio wave emission source 90 and the transmission power by maximum likelihood estimation. Therefore, even if the sensor 20 cannot detect the arrival direction of the radio wave, the radio wave emission source 90 can be estimated accurately. Therefore, the radio wave monitoring device 100 according to the first embodiment can accurately estimate the radio wave emission source 90 even in an environment where multipath can occur. Further, since it is configured as described above, the radio wave emission source 90 can be estimated accurately even if the number of sensors 20 is not as large as six. Therefore, the radio wave monitoring device 100 according to the first embodiment can estimate the position of the radio wave emission source 90 more accurately regardless of the radio wave environment.

(Modification example)
The present invention is not limited to the above embodiment, and can be appropriately modified without departing from the spirit. For example, in the above-mentioned flowchart, the order of each process (step) can be changed as appropriate. Further, one or more of the plurality of processes (steps) may be omitted. For example, the order of processing S124 and processing S126 in FIG. 7 may be reversed. Further, in FIG. 5, the processing of S130 to S160 may not be necessary.

Further, one of the above-mentioned components may be divided into a plurality of components. For example, the error distribution calculation unit 130 may be divided into a plurality of components. Further, a plurality of the above-mentioned components may be combined into one component. For example, the error distribution calculation unit 130 and the power distribution correction unit 140 may be combined into one component. Further, one or more of the processes performed by each component may be performed by other components. For example, although the processing of S134 to S136 in FIG. 10 is performed by the power distribution estimation unit 120 in the above-described embodiment, it may be performed by the error distribution calculation unit 130.

Further, in the above-described embodiment, the number of sensors 20 is set to 6, but the number of sensors 20 is not limited to 6. The number of sensors 20 may be plural. It should be noted that the larger the number of sensors 20, the better the estimation accuracy of the radio wave emission source 90 may be. However, in the present embodiment, as described above, it is possible to accurately estimate the radio wave emission source 90 even if the number of sensors 20 is not large.

In the above example, the program can be stored and supplied to the computer using various types of non-transitory computer readable medium. Non-temporary computer-readable media include various types of tangible storage media. Examples of non-temporary computer-readable media include magnetic recording media (eg, flexible disks, magnetic tapes, hard disk drives), optomagnetic recording media (eg, optomagnetic disks), CD-ROMs (Read Only Memory), CD-Rs. Includes CD-R / W, semiconductor memory (eg, mask ROM, PROM (Programmable ROM), EPROM (Erasable PROM), flash ROM, RAM (Random Access Memory)). The program may also be supplied to the computer by various types of transient computer readable medium. Examples of temporary computer readable media include electrical, optical, and electromagnetic waves. The temporary computer-readable medium can supply the program to the computer via a wired communication path such as an electric wire and an optical fiber, or a wireless communication path.

Some or all of the above embodiments may also be described, but not limited to:
(Appendix 1)
A measurement value acquisition means for acquiring the measured value of the reception intensity of the radio wave measured by each of the plurality of sensors arranged at each of the plurality of first positions from each of the plurality of sensors.
Calculate the first error indicating the error between the first estimated value and the measured value of the reception intensity of the radio wave at the first position when it is assumed that the radio wave is emitted from each of a plurality of arbitrary second positions. Error calculation means and
A radio wave monitoring device having a source estimation means for estimating the position of the source of radio waves at the second position where the first error is minimized.
(Appendix 2)
The radio wave monitoring device according to Appendix 1, wherein the error calculating means calculates the first estimated value based on the propagation loss between the first position and the second position.
(Appendix 3)
The error calculation means is
The first estimated value, which is a function of the second position and the assumed transmission output which is the transmission output when it is assumed that the radio wave is emitted at the second position, is calculated.
A function of the difference between the measured value of the plurality of sensors and the first estimated value is calculated as an error function.
The radio wave monitoring device according to Appendix 1 or 2, wherein the emission source estimation means estimates that the second position having the minimum error function among the plurality of second positions is the position of the emission source of the radio wave. ..
(Appendix 4)
The error calculating means calculates the minimum value of the error function at each of the plurality of second positions.
The radio wave monitoring according to Appendix 3, wherein the emission source estimation means estimates the position where the minimum value of the error function is the minimum among the plurality of second positions as the position of the emission source of the radio wave. Device.
(Appendix 5)
The emission source estimation means estimates that the hypothetical transmission output that minimizes the error function at the second position estimated to be the position of the emission source of the radio wave is the transmission output at the emission source. The radio wave monitoring device described.
(Appendix 6)
Intensity distribution that estimates the intensity distribution of the reception intensity in the space where the plurality of sensors are arranged when radio waves are emitted from the estimated position of the emission source at the estimated transmission output using the propagation loss. The radio wave monitoring device according to Appendix 5, further comprising an estimation means.
(Appendix 7)
The second error in the space, which is the error between the second estimated value at the first position and the measured value in the intensity distribution estimated by the intensity distribution estimation means by spatial interpolation, is used. An error distribution calculation means that calculates an error distribution by interpolating the error of 2 and
The radio wave monitoring device according to Appendix 6, further comprising an intensity distribution correction means for correcting the intensity distribution estimated by the intensity distribution estimation means using the error distribution calculated by the error distribution calculation means.
(Appendix 8)
With multiple sensors located in each of the multiple first positions,
It has a radio wave monitoring device that monitors radio waves.
The radio wave monitoring device is
The measured value acquisition means for acquiring the measured value of the reception intensity of the radio wave measured by each of the plurality of sensors from each of the plurality of sensors.
Calculate the first error indicating the error between the first estimated value and the measured value of the reception intensity of the radio wave at the first position when it is assumed that the radio wave is emitted from each of a plurality of arbitrary second positions. Error calculation means and
A radio wave monitoring system having a source estimation means for estimating the position of the source of radio waves at the second position where the first error is minimized.
(Appendix 9)
The radio wave monitoring system according to Appendix 8, wherein the error calculating means calculates the first estimated value based on the propagation loss between the first position and the second position.
(Appendix 10)
The error calculation means is
The first estimated value, which is a function of the second position and the assumed transmission output which is the transmission output when it is assumed that the radio wave is emitted at the second position, is calculated.
A function of the difference between the measured value of the plurality of sensors and the first estimated value is calculated as an error function.
The radio wave monitoring system according to Appendix 8 or 9, wherein the emission source estimation means estimates that the second position having the minimum error function among the plurality of second positions is the position of the emission source of the radio wave. ..
(Appendix 11)
The error calculating means calculates the minimum value of the error function at each of the plurality of second positions.
The radio wave monitoring according to Appendix 10, wherein the emission source estimation means estimates the position where the minimum value of the error function is the minimum among the plurality of second positions as the position of the emission source of the radio wave. system.
(Appendix 12)
The emission source estimation means estimates that the hypothetical transmission output that minimizes the error function at the second position estimated to be the position of the emission source of the radio wave is the transmission output at the emission source. The radio wave monitoring system described.
(Appendix 13)
The radio wave monitoring device is
Intensity distribution that estimates the intensity distribution of the reception intensity in the space where the plurality of sensors are arranged when radio waves are emitted from the estimated position of the emission source at the estimated transmission output using the propagation loss. The radio wave monitoring system according to Appendix 12, further comprising an estimation means.
(Appendix 14)
The radio wave monitoring device is
The second error in the space, which is the error between the second estimated value at the first position and the measured value in the intensity distribution estimated by the intensity distribution estimation means by spatial interpolation, is used. An error distribution calculation means that calculates an error distribution by interpolating the error of 2 and
The radio wave monitoring system according to Appendix 13, further comprising an intensity distribution correction means for correcting the intensity distribution estimated by the intensity distribution estimation means using the error distribution calculated by the error distribution calculation means.
(Appendix 15)
The measured value of the reception intensity of the radio wave measured by each of the plurality of sensors arranged at each of the plurality of first positions is acquired from each of the plurality of sensors.
Calculate the first error indicating the error between the first estimated value and the measured value of the reception intensity of the radio wave at the first position when it is assumed that the radio wave is emitted from each of a plurality of arbitrary second positions. death,
A radio wave monitoring method in which the second position where the first error is minimized is estimated to be the position of the radio wave emission source.
(Appendix 16)
The radio wave monitoring method according to Appendix 15, which calculates the first estimated value based on the propagation loss between the first position and the second position.
(Appendix 17)
The first estimated value, which is a function of the second position and the assumed transmission output which is the transmission output when it is assumed that the radio wave is emitted at the second position, is calculated.
A function of the difference between the measured value of the plurality of sensors and the first estimated value is calculated as an error function.
The radio wave monitoring method according to Appendix 15 or 16, wherein the second position having the minimum error function is estimated to be the position of the radio wave emission source among the plurality of second positions.
(Appendix 18)
The minimum value of the error function at each of the plurality of second positions is calculated.
The radio wave monitoring method according to Appendix 17, wherein the second position where the minimum value of the error function is the minimum among the plurality of second positions is estimated to be the position of the radio wave emission source.
(Appendix 19)
The radio wave monitoring method according to Appendix 17 or 18, wherein the hypothetical transmission output that minimizes the error function at the second position estimated to be the position of the radio wave emission source is estimated to be the transmission output at the emission source.
(Appendix 20)
Using the propagation loss, the intensity distribution of the reception intensity in the space where the plurality of sensors are arranged is estimated when the radio wave is emitted from the estimated position of the emission source with the estimated transmission output. Appendix 19 Radio wave monitoring method described in.
(Appendix 21)
By spatial interpolation, the second error in the space is interpolated using the second error, which is the error between the second estimated value at the first position in the estimated intensity distribution and the measured value. Calculate the error distribution
The radio wave monitoring method according to Appendix 20, wherein the estimated intensity distribution is corrected by using the calculated error distribution.
(Appendix 22)
A step of acquiring the measured value of the reception intensity of the radio wave measured by each of the plurality of sensors arranged at each of the plurality of first positions from each of the plurality of sensors.
Calculate the first error indicating the error between the first estimated value and the measured value of the reception intensity of the radio wave at the first position when it is assumed that the radio wave is emitted from each of a plurality of arbitrary second positions. Steps to do and
A program that causes a computer to perform a step of estimating the position of a radio wave emission source at the second position where the first error is minimized.

1 Radio monitoring device 2 Measurement value acquisition unit 4 Error calculation unit 6 Emission source estimation unit 10 Radio monitoring system 20 Sensor 90 Radio emission source 100 Radio monitoring device 110 Maximum likelihood estimation unit 112 Measurement value acquisition unit 114 Error calculation unit 116 Emission source estimation Unit 120 Power distribution estimation unit 130 Error distribution calculation unit 140 Power distribution correction unit

Claims (7)

A measurement value acquisition means for acquiring the measured value of the reception intensity of the radio wave measured by each of the plurality of sensors arranged at each of the plurality of first positions from each of the plurality of sensors.
Calculate the first error indicating the error between the first estimated value and the measured value of the reception intensity of the radio wave at the first position when it is assumed that the radio wave is emitted from each of a plurality of arbitrary second positions. Error calculation means and
The emission source estimation means for estimating the position of the emission source of the radio wave at the second position where the first error is minimized ,
Intensity distribution estimation means for estimating the intensity distribution of reception intensity
Have,
The error calculation means is
The first estimated value, which is a function of the second position and the assumed transmission output which is the transmission output when it is assumed that the radio wave is emitted at the second position, is calculated.
A function of the difference between the measured value of the plurality of sensors and the first estimated value is calculated as an error function.
The emission source estimation means is
Of the plurality of second positions, the second position that minimizes the error function is estimated to be the position of the radio wave emission source.
The assumed transmission output that minimizes the error function, which is a function of the difference between the measured value of the plurality of sensors and the first estimated value, at the second position estimated to be the position of the radio wave emission source. , Estimated as the transmission output at the source
The intensity distribution estimation means propagates the intensity distribution of the reception intensity in the space where the plurality of sensors are arranged when the radio wave is emitted from the estimated position of the emission source with the estimated transmission output. Estimate using
Radio monitoring device. The radio wave monitoring device according to claim 1, wherein the error calculating means calculates the first estimated value based on the propagation loss between the first position and the second position. The error calculating means calculates the minimum value of the error function at each of the plurality of second positions.
The radio wave according to claim 1, wherein the emission source estimation means estimates the position where the minimum value of the error function is the minimum among the plurality of second positions as the position of the emission source of the radio wave. Monitoring device. The second error in the space, which is the error between the second estimated value at the first position and the measured value in the intensity distribution estimated by the intensity distribution estimation means by spatial interpolation, is used. An error distribution calculation means that calculates an error distribution by interpolating the error of 2 and
The item according to any one of claims 1 to 3, further comprising an intensity distribution correction means for correcting the intensity distribution estimated by the intensity distribution estimation means using the error distribution calculated by the error distribution calculation means. The radio wave monitoring device described. With multiple sensors located in each of the multiple first positions,
It has a radio wave monitoring device that monitors radio waves.
The radio wave monitoring device is
The measured value acquisition means for acquiring the measured value of the reception intensity of the radio wave measured by each of the plurality of sensors from each of the plurality of sensors.
Calculate the first error indicating the error between the first estimated value and the measured value of the reception intensity of the radio wave at the first position when it is assumed that the radio wave is emitted from each of a plurality of arbitrary second positions. Error calculation means and
The emission source estimation means for estimating the position of the emission source of the radio wave at the second position where the first error is minimized ,
Intensity distribution estimation means for estimating the intensity distribution of reception intensity
Have,
The error calculation means is
The first estimated value, which is a function of the second position and the assumed transmission output which is the transmission output when it is assumed that the radio wave is emitted at the second position, is calculated.
A function of the difference between the measured value of the plurality of sensors and the first estimated value is calculated as an error function.
The emission source estimation means is
Of the plurality of second positions, the second position that minimizes the error function is estimated to be the position of the radio wave emission source.
The assumed transmission output that minimizes the error function, which is a function of the difference between the measured value of the plurality of sensors and the first estimated value, at the second position estimated to be the position of the radio wave emission source. , Estimated as the transmission output at the source
The intensity distribution estimation means propagates the intensity distribution of the reception intensity in the space where the plurality of sensors are arranged when the radio wave is emitted from the estimated position of the emission source with the estimated transmission output. Estimate using
Radio monitoring system. The measured value of the reception intensity of the radio wave measured by each of the plurality of sensors arranged at each of the plurality of first positions is acquired from each of the plurality of sensors.
It is a first estimated value of the reception intensity of the radio wave at the first position when it is assumed that the radio wave is emitted from each of a plurality of arbitrary second positions, and is the second position and the second position. The first estimated value, which is a function of the assumed transmission output which is the transmission output when it is assumed that the radio wave is emitted at the position, is calculated, and the measured value of the plurality of sensors and the first estimated value are used. Calculate the difference function as an error function and
Of the plurality of second positions, the second position that minimizes the error function is estimated to be the position of the radio wave emission source.
The assumed transmission output that minimizes the error function, which is a function of the difference between the measured value of the plurality of sensors and the first estimated value, at the second position estimated to be the position of the radio wave emission source. , Estimated as the transmission output at the source
The intensity distribution of the reception intensity in the space where the plurality of sensors are arranged when the radio wave is emitted from the estimated position of the emission source with the estimated transmission output is estimated by using the propagation loss.
Radio monitoring method. A step of acquiring the measured value of the reception intensity of the radio wave measured by each of the plurality of sensors arranged at each of the plurality of first positions from each of the plurality of sensors.
It is a first estimated value of the reception intensity of the radio wave at the first position when it is assumed that the radio wave is emitted from each of a plurality of arbitrary second positions, and is the second position and the second position. The step of calculating the first estimated value, which is a function of the assumed transmission output, which is the transmission output when it is assumed that the radio wave is emitted at the position, and
A step of calculating a function of the difference between the measured value of the plurality of sensors and the first estimated value as an error function, and
Among the plurality of second positions, the step of estimating the second position that minimizes the error function as the position of the radio wave emission source, and the step.
The assumed transmission output that minimizes the error function, which is a function of the difference between the measured value of the plurality of sensors and the first estimated value, at the second position estimated to be the position of the radio wave emission source. , The step of estimating the transmission output at the source, and
A step of estimating the intensity distribution of the reception intensity in the space where the plurality of sensors are arranged when the radio wave is emitted from the estimated position of the emission source with the estimated transmission output by using the propagation loss.
A program that causes a computer to run.

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