JP2020159705A - Position estimation device and position estimation method - Google Patents

Abstract

To provide a position estimation device capable of estimating a position or a transmission power of an unknown wave source.SOLUTION: A position estimation device 1 comprises: a received power acquisition unit 11 which receives a wave from an unknown wave source to acquire a received power; a receiving position acquisition unit 12 which acquires a receiving position where the wave corresponding to the received power is received; an estimation unit 13 which estimates an estimate position and an estimate transmission power by using a plurality of pairs of received powers and receiving positions, estimate positions of the unknown wave source, estimate transmission powers of the wave from the unknown wave source, and propagation loss of the wave to optimize an objective function associated with a difference between an estimate received power and a received power of each receiving position.SELECTED DRAWING: Figure 1

Description

The present invention relates to a position estimation device and the like that estimate the position of an unknown wave source and transmission power using received power.

With the widespread use of ICT equipment (Information and Communication Technology equipment) that performs wireless communication, various radio waves are flying around in the space. Some of these devices transmit without a license or proper certification. The radio waves may interfere with other devices and cause communication problems.

In order to grasp such a situation and take countermeasures, it is necessary to specify the position of the signal source that emits radio waves. The following methods are mainly known as the method.
-A method of measuring the RSSI (Received Signal Strength Indication) of radio waves emitted from a signal source at multiple points and estimating the position of the signal source from the results by a triangulation method-Transmitted from the signal source A method of simultaneously receiving a signal at multiple points and estimating the position of the signal source from the difference in delivery time (TDoA: Time Difference of Arrival).
-A method of simultaneously receiving signals transmitted from a signal source at multiple points and estimating the direction of arrival of the signals from the phase difference (DoA: Direction of Arrival).

When estimating the position of a signal source by TDoA or DoA, it is necessary to measure at a plurality of points at the same time. The radio wave propagates at an extremely high speed of 3 × ¹⁰⁸ (m / s). Therefore, in order to measure the propagation time difference and the phase difference at a plurality of points at the same time, a mechanism for receiving with extremely high time resolution is required. At that time, it will be difficult to realize "simultaneous" at multiple remote points. In the near case where simultaneous realization is easy to be realized, there is a problem that the propagation time difference and the phase difference become small and the estimation accuracy is lowered.

The method using RSSI also requires measurement at multiple points, but since it is not necessary to receive signals at those points at the same time, it is also possible to estimate the position by moving one receiver and recording RSSI. it can. Further, the method using RSSI has an advantage that only the strength of the received signal needs to be measured and can be realized by a simple circuit.

However, in addition to being transmitted directly from the signal source to the receiver, radio waves may be reflected and propagated by surrounding buildings or road surfaces. These multipaths are combined and input to the receiver. In addition, the phase relationship of the received synthetic radio waves changes due to the movement of reflectors and shields and the slight misalignment of the receiver. The RSSI fluctuates accordingly. When the position is estimated by the method of triangulation using such a fluctuating RSSI, there is a problem that a large displacement occurs.

Further, for position estimation using radio waves, for example, the methods described in Patent Documents 1 to 3 and Non-Patent Document 1 are also known.

Japanese Patent No. 6030976 Japanese Patent No. 5537284 Japanese Unexamined Patent Publication No. 2016-170032

Yuta Azuma, Takeshi Umezawa, Noritaka Osawa, "Indoor position estimation using relative position of position fingerprints based on radio field intensity observed at multiple points", Shingaku Giho, vol. 115, no. 436, MoNA2015-37, pp . 1-6, January 2016

In the invention of Patent Document 1, the position is estimated by measuring RSSI from the terminal at a plurality of base stations. However, on the premise that the position of the base station is unknown, the position of the base station is also estimated from the mutual received power between the base stations in order to determine it. If the position of the base station shifts in this process, the terminal position cannot be accurately grasped. It is also a method that requires multiple base stations.

In the invention of Patent Document 2, the terminal position is estimated with reference to a table in which the signal strength and the distance and angle to the access point are recorded. In this case, it is necessary to prepare a table corresponding to the terminal position and the received power in advance. Therefore, it is an inappropriate method for locating a signal source emitted from an unknown device in an unknown location.

In the invention of Patent Document 3, the deterioration of accuracy due to multipath, which is a drawback of the conventional calculation method by TDoA or DoA, which is a method of specifying the position of the signal source, is calculated a plurality of times and weighting is applied according to the propagation loss. It is designed to take measures such as. However, TDoA and DoA are the basic methods for estimating the position of the signal source. As described above, TDoA and DoA need to perform high-precision measurement at a plurality of distant points at the same time. There is a problem that it is extremely difficult to achieve this.

In Non-Patent Document 1, the triangulation method and the position fingerprint method are mentioned as the methods using RSSI, and the former is assumed to have a large error due to the influence of multipath and the like, and the correspondence between the position and RSSI as in Patent Document 2 (this is the position) It is said that the position estimation from the comparison between (called a fingerprint) and the actual RSSI is excellent. However, in the position fingerprint method, as in Patent Document 2, it is necessary to prepare a table (= position fingerprint) measured in advance, and there is a problem that it can be used only in a limited place.

Generally speaking, the position of an unknown wave source can be estimated even under the influence of multipath without using TDoA or DoA and without the need for prior preparation such as position fingerprint. There was a problem that I wanted to do.

The present invention has been made to solve these problems, and there is a case where there is an influence of multipath without using TDoA or DoA and without requiring prior preparation such as position fingerprint. However, it is an object of the present invention to provide a position estimation device or the like capable of estimating the position of an unknown wave source.

In order to achieve the above object, the position estimation device according to the present invention acquires a received power acquisition unit that acquires the received power of a wave from an unknown wave source and a reception position when a wave corresponding to the received power is received. Estimated reception power for each reception position using the reception position acquisition unit, multiple sets of reception power and reception position, estimated position of unknown wave source, estimated transmission power of wave from unknown wave source, and wave propagation loss. It is provided with an estimation unit that estimates the estimated position and the estimated transmission power by optimizing the objective function according to the difference between the power and the received power.
With such a configuration, it becomes possible to estimate the position of an unknown wave source and the transmission power without using TDoA or DoA and without requiring prior preparation such as a position fingerprint. As such, since TDoA or the like is not used, the position of the wave source can be estimated with a simple configuration. Furthermore, since the estimation is performed by optimizing the objective function, it is possible to estimate the position of the wave source while reducing the influence of multipath by using a sufficient number of sets of received power and receiving position. Will be.

Further, in the position estimation device according to the present invention, the received power acquisition unit receives a wave from an unknown wave source and acquires the received power, and the receiving position acquisition unit receives the wave according to the received power. The receiving position, which is the position of the position estimation device at the time of receiving the
With such a configuration, the position estimation device also receives waves from the wave source. Therefore, for example, the position estimation can be performed by moving the position estimation device and recording the reception position or the like. In that case, the position of the wave source can be estimated without using a plurality of receiving devices.

Further, in the position estimation device according to the present invention, there are one or more unknown wave sources, and the estimation unit optimizes the optimum value per wave source obtained by dividing the optimum value, which is the value of the optimized objective function, by the estimated number of wave sources. As such, the estimated number of wave sources may also be estimated.
With such a configuration, it becomes possible to estimate the number of wave sources.

Further, in the position estimation device according to the present invention, the estimation unit may optimize the objective function by using the propagation loss according to the spatial information regarding the space between the estimated position and the receiving position.
With such a configuration, it becomes possible to realize a more accurate estimation.

Further, in the position estimation device according to the present invention, the estimation unit weights the difference between the estimated reception power and the received power according to the spatial information regarding the space between the estimated position and the reception position used in the calculation of the estimated reception power. The attached objective function may be optimized.
With such a configuration, it becomes possible to realize a more accurate estimation.

Further, in the position estimation device according to the present invention, the wave from an unknown wave source is received by the device having directivity, and the direction of acquiring the direction of the device having directivity when the wave corresponding to the received power is received. An acquisition unit may be further provided, and the estimation unit may use the propagation loss according to the angle between the direction of the estimated position and the direction of the device having directivity.
With such a configuration, for example, estimation can be performed in consideration of the directivity of an antenna, a microphone, or the like, and more accurate estimation can be realized.

Further, in the position estimation device according to the present invention, the estimation unit may optimize the objective function by sequential arithmetic processing.
With such a configuration, the objective function can be optimized by a sequential operation such as Newton's method.

Further, in the position estimation device according to the present invention, the estimation unit may optimize the objective function by sequential arithmetic processing using a plurality of initial values.
With such a configuration, it is possible to prevent the optimum solution from corresponding to the local optimum value, and it becomes possible to realize a more accurate estimation.

Further, in the position estimation device according to the present invention, in the sequential arithmetic processing, when the objective function converges to the local optimum value, the estimation unit changes the step size to a larger value, and the objective function is global. The step size may be changed to a smaller value if it has converged to the optimum value.
With such a configuration, it is possible to prevent the optimum solution from corresponding to the local optimum value, and it becomes possible to realize a more accurate estimation.

Further, in the position estimation device according to the present invention, the unknown wave source is the transmission source of radio waves, and the radio waves may be received by the antenna.
With such a configuration, the position of the radio wave transmission source can be estimated, and for example, an illegal radio wave transmission source can be identified.

Further, in the position estimation device according to the present invention, the unknown wave source is a source of sound waves, and the sound waves may be received by a microphone or a hydrophone.
With such a configuration, the position of the sound wave source can be estimated, and for example, the position where abnormal noise is generated, the position of a desired sound source, and the like can be specified.

Further, the position estimation method according to the present invention includes a step of acquiring the received power of a wave from an unknown wave source, a step of acquiring a receiving position when a wave corresponding to the received power is received, and a received power and a receiving position. The estimated received power for each receiving position is calculated using multiple sets of and, the estimated position of the unknown wave source, the estimated transmission power of the wave from the unknown wave source, and the propagation loss of the wave. It includes a step of estimating the estimated position and the estimated transmission power by optimizing the objective function according to the difference from the received power.

According to the position estimation device and the like according to the present invention, the position of an unknown wave source and the transmission power can be estimated without using TDoA or DoA and without requiring prior preparation such as a position fingerprint. become.

A block diagram showing a configuration of a position estimation device according to an embodiment of the present invention. A flowchart showing the operation of the position estimation device according to the same embodiment. A block diagram showing another example of the configuration of the position estimation device according to the same embodiment. A block diagram showing another example of the configuration of the position estimation device according to the same embodiment. The figure for demonstrating the position estimation using the directional antenna in the same embodiment. A flowchart showing another example of the operation of the position estimation device according to the same embodiment. The figure for demonstrating the optimization of the number of wave sources in the same embodiment.

Hereinafter, the position estimation device according to the present invention will be described with reference to embodiments. In the following embodiments, the components and steps having the same reference numerals are the same or correspond to each other, and the description thereof may be omitted again. The position estimation device according to the present embodiment estimates the position of an unknown wave source and the transmission output by optimization using received power.

FIG. 1 is a block diagram showing a configuration of a position estimation device 1 according to the present embodiment. The position estimation device 1 according to the present embodiment includes a reception power acquisition unit 11, a reception position acquisition unit 12, and an estimation unit 13. As will be described later, the position estimation device 1 may or may not receive waves. In the former case, it is preferable that the position estimation device 1 is a device whose position can be changed (for example, a portable device, a device that can be mounted on a moving body such as an automobile, or the like). On the other hand, when the radio wave is not received, the position estimation device 1 may be, for example, a server device that receives received power or the like from one or two or more client devices. In the present embodiment, the case where the position estimation device 1 can change the position will be mainly described.

The received power acquisition unit 11 acquires the received power of the wave from the unknown wave source 5. The wave from the unknown source 5 may be, for example, a radio wave or a sound wave. In the former case, the unknown wave source 5 becomes a radio wave transmission source, and in the latter case, the unknown wave source becomes a sound wave transmission source. In the present embodiment, the case where the wave is a radio wave will be mainly described, and the case where the wave is a sound wave will be described later. Further, in the present embodiment, first, the case where the number of unknown wave sources 5 is one will be mainly described, and the case where the number of unknown wave sources 5 may be other than one will be described later.

The received power acquisition unit 11 may receive a wave from an unknown wave source 5 and acquire the received power, and may receive the received power of the wave received by the other device from the other device. It may be. In the present embodiment, as described above, the former case will be mainly described. That is, in the present embodiment, the received power acquisition unit 11 receives the radio wave by the antenna 11a and acquires the received power of the radio wave. The received power may be, for example, the received signal strength (RSSI). The received power acquisition unit 11 may be, for example, a spectrum analyzer that acquires the reception signal strength of the radio wave, or may have another configuration for receiving the radio wave. When the received power acquisition unit 11 is a spectrum analyzer, the received power acquisition unit 11 may also acquire the wavelength of the received radio wave. Further, the reception power acquisition unit 11 which is a spectrum analyzer may acquire the reception power of radio waves of a desired frequency, for example.

The reception position acquisition unit 12 acquires the reception position when a wave corresponding to the received power is received. That is, the position of the antenna or the like when the wave from the unknown wave source 5 is received by the antenna or the like is acquired. The reception position acquisition unit 12 may acquire the reception position which is the position of the position estimation device 1 at the time when the reception power acquisition unit 11 receives the wave corresponding to the received power, and the wave is generated by another device. The reception position, which is the position of the device at the time of reception, may be received from another device. In the present embodiment, the former case will be mainly described.

The method by which the receiving position acquisition unit 12 acquires the position does not matter. The reception position acquisition unit 12 may acquire the position using, for example, GPS (Global Positioning System), or may acquire the position using a quasi-zenith satellite system, and the position estimation device 1 may acquire a vehicle or the like. When mounted on the system, for example, the position may be acquired using an autonomous navigation device such as a gyro, and a code corresponding to the position information indicating the position (for example, a QR code (registered trademark)) may be obtained. When the image is arranged at the position indicated by the position information, for example, the position may be acquired by taking an image such as the code and reading the position information, or the position may be obtained by another method. You may get it. In the present embodiment, a case where the reception position acquisition unit 12 receives radio waves from GPS satellites via the antenna 12a and acquires the position using the received radio waves will be mainly described. The position acquired by the reception position acquisition unit 12 may be, for example, coordinates indicating latitude and longitude, or may be other coordinates.

With respect to the received power acquired by the received power acquisition unit 11 and the wave corresponding to the received power, it is preferable that the reception position acquired by the reception position acquisition unit 12 is linked and managed. In the present embodiment, the associated received power and the receiving position are referred to as a pair of the received power and the receiving position. The reception power is acquired by the reception power acquisition unit 11, and the reception position corresponding to the reception power is acquired by the reception position acquisition unit 12, so that a plurality of pairs of the reception power and the reception position are acquired. For example, when the position estimation device 1 is movable, even if a plurality of sets of received power and reception position are acquired by receiving waves from an unknown wave source 5 at a plurality of positions. Good.

The estimation unit 13 uses a plurality of sets of the received power and the receiving position, the estimated position of the unknown wave source 5, the estimated transmission power of the wave from the unknown wave source 5, and the estimated reception for each reception position using the wave propagation loss. The estimated position and the estimated transmission power are estimated by optimizing the objective function according to the difference between the power and the received power. That is, reception for each reception position is performed using a plurality of sets of the reception power and the reception position, which are the measurement results, the estimated values of the position of the unknown wave source and the transmission power, and the propagation loss of a general wave. Optimal solution (position of unknown wave source and unknown wave source) that optimizes the objective function so that the objective function is optimized according to the error between the estimated power value and the actual measured value of the received power (so that the error becomes small). Estimated value of transmission power) will be obtained. The estimation unit 13 can calculate the distance from the estimated position of the unknown wave source 5 to the reception position by using the reception position and the estimated position, and uses the distance, the estimated transmission power, and the propagation loss. The estimated received power at the receiving position can be estimated.

The objective function may be a function in which the value increases as the error between the estimated value of the received power and the actual measured value of the received power for each reception position increases, or a function in which the value decreases as the error increases. It may be. In the former case, the optimization will minimize the objective function, and in the latter case, the optimization will maximize the objective function. In the present embodiment, the former case will be mainly described. Further, various functions can be used as the function in which the value becomes smaller as the error between the estimated value of the received power for each reception position and the actual measured value of the received power becomes larger.

As the radio wave propagation loss, for example, a propagation loss according to a model according to the propagation path from the estimated position to the reception position (for example, a free space model, a model considering the influence of multipath, etc.) may be used. .. In the present embodiment, for the sake of simplicity, the case where the propagation loss of the free space model is used will be mainly described, and the model considering the influence of multipath will be briefly mentioned. Propagation loss may be considered as a function that takes transmission power and distance as arguments.

The estimation unit 13 may optimize the objective function by using the propagation loss according to the spatial information regarding the space between the estimation position and the reception position. The spatial information may indicate the type of propagation path from the estimated position to the receiving position. Therefore, the spatial information may be, for example, a prospect, an urban area, a mountainous area, or the like. For example, the estimation unit 13 uses map information to specify the reception position and the estimated position at that time, and when there is an urban area or a mountain between the two positions, the spatial information between the two positions is the urban area or If it is determined to be a mountainous area and there are no obstacles such as urban areas or mountains between the two positions, it may be determined that the spatial information between the two positions is a line of sight. Then, when the spatial information is a line-of-sight, for example, the propagation loss corresponding to the free space model is used, and when the spatial information indicates that there is an obstacle such as an urban area or a mountainous area, for example, a multipath Propagation loss corresponding to the model considering the influence may be used. The spatial information may be acquired, for example, by the estimation unit 13 accessing the map information held in the position estimation device 1 or accessing a server or the like that holds the map information. You may.

Hereinafter, the process of obtaining the estimated position and the estimated transmission power by optimizing the objective function will be specifically described. Here, the case where the number of wave sources 5 is one will be described, and the case where the number of wave sources 5 is one or more is indefinite will be described later.

First, let the estimated position of the unknown wave source 5 be (x ^e , y ^e , z ^e ), and let the estimated transmission power of the wave from the unknown wave source 5 be p ^e . Further, the reception position and the reception power acquired at the i-th position are (x _i , y _i , z _i ) and r _i , respectively. Therefore, i-th set of the received power and the reception position acquired by the reception power acquisition unit 11 and the reception position acquisition unit 12 is, for example, a _{(x i, y i, z} i, r i). In addition, i = 1, 2, ..., N. It is preferable that N is an integer exceeding the unknown number to be estimated. For example, when there is one wave source 5, the unknown number is 4, so it is preferable that N is 5 or more. If N is the same as the unknown, the estimated position and estimated transmission power can be obtained, but the estimation will be performed with substantially the same accuracy as triangulation, and the effect of multipath will be reduced. Is difficult. Further, the larger N is, the better the influence of multipath can be reduced. Therefore, when there is one wave source 5, N is sufficiently larger than 5 such as 10 or more or 20 or more. It is more preferable that it is a value.

Reception calculated using the estimated transmission power ^pe , propagation loss, estimated position (x ^e , y ^e , z ^e ), and reception position (x _i , y _i , z _i ) for the wave from the unknown wave source 5. The estimated received power r _i ^{e at the} position (x _i , y _i , z _i ) is as follows. G _r is the gain of the antenna 11a and is a known value. Here, the case where the antenna 11a has no directivity and the antenna gain _Gr is a constant value will be described, and the case where the antenna has directivity, that is, the case where the antenna gain _Gr has an angle as an argument will be described later. ..

In the above equation, d _i is the distance of the estimated position of the unknown wave source ^{5 (x e, y e,} z e) from to the receiving position _{(x i, y i, z} i), are as follows ..

Further, λ is the wavelength of the received wave, and for example, when the received power acquisition unit 11 is a spectrum analyzer, it may be acquired by the received power acquisition unit 11. Further, the received wave may be Fourier transformed to obtain the wavelength λ of the peak in the frequency band. Since the wave source 5 is unintended, it is said to be omnidirectional. Therefore, a value corresponding to the antenna gain will be included in the estimated transmit power p ^e as effective radiated power.

Further, in the above equation, the estimated received power using the equation of the propagation loss of the radio wave in the free space is shown, but the equation of the other propagation loss depends on the spatial information from the position of the wave source 5 to the receiving position. May be used as described above. For example, when the spatial information from the estimated position of the wave source 5 to the reception position indicates the existence of an obstacle such as a mountainous area or an urban area, the propagation loss considering the influence of multipath is used and the following equation is used. The estimated received power r _i ^e may be calculated. Further, instead of the d _i ² of the formula: may be used d _i ^m such d _i ^3/2. However, m is a real number from 1 to 2.

As described above, when the received power and the receiving position are acquired at N points, the objective function (evaluation function) f according to the difference between the estimated received power and the received power for each receiving position is, for example, as follows. become that way.

Here, the case where the objective function is the sum of squares of the difference between the received power and the receiving position is shown, but the objective function is, for example, for each receiving position of the absolute value of the difference between the estimated received power and the received power. Needless to say, it may be the sum of the estimated received power and the difference between the received power and each receiving position of the fourth or sixth power. Further, in the sum (sum), the difference between the estimated received power and the received power may be weighted as in the equation of the objective function f.

Weighting the difference between the estimated received power and the received power means that the value corresponding to the difference between the estimated received power and the received power, for example, the square of the difference, the absolute value of the difference, the fourth power of the difference, and the difference. It may be to multiply the sixth power or the like by a weight. The weight w _i is a weight related to the measurement result at the i-th reception position, and is usually a positive real number. For example, the difference between the estimated received power r _i ^e and the received power r _i according to the i-th receiving position is the estimated position (x ^e , y ^e , z ^e ) used in the calculation of the estimated received power r _i ^e. A weight w _i may be added according to the spatial information regarding the space between the reception position (x _i , y _i , z _i ). Specifically, the weight w _i corresponding to the spatial information indicating the line-of-sight is set to a large value, for example, "1", and the weight corresponding to the spatial information indicating the existence of obstacles such as urban areas and mountains. w _i may be set to a value smaller than the weight corresponding to the spatial information of the line of sight, for example, "0.3" or "0.5". In addition, the weight may be changed according to the degree of the obstacle. In that case, the more obstacles indicated by the spatial information, the smaller weights may be used. For example, the weight according to the spatial information indicating the existence of a small number of high-rise buildings is set to a larger value such as "0.5", and the spatial information indicating the existence of a large number of high-rise buildings is used. The corresponding weight may be set to a smaller value, such as "0.2". As such, the weight w _i is set to a smaller value, for example, if spatial information indicates more multipaths, and to a larger value if less multipaths are indicated. May be done. Further, the weight w _i may be changed according to, for example, the magnitude and accuracy of the received signal. In that case, for example, the closer to the ideal reception, the larger the weight may be used. The weight w _i may be a constant. That is, the objective function may not use the weight for each reception position. In that case, the w _i can be, for example, it may be one, or may be 1 / N.

The x ^e , y ^e , z ^e , and p ^e that minimize the above objective function f are the position of the wave source 5 to be estimated and the transmission power. Since the solution that minimizes the objective function f, that is, the optimum solution corresponds to the minimum point, the partial differential of each variable of the objective function f becomes 0. Therefore, to obtain the estimated position and the estimated transmission power, the following equation holds (x ^e , y ^e , z ^e , p ^e ).

Various algorithms can be considered as a method for calculating such (x ^e , y ^e , z ^e , p ^e ), that is, a method for optimizing the objective function, and examples thereof include the Newton method and the steepest descent method. However, the optimization is not limited to this, and optimization may be performed using, for example, a parameter estimation method such as a Kalman filter. For example, when performing sequential operations using the steepest descent method, set (x ₀ ^e , y ₀ ^e , z ₀ ^e , p ₀ ^e ) as the initial value, and an appropriate positive real number is set. The objective function f can be optimized by setting the step size α _k and repeating the sequential operation of the following equation. It should be noted that k = 0, 1, 2, ... Further, ∇f (x ^e , y ^e , z ^e , p ^e ) required for the sequential operation may be calculated in advance and the calculation result may be used for the sequential operation. Further, the number of operations may be reduced by setting the step size α _k to a large value at first and a small value according to the convergence state.

In this way, the estimation unit 13 may optimize the objective function f by sequential arithmetic processing. In that case, the optimization process may be terminated when a predetermined termination condition is satisfied. The end condition may be, for example, that the convergence condition is satisfied, k may exceed a predetermined maximum number of sequential operations, or may be another condition. The estimation unit 13 determines, for example, the absolute value of the change in the value of the objective function f when k is incremented by 1 | f (x _{k + 1} ^e , y _{k + 1} ^e , z _{k + 1} ^e , p _{k + When 1} ^e ) −f (x _k ^e , y _k ^e , z _k ^e , p _k ^e ) | becomes smaller than a predetermined threshold, it may be determined that the convergence condition is satisfied. The threshold is a positive real number and is usually set to a small value. Further, the estimation unit 13 may determine that the convergence condition is satisfied when, for example, the value of the objective function f is smaller than a predetermined value. The predetermined value is a positive real number and is usually set to a small value.

The estimation unit 13 may optimize the objective function f by, for example, sequential arithmetic processing using a plurality of initial values in order to prevent the optimization of the objective function f from becoming a local optimization. For example, the estimation unit 13 sets a plurality of initial values and performs optimization using each initial value, so that the optimum solution and the optimum solution are substituted into the objective function for each initial value. You can get the value and. After that, the estimation unit 13 may use the optimum solution corresponding to the most appropriate optimum value among the plurality of optimum values as the final estimated position and the estimated transmission power. The optimum solution is a solution (here, an estimated position and an estimated transmission power) obtained by optimizing the objective function. Also, the most appropriate optimum value means that the optimum value is the smallest when the optimization is the minimum, and the optimum value is the largest when the optimization is the maximum. is there. Strictly speaking, the initial values are the initial values of the estimated position and the estimated transmission power. The initial value of the estimated position may be randomly specified, for example, in a region including N reception positions (for example, it may be the smallest region including N reception positions). Further, the initial value of the estimated transmission power may be randomly selected from, for example, a plurality of predetermined values or a range of predetermined values.

Further, in order to prevent the optimization of the objective function f from becoming a local optimum, the estimation unit 13 determines, for example, in a sequential arithmetic process, when the objective function f converges to the local optimum value, the step size. If α _k is changed to a larger value and the objective function f converges to the global optimum value, the step size α _k may be changed to a smaller value. Whether the objective function f has converged to the local optimum value or the global optimum value may be determined by, for example, whether the value of the objective function f is close to the ideal optimum value. Good. When the value of the objective function f is close to the ideal optimum value, it is judged that it has converged to the global optimum value, and when it is far from the ideal optimum value, it is judged that it has converged to the local optimum value. You may. More specifically, when the optimization is minimized, for example, when the value of the objective function f converges to a value larger than the first threshold value, it is determined that the value has converged to the local optimum value. Then, when the value of the objective function f converges to a value smaller than the first threshold value, it may be determined that the value converges to the global optimum value. When the optimization is maximized, for example, when the value of the objective function f converges to a value smaller than the second threshold value, it is determined that the value has converged to the local optimum value, and the objective function f When the value converges to a value larger than the second threshold value, it may be determined that the value has converged to the global optimum value. The first and second threshold values may be the same value or may be different. Both thresholds are usually positive real numbers. Step size alpha _k used when the objective function f is converging to a local optimum, and the step size alpha _k used when the objective function f is converging to the global optimum, can be predetermined Well or not. In the latter case, for example, when the objective function f converges to the local optimum value, a step size α _k that gradually increases with each update of _k is used, and the objective function f converges to the global optimum value. If so, a step size α _k that gradually decreases with each update of _k may be used. Even in that case, the upper limit value and the lower limit value of the step size may be set.

The estimated position and estimated transmission power of the wave source 5 acquired by the estimation unit 13 may be output by, for example, an output unit (not shown). The output may be displayed on a display device (for example, a liquid crystal display or an organic EL display), may be transmitted via a communication line to a predetermined device, may be printed by a printer, or may be stored in a recording medium. It may be.

Next, the operation of the position estimation device 1 will be described with reference to the flowchart of FIG. Here, a case where the objective function f is optimized by a sequential operation will be described.

(Step S101) The reception power acquisition unit 11 and the reception position acquisition unit 12 acquire a plurality of sets of the reception power and the reception position of the wave from the unknown wave source 5. The plurality of sets may be stored, for example, on a recording medium (not shown).

(Step S102) The estimation unit 13 sets the initial values of the estimated position and the estimated transmission power. The setting of this initial value may be, for example, reading out a predetermined value.

(Step S103) The estimation unit 13 sets the counter k to 1. The value of the counter k indicates the number of sequential operations.

(Step S104) The estimation unit 13 calculates the provisional estimated position and the estimated transmission power. The calculation of this provisional estimated value may be performed by updating the estimated position and the estimated transmission power so as to approach the optimum solution, for example, as in the above equation.

(Step S105) The estimation unit 13 calculates the value of the objective function f according to the estimated position and the estimated transmission power acquired in step S104.

(Step S106) The estimation unit 13 determines whether or not the convergence condition is satisfied. Then, when the convergence condition is satisfied, a series of processes for estimating the estimated position and the estimated transmission power are completed, and if not, the process proceeds to step S107.

(Step S107) The estimation unit 13 increments the counter k by 1.

(Step S108) The estimation unit 13 determines whether or not the counter k has exceeded the maximum number of sequential operations. Then, when k exceeds the maximum number of sequential operations, the series of processes for estimating the estimated position and the estimated transmission power ends, and if not, the process returns to step S104.

When a series of processes for estimating the estimated position and the estimated transmission power are completed, the estimated position and the estimated transmission power finally calculated in step S104 become the final estimation result.

In addition, in the flowchart of FIG. 2, sequential calculation using a plurality of initial values may be performed. In that case, the processes of steps S102 to S108 are repeated for each initial value, and after each process is completed, the optimum solution corresponding to the optimum optimum value may be used as the estimated position of the wave source 5 and the estimated transmission power. .. Further, the flowchart of FIG. 2 shows a case where the received power and the receiving position are first acquired, and then the position of the wave source 5 and the like are estimated by optimizing the objective function. It does not have to be. For example, when the acquisition of the received power and the received position at a predetermined number of points is completed, the estimated position and the estimated transmission power are estimated, and the estimation process is repeated every time the number of acquired received powers and the received positions increases. You may do so. Then, when the estimated position and the estimated transmission power with sufficient accuracy can be acquired, the acquisition of the received power and the like and the process of estimating the estimated position and the like may be terminated. Further, the order of processing in the flowchart of FIG. 2 is an example, and the order of each step may be changed as long as the same result can be obtained.

As described above, according to the position estimation device 1 according to the present embodiment, the position and transmission of the unknown wave source 5 are performed without using TDoA or DoA and without requiring prior preparation such as a position fingerprint. The power can be estimated. As such, since TDoA or the like is not used, the position of the wave source 5 can be estimated with a simple configuration. Furthermore, since the estimation is performed by optimizing the objective function, it is possible to perform position estimation and the like with reduced effects of errors due to multipath and the like by using a sufficient number of sets of received power and receiving positions. Further, when the position estimation device 1 is moved to a plurality of positions to receive radio waves from an unknown wave source 5 and acquire a plurality of pairs of received power and reception position, it is not necessary to use a plurality of receiving devices. , The position of the wave source 5 can be estimated. Further, even if unreliable value, by adjusting the weights w _i, it also becomes possible to reduce the influence. As a result, the estimation accuracy can be improved. Further, the estimation accuracy can be improved by making the propagation loss of the equation for obtaining the estimated received power correspond to the spatial information.

Next, a modification of the position estimation device 1 according to the present embodiment will be described.

[Acquisition of position according to measurement trigger]
The unknown wave source 5 does not always output a wave. Therefore, as shown in FIG. 3, when the received power acquisition unit 11 receives the wave from the target wave source 5, the received power acquisition unit 11 acquires the received power and triggers the reception position acquisition unit 12 to measure. May be output. Then, the reception position acquisition unit 12 may acquire the reception position which is the position at the time when the measurement trigger is received. In this way, even when the wave from the wave source 5 is output intermittently, the pair of the received power and the receiving position can be appropriately acquired. The received power acquisition unit 11 receives a wave from the target wave source 5 when it receives a wave having a preset frequency or when it receives a wave having the same frequency as a wave received in the past. You may judge that it was done. Further, the received power acquisition unit 11 targets the wave source 5 when the intensity of the received wave is equal to or higher than a predetermined threshold value, for example, when the received signal strength (RSSI) of the received wave is equal to or higher than the threshold value. It may be determined that the wave from is received.

[Estimation according to directivity]
In the above embodiment, the case where the wave from the unknown wave source 5 is received by the antenna 11a having no directivity has been mainly described, but it is not necessary. When the omnidirectional antenna 11a is used, measurement and calculation are facilitated, but since multipath from surrounding structures and the like is also received, an error may occur in the estimated position and the like. In order to solve such a problem, the wave from the wave source 5 may be received by a device having directivity.

The device having the directivity may be, for example, an antenna having a directivity when the wave is a radio wave, and a microphone or a hydrophone having the directivity when the wave is a sound wave. May be good. The directional antenna may be directional due to an antenna structure such as a Yagi antenna or a parabolic antenna, and the received signals of a plurality of antennas, such as an array antenna, depend on the amplitude and phase. The antenna may have directivity by multiplying the weights.

FIG. 4 is a block diagram showing a configuration of a position estimation device 1 that receives radio waves via a directional antenna 11b. In FIG. 4, the position estimation device 1 further includes a direction acquisition unit 14.

The direction acquisition unit 14 acquires the direction of the device (antenna 11b in FIG. 4) having directivity when a wave corresponding to the received power is received. It is preferable that the direction acquisition unit 14 can acquire the direction of the antenna 11b, such as a geomagnetic sensor. Further, it is preferable that the direction acquisition unit 14 can acquire the direction of the antenna 11b so as not to be affected by the metal of the antenna 11b having directivity. The direction of the antenna 11b acquired by the direction acquisition unit 14 may be, for example, the direction of the antenna 11b with respect to the reference direction. The reference direction may be, for example, the north direction. The direction acquisition unit 14 may acquire, for example, an azimuth angle indicating the direction of directivity of the antenna 11b.

When receiving radio waves using the directional antenna 11b, the estimation unit 13 calculates the estimated reception power calculated by the propagation loss according to the angle between the direction of the estimated position and the direction of the directional device. You may use it. The propagation loss according to the angle between the direction of the estimated position and the direction of the device having directivity is the propagation loss according to the antenna gain of the angle between the direction of the estimated position with respect to the receiving position and the direction of the device having directivity. There may be. That is, the estimation unit 13 may use the directional antenna gain G _r (θ _i ) as shown in the following equation instead of the non-directional antenna gain G _r for calculating the estimated received power.

Note that θ _i is the angle formed by the direction of the estimated position at the i-th receiving position (x _i , y _i , z _i ) and the direction of the directional antenna 11b. The direction of the estimated position is the direction of a straight line connecting the receiving position (x _i , y _i , z _i ) and the estimated position (x ^e , y ^e , z ^e ). A method of obtaining the angle θ _i will be described with reference to FIG. 5, the receiving position _{(x i, y i, z} i) in, it is assumed that antenna 11b having directivity are arranged. The angle φ ₁ of the antenna 11b with respect to the reference direction is acquired by the direction acquisition unit 14. Further, by using the coordinates of the receiving position (x _i , y _i , z _i ) and the coordinates of the estimated position (x ^e , y ^e , z ^e ), the reference direction and the receiving position and the estimated position are connected. The angle φ ₂ with the straight line can also be obtained. Then, by using both angles φ ₁ and φ ₂ , the angle θ _i (= φ _{2 −} φ ₁ ) formed by the direction of the antenna 11b and the straight line connecting the receiving position and the estimated position can be calculated. By using the antenna gain G _r (θ _i ) corresponding to the angle θ _i , it becomes possible to acquire the estimated received power according to the direction of the directional antenna 11b. It is assumed that the direction dependence of the antenna gain G _r (θ _i ) (the directivity pattern of the antenna shown in FIG. 5) has been acquired in advance.

The objective function f is optimized in the same manner as above except that the antenna gain G _r (θ _i ) according to the direction of the antenna 11b is used instead of the constant antenna gain G _r. Is omitted. In this case as well, the direction acquisition unit 14 may acquire the direction according to the measurement trigger.

As described above, by using the antenna 11b having directivity, the influence of multipath from the peripheral structure can be reduced. Further, since the directional antenna has a higher gain than the omnidirectional antenna, the received power of the signal from the directional direction becomes stronger, and the influence of noise can be reduced. As a result, the estimation accuracy between the position of the wave source 5 and the transmission power can be improved.

Although the case where the direction acquisition unit 14 directly acquires the direction of the antenna 11b having directivity has been described here, it may not be the case. As described above, when the received power acquisition unit 11 and the reception position acquisition unit 12 receive the received power and the reception position from another device or the like, the direction acquisition unit 14 also receives the wave from the wave source 5. The direction of the device having directivity in the above may be received from another device or the like. In that case, in another device or the like, the direction of the device having directivity may be acquired by using the geomagnetic sensor or the like as described above.

[Estimation of the number of wave sources]
In the above embodiment, the case where the number of wave sources 5 is one has been mainly described, but it is not necessary. The number of wave sources 5 may be plural or indefinite. If the number of wave sources 5 is indefinite, the number of wave sources 5 may also be estimated.

If the number of wave sources 5 is indefinite, the estimation unit 13 may estimate the position and transmission power of each wave source 5 by optimizing each estimated number of wave sources from the minimum number of wave sources to the maximum number of wave sources. Good. Then, the estimation unit 13 may also estimate the estimated number of wave sources so that the optimum value per wave source obtained by dividing the optimum value, which is the value of the optimized objective function, by the estimated number of wave sources is optimized. That is, the number of wave sources may be estimated so as to optimize the objective function with the objective function for estimating the number of wave sources as the optimum value per wave source. For example, when there is one or more unknown wave sources 5, the minimum number of wave sources is 1. The minimum number of wave sources may be 2 or more.

Estimating the estimated number of wave sources so that the optimum value per wave source is optimized means that, for example, when the optimization of the objective function f is minimized, the optimum value per wave source becomes the smallest. The estimated number of wave sources may be obtained, and when the optimization of the objective function f is maximized, the number of estimated wave sources having the largest optimum value per wave source may be obtained. For example, when the optimization of the objective function f is minimized and the change in the optimum value per wave source with respect to the number of wave sources is shown in FIG. 7, the estimation unit 13 performs the optimization per wave source. It may be estimated that the number of wave sources "3" having the smallest value is the number of unknown wave sources 5. In that case, the estimated position and estimated transmission power, which are the optimum solutions obtained by the optimization performed with the number of wave sources set to "3", become the estimated position and estimated transmission power of the three unknown wave sources 5. Note that FIG. 7 does not show the measured value, but is a diagram showing the change of the optimum value per wave source for the sake of explanation.

In this case, assuming that the number of temporary wave sources is M, there are only 4 × M unknowns. Therefore, it is preferable that the number N of the receiving positions for acquiring the received power exceeds 4 × M. In addition, M is an integer of 1 or more. Further, assuming that the maximum number of wave sources is M _max , it is preferable that the number N of reception positions for acquiring received power exceeds 4 × M _max . For example, as shown in FIG. 7, when the maximum number of wave sources M _max = 6, it is preferable that the received power is acquired at 25 or more positions.

When one or more wave sources 5 are present, the estimated received power at the i-th reception position of the wave from the j-th wave source 5 is as follows. Note that j is an integer of 1 or more, and when there are M wave sources 5, j = 1, 2, ..., M.

In the above equation, di _{, j} is the estimated position (x _j ^e , y _j ^e , z _j ^e ) of the _jth wave source 5 from the i-th reception position (x _i , y _i , z _i ). It is the distance to, and is as shown in the following equation.

Further, when the number of wave sources 5 is M, the estimation unit 13 may use the objective function f of the following equation.

In the objective function f, the estimated received power at the i-th receiving position is the sum of the estimated received powers for the waves from the first to Mth wave sources 5. The process of estimating the estimated position and the estimated transmission power by optimizing the objective function is to estimate the waves from M wave sources 5 instead of the estimated received power of the waves from one wave source 5 in the objective function. It is the same as the above-described embodiment except that the total received power is used, and detailed description thereof will be omitted. In this case, the number of variables obtained by optimizing the objective function can be increased as compared with the case where the number of wave sources 5 is one. When M wave sources 5 are assumed, the estimated M positions and the estimated transmission power for each estimated position are estimated. That is, M sets of the estimated position and the estimated transmission power are acquired.

FIG. 6 is a flowchart showing the operation of the position estimation device 1 when estimating the number of wave sources 5. The processing of steps S101 to S108 is the same as the flowchart of FIG. 2 except that the equation of the estimated received power and the equation of the objective function f are changed as described above, and detailed description thereof will be omitted.

(Step S201) The estimation unit 13 sets the counter M to the minimum number of wave sources. The value of the counter M indicates the number of tentative wave sources.

(Step S202) The estimation unit 13 sets a value obtained by dividing the optimum value of the objective function at that time by the counter M at that time, that is, an optimum value per wave source in G (M). The G (M) value may be stored in a recording medium (not shown).

(Step S203) The estimation unit 13 increments the counter M by 1.

(Step S204) The estimation unit 13 determines whether or not the counter M exceeds the maximum number of wave sources. Then, if the counter M exceeds the maximum number of wave sources, the process proceeds to step S205, and if not, the process returns to step S102. For example, when the minimum number of wave sources is 1, the maximum number of wave sources is 6, and the process proceeds from step S204 to step S205, the values of G (1), G (2), ..., G (6) are obtained. Will have been acquired.

(Step S205) The estimation unit 13 specifies the number of estimated wave sources for which the optimum value G (M) per wave source calculated so far is optimized. For example, when the optimization is minimization and each value of G (1), G (2), ..., G (6) is acquired, the minimum value of G (M) M ( (This value becomes the final estimated number of wave sources) is specified, and the set of the estimated position and the estimated transmission power specified when the counter M is the final estimated number of wave sources is the estimated position of each wave source 5. And the estimated transmission power. In this way, a series of processing of estimating the number of wave sources 5 and estimating the position and transmission power of the estimated number of each wave source 5 is completed.

In the flowchart of FIG. 6, the case where the value of M is incremented by 1 has been described, but it may not be the case. For example, M is changed by a discrete value, and among the G (M) values obtained in this way, the optimum one or two M values are specified, and the specified one or two values are specified. The estimated number of wave sources may be obtained by calculating G (M) in the vicinity of the value of M of. The optimum one or two M values may be, for example, one or two M values having the smallest G (M) values when the optimization is minimized. Good. For example, if the absolute value of the difference between the minimum value of G (M) and the next smallest value is smaller than a predetermined threshold, the values of both Ms are specified, otherwise the minimum G ( Only the value of M in M) may be specified. By doing so, for example, when there are many candidates for M from the minimum number of wave sources to the maximum number of wave sources, the estimated number of wave sources can be obtained with less processing. Further, the order of processing in the flowchart of FIG. 6 is an example, and the order of each step may be changed as long as the same result can be obtained.

In this way, even when the number of wave sources 5 is unknown, the number of wave sources 5 can be estimated. Although the case where the processing is performed until the number of wave sources 5 reaches the maximum number of wave sources has been described here, it is not necessary. A convergence condition may be set for optimizing the optimum value per wave source, and the process may be terminated when the convergence condition is satisfied. For example, when the optimum value per wave source is on the appropriate side of the predetermined threshold value (for example, if the optimization is minimized, it is smaller than the threshold value, and the optimization is maximized. If it becomes larger than the threshold value), it may be determined that the convergence condition is satisfied.

Further, here, the case where the number of wave sources 5 is unknown has been mainly described, but even when the number of wave sources 5 is known, the position and transmission power of each wave source 5 are estimated as described above. be able to. In that case, it is sufficient to perform the process of optimizing the objective function only for the value of M that is known in advance.

[Wave source that emits sound waves]
As described above, the wave source may be one that emits sound waves instead of transmitting radio waves. Even if the wave from the wave source is a sound wave, the position of the wave source of the sound wave and the transmission power (transmission power) of the sound wave can be estimated in the same manner as in the case of the above radio wave. In that case, sound waves are received by a microphone or a hydrophone instead of the antenna. As for the propagation loss or the like, the propagation loss or the like according to the sound wave may be used. Then, it is clear that the position of the sound wave source and the sound wave transmission output can be estimated by optimizing the objective function in the same manner as in the case of the radio wave, and detailed description thereof will be omitted.

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

Further, in the above embodiment, the transfer of information performed between the components is performed by, for example, one component when the two components that transfer the information are physically different. It may be performed by outputting information and accepting information by the other component, or if the two components that pass the information are physically the same, one component. It may be performed by moving from the processing phase corresponding to the above to the processing phase corresponding to the other component.

Further, in the above embodiment, information related to the processing executed by each component, for example, information received, acquired, selected, generated, transmitted, or received by each component. In addition, information such as threshold values, mathematical formulas, and addresses used by each component in processing may be temporarily or for a long period of time in a recording medium (not shown) even if it is not specified in the above description. In addition, each component or a storage unit (not shown) may store information on a recording medium (not shown). Further, the information may be read from the recording medium (not shown) by each component or a reading unit (not shown).

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

Further, in the above embodiment, when two or more components included in the position estimation device 1 have a communication device, an input device, or the like, even if the two or more components have a physically single device. Well, 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 or the recording medium. Further, the program may be executed by being downloaded from a server or the like, or may be executed by reading a program recorded on a predetermined recording medium (for example, an optical disk, a magnetic disk, a semiconductor memory, etc.). Good. Further, this program may be used as a program constituting a program product. Further, the number of computers that execute the program may be singular or plural. That is, centralized processing may be performed, or distributed processing may be performed.

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

From the above, the position estimation device or the like according to the present invention has the effect of being able to estimate the position of an unknown wave source and the transmission power, and is useful as, for example, a device for identifying the source of illegal radio waves.

1 Position estimation device 11 Received power acquisition unit 12 Reception position acquisition unit 13 Estimating unit 14 Direction acquisition unit

Claims (12)

A received power acquisition unit that acquires the received power of a wave from an unknown wave source,
A reception position acquisition unit that acquires a reception position when a wave corresponding to the received power is received, and a reception position acquisition unit.
Using a plurality of sets of received power and receiving position, the estimated position of the unknown wave source, the estimated transmission power of the wave from the unknown wave source, and the wave propagation loss, the estimated received power and the received power for each receiving position A position estimation device including an estimation unit that estimates an estimated position and an estimated transmission power by optimizing an objective function according to the difference between the two. The received power acquisition unit receives a wave from the unknown wave source, acquires the received power, and obtains the received power.
The position estimation device according to claim 1, wherein the reception position acquisition unit acquires a reception position which is the position of the position estimation device at the time when the reception power acquisition unit receives a wave corresponding to the received power. There is one or more of the unknown wave sources,
Claim 1 or claim that the estimation unit also estimates the estimated number of wave sources so that the optimum value per wave source obtained by dividing the optimum value, which is the value of the optimized objective function, by the estimated number of wave sources is optimized. Item 2. The position estimation device according to item 2. The position estimation according to any one of claims 1 to 3, wherein the estimation unit optimizes the objective function by using the propagation loss according to the spatial information regarding the space between the estimation position and the reception position. apparatus. The estimation unit optimizes an objective function in which the difference between the estimated reception power and the reception power is weighted according to the spatial information regarding the space between the estimated position and the reception position used in the calculation of the estimated reception power. , The position estimation device according to any one of claims 1 to 4. Waves from the unknown source are received by a directional device and
Further provided with a direction acquisition unit that acquires the direction of the device having the directivity when a wave corresponding to the received power is received.
The position estimation device according to any one of claims 1 to 5, wherein the estimation unit uses a propagation loss according to an angle between the direction of the estimated position and the direction of the device having the directivity. The position estimation device according to any one of claims 1 to 6, wherein the estimation unit optimizes the objective function by sequential arithmetic processing. The position estimation device according to claim 7, wherein the estimation unit optimizes the objective function by the sequential arithmetic processing using a plurality of initial values. In the sequential arithmetic processing, the estimation unit changes the step size to a larger value when the objective function has converged to the local optimum value, and when the objective function has converged to the global optimum value. 7. The position estimation device according to claim 7 or 8, wherein the step size is changed to a smaller value. The unknown wave source is a radio wave transmission source.
The position estimation device according to any one of claims 1 to 9, wherein the radio wave is received by an antenna. The unknown wave source is a source of sound waves and
The position estimation device according to any one of claims 1 to 9, wherein the sound wave is received by a microphone or a hydrophone. Steps to get the received power of a wave from an unknown wave source,
The step of acquiring the reception position when a wave corresponding to the received power is received, and
Using a plurality of sets of received power and receiving position, the estimated position of the unknown wave source, the estimated transmission power of the wave from the unknown wave source, and the wave propagation loss, the estimated received power and the received power for each receiving position A position estimation method comprising a step of estimating an estimated position and an estimated transmission power by optimizing an objective function according to the difference between the two.

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