JP7610243B2 - Position estimation device and position estimation method - Google Patents

Description

The present invention relates to a position estimation device that estimates the position of an unknown wave source using the direction of arrival of radio waves.

With the widespread use of ICT (Information and Communication Technology) devices that perform wireless communications, various radio waves are flying around in the air. Some of these devices transmit without a license or proper certification. These radio waves can interfere with other devices, causing communication problems.

In order to understand such situations and take measures, it is necessary to identify the location of the signal source emitting radio waves. The following methods are mainly known as the methods for doing so:
- A method of measuring the RSSI (Received Signal Strength Indication) of radio waves emitted from a signal source at multiple points and estimating the location of the signal source from the results using a triangulation method. - A method of receiving a signal transmitted from a signal source simultaneously at multiple points and estimating the location of the signal source from the difference in the delivery time (TDoA: Time Difference of Arrival).
A method in which a signal transmitted from a signal source is received simultaneously at multiple points and the direction of arrival of the signal is estimated from the phase difference (DoA: Direction of Arrival)

When estimating the position of a signal source using TDoA or DoA, it is necessary to perform measurements at multiple locations simultaneously. Radio waves propagate at an extremely fast speed of 3 x 10 ⁸ (m/s). Therefore, in order to measure the propagation time difference or phase difference at multiple locations simultaneously, a receiving mechanism with extremely high time resolution is required. In such cases, it is difficult to achieve "simultaneity" at multiple distant locations. In the case of nearby locations where it is easy to achieve simultaneous measurement, the propagation time difference and phase difference become small, resulting in a problem of reduced estimation accuracy.

Although the method using RSSI still requires measurements at multiple locations, it is not necessary to receive signals at those locations simultaneously, so location estimation can be performed by moving a single receiver and recording the RSSI. Another advantage of the method using RSSI is that it is only necessary to measure the strength of the received signal, and it can be implemented with simple circuitry.

In addition, a method for estimating position using radio waves is known, for example, as described in Patent Document 1.

Patent No. 6030976

In the invention of Patent Document 1, multiple base stations measure the RSSI from the terminal to estimate the location. However, since the base station's location is assumed to be unknown, a process is performed in which the base station's location is also estimated from the mutual received power between base stations in order to determine it. If the base station's location shifts during this process, the terminal's location cannot be accurately determined. This method also requires multiple base stations.

Although the method of estimating the position of a signal source using RSSI has advantages as described above, there is a problem in that if an approximation is made to the propagation loss of radio waves from the position of the wave source to the receiving position, an estimation error occurs according to the approximation. Furthermore, if the output of the signal source changes during the measurement, there is also a problem in that an estimation error occurs according to the change.

The present invention has been made to solve the above problems, and its purpose is to provide a position estimation device and a position estimation method that can estimate the position of an unknown wave source with higher accuracy without using TDoA or DoA.

In order to achieve the above object, a position estimation device according to one embodiment of the present invention includes an arrival direction acquisition unit that acquires the arrival direction of radio waves from an unknown wave source, a reception position acquisition unit that acquires the reception position when the radio waves whose arrival direction is acquired are received, and an estimation unit that estimates an estimated position by optimizing an objective function according to the difference between the estimated arrival direction and the arrival direction for each reception position using multiple pairs of arrival directions and reception positions and the estimated position of the unknown wave source.
With this configuration, it is possible to estimate the position of an unknown wave source using the direction of arrival of radio waves without using TDoA or DoA. In this way, since TDoA and the like are not used, it is possible to estimate the position of the wave source with a simple configuration. In addition, since there is no need to approximate the propagation loss of radio waves, it is possible to estimate the position with higher accuracy. In addition, even if the output of the signal source changes during the measurement, it is possible to perform more appropriate position estimation. Furthermore, since 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 pairs of the direction of arrival and the receiving position.

In addition, in a position estimation device according to one aspect of the present invention, there are one or more unknown wave sources, and the estimation unit may also estimate the number of estimated wave sources so that an optimal value per wave source, which is the value of the optimized objective function, is divided by the number of estimated wave sources, is optimized.
With this configuration, it is also possible to estimate the number of wave sources.

In addition, in a position estimation device according to one aspect of the present invention, the estimation unit may optimize an objective function in which a weight is applied to the difference between the estimated arrival direction and the arrival direction according to spatial information regarding the space between the estimated position and the receiving position used in calculating the estimated arrival direction.
With this configuration, it is possible to achieve more accurate estimation.

In addition, in a position estimation device according to one aspect of the present invention, the arrival direction acquisition unit may also acquire the received power of the radio waves from which the arrival direction is acquired, and the estimation unit may optimize an objective function in which a weight is applied to the difference between the estimated arrival direction and the arrival direction according to the received power of the radio waves from which the arrival direction is acquired.
With this configuration, it is possible to achieve more accurate estimation.

In addition, in a position estimation device according to one aspect of the present invention, the arrival direction acquisition unit also acquires the received power of the radio waves from which the arrival direction is acquired, and the estimation unit may estimate the estimated position and estimated transmission power by optimizing an objective function according to the difference between the estimated arrival direction and the arrival direction for each receiving position and the difference between the estimated received power and the received power for each receiving position, using a pair of the arrival direction, receiving position, and received power, the estimated position of the unknown wave source, the estimated transmission power of the radio waves from the unknown wave source, and the propagation loss of the radio waves.
With this configuration, the position of the wave source is estimated using the received power in addition to the direction of arrival, so that it is possible to realize more accurate estimation. Also, the transmission power of the wave source can be estimated.

In the position estimation device according to an aspect of the present invention, the estimation unit may optimize the objective function by sequential calculation processing.
With this configuration, it becomes possible to optimize the objective function by sequential calculations such as the Newton method.

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

In addition, in a position estimation device according to one aspect of the present invention, the estimation unit may change the step size to a larger value when the objective function converges to a local optimum value in the sequential calculation process, and may change the step size to a smaller value when the objective function converges to a global optimum value.
With this configuration, it is possible to prevent the optimum solution from corresponding to a local optimum value, and it is possible to realize more accurate estimation.

In addition, a position estimation method according to one aspect of the present invention includes a step of acquiring the direction of arrival of radio waves from an unknown wave source, a step of acquiring a receiving position when the radio waves whose direction of arrival is acquired are received, and a step of estimating an estimated position by optimizing an objective function according to the difference between the estimated direction of arrival and the direction of arrival for each receiving position, using multiple pairs of the direction of arrival and the receiving position and the estimated position of the unknown wave source.

According to one aspect of the present invention, a location estimation device can estimate the location of an unknown wave source using the direction of arrival, which is information about radio waves, without using TDoA or DoA.

FIG. 1 is 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 embodiment.

The following describes a position estimation device and a position estimation method according to the present invention using an embodiment. The position estimation device and the position estimation method according to the present embodiment estimate the position of an unknown wave source by optimization using the direction of arrival of radio waves.

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

The arrival direction acquisition unit 11 acquires the arrival direction of radio waves from the unknown wave source 5. The number of unknown wave sources 5 may be one or more. In this 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 arrival direction acquisition unit 11 may receive radio waves from the unknown wave source 5 and acquire the arrival direction of the radio waves, or may receive from another device the arrival direction of radio waves received by another device. In this embodiment, as described above, the former case will be mainly described. That is, in this embodiment, the arrival direction acquisition unit 11 receives radio waves with the antenna 11a and acquires the arrival direction of the radio waves.

It is preferable that antenna 11a be a directional antenna. The directional antenna may be one that has directionality due to the antenna structure, such as a Yagi antenna or a parabolic antenna, or may be an antenna that has directionality by multiplying the received signals of multiple antennas by weights based on the amplitude and phase, such as an array antenna. In order to properly estimate the direction of arrival of radio waves, it is preferable that antenna 11a has a sharp directivity.

The arrival direction acquisition unit 11 may rotate the directional antenna 11a such as a Yagi antenna, and may set the direction of the main lobe of the antenna 11a at the time when the received signal strength (RSSI) of the radio wave from the unknown wave source 5 becomes maximum as the arrival direction of the radio wave. In this case, the arrival direction acquisition unit 11 may have a rotation mechanism for rotating the antenna 11a. The arrival direction acquisition unit 11 may also acquire the arrival direction of the radio wave for the antenna 11a by using the phase of the radio wave received by each antenna of the antenna 11a, which is an array antenna, for example. The arrival direction of the radio wave acquired by the arrival direction acquisition unit 11 may be the arrival direction of the radio wave based on a reference direction. The reference direction may be a predetermined direction in the world coordinate system, such as the north direction or the east direction. The arrival direction acquisition unit 11 may have, for example, a geomagnetic sensor for identifying the reference direction. Then, when the direction of arrival of the radio waves relative to the antenna 11a is acquired, the direction of arrival acquisition unit 11 may acquire the absolute direction of arrival of the radio waves relative to the reference direction by using the relationship between the reference direction and the direction of the antenna 11a.

The receiving position acquisition unit 12 acquires the receiving position when the radio waves from which the direction of arrival is acquired are received. That is, the position of the antenna or the like when the radio waves from the unknown wave source 5 are received by the antenna or the like is acquired. The receiving position acquisition unit 12 may acquire the receiving position, which is the position of the position estimation device 1 at the time when the direction of arrival acquisition unit 11 received the radio waves to acquire the direction of arrival, or may receive from another device the receiving position, which is the position of that device at the time when the radio waves were received by that device. In this 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 receiving position acquisition unit 12 may acquire the position using, for example, the Global Positioning System (GPS), or may also acquire the position using the Quasi-Zenith Satellite System. If the position estimation device 1 is mounted on a vehicle, for example, the receiving position may be acquired using an autonomous navigation device such as a gyro. If an image of a code or the like (e.g., a QR code (registered trademark), etc.) corresponding to the position information indicating the position is placed at the position indicated by the position information, for example, the image of the code or the like may be photographed and the position information may be read to acquire the position, or the position may be acquired by other methods. The receiving position acquisition unit 12 may accept, for example, a receiving position measured manually using a tape measure or the like, via an input means such as a keyboard or a touch panel. In this embodiment, the receiving position acquisition unit 12 mainly describes a case in which the receiving position acquisition unit 12 receives radio waves from a GPS satellite via the antenna 12a and acquires the position using the received radio waves. The position acquired by the receiving position acquisition unit 12 may be, for example, coordinates indicating latitude and longitude, or other coordinates.

It is preferable that the direction of arrival acquired by the direction of arrival acquisition unit 11 and the receiving position acquired by the receiving position acquisition unit 12 for the radio waves acquired in that direction of arrival are linked and managed. In this embodiment, the linked direction of arrival and receiving position are referred to as a pair of direction of arrival and receiving position. The direction of arrival is acquired by the direction of arrival acquisition unit 11, and the receiving position corresponding to the acquired direction of arrival is acquired by the receiving position acquisition unit 12, thereby acquiring multiple pairs of direction of arrival and receiving position. For example, if the position estimation device 1 is mobile, multiple pairs of direction of arrival and receiving position may be acquired by receiving radio waves from an unknown wave source 5 at multiple positions.

The estimation unit 13 estimates the estimated position by optimizing an objective function according to the difference between the estimated direction of arrival and the direction of arrival for each receiving position, using multiple pairs of the direction of arrival and the receiving position, and the estimated position of the unknown wave source 5. That is, using multiple pairs of the direction of arrival and the receiving position, which are the measurement results, an optimal solution (i.e., the position of the unknown wave source 5) that optimizes the objective function (error function) according to the error between the estimated value of the direction of arrival for each receiving position and the actual measured value of the direction of arrival is found so that the error is optimized (i.e., the error is reduced). The estimation unit 13 can estimate the direction of the unknown wave source 5 based on the receiving position, i.e., the estimated direction of arrival, using the receiving position and the estimated position.

The objective function may be a function whose value increases as the error between the estimated value of the direction of arrival for each receiving position and the actual measured value of the direction of arrival increases, or may be a function whose value decreases as the error increases. In the former case, optimization involves minimizing the objective function, and in the latter case, optimization involves maximizing the objective function. In this embodiment, the former case will be mainly described. Also, various functions can be used as a function whose value decreases as the error between the estimated value of the direction of arrival for each receiving position and the actual measured value of the direction of arrival increases.

Hereinafter, a process of obtaining an estimated position of the unknown wave source 5 by optimizing the objective function will be specifically described. First, the estimated position of the unknown wave source 5 is (x ^e , y ^e ). The reception position and the arrival direction acquired at the i-th position are (x _i , y _i ) and θ _i , respectively. Therefore, the i-th pair of the arrival direction and the reception position acquired by the arrival direction acquisition unit 11 and the reception position acquisition unit 12 is, for example, (x _i , y _i , θ _i ). Note that i=1, 2, ..., N. It is preferable that N is an integer that exceeds the unknown number of the estimation target. For example, when there is one wave source 5, the unknown number is 2, so that N is preferably 3 or more. This is because, although an estimated position can be obtained when N is the same as the unknown number, the estimation is performed with substantially the same accuracy as triangulation, making it difficult to reduce the influence of multipath. Furthermore, since the larger N is, the better the effect of multipath can be reduced, when there is one wave source 5, it is more preferable that N be a value sufficiently larger than 3, such as 10 or more, 20 or more.

For a wave from an unknown wave source 5, the estimated arrival direction θ i e at the receiving position ( ^xi , ^yi ) calculated using the estimated position ( _xe , _ye ) and the receiving position ( _xi , _yi ) is given by the following equation: In this case, ^the estimated arrival direction _{θ i e} ^is an angle with the x-axis direction as the reference direction.

As described above, when the arrival direction and reception position are acquired at N locations, the objective function (evaluation function) f according to the difference between the estimated arrival direction and the arrival direction for each reception position is, for example, as follows:

Note that, although the objective function is shown here as the sum of the squares of the difference between the estimated direction of arrival and the direction of arrival, it goes without saying that the objective function may be, for example, the sum of the absolute value of the difference between the estimated direction of arrival and the direction of arrival for each receiving position, or the sum of the fourth or sixth power of the difference between the estimated direction of arrival and the direction of arrival for each receiving position. Furthermore, in the sum (total sum), the difference between the estimated direction of arrival and the direction of arrival may be weighted, as in the formula for the objective function f above.

Weighting the difference between the estimated arrival direction and the arrival direction may mean multiplying a value corresponding to the difference between the estimated arrival direction and the arrival direction, such as the square of the difference, the absolute value of the difference, the fourth power of the difference, or the sixth power of the difference. The weight w _i is a weight related to the measurement result at the i-th receiving position, and is usually a positive real number. For example, the difference between the estimated arrival direction θ _i ^e corresponding to the i-th receiving position ^and the arrival direction _{θ i may} be weighted by a weight w _i corresponding to the space information related to the space between the estimated position (x ^e , y ^e ) and the receiving position (x _i , y _i ) used in calculating the estimated arrival direction θ i e. Specifically, the weight w _i corresponding to the space information indicating visibility is set to a large value, such as "1", and the weight w _i corresponding to the space information indicating the presence of an obstacle, such as an urban area or a mountainous area, may be set to a value smaller than the weight corresponding to the space information of visibility, such as "0.3" or "0.5". The weight may also be changed depending on the level of the obstacle. In this case, the more obstacles indicated by the spatial information, the smaller the weight may be used. For example, the weight according to the spatial information indicating the presence of a small number of high-rise buildings may be set to a larger value such as "0.5", and the weight according to the spatial information indicating the presence of a large number of high-rise buildings may be set to a smaller value such as "0.2". In this way, the weight w _i may be set to a smaller value when the spatial information indicates that there is a large number of multipaths, and may be set to a larger value when the spatial information indicates that there is a small number of multipaths. The estimation unit 13 may acquire the spatial information, for example, by using map information. A method for acquiring the spatial information will be described later. The weight w _i may also be changed according to, for example, the magnitude or accuracy of the received signal. In that case, for example, the closer to ideal reception, the larger the weight may be used. The estimation unit 13 may also optimize an objective function in which a weight according to the received power of the radio wave acquired in the arrival direction is applied to the difference between the estimated arrival direction and the arrival direction. In this case, the larger the received power, the larger the weight may be used. This is because it is considered that the higher the received power is, the more appropriately the radio waves are received, and therefore it is preferable to increase the weighting for the direction of arrival. The weighting w _i may be a constant. In this way, the objective function may not use a weighting for each receiving position. In this case, the above w _i may be, for example, 1 or 1/N.

The x ^e , y ^e that minimize the above objective function f is the position of the wave source 5 to be estimated. The solution that minimizes the objective function f, i.e., the optimal solution, corresponds to a local minimum, and therefore the partial differentials of each variable of the objective function f are 0. Therefore, finding an estimated position is equivalent to finding (x ^e , y ^e ) for which the following equation holds:

As a method for calculating such (x ^e , y ^e ), that is, a method for optimizing the objective function, various algorithms can be considered, and examples thereof include the Newton method and the steepest descent method, but are not limited thereto. For example, optimization may be performed using a parameter estimation method such as a Kalman filter. For example, when performing sequential calculations using the steepest descent method, the objective function f can be optimized by setting (x ₀ ^e , y ₀ ^e ) as an initial value, setting an appropriate step size α _k that is a positive real number, and repeating the sequential calculation of the following formula. Note that k=0, 1, 2, .... In addition, ∇f(x ^e , y ^e ) required for the sequential calculation may be calculated in advance, and the calculation result may be used for the sequential calculation. In addition, the step size α _k may be set to a large value at first, and then to a small value depending on the convergence situation, thereby reducing the number of calculations. Note that a constant may be used as the step size.

Here, ∇f( ^xek , ^yek ) is _expressed by the _following equation from the above equations.

In this way, the estimation unit 13 may optimize the objective function f by sequential calculation processing. In this case, the optimization processing may be terminated when a predetermined termination condition is satisfied. The termination condition may be, for example, that a convergence condition is satisfied, that k exceeds a predetermined maximum number of sequential calculations, or other conditions. The estimation unit 13 may determine that the convergence condition is satisfied when, for example, the absolute value |f(x _k+1 ^e , y _k+1 ^e )−f(x _k ^e , y _k ^e )| of the change in the value of the objective function f when k is incremented by 1 becomes smaller than a predetermined threshold value. The threshold value is a positive real number and is usually set to a small value. The estimation unit 13 may also determine that the convergence condition is satisfied when, for example, the value of the objective function f becomes smaller than a predetermined value. The predetermined value is a positive real number and is usually set to a small value.

Note that, in order to prevent the optimization of the objective function f from becoming a local optimum, the estimation unit 13 may optimize the objective function f by, for example, sequential calculation processing using multiple initial values. For example, the estimation unit 13 may set multiple initial values and perform optimization using each initial value, thereby obtaining an optimal solution for each initial value and an optimal value obtained by substituting the optimal solution into the objective function. Thereafter, the estimation unit 13 may set the optimal solution corresponding to the most appropriate optimal value among the multiple optimal values as the final estimated position. The optimal solution is a solution (here, the estimated position) obtained by optimizing the objective function. In addition, the most appropriate optimal value means that the optimal value is the smallest when the optimization is minimization, and that the optimal value is the largest when the optimization is maximization. Note that, strictly speaking, the initial value is the initial value of the estimated position. The initial value of the estimated position may be randomly specified, for example, in an area including N receiving positions (for example, it may be the smallest area including N receiving positions).

In addition, in order to prevent the optimization of the objective function f from becoming a local optimum, for example, in sequential calculation processing, the estimation unit 13 may change the step size α _k to a larger value when the objective function f converges to a local optimum value, and may change the step size α _k to a smaller value when the objective function f converges to a global optimum value. Whether the objective function f converges to a local optimum value or a global optimum value may be determined, for example, based on whether the value of the objective function f is close to an ideal optimum value. When the value of the objective function f is close to the ideal optimum value, it may be determined that the objective function f has converged to a global optimum value, and when the value of the objective function f is far from the ideal optimum value, it may be determined that the objective function f has converged to a local optimum value. More specifically, when the optimization is minimization, for example, when the value of the objective function f converges to a value larger than a first threshold value, it may be determined that the objective function f has converged to a local optimum value, and when the value of the objective function f converges to a value smaller than a first threshold value, it may be determined that the objective function f has converged to a global optimum value. In the case where the optimization is maximization, for example, it may be determined that the objective function f has converged to a local optimum when the value of the objective function f has converged to a value smaller than the second threshold, and that the objective function f has converged to a global optimum when the value of the objective function f has converged to a value larger than the second threshold. The first and second thresholds may be the same value or may be different. Both thresholds are usually positive real numbers. The step size α _k used when the objective function f has converged to a local optimum and the step size α _k used when the objective function f has converged to a global optimum may or may not be determined in advance. In the latter case, for example, when the objective function f has converged to a local optimum, a step size α _k that gradually increases with each update of k may be used, and when the objective function f has converged to a global optimum, a step size α _k that gradually decreases with each update of k may be used. Even in this case, an upper limit value and a lower limit value of the step size may be set.

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

Next, the operation of the position estimation device 1 will be described with reference to the flowchart in FIG. 2. Here, we will explain the case where the objective function f is optimized by sequential calculations.

(Step S101) The arrival direction acquisition unit 11 and the reception position acquisition unit 12 acquire multiple pairs of arrival directions and reception positions of radio waves from an unknown wave source 5. The multiple pairs may be stored, for example, in a recording medium (not shown).

(Step S102) The estimation unit 13 sets an initial value for the estimated position. This initial value may be set by, for example, reading out a predetermined value.

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

(Step S104) The estimation unit 13 calculates a provisional estimated position. This provisional estimated value may be calculated, for example, by updating the estimated position to approach the optimal solution, as shown in the above formula.

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

(Step S106) The estimation unit 13 determines whether the convergence condition is satisfied. If the convergence condition is satisfied, the process of estimating the estimated position ends. 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 the counter k has exceeded the maximum number of sequential calculations. If k has exceeded the maximum number of sequential calculations, the process of estimating the estimated position ends. If not, the process returns to step S104.

When the series of processes for estimating the estimated position has been completed, the last estimated position calculated in step S104 becomes the final estimation result.

In the flowchart of FIG. 2, sequential calculations using multiple 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 optimal solution corresponding to the optimal value may be set as the estimated position of the wave source 5. In addition, the flowchart of FIG. 2 shows a case in which the arrival direction and reception position are first acquired, and then the position of the wave source 5 is estimated by optimizing the objective function, but this is not necessary. For example, when the arrival direction and reception position acquisition at a predetermined number of points is completed, the estimated position may be estimated, and the estimation process may be repeated each time the number of arrival directions and reception positions acquired increases. Then, when an estimated position with sufficient accuracy is acquired, the acquisition of the arrival direction, etc. and the process of estimating the estimated position may be terminated. In addition, the order of the processes in the flowchart of FIG. 2 is one 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 of this embodiment, the position of the unknown wave source 5 can be estimated without using TDoA or DoA. In addition, since there is no need to approximate the propagation loss of the radio wave, more accurate position estimation is possible compared to the case where the approximation is inappropriate. In addition, even if the output of the signal source changes during the measurement, the position of the wave source 5 can be estimated more appropriately. In this way, since TDoA and the like are 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, by using a sufficient number of pairs of the arrival direction and the reception position, it is possible to perform position estimation with reduced influence of errors due to multipath, etc. In addition, when the position estimation device 1 is moved to multiple positions, receives radio waves from the unknown wave source 5, and obtains multiple pairs of the arrival direction and the reception position, it becomes possible to estimate the position of the wave source 5 without using multiple receiving devices. In addition, even if there is an unreliable value, it is possible to reduce the influence by adjusting the weight w _i . As a result, the estimation accuracy can be improved.

Next, a modification of the position estimation device 1 according to the present embodiment will be described.
[Estimation of the positions of multiple wave sources and 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 this is not essential. The number of wave sources 5 may be multiple or may be indefinite. When the number of wave sources 5 is indefinite, the number of wave sources 5 may also be estimated.

When the number of unknown wave sources 5 is two, the estimated positions of the wave sources 5 can be (x ^(1)e , y ^(1)e ), (x ^(2)e , y ^(2)e ). The objective function is expressed by the following equation. In this case, the i-th pair of the arrival direction and reception position acquired by the arrival direction acquisition unit 11 and the reception position acquisition unit 12 is, for example, (x(1 _)e , _y ⁽¹⁾ _e , θ ⁽²⁾ _i ). The two arrival directions θ ⁽¹⁾ _i , θ ⁽²⁾ _i may be, for example, the direction with the strongest and second strongest received signal strengths for radio waves from the unknown wave source 5. The estimated arrival direction θ ⁽¹⁾ _i of the first wave source 5 is calculated using the estimated position (x ^(1)e , y ^(1)e ) of the first wave source 5. The same applies to the estimated arrival direction of the second wave source 5. In addition, when two wave sources 5 can be distinguished (for example, when two wave sources 5 can be distinguished by characteristics of radio waves such as frequency), the objective function may be the sum of two objective functions of one wave source 5. In this case, the weight may be different for each wave source 5. Furthermore, when two wave sources 5 can be distinguished, the position may be estimated for each wave source 5.

Even when the number of unknown wave sources 5 is two, it is possible to perform sequential calculations using the steepest descent method as shown in the following equation, for example.

When the number of wave sources 5 is two, ∇f(x ⁽¹⁾ _ek , y ⁽¹⁾ _ek , x ⁽²⁾ _ek , y ⁽²⁾ _ek ) is expressed by the following equation.

In this way, even when there are two wave sources 5, the position of each of the wave sources 5 can be estimated by optimizing the objective function in the same way as for a single wave source 5. Also, when there are three or more unknown wave sources 5, the position of each of the wave sources 5 can be estimated by similarly extending the formula.

Next, when the number of wave sources 5 is indefinite, the estimation unit 13 may estimate the position of each wave source 5 by optimization for each estimated number of wave sources from the minimum number of wave sources to the maximum number of wave sources. The estimation unit 13 may also estimate the estimated number of wave sources so that an optimal value per wave source obtained by dividing the optimal value, which is the value of the optimized objective function, by the estimated number of wave sources is optimized. In other words, the number of wave sources may be estimated so that the objective function for estimating the number of wave sources is set as the optimal value per wave source and the objective function is optimized. Note that, 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.

Note that estimating the estimated number of wave sources so that the optimal value per wave source is optimized may mean, for example, finding the estimated number of wave sources that results in the smallest optimal value per wave source when the optimization of the objective function f is minimization, or finding the estimated number of wave sources that results in the largest optimal value per wave source when the optimization of the objective function f is maximization.

In this way, even if the number of wave sources 5 is unknown, it is possible to estimate the number of wave sources 5. Note that, although a case has been described here in which processing is performed until the number of wave sources 5 reaches the maximum number of wave sources, this is not essential. A convergence condition may be set for optimizing the optimal value per wave source, and processing may be terminated when the convergence condition is satisfied. For example, it may be determined that the convergence condition is satisfied when the optimal value per wave source becomes more appropriate than a predetermined threshold value (for example, when the optimal value becomes smaller than the threshold value if the optimization is minimization, or when the optimal value becomes larger than the threshold value if the optimization is maximization).

[Optimization of objective function using received power]
The estimation unit 13 may estimate the estimated position and the estimated transmission power by optimizing an objective function according to the difference between the estimated direction of arrival and the direction of arrival for each receiving position and the difference between the estimated received power and the received power for each receiving position, using a pair of the direction of arrival, the receiving position, and the received power, the estimated position of the unknown wave source 5, the estimated transmission power of the radio waves from the unknown wave source 5, and the propagation loss of the radio waves.

The received power may be, for example, received signal strength indicator (RSSI). In this case, the arrival direction acquisition unit 11 may also acquire the received power of the radio waves from which the arrival direction is acquired. The arrival direction acquisition unit 11 may acquire the received signal strength of the radio waves, for example, by a spectrum analyzer, or may acquire the received signal strength of the radio waves by other configurations.

The propagation loss of the radio waves may be, for example, a propagation loss according to a model corresponding to the propagation path from the estimated position to the receiving position (e.g., a free space model or a model that takes into account the effects of multipath). For simplicity of explanation, the following mainly describes the case where the propagation loss of the free space model is used. The propagation loss may be considered to be a function that takes the transmission power and distance as arguments.

The estimation unit 13 may optimize the objective function using a propagation loss according to spatial information regarding the space between the estimated position and the receiving 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, line of sight, urban area, mountain area, etc. The estimation unit 13 may, for example, use map information to identify the receiving position and the estimated position at that time, and if there is an urban area or a mountain between the two positions, determine that the spatial information between the two positions is an urban area or a mountain area, and if there is no obstacle such as an urban area or a mountain between the two positions, determine that the spatial information between the two positions is line of sight. If the spatial information is line of sight, for example, a propagation loss corresponding to a free space model may be used, and if the spatial information indicates that there is an obstacle such as an urban area or a mountain area, for example, a propagation loss corresponding to a model that takes into account the effect of multipath may be used. Note that the spatial information may be obtained by the estimation unit 13 accessing map information stored in the position estimation device 1, or by accessing a server or the like that stores the map information.

First, the estimated position of the unknown wave source 5 is (x ^e , y ^e ), and the estimated transmission power of the wave from the unknown wave source 5 is p ^e . In addition, the received power acquired at the i-th position is r _i . Therefore, the i-th set of the arrival direction, received power, and receiving position acquired by the arrival direction acquisition unit 11 and the receiving position acquisition unit 12 is, for example, (x _i , y _i , θ _i , r _i ).

For radio waves from an unknown wave source 5, the estimated received power r i e at the receiving position (x i , y ⁱ _{) calculated using the estimated transmission power p e , propagation loss, estimated position (x e , y e ), and receiving position (x i ,} ^{y i} ₎ ^is _{given by} the following equation: G _r is the gain of the antenna 11 a and is a known value.

In the above equation, d _i is the distance from the estimated position (x ^e , y ^e ) of the unknown wave source 5 to the receiving position (x _i , y _i ), as given by the following equation:

Also, λ is the wavelength of the received wave, and may be acquired by the direction of arrival acquisition unit 11, for example, when the direction of arrival acquisition unit 11 acquires the received power by a spectrum analyzer. Also, the received wave may be Fourier transformed to acquire the wavelength λ of the peak in the frequency band. Note that the wave source 5 is unintentional and therefore omnidirectional. Therefore, a value equivalent to the antenna gain is included in the estimated transmission power p ^e as the effective radiated power.

In addition, the above formula shows the estimated received power using the formula for the propagation loss of radio waves in free space, but as described above, other formulas for propagation loss may be used depending on the spatial information from the position of the wave source 5 to the receiving position. For example, when the spatial information from the estimated position of the wave source 5 to the receiving position indicates the presence of obstacles such as mountainous areas or urban areas, the estimated received power r _i ^e may be calculated as in the following formula using a propagation loss that takes into account the effects of multipath. Also, d _i ^m, such as d _i ^3/2 , may be used instead of d _i ² in the following formula, where m is a real number from 1 to 2.

As described above, when the arrival direction, reception power, and reception position are acquired at N points, the objective function (evaluation function) f according to the difference between the estimated arrival direction and the arrival direction for each reception position and the difference between the estimated reception power and the reception power for each reception position is, for example, as follows. Note that β is an arbitrary real number from 0 to 1, and is a weight for the function according to the difference between the estimated arrival direction and the arrival direction for each reception position and the function according to the difference between the estimated reception power and the reception power for each reception position. For example, if the function according to the difference between the estimated arrival direction and the arrival direction for each reception position is more accurate, a value close to 1 may be used as β. If the accuracy of both functions is about the same, 0.5 may be used as β. In addition, here, the weight w _i used in both functions is the same, but it goes without saying that different weights may be used in both functions.

In this case as well, x ^e , y ^e , and p ^e that minimize the above objective function f become the position and transmission power of the wave source 5 to be estimated. The solution that minimizes the objective function f, i.e., the optimal solution, corresponds to a local minimum point, and therefore the partial differentials of each variable of the objective function f become 0. Therefore, finding the estimated position and estimated transmission power is equivalent to finding (x ^e , y ^e , p ^e ) for which the following equation holds:

The method for estimating the estimated position and estimated transmission power to optimize the objective function is the same as described above, and detailed description thereof will be omitted.

[3D Position Estimation]
In the above description, the case where the position of the unknown wave source 5 is estimated on a two-dimensional plane has been described, but the position of the unknown wave source 5 can also be estimated in a three-dimensional space in a similar manner. When estimating the position of the wave source 5 in a three-dimensional space, the arrival direction of the radio wave may be acquired by measuring the azimuth angle θ _i and the elevation angle φ _i of the radio wave. In addition, the objective function according to the difference between the estimated arrival direction and the arrival direction for each receiving position may be, for example, an objective function according to the difference between the estimated azimuth angle and the measured azimuth angle for each receiving position, and the difference between the estimated elevation angle and the measured elevation angle. In addition, it is clear that the two-dimensional position in the above description can be easily extended to a three-dimensional position even when the objective function includes a function according to the difference between the estimated reception power and the reception power for each receiving position.

In addition, in the above embodiments, each process or function may be realized by centralized processing in a single device or a single system, or may be realized by distributed processing in multiple devices or multiple systems.

In addition, in the above embodiment, the transfer of information between components may be performed, for example, by one component outputting information and the other component receiving information if the two components transferring the information are physically different, or, if the two components transferring the information are physically the same, by shifting from a processing phase corresponding to one component to a processing phase corresponding to the other component.

In addition, in the above embodiment, information related to the processing performed by each component, such as information accepted, acquired, selected, generated, transmitted, or received by each component, and information such as thresholds, formulas, and addresses used by each component in processing, may be temporarily or long-term stored in a recording medium (not shown) even if not specified in the above description. Furthermore, each component or a storage unit (not shown) may store information in the recording medium (not shown). Furthermore, each component or a reading unit (not shown) may read information from the recording medium (not shown).

In the above embodiment, if the information used by each component, such as the thresholds, addresses, and various setting values used by each component in processing, may be changed by the user, the user may or may not be able to change the information as appropriate, even if not specified in the above description. If the information is changeable by the user, the change may be realized, for example, by 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. The reception unit (not shown) may receive the change instruction from an input device, may receive information transmitted via a communication line, or may receive information read from a specified recording medium.

In addition, in the above embodiment, when two or more components included in the position estimation device 1 have a communication device, an input device, etc., the two or more components may have a single physical device, or may have separate devices.

In each of the above embodiments, each component may be configured with dedicated hardware, or a component that can be realized by software may be realized by executing a program. For example, each component may 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 semiconductor memory. During execution, the program execution unit may execute the program while accessing the storage unit or recording medium. 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 (e.g., an optical disk, a magnetic disk, a semiconductor memory, etc.). The program may be used as a program that constitutes a program product. The computer that executes the program may be a single computer or multiple computers. In other words, centralized processing or distributed processing may be performed.

As described above, the position estimation device according to one aspect of the present invention has the effect of being able to estimate the position of an unknown wave source, and is useful, for example, as a device for identifying the source of illegal radio waves.

REFERENCE SIGNS LIST 1 Position estimation device 5 Wave source 11 Arrival direction acquisition unit 12 Reception position acquisition unit 13 Estimation unit

Claims (8)

an arrival direction acquisition unit that acquires arrival directions of radio waves from a plurality of unknown wave sources;
a reception position acquisition unit that acquires a reception position when the radio wave whose arrival direction is acquired is received;
and an estimation unit that estimates a plurality of estimated positions by optimizing an objective function having as an argument a sum of differences between the estimated directions of arrival and directions of arrival for the plurality of wave sources for each receiving position, using a plurality of pairs of directions of arrival and receiving positions and the estimated positions of the unknown wave sources. The position estimation device according to claim 1 , wherein the estimation unit optimizes an objective function in which the sum is weighted according to spatial information relating to a space between the estimated position used in calculating the estimated direction of arrival and the receiving position. The arrival direction acquisition unit also acquires a received power of a radio wave for acquiring the arrival direction,
3. The position estimation device according to claim 1, wherein the estimation unit optimizes an objective function in which the sum is weighted according to a received power of the radio wave acquired in the arrival direction. The arrival direction acquisition unit also acquires a received power of a radio wave for acquiring the arrival direction,
3. The position estimation device according to claim 1, wherein the estimation unit estimates the estimated position and the estimated transmission power by optimizing an objective function according to the sum for each reception position and the difference between the estimated reception power and the received power for each reception position, using a set of the direction of arrival, the reception position, and the received power, the estimated position of the unknown wave source, the estimated transmission power of the radio waves from the unknown wave source, and a propagation loss of the radio waves. The position estimation device according to any one of claims 1 to 4, wherein the estimation unit optimizes the objective function by sequential calculation processing. The position estimation device according to claim 5, wherein the estimation unit optimizes the objective function by the sequential calculation process using multiple initial values. The position estimation device according to claim 5 or 6, wherein the estimation unit changes the step size to a larger value when the objective function converges to a local optimum value in the sequential calculation process, and changes the step size to a smaller value when the objective function converges to a global optimum value. obtaining directions of arrival of radio waves from a plurality of unknown sources;
acquiring a reception position when the radio wave whose arrival direction is acquired is received;
and estimating a plurality of estimated positions by optimizing an objective function having an argument of a sum of differences between the estimated directions of arrival and directions of arrival for the plurality of wave sources for each receiving position, using a plurality of pairs of directions of arrival and receiving positions and the estimated positions of the unknown wave sources.

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