WO2020208987A1 - Position estimation device, position estimation method, and program - Google Patents

Abstract

[Problem] To provide a position estimation device that reduces the number of location fingerprints to be acquired in a training stage. [Solution] This position estimation device comprises a prediction model generation unit, error group calculation unit, error combination unit, pseudo measurement value correction unit, and position estimation unit. The prediction model generation unit generates a prediction model for predicting a transmission-position-dependent feature value that will be obtained from a reception signal. The error group calculation unit calculates an error group of measured feature values from reference transmission sources having known positions and predicted feature values calculated using the prediction model. The error combination unit combines the error group according to the positional relationship between a pseudo transmission source at a given position and the reference transmission sources and outputs a combined error. The pseudo measurement value correction unit uses the combined error to correct a predicted feature value predicted by the prediction model for signal reception from the pseudo transmission source. The position estimation unit inputs a measured transmission-position-dependent feature value into a learning model learned on the basis of predicted pseudo-transmission-source feature values that have been corrected and estimates a transmission source position.

Description

Position estimation device, position estimation method and program

The present invention relates to a position estimation device, a position estimation method and a program.

An example of an existing source position estimation system is described in Patent Document 1. As disclosed in Patent Document 1, the existing source position estimation system includes a receiving means, a signal processing means, a storage means, and a position estimating means.

The receiving means receives radio waves from the source. The receiving means are arranged at different positions from each other. The signal processing means acquires signals transmitted from each of the plurality of candidate positions and performs signal processing. The storage means holds a set of features obtained as a result of signal processing by the signal processing means. The position estimation means compares the set of features obtained by measuring the signal transmitted from the position to be estimated by the receiving means with the set of features held by the storage means to determine the position of the source. presume.

The existing source position estimation system having the above configuration operates in the following two steps.

The first step is the "training" step.

In the training stage, which is the first step, radio waves are transmitted from known positions that are candidates for source positions, and are received by receiving means arranged at different known positions. The signal processing means performs signal processing on the received signal to acquire the feature amount. A set of features equal to the number of receiving means is also called a position fingerprint with respect to its source position. The training data is acquired for a plurality of positions that are candidates for the source position and is stored in the storage means.

The second step is the "estimation" step.

In the estimation stage, which is the second step, a position fingerprint is acquired for a source whose position is unknown by the same procedure as in the training stage. Then, among the position fingerprints created in advance during training, the position corresponding to the position fingerprint closest to the position fingerprint to be estimated is treated as the estimated position of the source.

Patent Document 1 discloses that reception strength (RSS; Received Signal Strength) and channel impulse response (CIR; Channel Impulse Response) are used as feature quantities. In addition, the document also states that by interpolating the center frequency, bandwidth, and position of the transmitted signal with respect to the CIR data set, a signal different from the transmitted signal used during training is transmitted. A method for expanding the position fingerprint data so that it can be estimated is disclosed. As an algorithm for performing interpolation for a position, there are a method using kriging in addition to linear, solid, and spline interpolation.

Japanese Unexamined Patent Publication No. 2016-080589

An existing source position estimation system as disclosed in Patent Document 1 has a problem that it is necessary to acquire position fingerprints for a sufficient number of candidate positions at the training stage when interpolating positions. There is.

The reason is that if the number of candidate positions is not sufficient, it may not be possible to synthesize the position fingerprints corresponding to the sources located in between by simply superimposing the position fingerprints for each candidate position. For example, a position fingerprint that is acquired when radio waves are simultaneously transmitted from each candidate position may be synthesized.

However, acquiring a large number of position fingerprints causes an increase in cost.

A main object of the present invention is to provide a position estimation device, a position estimation method, and a program that contribute to reducing the number of position fingerprints acquired in the training stage.

According to the first viewpoint of the present invention, a prediction model generation that predicts a feature amount depending on a transmission position, which is obtained when a signal from a source at an arbitrary position is received at a specific position. A unit, a measured value of a feature amount acquired based on a signal from a reference source at a known position, and a predicted value of a feature amount related to the reference source at a known position calculated using the prediction model. The error group is calculated according to the positional relationship between the error group calculation unit, the pseudo source at an arbitrary position, and each of the reference sources, which calculates the error group by calculating the error for a plurality of reference source positions. Pseudo-measured value correction that uses the synthesis error to correct the predicted value of the feature amount by the prediction model when the signal from the pseudo source and the error synthesis unit, which synthesizes and outputs as a synthesis error, is received. The source position is estimated by inputting the measured value of the feature amount depending on the unit and the transmission position into the learning model learned based on at least the predicted value of the feature amount from the corrected pseudo source. A position estimation device including a position estimation unit is provided.

According to the second viewpoint of the present invention, in the position estimation device, a prediction model for predicting a feature amount depending on the transmission position obtained when a signal from a source at an arbitrary position is received at a specific position is generated. Steps to be performed, the measured value of the feature amount acquired based on the signal from the reference source at the known position, and the predicted value of the feature amount related to the reference source at the known position calculated using the prediction model. The error group is calculated by calculating the error of the above for a plurality of reference source positions, and the error group is synthesized according to the positional relationship between the pseudo source at an arbitrary position and each of the reference sources. A step of outputting as a synthesis error, a step of correcting the predicted value of the feature amount by the prediction model when a signal from the pseudo transmission source is received by using the synthesis error, and a feature amount depending on the transmission position. Provided is a position estimation method including a step of estimating the source position by inputting the measured value of the above into a learning model learned based on at least the predicted value of the feature amount from the corrected pseudo source. Will be done.

According to the third viewpoint of the present invention, the computer mounted on the position estimation device predicts the feature amount depending on the transmission position obtained when a signal from a source at an arbitrary position is received at a specific position. The process of generating the prediction model to be performed, the measured value of the feature amount acquired based on the signal from the reference source at the known position, and the feature amount related to the reference source at the known position calculated using the prediction model. The error group is calculated by calculating the error between the predicted value and the reference source positions for a plurality of reference source positions, and the error is calculated according to the positional relationship between the pseudo source at an arbitrary position and each of the reference sources. A process of synthesizing a group and outputting it as a synthesis error, a process of correcting a predicted value of a feature amount by the prediction model when a signal from the pseudo source is received by using the synthesis error, and a process of correcting the transmission position. By inputting the measured value of the feature amount depending on the above into the learning model learned based on at least the predicted value of the feature amount from the corrected pseudo source, the process of estimating the source position is executed. The program is provided.

According to each viewpoint of the present invention, a position estimation device, a position estimation method, and a program that contribute to reducing the number of position fingerprints acquired in the training stage are provided. According to the present invention, other effects may be produced in place of or in combination with the effect.

FIG. 1 is a diagram for explaining an outline of one embodiment. FIG. 2 is a diagram showing an example of a schematic configuration of a source position estimation system according to the first embodiment. FIG. 3 is a diagram for explaining the operation of the source position estimation system according to the first embodiment. FIG. 4 is a diagram showing an example of a processing configuration (processing module) of the position estimation device according to the first embodiment. FIG. 5 is a flowchart showing an example of the operation of the training stage of the source position estimation system according to the first embodiment. FIG. 6 is a diagram for explaining the concept of an RSS measurement value set. FIG. 7 is a flowchart showing an example of an operation of creating training data by a reference source. FIG. 8 is a diagram for explaining the operation of the propagation model generation unit according to the first embodiment. FIG. 9 is a diagram for explaining the operation of the reference source error set creating unit according to the first embodiment. FIG. 10 is a flowchart showing an example of an operation of creating training data by a pseudo source. FIG. 11 is a diagram for explaining the operation of the error set synthesis unit for the pseudo source according to the first embodiment. FIG. 12 is a diagram for explaining the operation of the pseudo measurement value set correction unit according to the first embodiment. FIG. 13 is a flowchart showing an example of the operation of the estimation stage of the source position estimation system according to the first embodiment. FIG. 14 is a diagram showing an example of a processing configuration (processing module) of the position estimation device according to the second embodiment. FIG. 15 is a diagram showing an example of a processing configuration of the source position estimation system according to the third embodiment. FIG. 16 is a diagram showing an example of a processing configuration of the source position estimation system according to the fourth embodiment. FIG. 17 is a diagram showing an example of a processing configuration of the source position estimation system according to the fifth embodiment. FIG. 18 is a diagram showing an example of the hardware configuration of the position estimation device.

First, the outline of one embodiment will be explained. It should be noted that the drawing reference reference numerals added to this outline are added to each element for convenience as an example to aid understanding, and the description of this outline is not intended to limit anything. In the present specification and the drawings, elements that can be similarly described may be given the same reference numerals, so that duplicate description may be omitted.

The position estimation device 100 according to one embodiment includes a prediction model generation unit 101, an error group calculation unit 102, an error synthesis unit 103, a pseudo measurement value correction unit 104, and a position estimation unit 105 (FIG. 1). reference). The prediction model generation unit 101 generates a prediction model that predicts a feature amount depending on the transmission position, which is obtained when a signal from a source at an arbitrary position is received at a specific position. The error group calculation unit 102 includes a measured value of the feature amount acquired based on the signal from the reference source at the known position, and a predicted value of the feature amount related to the reference source at the known position calculated using the prediction model. The error group is calculated by calculating the error of, for a plurality of reference source positions. The error synthesis unit 103 synthesizes an error group according to the positional relationship between the pseudo transmission source at an arbitrary position and each of the reference transmission sources, and outputs it as a synthesis error. The pseudo-measured value correction unit 104 corrects the predicted value of the feature amount by the prediction model when the signal from the pseudo-source is received by using the synthesis error. The position estimation unit 105 estimates the source position by inputting the measured value of the feature amount depending on the transmission position into the learning model learned at least based on the predicted value of the feature amount from the corrected pseudo source. To do.

The position estimation device 100 receives, for example, a transmitted radio wave by sensors arranged around it, and estimates the source position using a feature amount depending on the transmission position obtained from the received waveform. The position estimation device 100 does not simply superimpose the position fingerprints corresponding to the plurality of candidate positions, but superimposes the spatial distribution of the error between the measured value and the predicted value at the plurality of candidate positions, and the space of the error of the predicted value. Correct the predicted value using the distribution. That is, the position estimation device 100 takes into consideration the usual tendency that the feature amount (for example, RSS) becomes smaller as the distance from the source is increased, so that the position fingerprints at a small number of candidate positions can be moved to an arbitrary transmission position. Create a corresponding position fingerprint. The created position fingerprint expands the training data based on the measured values. As a result, the number of position fingerprints actually measured and acquired at the training stage can be reduced.

Furthermore, by considering the usual tendency that RSS becomes smaller as the distance from the source increases, the position fingerprint corresponding to the transmission position outside the candidate position for which the position fingerprint was acquired in the training stage is accurately created. As a result, even when the source exists outside the candidate position where the position fingerprint was acquired in the training stage, the degree of deterioration of the estimation accuracy can be reduced.

The specific embodiment will be described in more detail below with reference to the drawings.

[First Embodiment]
The first embodiment will be described in more detail with reference to the drawings.

[Description of configuration]
First, the configuration of the source position estimation system according to the first embodiment will be described. FIG. 2 is a diagram showing an example of a schematic configuration of a source position estimation system according to the first embodiment.

Referring to FIG. 2, the source position estimation system includes a plurality of receiving devices 10-1 to 10-M, a plurality of signal processing devices 20-1 to 20-M, a storage device 30, and a position estimating device 40. And are included (M is a positive integer, the same applies hereinafter). In the following description, if there is no particular reason for distinguishing the receiving devices 10-1 to 10-M, it is simply referred to as "receiving device 10". Similarly, unless there is a particular reason for distinguishing the signal processing devices 20-1 to 20-M, the term "signal processing device 20" is simply used.

The receiving device 10 is arranged in the field to be the target of the source position estimation. The receiving device 10 is exemplified by a radio wave sensor or the like that receives radio waves.

The signal processing device 20 is a device that performs signal processing using the signal received by the receiving device 10. Specifically, the signal processing device 20 calculates a feature amount (for example, reception intensity RSS) from a received signal (radio signal).

The storage device 30 stores the position of the receiving device 10 in association with the feature amount calculated by the signal processing device 20.

The position estimation device 40 estimates the position in the field of a signal source whose position is unknown based on the information stored in the storage device 30.

The position estimation device 40 estimates the position of the source in the field as shown in FIG. In FIG. 3, the radio wave sensor corresponds to the receiving device 10. The position estimation device 40 generates a feature amount map (for example, a radio wave intensity map; position fingerprint) for each position of the reference source, and collates the map with the feature amount map (position fingerprint) obtained from an unknown source. , Estimate the location of an unknown source.

FIG. 4 is a diagram showing an example of a processing configuration (processing module) of the position estimation device 40 according to the first embodiment.

Referring to FIG. 4, the position estimation device 40 includes an input unit 201, a data classification unit 202, a training data expansion unit 203, a training data combination unit 204, a learning unit 205, a position estimation unit 206, and an output unit. 207 and.

The input unit 201 inputs an RSS measurement value set when a signal from a source at an arbitrary position is received at a specific position.

The data classification unit 202 classifies the input data as training data or estimation data.

The training data expansion unit 203 generates pseudo data (training data) based on the training data.

The training data combination unit 204 combines the training data obtained by actually measuring and the training data generated in a pseudo manner. The training data combining unit 204 generates the above two training data (training data based on actual measurement values, training data generated in a pseudo manner) as training data for training.

The learning unit 205 learns the correspondence between the RSS measurement value set and the correct position based on the combined training data. More specifically, the learning unit 205 has a measured value of the feature amount acquired based on the signal from the reference source (training data based on the measured value) and a predicted value of the feature amount from the pseudo source (pseudo source). Based on the training data), the above correspondence is learned.

The position estimation unit 206 estimates the source position corresponding to the input estimation data based on the result learned by the learning unit 205. The position estimation unit 206 is a learning model (learning model generated by the learning unit 205) in which the measured value of the feature amount depending on the transmission position is learned based on at least the predicted value of the feature amount from the corrected pseudo source. The source position is estimated by inputting to.

The output unit 207 outputs the estimated source position.

Here, RSS is an example of a feature amount depending on the transmission position. A set of RSS measurement values [RSS ₁ , RSS ₂ , ..., RSS _M ] measured at M different positions is an example of a position fingerprint. For example, in the example of FIG. 3, an RSS measurement value set consisting of 9 RSSs is calculated.

The training data is a set of pairs of RSS position fingerprint Xi (= [RSS ₁ , RSS ₂ , ..., RSS _M ]) and the corresponding training reference source position Yi {(Xi, Yi). }.

Note that the number of reference sources at the training stage is N (N is a positive integer. The same applies hereinafter). The suffix i is 1 to N. In the example of FIG. 3, one reference source (N = 1) is described.

As described above, RSS is an example of the feature amount that can be used in the disclosure of the present application, and as another feature amount, CIR or the difference between the reference time and the arrival time may be used.

The input unit 201 may include preprocessing accompanied by monotonic mapping such as mutual conversion between linear units and logarithmic units of RSS measurement values, scaling such as normalization and standardization.

The data classification unit 202 distributes the data acquired from the input unit 201 into "training data" or "estimation data" according to the mode of the source position estimation system. The mode of the source position estimation system is either "training mode" or "estimation mode", and the system administrator or the like determines and inputs the mode of the source position estimation system.

The training data expansion unit 203 includes a propagation model generation unit 211, a reference source error set creation unit 212, a pseudo source position determination unit 213, a model-based pseudo measurement value set generation unit 214, and a pseudo source error set. It includes a synthesis unit 215 and a pseudo measurement value set correction unit 216.

The propagation model generation unit 211 generates a radio wave propagation model using the training data. The propagation model generation unit 211 obtains a feature amount (for example, radio field intensity) depending on the transmission position, which is obtained when the receiving device 10 receives a signal from a transmission source (reference transmission source) at an arbitrary position at a specific position. Generate a model to predict. The details of the prediction model will be described later.

The reference source error set creation unit 212 creates a set of errors between the RSS pseudo-measurement value set predicted from the generated propagation model and the RSS measurement value set actually obtained. The reference source error set creation unit 212 uses the measured value (actual measurement value) of the feature amount acquired based on the signal from the reference source at the known position and the reference transmission at the known position calculated using the above prediction model. Calculate the predicted value of the feature quantity for the source and the error. The reference source error set creation unit 212 calculates an error group (plurality of error maps) by executing the above error calculation for a plurality of reference source positions.

The pseudo source position determination unit 213 determines the position of the pseudo source provided for training data expansion.

The model-based pseudo measurement value set generation unit 214 generates a pseudo RSS measurement value set based on the pseudo source position and the propagation model.

The error set synthesis unit 215 for the pseudo source synthesizes an error group (plurality of error maps) according to the positional relationship between the pseudo source at an arbitrary position and each of the reference sources, and outputs it as a composite error. For example, the error set synthesis unit 215 for a pseudo source synthesizes an error set based on the degree of spatial correlation between the pseudo source position and the reference source position, and synthesizes the error set for the pseudo source.

The pseudo measurement value set correction unit 216 corrects the generated model-based pseudo measurement value set with the combined error set for the pseudo source and outputs it. The pseudo measurement value set correction unit 216 corrects the predicted value of the feature amount by the prediction model when the signal from the pseudo transmission source is received by using the above synthesis error.

Here, the propagation model generation unit 211 is an example of the prediction model generation unit. Further, the reference source error set creation unit 212 is an example of an error group calculation unit. Further, the error set synthesis unit 215 for a pseudo transmission source is an example of an error synthesis unit.

[Explanation of operation]
Next, the operation of the source position estimation system according to the first embodiment will be described in detail with reference to the flowchart. FIG. 5 is a flowchart showing an example of the operation of the training stage of the source position estimation system according to the first embodiment. First, the operation of the training stage will be described in detail with reference to the flowchart of FIG.

Step S31 is a preparatory step for the training stage. In this step, the source position estimation system receives a signal from the source (reference source) and generates a set of position coordinates generated. The reception position coordinates may be input to the system as a distance from the reference point using a laser range finder or the like, or may be input by using a satellite positioning system or the like. It is desirable to set the reception position so that radio waves can be received at a plurality of locations when the transmission source is located at an arbitrary position in the area. For example, in the example of FIG. 3, the position where the nine radio wave sensors are arranged is input to the system.

Next, the source position estimation system creates training data using a reference source whose position is known (step S32).

The training data is a set of multiple reference source positions and RSS measurement value sets obtained correspondingly. For example, in the example of FIG. 3, the position of the reference transmission source is changed, and the received signal is collected from the radio wave sensor (reception device 10) at each position. A feature amount (for example, RSS) is calculated from the received signal for each position of the reference source, and an RSS measurement value set (position fingerprint) is obtained.

FIG. 6 is a diagram for explaining the concept of the RSS measurement value set. In FIG. 6, when nine radio wave sensors are installed in the field as shown in FIG. 3, the radio wave intensity obtained from the sensors is expressed by shades of color. Referring to FIG. 6, the radio wave sensor (receiver 10) receives the radio wave transmitted from the reference source, and the information relating the position of each radio wave sensor and the feature amount obtained from the sensor is the RSS measurement value set (position). Fingerprint). The information in which the position fingerprint is associated with the position of the reference source is the training data.

Return the explanation to Fig. 5. The source position estimation system creates training data by a pseudo source based on the training data obtained by actually measuring (step S33). Details regarding the creation of training data by the pseudo source will be described later.

Further, the source position estimation system uses the training data created by combining the training data created in step S32 and the training data created by the pseudo source created in step S33 to obtain a position estimator. Train (step S34). That is, the source position estimation system generates a learning model using two training data (training data by an actual reference source and training data by a pseudo source).

FIG. 7 is a flowchart showing an example of an operation of creating training data by the reference source in step S32. The operation of step S32 will be described in detail with reference to FIG. 7.

First, the radio waves transmitted by the reference source are received by the receiving device 10 at a plurality of positions, and the RSS is measured by the signal processing device 20 (step S41).

Next, the source position estimation system acquires the position of the reference source (step S42).

A set of a plurality of RSS measurement values obtained in step S41 is a position fingerprint. There is a 1: 1 correspondence between the position fingerprint and the reference source position acquired in step S42. That is, training data is obtained by executing step S41 and step S42.

It is desirable that the number of reference transmission sources is about the same as the number of reception positions to about 5 times as many. If it is less than that, the accuracy when generating the training data by the pseudo source from the training data by the reference source deteriorates, and high position accuracy cannot be obtained. Further, if it is more than that, it is desirable from the viewpoint of improving the position estimation accuracy, but the effect of reducing the amount of data required at the training stage is reduced.

Next, the following processing is performed for each reference source position of the obtained training data.

The propagation model generation unit 211 of the training data expansion unit 203 creates (estimates) a propagation model based on the reference source position and the actual RSS measurement value set (step S43). Specifically, the propagation model generation unit 211 models how much RSS is attenuated according to the distance between the source and the reception position.

FIG. 8 is a diagram for explaining the operation of the propagation model generation unit 211. The propagation model generation unit 211 sets the position of the reference source as the center (origin), sets the distance between the position of the reference source whose position is known and the radio wave sensor (receiver 10) on the X-axis, and each radio wave. The radio field intensity in the sensor is set on the Y-axis, and a data set (graph) is generated. The propagation model generation unit 211 performs regression analysis on the data set to generate a propagation model. In the example of FIG. 8, a straight line is generated as a propagation model. The propagation model generation unit 211 calculates a constant (propagation model constant) representing the straight line shown in FIG.

Return the explanation to Fig. 7. The reference source error set creation unit 212 calculates the predicted RSS value at each reception position based on the propagation model created above (step S44).

FIG. 9 is a diagram for explaining the operation of the reference source error set creation unit 212. The reference source error set creation unit 212 generates a radio field intensity map as shown in the lower left of FIG. The reference source error set creation unit 212 inputs the distance between the reference source and the radio wave sensor (receiver 10) into the propagation model estimated in step S43, and calculates the radio wave intensity at the radio wave sensor position. The reference source error set creation unit 212 calculates the radio wave intensity of each radio wave sensor arranged in the field, and calculates a radio wave intensity map (RSS predicted value) as shown in the lower left of FIG.

After that, the reference source error set creation unit 212 calculates the difference between the actual RSS measurement value and the predicted value calculated in step S44, and saves it as an error set (step S45). In the example of FIG. 9, the difference between the upper left radio field intensity map (actual RSS measurement value) and the lower left radio wave intensity map (RSS predicted value) is calculated, and the error map of the radio wave intensity for each reference source position is calculated. .. Referring to FIG. 9, the radio field intensity map generated by the propagation model described in the lower left of the drawing is a predicted value that is not affected by obstacles existing in the actual field, and therefore the radio field strength increases as the distance from the source increases. Will be low. On the other hand, since the radio field intensity map on the upper left of the drawing is an actually measured value, it is affected by obstacles existing in the field. When the difference between the measured value and the predicted value regarding the radio field strength is calculated, the influence of obstacles or the like at each reference source position is calculated as an error. The shading related to the error of the radio field intensity shown in FIG. 9 and the like indicates that the center color has a small error, and the edge color has a large error (positive error, negative error).

FIG. 10 is a flowchart showing an example of an operation of creating training data by the pseudo source in step S33. The operation of step S33 will be described in detail with reference to FIG.

First, the pseudo source position determination unit 213 sets the position of the pseudo source (step S51). The pseudo source position determination unit 213 sets the position of the pseudo source within a region where an unknown source, which is a position estimation target, can exist. At that time, it is desirable that the pseudo source position determination unit 213 sets a position different from the position where the reference source already exists as the pseudo source position.

Further, it is desirable that the pseudo source position determination unit 213 sets the pseudo source at a plurality of positions so as to cover the entire area. Specifically, the number of pseudo-sources is preferably about 5 to 10 times the number of reference sources. If it is less than that, it may not be possible to cover the entire region with sufficient density, and if it is more than that, the amount of calculation will increase and the improvement in accuracy will be limited.

Next, the following processing is performed for each pseudo source position.

The model-based pseudo-measurement value set generation unit 214 pseudo-measures the RSS measurement value set obtained when the radio wave transmitted from the pseudo-source position is received at each reception position based on the propagation model generated in step S43. Calculated as a value set (step S52). The model-based pseudo-measurement value set generator 214 inputs the difference between the position of the pseudo-source and the position of the radio wave sensor into the propagation model of the reference source closest to the position of the selected pseudo-source, and RSS for each pseudo-source. Generate a measurement value set (radio field intensity map).

Alternatively, the RSS measurement value set for each pseudo source may be generated from a propagation model that is commonly used for all pseudo sources. Specifically, the propagation model generation unit 211 plots the data for all the reference sources as shown in FIG. 8, and the propagation model commonly used for all the pseudo sources from the plotted data. To generate.

Alternatively, the RSS measurement value set for each pseudo source may be generated from a propagation model obtained by weighted averaging with a weighting coefficient determined according to the distance between the pseudo source position and the reference source. .. The method for generating the propagation model in this case can be the same as the method for generating the error set by the error set synthesis unit 215 for the pseudo source, which will be described later.

Next, the error set synthesis unit 215 for the pseudo source synthesizes the error set for each reference source position saved in step S45, and creates an error set according to the pseudo source position (step S53). For example, the error set synthesis unit 215 for a pseudo source weights and averages the error set with a predetermined weighting coefficient based on the relative relationship between the reference source source position and the pseudo source position (positional relationship between the two sources). By doing so, the error set corresponding to the pseudo source position is synthesized.

FIG. 11 is a diagram for explaining the operation of the error set synthesis unit 215 for a pseudo source. The error set synthesis unit 215 for the pseudo source synthesizes (adds the radio field intensity) the error set of each reference source position calculated earlier. At that time, the error set synthesis unit 215 for the pseudo source synthesizes the error set by the weighted average reflecting the position of the pseudo source and the position of the reference source. For example, in the upper left corner of FIG. 11, since the distance between the reference source and the pseudo source is long, the weight of the reference source is reduced. On the other hand, in the lowermost row on the left side, the distance between the reference source and the pseudo source is short, so the weight of the reference source is increased. By synthesizing such an error set, an error (error of radio field intensity) at the pseudo source position as shown on the right side of FIG. 11 can be obtained.

In the example of FIG. 11, as shown in the lowermost part on the left side, if the pseudo source and the reference source are close to each other, the degree of similarity between the error map of the reference source and the error map of the pseudo source should be high. On the other hand, as shown in the uppermost row on the left side, if the pseudo source and the reference source are far from each other, the similarity between the error map of the reference source and the error map of the pseudo source should be low. The error set synthesis unit 215 for the pseudo source generates an error map of the pseudo source in consideration of the positions of the above two types of sources.

In the inverse distance weighting method, a weighting coefficient proportional to the reciprocal of the distance between the reference source position and the pseudo source position is used. For example, a weighting factor proportional to the -1.5th power or -2nd power of the distance may be used.

As another example of the error set synthesis method, first, the error set synthesis unit 215 for a pseudo source sets the similarity of each error set to the distance between two points for any two reference sources. Create a spatial correlation model of how it changes accordingly. Then, the error set synthesis unit 215 for the pseudo source determines the weighting coefficient according to the distance between the reference source position and the pseudo source position so as to be consistent with the spatial correlation model. As described above, there is kriging as a method of determining the weighting coefficient in consideration of the spatial correlation.

The pseudo measurement value set correction unit 216 corrects the pseudo measurement value set generated in step S52 by the error set created in step S53 (step S54). Specifically, the pseudo measurement value set correction unit 216 corrects the pseudo measurement value set generated in step S52 by adding the pseudo measurement value set and the error set for each pseudo transmission position.

FIG. 12 is a diagram for explaining the operation of the pseudo measurement value set correction unit 216. When the pseudo measurement value set correction unit 216 adds the radio field intensity of the pseudo measurement value set of the pseudo source position and its error, a radio field intensity map at the corrected pseudo source position as shown on the right side of FIG. 12 is obtained. Be done. The radio wave intensity map becomes pseudo position fingerprint data.

FIG. 13 is a flowchart showing an example of the operation of the estimation stage of the source position estimation system according to the first embodiment. The operation of the estimation stage will be described in detail with reference to the flowchart of FIG.

First, the reception position is acquired in the same manner as in step S31 (step S61).

Next, the input unit 201 acquires the RSS measurement value set calculated by the signal processing means in the same manner as in step S41 (step S62).

Next, the position estimation unit 206 collates the RSS measurement value set obtained for the unknown source with the RSS measurement value set included in the training data by using the position estimator trained in step S34. (Step S63).

After that, the output unit 207 outputs the source position corresponding to the RSS measurement value set of the nearest training data as the estimated position of the unknown source (step S64).

In the first embodiment, a case where a multi-class classification method of selecting and outputting one of the closest candidate positions from a large number of candidate positions is used has been described. However, in the disclosure of the present application, a regression analysis method may be used in which the position coordinates of the source are treated as continuous numerical values and output.

Alternatively, a weighted coefficient of similarity is used for a plurality of candidate positions corresponding to the RSS measurement value set obtained for an unknown source and the RSS measurement value set of a plurality of training data having a large degree of similarity. The average may be calculated and treated as an estimated position.

Examples of multi-class classification methods include logistic regression, random forest, support vector machine, decision tree, neural network, k-nearest neighbor method, etc. Examples of regression analysis methods include linear regression, logistic regression, support vector machines, random forests, and neural networks. However, the position estimation method to which the disclosure of the present application is applicable is not limited to the above examples.

[Explanation of effect]
Next, the effect of the first embodiment will be described.

In the first embodiment, the training data is expanded by creating the training data by the pseudo source based on the training data by the reference source. As a result, the number of RSS measurement value sets that are actually measured and acquired can be reduced. At that time, instead of simply superimposing the RSS measurement value sets corresponding to the plurality of reference source positions, the error sets of the measured values and the predicted values for the plurality of reference source positions are superimposed, and further, the error sets are superimposed. The predicted value is corrected using. Therefore, it is possible to avoid synthesizing RSS measurement value sets in which radio waves are simultaneously transmitted from a plurality of candidate positions. That is, it is rare that radio waves are transmitted from a plurality of candidate positions at the same time during system operation, and even if a learning model is generated using such a rare RSS measurement value set, the estimation result by the learning model is obtained. The accuracy will be low.

Further, in the first embodiment, a propagation model is created based on the RSS measurement value set actually measured using the reference source. Therefore, the RSS measurement value set obtained when the pseudo source is placed outside the reference source position is accurately created. As a result, the degree of deterioration of the estimation accuracy is reduced even when an unknown source exists outside the reference source position in the training stage.

[Second Embodiment]
Next, the second embodiment will be described in detail with reference to the drawings.

[Description of configuration]
FIG. 14 is a diagram showing an example of a processing configuration (processing module) of the position estimation device 40 according to the second embodiment. Referring to FIG. 14, the position estimation device 40 according to the second embodiment is different from the position estimation device 40 according to the first embodiment in that it further has a plurality of wave source pseudo measurement value set synthesis unit 701. .. Here, the plurality of wave source pseudo measurement value set synthesis unit 701 is an example of the pseudo measurement value synthesis unit.

[Explanation of operation]
The multi-wave source pseudo-measured value set synthesis unit 701 operates as follows.

Multiple wave source pseudo measurement value set Since the synthesis unit 701 pseudo-creates training data when a plurality of sources are transmitting signals from different points at the same time, an RSS measurement value set when the number of wave sources is 1. To create an RSS measurement value set when multiple wave sources exist. The RSS measurement value set to be superimposed may be either an RSS measurement value set by a reference source or an RSS measurement value set by a pseudo source. Further, in the case of RSS, it is desirable to add the power level in a linear representation as the superposition method. However, monotonic mapping processing such as conversion to logarithmic representation after addition may be performed.

Note that in the training data in the second embodiment, one RSS measurement value set corresponds to one or more source positions. Therefore, the position estimation unit 206 needs to be configured so that it can output one or more source positions. For example, a multi-label classification method can be used in which a plurality of candidate positions are selected and output for one RSS measurement value set.

[Explanation of effect]
The effect of the second embodiment will be described. In the second embodiment, an RSS measurement value set when two or more transmission sources are transmitting radio waves at the same time (substantially at the same time) is created, and learning is performed using the RSS measurement value set. As a result, even when there are a plurality of transmission sources in the area and radio waves are transmitted at the same time, the positions of the respective transmission sources can be estimated and output.

[Third Embodiment]
Next, the third embodiment will be described in detail with reference to the drawings.

[Description of configuration]
FIG. 15 is a diagram showing an example of a processing configuration of the source position estimation system according to the third embodiment. Referring to FIG. 15, in the third embodiment, instead of the input unit 201 of the first and second embodiments, M sensors 801-1 to 801-M that receive signals from the source are used. It differs from the communication network 802 in that it has a communication unit 803.

Each of the plurality of sensors 801-1 to 801-M includes a radio wave intensity measuring unit 804, a position measuring unit 805, and a communication unit 806 for transmitting the measured data. Here, the radio wave intensity measuring unit 804 is an example of a measuring unit that measures a feature amount depending on the transmission position.

[Explanation of operation]
Each of the above components operates as follows.

The radio wave intensity measuring unit 804 receives the radio wave from the source and measures its RSS. The position measurement unit 805 measures its own position. The communication unit 806 transmits the measured data to the communication unit 803 via the communication network 802.

[Explanation of effect]
The effect of the third embodiment will be described. In the third embodiment, the sensors 801-1 to 801-M measure the RSS and the self-position, and the measured data is connected to the data classification unit 202 via the communication network 802. , Training and estimation process can be carried out online.

[Fourth Embodiment]
Next, the fourth embodiment will be described in detail with reference to the drawings.

[Description of configuration]
FIG. 16 is a diagram showing an example of a processing configuration of the source position estimation system according to the fourth embodiment. Referring to FIG. 16, the fourth embodiment is different in that it has a sensor position holding unit 901 and a sensor position adding unit 902 instead of the position measuring unit 805 of the third embodiment.

[Explanation of operation]
Each of the above components operates as follows.

The sensor position holding unit 901 holds the position of each sensor installed in the area. The sensor position addition unit 902 adds the position of each sensor to the data measured by the sensors 801-1 to 801-M obtained via the communication unit 803 and outputs the data.

[Explanation of effect]
The effect of the fourth embodiment will be described. In the fourth embodiment, the sensor position held by the sensor position holding unit 901 is added to the RSS measurement value set measured by the sensors 801-1 to 801-M so as to be connected to the data classification unit 202. ing. Therefore, the position measurement unit 805 of the sensor becomes unnecessary, and the sensor can be manufactured at low cost.

[Fifth Embodiment]
Next, the fifth embodiment will be described in detail with reference to the drawings.

[Description of configuration]
FIG. 17 is a diagram showing an example of a processing configuration of the source position estimation system according to the fifth embodiment. Referring to FIG. 17, the fifth embodiment is different from the fourth embodiment in that it has a time / weather measurement unit 1001 and a time / weather label addition unit 1002.

[Explanation of operation]
Each of the above components operates as follows.

The time / weather measurement unit 1001 acquires calendar information such as the date and time of measurement, the day of the week, and public holidays, as well as the weather, temperature, and humidity of that day. The time / weather label addition unit 1002 adds time information and weather information to the data measured by the sensors 801-1 to 801-M obtained via the communication unit 803 and outputs the data.

[Explanation of effect]
The effect of the fifth embodiment will be described. In the fifth embodiment, a time label or a weather label is added to the RSS measurement value set measured by the sensors 801-1 to 801-M. Therefore, the data classification unit 202 can classify according to time and weather. That is, training and estimation can be performed according to the assigned time label and weather label. For example, with regard to time, since the vegetation changes according to the season with a cycle of one year, radio waves are easily absorbed and attenuated by the vegetation in the summer when the leaves are overgrown, and the radio waves are blocked in the winter when the leaves fall. It disappears and is easy to reach long distances.

In addition, in the daily cycle and the weekly cycle, there is a flow of humans and the accompanying increase and decrease of vehicles. Since both humans and vehicles are absorbers and reflectors for radio waves, changes such as difficulty in flying radio waves during the daytime on weekdays when human activities are active are expected. Similarly, when it rains, radio waves are easily absorbed by the rain and attenuated, and when it is sunny and dry, the radio waves tend to fly. The position estimation accuracy can be improved by performing the position estimation in consideration of such a change. The sensors 801-1 to 801-M may have the time / weather measurement unit 1001.

Next, the hardware of the position estimation device 40 will be described. FIG. 18 is a diagram showing an example of the hardware configuration of the position estimation device 40.

The position estimation device 40 can be configured by an information processing device (so-called computer), and includes the configuration illustrated in FIG. For example, the position estimation device 40 includes a processor 311, a memory 312, an input / output interface 313, a communication interface 314, and the like. The components such as the processor 311 are connected by an internal bus or the like so that they can communicate with each other.

However, the configuration shown in FIG. 18 does not mean to limit the hardware configuration of the position estimation device 40. The position estimation device 40 may include hardware (not shown), or may not include an input / output interface 313 if necessary. Further, the number of processors 311 and the like included in the position estimation device 40 is not limited to the example of FIG. 18, and for example, a plurality of processors 311 may be included in the position estimation device 40.

The processor 311 is a programmable device such as a CPU (Central Processing Unit), an MPU (Micro Processing Unit), or a DSP (Digital Signal Processor). Alternatively, the processor 311 may be a device such as an FPGA (Field Programmable Gate Array) or an ASIC (Application Specific Integrated Circuit). The processor 311 executes various programs including an operating system (OS; Operating System).

The memory 312 is a RAM (RandomAccessMemory), a ROM (ReadOnlyMemory), an HDD (HardDiskDrive), an SSD (SolidStateDrive), or the like. The memory 312 stores an OS program, an application program, and various data.

The input / output interface 313 is an interface of a display device or an input device (not shown). The display device is, for example, a liquid crystal display or the like. The input device is, for example, a device that accepts user operations such as a keyboard and a mouse.

The communication interface 314 is a circuit, module, or the like that communicates with another device. For example, the communication interface 314 includes a NIC (Network Interface Card) and the like.

The function of the position estimation device 40 is realized by various processing modules. The processing module is realized, for example, by the processor 311 executing a program stored in the memory 312. The program can also be recorded on a computer-readable storage medium. The storage medium may be a non-transient such as a semiconductor memory, a hard disk, a magnetic recording medium, or an optical recording medium. That is, the present invention can also be embodied as a computer program product. In addition, the program can be downloaded via a network or updated using a storage medium in which the program is stored. Further, the processing module may be realized by a semiconductor chip.

[Modification example]
It should be noted that the configuration, operation, and the like of the source position estimation system described in the above embodiment are examples, and are not intended to limit the system configuration and the like. For example, the receiving device 10 and the signal processing device 20 may be integrated and these functions may be realized by a single device.

Further, in the plurality of flowcharts used in the above description, a plurality of steps (processes) are described in order, but the execution order of the steps executed in each embodiment is not limited to the order of description. In each embodiment, the order of the illustrated steps can be changed within a range that does not hinder the contents, for example, each process is executed in parallel. In addition, the above-described embodiments can be combined as long as the contents do not conflict with each other.

Although the industrial applicability of the present invention is clear from the above description, the present invention is suitable for applications such as estimating the position of an illegal / illegal radio wave transmission source and taking appropriate measures. It is also suitable for applications such as detecting and tracking the position of a person or object equipped with a radio wave transmitter (beacon).

Some or all of the above embodiments may also be described, but not limited to:
[Appendix 1]
Prediction model generation units (101, 211) that generate a prediction model that predicts a feature amount depending on the transmission position, which is obtained when a signal from a source at an arbitrary position is received at a specific position.
Multiple errors between the measured value of the feature amount acquired based on the signal from the reference source at the known position and the predicted value of the feature amount for the reference source at the known position calculated using the prediction model. The error group calculation unit (102, 212), which calculates the error group by calculating with respect to the reference source position of
An error synthesizing unit (103, 215) that synthesizes the error group according to the positional relationship between the pseudo transmission source at an arbitrary position and each of the reference transmission sources and outputs the combined error.
Pseudo-measured value correction units (104, 216) that correct the predicted value of the feature amount by the prediction model when the signal from the pseudo-source is received by using the synthesis error.
A position estimation unit that estimates the source position by inputting the measured value of the feature amount depending on the transmission position into a learning model learned based on at least the predicted value of the feature amount from the corrected pseudo source. (105, 206) and
Position estimation devices (40, 100).
[Appendix 2]
The error synthesizing unit (103, 215) weighted and averages the error group using a weighting coefficient determined according to the positional relationship between the pseudo source at the arbitrary position and each of the reference sources, and the combined error. The position estimation device (40, 100) according to Appendix 1 for calculating the above.
[Appendix 3]
Based on the measured value of the feature amount acquired based on the signal from the reference source of the known position and the predicted value of the feature amount from the pseudo source after the correction, the feature amount and the correct answer position depending on the transmission position The position estimation device (40, 100) according to Appendix 1 or 2, further comprising a learning unit (205) that learns correspondences and generates a learning model.
[Appendix 4]
The position estimation device (40, 100) according to Appendix 2, wherein the weighting factor is expressed as a power of the distance between the pseudo source and the reference source.
[Appendix 5]
The weighting coefficient creates a spatial correlation model of the similarity of the error with respect to the distance between two points for any two reference sources, and pseudo-transmits with the reference source so as to be consistent with the spatial correlation model. The position estimation device (40, 100) according to Appendix 2, which is determined according to the distance between the sources.
[Appendix 6]
In any one of Appendix 1 to 5, further including a pseudo-measurement value synthesizer (701) that synthesizes and outputs one or more of the measurement values corresponding to different source positions or the pseudo-measurement values by the pseudo-source. The position estimation device (40, 100) described.
[Appendix 7]
The position estimation device (40) according to any one of Supplementary note 1 to 6, further comprising a sensor including a measurement unit for measuring a feature amount depending on the transmission position and a communication unit (803) connected via a network. , 100).
[Appendix 8]
The position estimation device (40, 100) according to any one of Supplementary notes 1 to 7, wherein the feature amount is a radio wave intensity.
[Appendix 9]
A sensor position holding unit (901) that holds the position of each of the sensors installed in the area, and
The position estimation according to Appendix 7, further comprising a sensor position addition unit (902) that adds the position of the sensor to the data measured by the sensor and outputs the data obtained via the communication unit (803). Equipment (40, 100).
[Appendix 10]
The time / weather measurement unit (1001) that acquires time information related to the time when the measurement was performed or weather information related to the weather on the day when the measurement was performed.
A time / weather label addition unit (1002) that adds the time information or the weather information to the data measured by the sensor obtained via the communication unit.
The position estimation device (40, 100) according to Appendix 7, further comprising.
[Appendix 11]
In the position estimation device (40, 100)
A step to generate a prediction model that predicts a feature amount depending on the transmission position, which is obtained when a signal from a source at an arbitrary position is received at a specific position.
Multiple errors between the measured value of the feature amount acquired based on the signal from the reference source at the known position and the predicted value of the feature amount for the reference source at the known position calculated using the prediction model. The step of calculating the error group by calculating for the reference source position of
A step of synthesizing the error group according to the positional relationship between the pseudo source at an arbitrary position and each of the reference sources and outputting it as a combined error.
A step of correcting the predicted value of the feature amount by the prediction model when the signal from the pseudo transmission source is received by using the synthesis error, and
A step of estimating the source position by inputting the measured value of the feature amount depending on the transmission position into a learning model learned based on at least the predicted value of the feature amount from the corrected pseudo source.
Location estimation methods, including.
[Appendix 12]
In the computer mounted on the position estimation device (40, 100),
Processing to generate a prediction model that predicts the feature amount depending on the transmission position, which is obtained when a signal from a source at an arbitrary position is received at a specific position,
Multiple errors between the measured value of the feature amount acquired based on the signal from the reference source at the known position and the predicted value of the feature amount for the reference source at the known position calculated using the prediction model. The process of calculating the error group by calculating for the reference source position of
A process of synthesizing the error group according to the positional relationship between the pseudo source at an arbitrary position and each of the reference sources and outputting it as a combined error.
A process of correcting the predicted value of the feature amount by the prediction model when a signal from the pseudo transmission source is received by using the synthesis error, and
A process of estimating the source position by inputting the measured value of the feature amount depending on the transmission position into a learning model learned based on at least the predicted value of the feature amount from the corrected pseudo source.
A program that executes.
Note that the form of Appendix 11 and the form of Appendix 12 can be expanded to the forms of Appendix 2 to the form of Appendix 10 in the same manner as the form of Appendix 1.

Although the embodiments of the present invention have been described above, the present invention is not limited to these embodiments. It will be appreciated by those skilled in the art that these embodiments are merely exemplary and that various modifications are possible without departing from the scope and spirit of the invention.

This application claims priority based on Japanese application Japanese Patent Application No. 2019-076361 filed on April 12, 2019, and incorporates all of its disclosures herein.

10, 10-1 to 10-M receiver 20, 20-1 to 20-M signal processing device 30 storage device 40, 100 position estimation device 101 prediction model generation unit 102 error group calculation unit 103 error synthesis unit 104 pseudo measurement value Correction unit 105, 206 Position estimation unit 201 Input unit 202 Data classification unit 203 Training data expansion unit 204 Training data coupling unit 205 Learning unit 207 Output unit 211 Propagation model generation unit 212 Reference source error set creation unit 213 Pseudo source position determination Unit 214 Model-based pseudo measurement value set generation unit 215 Pseudo source error set synthesis unit 216 Pseudo measurement value set correction unit 311 Processor 312 Memory 313 Input / output interface 314 Communication interface 701 Multiple wave source pseudo measurement value set synthesis unit 801-1 801-M Sensor 802 Communication network 803, 806 Communication unit 804 Radio strength measurement unit 805 Position measurement unit 901 Sensor position holding unit 902 Sensor position addition unit 1001 Time / weather measurement unit
1002 hours / weather label addition part

Claims (12)

1. A prediction model generator that generates a prediction model that predicts features depending on the transmission position, which is obtained when a signal from a source at an arbitrary position is received at a specific position.
   Multiple errors between the measured value of the feature amount acquired based on the signal from the reference source at the known position and the predicted value of the feature amount related to the reference source at the known position calculated using the prediction model. The error group calculation unit, which calculates the error group by calculating for the reference source position of
   An error synthesizer that synthesizes the error group according to the positional relationship between the pseudo source at an arbitrary position and each of the reference sources and outputs it as a composite error.
   A pseudo-measurement value correction unit that corrects the predicted value of the feature amount by the prediction model when a signal from the pseudo-source is received by using the synthesis error.
   A position estimation unit that estimates the source position by inputting the measured value of the feature amount depending on the transmission position into a learning model learned based on at least the predicted value of the feature amount from the corrected pseudo source. When,
   A position estimation device.
2. The error synthesizing unit calculates the combined error by weighted averaging the error group using a weighting coefficient determined according to the positional relationship between the pseudo source at an arbitrary position and each of the reference sources. Item 1. The position estimation device according to item 1.
3. Based on the measured value of the feature amount acquired based on the signal from the reference source of the known position and the predicted value of the feature amount from the pseudo source after the correction, the feature amount and the correct answer position depending on the transmission position The position estimation device according to claim 1 or 2, further comprising a learning unit that learns correspondences and generates a learning model.
4. The position estimation device according to claim 2, wherein the weighting coefficient is expressed by a power of the distance between the pseudo source and the reference source.
5. The weighting coefficient creates a spatial correlation model of the similarity of the error with respect to the distance between two points for any two reference sources, and pseudo-transmits with the reference source so as to be consistent with the spatial correlation model. The position estimation device according to claim 2, which is determined according to the distance between the sources.
6. The one according to any one of claims 1 to 5, further comprising a pseudo-measurement value synthesizer that synthesizes and outputs one or more of the measurement values corresponding to different source positions or the pseudo-measurement values by the pseudo-source. Position estimator.
7. The position estimation device according to any one of claims 1 to 6, further comprising a sensor including a measuring unit for measuring a feature amount depending on the transmission position and a communication unit connected via a network.
8. The position estimation device according to any one of claims 1 to 7, wherein the feature amount is a radio wave intensity.
9. A sensor position holding unit that holds the position of each of the sensors installed in the area,
   The position estimation device according to claim 7, further comprising a sensor position addition unit that adds the position of the sensor to the data measured by the sensor and outputs the data obtained via the communication unit.
10. The time / weather measurement unit that acquires time information related to the time of measurement or weather information related to the weather on the day of measurement,
    A time / weather label addition unit that adds the time information or the weather information to the data measured by the sensor obtained via the communication unit.
    7. The position estimation device according to claim 7.
11. In the position estimation device
    A step to generate a prediction model that predicts a feature amount depending on the transmission position, which is obtained when a signal from a source at an arbitrary position is received at a specific position.
    Multiple errors between the measured value of the feature amount acquired based on the signal from the reference source at the known position and the predicted value of the feature amount for the reference source at the known position calculated using the prediction model. The step of calculating the error group by calculating for the reference source position of
    A step of synthesizing the error group according to the positional relationship between the pseudo source at an arbitrary position and each of the reference sources and outputting it as a combined error.
    A step of correcting the predicted value of the feature amount by the prediction model when the signal from the pseudo transmission source is received by using the synthesis error, and
    A step of estimating the source position by inputting the measured value of the feature amount depending on the transmission position into a learning model learned based on at least the predicted value of the feature amount from the corrected pseudo source.
    Location estimation methods, including.
12. On the computer installed in the position estimation device,
    Processing to generate a prediction model that predicts the feature amount depending on the transmission position, which is obtained when a signal from a source at an arbitrary position is received at a specific position,
    Multiple errors between the measured value of the feature amount acquired based on the signal from the reference source at the known position and the predicted value of the feature amount for the reference source at the known position calculated using the prediction model. The process of calculating the error group by calculating for the reference source position of
    A process of synthesizing the error group according to the positional relationship between the pseudo source at an arbitrary position and each of the reference sources and outputting it as a combined error.
    A process of correcting the predicted value of the feature amount by the prediction model when a signal from the pseudo transmission source is received by using the synthesis error, and
    A process of estimating the source position by inputting the measured value of the feature amount depending on the transmission position into a learning model learned based on at least the predicted value of the feature amount from the corrected pseudo source.
    A program that executes.
    

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