JP2022079868A - Data interpolation processing method, data interpolation processing apparatus, program, learning processing device and prediction processing device - Google Patents

Abstract

To provide a wireless state prediction device capable of acquiring data obtained by appropriately interpolating observation data even under a situation where the observation data is acquired as intermittent data and by using the data, highly accurately and appropriately performing learning processing of a model predicting a future communication quality state.SOLUTION: In a case where observation data is intermittently acquired, a wireless state prediction device 100 is configured to, no matter where a missing part of the observation data is, when data interpolation processing is performed for the same waveform pattern, perform the data interpolation processing so as to acquire substantially the same waveform pattern, In other words, the wireless state prediction device 100 generates Hankel matrix R from the observation data, using the Hankel matrix R to acquire an optimization matrix R_opt acquired by performing optimization processing and performs the data interpolation processing based on the optimization matrix R_opt.SELECTED DRAWING: Figure 1

Description

The present invention relates to a technique for estimating communication status and communication status such as wireless communication.

In a narrow space such as a factory, the wireless environment situation changes complicatedly and dynamically due to changes in the propagation environment due to the movement of machine tools, products, workers, etc., and interference between multiple wireless applications. In a narrow space such as a factory, it is difficult to grasp the position information of moving objects such as machine tools, and since the radio wave propagation is a multipath-rich environment, unexpected effects may occur in unexpected places. Occurs. In this way, if an unexpected impact occurs in an unexpected place in a narrow space, stable communication cannot be maintained in the worst case, and the manufacturing site may take measures such as stopping the manufacturing line. Productivity is reduced. That is, in a narrow space such as a factory, unexpected deterioration in communication quality (QoS: Quality of Service) may occur, resulting in a decrease in productivity.

Therefore, it is necessary to take evasive action before the extreme deterioration of QoS (communication failure) occurs, and in order to realize it, there is a demand for a technique for predicting the occurrence of communication failure with high accuracy. In order to realize such a technique, for example, a technique for acquiring a distribution of values indicating communication quality in time series and predicting a future communication quality status based on the distribution (for example, disclosed in Patent Document 1). It is conceivable to use the technology that is used. In addition, a technique for predicting such a future communication quality situation has been developed by using a neural network model or the like.

Japanese Unexamined Patent Publication No. 2005-18304

For example, when predicting a future communication quality situation by a technique using a neural network model or the like, it is necessary to perform learning processing and acquire a trained model. For this purpose, in a wireless communication environment, observation data is acquired by receiving radio waves by a sensor, and the observation data is used to perform learning processing of a model for predicting future communication quality status. At this time, the sensor cannot always receive radio waves, and radio wave reception (frame reception) becomes intermittent, and as a result, there is a problem that the acquired observation data also becomes intermittent data. If the learning process of a model for predicting the communication quality status is performed using such intermittent observation data (observation data with missing parts), the learning efficiency is poor and the optimum model cannot be obtained.

Therefore, in view of the above problems, the present invention acquires data obtained by appropriately interpolating the observation data even in a situation where the observation data is acquired as intermittent data, and uses the data to determine the future communication quality status. It is an object of the present invention to realize a radio condition prediction device capable of performing training processing of a prediction model with high accuracy and appropriately, and a data interpolation processing method and program used for the radio condition prediction device.

In order to solve the above problems, the first invention is a data interpolation processing method for performing an interpolation process on intermittently acquired observation data, which includes an observation data acquisition step and a data retention step. , A matrix generation step, a matrix factorization processing step, an optimization processing step, and an interpolation data processing step.

The observation data acquisition step acquires observation data of data related to communication quality from the radio signal.

The data retention step stores and retains the observation data acquired by the observation data acquisition step for a predetermined period of time.

In the matrix generation step, when the window corresponding to a predetermined unit period is shifted by the first hour, which is a predetermined period in the time direction, the data group included in the period corresponding to the window becomes an element of one row. The Hankel matrix R is generated in. Then, in the matrix generation step, (1) when the data corresponding to the element of the Hankel matrix R is the observation data stored and held in the data holding step, the data corresponding to the element is set in the observation data, and (2). ) When the data corresponding to the element of the Hankel matrix R is not stored and retained in the data retention step, the Hankel matrix R is generated by setting the data corresponding to the element to a value indicating that it is the data of the missing part. do.

The matrix factorization processing step performs matrix factorization on the Hankel matrix R generated by the matrix factorization step and acquires a factorization matrix.

The optimization processing step is based on the value of the element obtained by the product of the matrices decomposed by the matrix factorization processing step and the value of the element of the Hankel matrix, and the difference between the adjacent values in the time series is determined. The optimization matrix is acquired by performing the optimization process based on the evaluation formula indicating that the product falls within the range of.

The interpolation data processing step interpolates the data of the part where the observation data is missing based on the optimization matrix.

In this data interpolation processing method, the Hankel matrix R is acquired by stacking the acquired data while shifting the window corresponding to the predetermined unit period by the first time (for example, the sample period) in the time direction. In a wireless application such as an AGV (Automated guided vehicle), a wireless terminal (for example, a wireless terminal mounted on an AGV) repeatedly moves on a fixed route, so that the communication quality information to be interpolated also changes periodically. Therefore, the Hankel matrix R acquired as described above has a high correlation between rows and therefore has a low rank. Therefore, by decomposing the Hankel matrix R into a matrix, it can be decomposed into a low-ranked matrix. Then, in this data interpolation processing method, based on the value of the element acquired by the product of the matrices decomposed by the matrix factorization processing step and the value of the element of the Hankel matrix, the values adjacent to each other in the time series are further increased. Since the optimization process is performed based on the evaluation formula indicating that the difference is within a predetermined range, the optimization process can be executed while reducing the amount of calculation.

Then, in this data interpolation method, the data in the missing portion can be interpolated with high accuracy by using the optimization matrix acquired by the optimization process.

As a result, in this data interpolation processing method, an appropriate waveform pattern (waveform pattern after interpolation processing) can be obtained, and the waveform pattern can be used, for example, in a PNN (Probabilistic neural network) model for predicting future values. By performing the learning process, it is possible to perform the learning process with high accuracy and efficiency. Further, by performing the prediction processing using the trained model acquired by the learning process on the waveform pattern acquired by this data interpolation processing method, highly accurate prediction processing can be realized.

Further, in this data interpolation processing method, optimization processing is performed based on an evaluation formula indicating that the difference between adjacent values (sample values defined by a predetermined sample period) in a time series falls within a predetermined range. Therefore, the acquired waveform pattern after interpolation becomes smooth. That is, in this data interpolation processing method, the data interpolation processing is performed so that the difference between the values of adjacent samples in the time series is within a predetermined range, so that the acquired waveform pattern after interpolation becomes smooth. , Appropriate interpolation data can be obtained.

The "observation data" is, for example, data (QoS data) indicating communication quality, and is, for example, an RSSI value.

Further, the "evaluation formula indicating that the difference between adjacent values in a time series falls within a predetermined range" is, for example, quantitatively the difference between the values (sample values) of adjacent samples in a time series. For example, the term (expression) included in the loss function when performing optimization processing (the change in the value between adjacent samples is small in the time series (the change in power between adjacent samples in the time series) It is a regularization term (restriction term) that makes it possible to obtain the optimum solution when there are few). The term (expression) included in the loss function when performing this optimization process is, for example, the value of an element obtained by the product of the matrices decomposed by the matrix decomposition process step, and is a sample value adjacent in time series. It is an equation (for example, (Equation 4) shown in the embodiment corresponds to this) for obtaining the sum of the absolute values of the differences between the values of the elements corresponding to (for example, the sum of the samples to be processed). By performing the optimization process by the loss function including such a regularization term, the optimum solution is the solution when the difference between adjacent values in the time series falls within a predetermined range (waveform pattern (time series). In, the change in the value between adjacent samples is gradual, and the probability of a smooth waveform pattern)) increases, and as a result, high-precision interpolation processing can be performed.

The second invention is the first invention, and the matrix factorization processing step acquires a decomposition matrix by performing singular value decomposition on the Hankel matrix R.

As a result, in this data interpolation processing method, a decomposition matrix can be obtained by singular value decomposition.

The third invention is the first or second invention, and the optimization processing step is an element R _ij (i, j: natural number, R) in which observation data exists among the elements of the Hankel matrix R. _ij : The first extraction process for extracting only the elements of the Hankel matrix R in row i and column j) is executed.

Then, the optimization processing step is an element A _ij (A _ij : i row of the product of the matrix decomposed by the matrix factorization processing step), which is an element of the product of the matrix decomposed by the matrix factorization processing step corresponding to the element. The second extraction process for extracting only the elements in column j) is executed.

Then, in the optimization processing step, the optimization processing is performed so that the error between the extracted element R _ij and the element A _ij is reduced.

Thereby, in this data interpolation processing method, for example, the optimization processing can be performed by evaluating the loss function regarding the error between the extracted element R _ij and the element A _ij .

A fourth aspect of the invention is the third aspect, wherein the optimization processing step is for the product of the Hankel matrix R and / or the matrix decomposed by the matrix factorization processing step by the selection matrix that selects a predetermined element. By performing the matrix operation, the first extraction process and / or the second extraction process is executed.

As a result, in this data interpolation processing method, only the elements necessary for the optimization processing can be easily extracted by using the selection matrix.

A fifth aspect of the invention is any one of the first to fourth aspects, wherein the interpolation data processing step is an element corresponding to a portion where observation data is missing, and is in the opposite angle direction of the optimization matrix. The average value or weighted average value of the arranged elements is acquired, and the data of the part where the observation data is missing is interpolated based on the acquired average value or weighted average value.

As a result, in this data interpolation processing method, the data of the part where the observation data is missing is obtained by a simple method of acquiring the average value or the weighted average value of the elements arranged in the opposite angle direction of the optimization matrix. Can be obtained.

The sixth invention is a data interpolation processing device for performing interpolation processing on intermittently acquired observation data, which includes an observation data acquisition unit, a data holding unit, a matrix generation unit, and a matrix factorization. It includes a processing unit, an optimization processing unit, and an interpolation data processing unit.

The observation data acquisition unit acquires observation data of data related to communication quality from the radio signal.

The data holding unit stores and holds the observation data acquired by the observation data acquisition unit for a predetermined period of time.

In the matrix generation unit, when the window corresponding to a predetermined unit period is shifted by the first hour, which is a predetermined period in the time direction, the data group included in the period corresponding to the window becomes an element of one row. The Hankel matrix R is generated in.

Then, when the data corresponding to the element of the Hankel matrix R is the observation data stored and held in the data holding unit, the matrix generation unit sets the data corresponding to the element in the observation data (1). 2) When the data corresponding to the element of the Hankel matrix R is not stored and held in the data holding unit, the Hankel matrix R is set to a value indicating that the data corresponding to the element is the data of the missing part. Generate.

The matrix factorization processing unit performs matrix factorization on the Hankel matrix R generated by the matrix factorization unit and acquires a decomposition matrix.

The optimization processing unit acquires an optimization matrix by performing optimization processing based on the element values acquired by the product of the matrices decomposed by the matrix factorization processing unit and the element values of the Hankel matrix. do.

The interpolation data processing unit interpolates the data of the portion where the observation data is missing based on the optimization matrix.

This makes it possible to realize a data interpolation processing device having the same effect as that of the first invention.

The seventh invention is a program for causing a computer to execute the data interpolation processing method according to any one of the first to fourth inventions.

This makes it possible to realize a program for causing a computer to execute a data interpolation processing method having the same effect as that of the first invention.

The eighth invention is a learning processing apparatus that performs learning processing of a model for predicting future values of observation data using the interpolation data acquired by the data interpolation processing method according to any one of the first to fifth inventions. be.

Thereby, in this learning processing apparatus, the learning processing can be performed using the interpolation data acquired by the data interpolation processing method according to any one of the first to fifth inventions.

The ninth invention is acquired by performing a learning process of a model for predicting future values of observation data using the interpolation data acquired by the data interpolation processing method according to any one of the first to fifth inventions. Equipped with a trained model
It is a prediction processing apparatus that predicts the future value of observation data by inputting the interpolation data acquired by the data interpolation processing method according to any one of the first to fifth inventions into the trained model.

As a result, in this learning processing device, the interpolated data acquired by the data interpolation processing method according to any one of the first to fifth inventions is input to the trained model to predict the future value of the observed data with high accuracy. It can be performed.

According to the present invention, even in a situation where observation data is acquired as intermittent data, a model that acquires data obtained by appropriately interpolating observation data and predicts future communication quality status using the data. It is possible to realize a radio condition prediction device capable of performing learning processing with high accuracy and appropriateness, and a data interpolation processing method and program used for the radio condition prediction device.

The schematic block diagram of the wireless condition prediction apparatus 100 which concerns on 1st Embodiment. The schematic block diagram of the data interpolation processing unit 1 of the radio state prediction apparatus 100 which concerns on 1st Embodiment. The figure for demonstrating the linear interpolation processing for the same waveform pattern when observation data is acquired intermittently. The figure for demonstrating the data interpolation processing for the same waveform pattern when observation data is acquired intermittently. The figure for demonstrating the process of acquiring the Hankel matrix from the observation data intermittently acquired in the waveform pattern of an RSSI value. The figure for demonstrating the matrix factorization process. The flowchart of the data interpolation processing executed by the wireless condition prediction apparatus 100. The figure for demonstrating the process of extracting the element which exists the observation data from the matrix R by the selection matrix Sk. The figure for demonstrating the process of extracting the data of the same row as the element which the observation data exists in the matrix R from the matrix P by the selection matrix Sk. The figure for demonstrating the process of extracting the element which exists the observation data from the matrix R by the selection matrix Si. The figure for demonstrating the process of extracting the data of the same column as the element which the observation data exists in the matrix R from the matrix P by the selection matrix Si. It is a figure for demonstrating the data interpolation process, and is the figure which showed the observation data (RSSI value) acquired intermittently, and the optimization matrix R_opt (the matrix acquired by the optimization process for Hankel matrix R). It is a figure for demonstrating the data interpolation process, and is the figure which showed the observation data (RSSI value) acquired intermittently, and the interpolation data acquired by the optimization matrix R_opt. In an environment where an AGV controlled by wireless communication patrols a predetermined route in a warehouse, the RSSI value (data acquired intermittently) of the acquired wireless signal is interpolated at an access point installed at a predetermined position. The figure which shows the data acquired in. In an environment where an AGV controlled by wireless communication patrols a predetermined route in a warehouse, the RSSI value (data acquired intermittently) of the acquired wireless signal is interpolated at an access point installed at a predetermined position. The figure which shows the prediction result data at the time of performing the prediction processing (prediction of RSSI value 10 seconds ahead) by the PNN model using the data acquired in the above. The figure which shows the CPU bus configuration.

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

<1.1: Configuration of wireless communication system>
FIG. 1 is a schematic configuration diagram of the radio condition prediction device 100 according to the first embodiment.

FIG. 2 is a schematic configuration diagram of the data interpolation processing unit 1 of the radio condition prediction device 100 according to the first embodiment.

As shown in FIG. 1, the radio condition prediction device 100 includes an antenna Ant1, a demodulation processing unit Dm1, an observation data acquisition unit FE1, a data interpolation processing unit 1, and a prediction processing unit 2.

The antenna Ant1 is an antenna for receiving an RF signal (for example, a carrier band OFDM signal) from the outside. The antenna Ant1 outputs the received RF signal (for example, a carrier band OFDM signal) as a signal RFin to the demodulation processing unit Dm1. The antenna Ant1 may be an antenna (transmission / reception antenna) that also functions as a transmission antenna.

The demodulation processing unit Dm1 includes an RF processing unit Dm11 and a BB processing unit Dm12.

The RF processing unit Dm11 executes RF demodulation processing on the signal RFin and acquires a baseband signal.

The BB processing unit Dm12 executes baseband demodulation processing on the baseband signal demodulated by the RF processing unit Dm11, acquires the signal (data) after the baseband demodulation processing as data D0, and acquires the acquired data D0. Is output to the observation data acquisition unit FE1.

The observation data acquisition unit FE1 inputs the data D0 output from the demodulation processing unit Dm1, and from the data D0, data indicating the QoS (Quality of Service) of the wireless communication environment in which the wireless condition prediction device 100 is placed (Quality of Service). Acquires a QoS value (data representing communication quality). Then, the observation data acquisition unit FE1 outputs the data including the acquired QoS value as the data D1 to the data interpolation processing unit 1.

The QoS value is an index value indicating communication quality such as received signal strength (RSSI: Received Signal Strength Indicator), throughput, number of (continuous) packet losses, delay amount, and the like.

As shown in FIG. 2, the data interpolation processing unit 1 includes a data holding unit 11, a matrix generation unit 12, a matrix factorization processing unit 13, an optimization processing unit 14, and an interpolation data acquisition unit 15.

The data holding unit 11 inputs the data D1 from the observation data acquisition unit FE1. The data holding unit 11 stores and holds the input data D1 for a predetermined period. The data holding unit 11 is realized by using, for example, a FIFO (First in First out) memory. The data holding unit 11 reads the data stored at a predetermined address according to the command from the matrix generation unit 12, and outputs the read data as data D_ptn to the matrix generation unit 12.

The matrix generation unit 12 reads data stored at a predetermined address to the data holding unit 11, and inputs the read data as data D_ptn from the data holding unit 11. The matrix generation unit 12 acquires the matrix R from the data D_ptn, and outputs the acquired matrix R (data including the matrix R) to the matrix factorization processing unit 13 and the optimization processing unit 14.

The matrix factorization processing unit 13 inputs data including the matrix R output from the matrix generation unit 12, and performs matrix factorization processing on the matrix R. The matrix factorization processing unit 13 outputs the data including the matrices R and Q acquired by the matrix factorization processing to the optimization processing unit 14.

The optimization processing unit 14 inputs data including the matrix R output from the matrix generation unit 12 and data including the matrices R and Q output from the matrix factorization processing unit 13. The optimization processing unit 14 performs optimization processing using the matrix R, the matrix P, and the Q (matrix P and Q obtained by matrix factorization of the matrix R), and acquires the optimization matrix R_opt. Then, the optimization processing unit 14 outputs the data including the acquired optimization matrix R_opt to the interpolation data acquisition unit 15.

The interpolation data acquisition unit 15 inputs the optimization matrix R_opt output from the optimization processing unit 14, performs interpolation processing based on the optimization matrix R_opt, and acquires interpolation data. Then, the interpolation data acquisition unit 15 outputs the data including the acquired interpolation data to the prediction processing unit 2 as data D1_intpl.

The prediction processing unit 2 has data D1_input output from the data interpolation processing unit 1 and a processing mode (for example, (1) learning processing mode and (2) prediction processing execution mode) output from the control unit (not shown). ) Is specified as a mode signal Mode.

When the mode signal Mode is a signal that specifies the learning processing mode, the prediction processing unit 2 uses the data D1_intpl for learning processing (for example, learning processing (training processing) for a learning model using a PNN model or a neural network model). ) Is executed.

When the mode signal Mode is a signal for designating the prediction processing execution mode, the prediction processing unit 2 executes the prediction processing for the data D1_intpl and outputs the data including the result data of the prediction processing as data Dout.

The "data interpolation processing device" is realized by the data interpolation processing unit.

<1.2: Operation of wireless condition prediction device>
The operation of the radio condition prediction device 100 configured as described above will be described below.

FIG. 3 is a diagram for explaining linear interpolation processing for the same waveform pattern when observation data is acquired intermittently. The upper figure of FIG. 3 is a diagram showing a waveform pattern (waveform pattern of RSSI value) when observation data is acquired intermittently, and the horizontal axis is time and the vertical axis is RSSI value. The lower figure of FIG. 3 is a diagram showing a waveform pattern (RSSI value waveform pattern) of observation data acquired by linear interpolation with respect to the waveform pattern of the upper figure of FIG. 3, where the horizontal axis is time and the vertical axis is vertical. The axis is the RSSI value.

FIG. 4 is a diagram for explaining data interpolation processing for the same waveform pattern when observation data is acquired intermittently. The upper figure of FIG. 4 is a diagram showing a waveform pattern (waveform pattern of RSSI value) when observation data is intermittently acquired, and the horizontal axis is time and the vertical axis is RSSI value. The lower figure of FIG. 4 shows the waveform pattern of the observation data (RSSI value waveform pattern) acquired by the data interpolation process (data interpolation process executed by the radio condition prediction device 100) with respect to the waveform pattern of the upper figure of FIG. ), The horizontal axis is time, and the vertical axis is RSSI value.

FIG. 5 is a diagram for explaining a process of acquiring a Hankel matrix from observation data intermittently acquired in a waveform pattern of RSSI values.

FIG. 6 is a diagram for explaining the matrix factorization process.

FIG. 7 is a flowchart of the data interpolation process executed by the radio condition prediction device 100.

FIG. 8 is a diagram for explaining a process of extracting an element in which observation data exists from the matrix R by the selection matrix _Sk .

FIG. 9 is a diagram for explaining a process of extracting data in the same row as an element in which observation data exists in the matrix R from the matrix P by the selection matrix _Sk .

FIG. 10 is a diagram for explaining a process of extracting an element in which observation data exists from the matrix R by the selection matrix _Si .

FIG. 11 is a diagram for explaining a process of extracting data in the same column as an element in which observation data exists in the matrix R from the matrix P by the selection matrix _Si .

First, interpolation processing for a waveform pattern in which observation data (for example, RSSI value) is intermittently acquired will be described.

For example, as shown in FIG. 3, when the waveform pattern of the RSSI value at time tt ₁ to time tt ₂ and the waveform pattern of the RSSI value at time tt ₃ to time tt ₄ are the same, the observed data is used. The case where linear interpolation is performed will be described. As shown in the left figure of FIG. 3, it is assumed that the data of the parts shown by D1_observed and D2_observed were observed (data could be acquired) from the time tt ₁ to the time tt ₂ , and the right figure of FIG. As shown in the above, it is assumed that the data of the parts indicated by D3_observed and D4_observed were observed (data could be acquired) from time tt ₃ to time tt ₄ .

In this case, when linear interpolation is performed using the observation data (data of the portion shown by D1_observed and D2_observed) in the left figure of FIG. 3, the waveform pattern as shown in the lower left figure of FIG. 3 (after linear interpolation) is performed. Waveform pattern) is acquired.

Further, when linear interpolation is performed using the observation data (data of the portion shown by D3_observed and D4_observed) in the right figure of FIG. 3, the waveform pattern as shown in the lower right figure of FIG. 3 (waveform pattern after linear interpolation) is performed. ) Is acquired.

In this way, when the data of the data missing part is interpolated by linear interpolation for the same waveform pattern, the linear interpolation is performed depending on which part of the waveform pattern the observed data is (depending on the position of the missing part of the observed data). The acquired waveform pattern will be different. If the same waveform pattern is linearly interpolated and becomes a different waveform pattern (different waveform pattern) when the missing part of the observation data is different, the future value will be used using the waveform pattern obtained by linear interpolation. When learning processing such as a PNN model for prediction is performed, the accuracy and efficiency of the learning processing deteriorate. In other words, if the waveform patterns obtained by linear interpolation are different waveform patterns even though they are originally the same waveform pattern, the learning process will be executed as different waveform patterns, which is an appropriate future. It becomes impossible to acquire a trained model that performs value prediction. Further, if the waveform patterns acquired by linear interpolation become different waveform patterns even though they are originally the same waveform patterns, the number of waveform patterns increases inappropriately, and the efficiency of the learning process becomes high. Getting worse.

In order to solve such a problem of linear interpolation, in the radio condition prediction device 100, as shown in FIG. 4, when the observation data is intermittently acquired, the observation data acquisition portion (missing data portion). However, when the data interpolation processing is performed on the same waveform pattern, the data interpolation processing is performed so that substantially the same waveform pattern (wave pattern after the interpolation processing) is acquired. As a result, the wireless condition prediction device 100 can acquire an appropriate waveform pattern (waveform pattern after interpolation processing), and is highly accurate and efficient learning processing (learning processing such as a PNN model for predicting future values). )It can be performed.

In the following, the operation of the wireless condition prediction device 100 will be described separately for (1) operation of learning processing (operation in learning processing mode) and (2) operation of prediction processing (operation in prediction processing execution mode). do. Further, it will be described with reference to the flowchart of FIG.

(1.2.1: Learning process (operation in learning process mode))
First, the learning process (operation in the learning process mode) will be described.

The demodulation processing unit Dm1 of the radio condition prediction device 100 executes demodulation processing on the radio signal received via the antenna Ant1 and acquires an RF demodulation signal and a BB demodulation signal. The observation data acquisition unit FE1 is an index indicating communication quality such as a QoS value (throughput, (continuous) packet loss number, delay amount, etc.) from the RF demodulation signal and / or the BB demodulation signal acquired by the demodulation processing unit Dm1. Value). For convenience of explanation, the QoS value will be described below as an RSSI value (signal reception strength).

Then, the observation data acquisition unit FE1 outputs the data including the acquired RSSI value as the data D1 to the data interpolation processing unit 1.

The data holding unit 11 of the data interpolation processing unit 1 stores and holds the input data D1 for a predetermined period. Here, it is assumed that the data holding unit 11 is realized by using a FIFO (First in First out) memory. The FIFO memory may be realized by using, for example, a dual-port RAM.

The data holding unit 11 stores and holds data for a period corresponding to Ts × (Nw + Ns-1), where the sample cycle Ts is the cycle for acquiring one sample of the FIFO memory (the cycle for inputting one data to the FIFO memory). do. That is, the data holding unit 11 stores and holds (Nw + Ns-1) sample data.

The data holding unit 11 inputs data having a value of "0" (RSSI value) into the FIFO memory during a period in which observation data cannot be acquired (data missing period) from the observation data acquisition unit FE1, and the observation data is generated. During the acquisition period, the RSSI value of the observation data shall be input to the FIFA memory.

The matrix generation unit 12 reads the data stored in the data retention unit 11 for a predetermined period as data D_ptn to the data retention unit 11. Specifically, the matrix generation unit 12 reads out (Nw + Ns-1) sample data stored in the data holding unit 11 and acquires Ns row data as shown below to obtain Ns rows and Nw columns. (Hankel matrix R) is acquired (step S1 in FIG. 7).
(1) The data (sample) r ₁ to r _Nw stored (input) in the FIFO memory of the data holding unit 11 during the period from time t ₁₁ to t ₁₂ are the elements of the first row of the matrix R (Nw elements). ).
( ₂ ) Data (samples) r2 to _{rNw + 1} stored (input) in the FIFO memory of the data holding unit 11 during the period of time t ₁₁ + Ts to t ₁₂ + Ts are the elements (Nw) in the second row of the matrix R. Element). Note that Ts is a sample cycle when data is acquired in the FIFO memory of the data holding unit 11.
( ₃ ) The data (sample) r3 to _{rNw + 2} stored (input) in the FIFO memory of the data holding unit 11 during the period of time t ₁₁ + Ts × 2 to t ₁₂ + Ts × 2 is the third row of the matrix R. Let it be an element (Nw elements).
・ ・ ・
(K) Data (sample) r _k to r _{Nw + k-} stored (input) in the FIFO memory of the data holding unit 11 during the period from time t ₁₁ + Ts × (k-1) to t ₁₂ + Ts × (k-1). Let ₁ be an element (Nw elements) of the kth row (k: natural number, 1 ≦ k ≦ Ns) of the matrix R.
・ ・ ・
Data (sample) r _Ns to r _{Nw +} Ns- stored (input) in the FIFO memory of the data holding unit 11 during the period (Ns) time t ₁₁ + Ts × (Ns-1) to t ₁₂ + Ts × (Ns-1). Let ₁ be an element (Nw elements) of the Nsth row (k: natural number, 1 ≦ k ≦ Ns) of the matrix R.

The matrix R (Hankel matrix R) of Ns rows and Nw columns acquired by the matrix generation unit 12 as described above shifts the sliding window Win1 shown in FIG. 5 by one sample period in the direction of the arrow Dir1 in FIG. It corresponds to the matrix obtained by making the data in the sliding window an element in one row. As can be seen from FIG. 5, the matrix R is a matrix in which the observed data moves diagonally downward to the left, and the element of the portion without the observed data (element of the missing data portion) has a value of “0”. In the Hankel matrix R shown in the lower left figure of FIG. 5, the data in the portion shown by the solid line is an element of the RSSI value of the observation data, and the white background portion is an element of the value “0”. In the Hankel matrix R shown in the lower right figure of FIG. 5, the data in the gray portion is an element of the RSSI value of the observation data, and the white portion is an element of the value “0”.

That is, the matrix R of the Ns row and Nw column acquired as described above is a Hankel matrix in which only the anti-diagonal component is a value other than "0". The Hankel matrix is defined by a square matrix, but even in the case of a matrix other than the square matrix, when the opposite angle components are the same (elements of i-row j-column (observation data) and i + 1-row j). (When the elements in column -1 are the same), assuming that it is a Hankel matrix in a broad sense, such a matrix is hereinafter referred to as a Hankel matrix.

The matrix generation unit 12 outputs the data including the Hankel matrix R acquired as described above to the matrix factorization processing unit 13 and the optimization processing unit 14.

The matrix factorization processing unit 13 performs a matrix factorization process on the Hankel matrix R acquired by the matrix factorization unit 12. Specifically, the matrix factorization processing unit 13 performs a process of acquiring (calculating) the effective rank number (rank) L of the Hankel matrix R by a known method, and the effective rank number of the Hankel matrix R. Get L.

Then, the matrix factorization processing unit 13 performs singular value decomposition on the Hankel matrix R. The effective number of ranks refers to the number of non-zero singular values after considering a singular value that is very small compared to the maximum singular value (the one with the maximum absolute value of the singular value) as 0. The singular value regarded as 0 is determined as, for example, a singular value having an absolute value of 1/10 or less of the absolute value of the maximum singular value. By using an effective number of ranks, it is possible to reduce the influence of noise caused by error factors such as the deviation of the observation timing and the deviation of the route to which the wireless terminal has moved. In general, the matrix R can be expressed as follows by performing a singular value decomposition on the matrix R having an effective number of ranks L.
R = UΣV ^T
U: Unitary matrix composed of left singular vectors Σ: Matrix whose diagonal components have singular values (hereinafter referred to as "singular value matrix")
V: Unitary matrix composed of right singular vectors Here, in the singular value matrix Σ, when the effective number of ranks is L, the elements from the first row to the Lth row of the diagonal components are non-zero. And the values of the other elements are "0". That is, the values of the diagonal components σ ₁₁ , σ ₂₂ , ..., Σ _LL of the singular value matrix Σ are non-zero. Note that σ _ij represents an element of i rows and j columns. Further, ^{AT represents the transpose of the matrix A (AT is} the transpose matrix of the matrix A).

The matrix factorization processing unit 13 performs singular value decomposition and acquires the unitary matrix U, the singular value matrix Σ, and the unitary matrix ^VT . Then, the matrix factorization processing unit 13
P = U _{:, 1: L} Σ ^0.5 _{1: L, 1: L}
Q = Σ ^0.5 _{1: L, 1} : L ^VT _{1: L ,:}
L: Performs processing corresponding to the effective number of ranks of the matrix R, and acquires the matrix P and the matrix Q. Assuming that the matrix A is an m × n (m rows and n columns) matrix having a real number as an element, and the component of the i rows and j columns of the matrix A is x _ij , (1) A ^0.5 , (2). ) A _{a: b, c: d} , (3) A _{a ,:} , and (4) A _{:, a} shall mean the following contents.
(1) A ^0.5 : A matrix in which the components of i-row and j-column are sqrt (x _ij ) (matrix of m × n) (sqrt (x) represents the square root of x)
(2) A _{a: b, c: d :} A matrix in which the elements in rows a to b of the matrix A and the elements in the c column of the matrix A are extracted from the elements in the d column. Matrix from which elements in row a are extracted (4) A _{:, a} : Matrix from which elements in column a of matrix A are extracted As shown in FIG. 6, the matrix R of m × n is the unitary matrix U of n × n. , N × m singular value matrix Σ and m × m unitary matrix V ^transposed matrix VT can be expressed as a product. Then, when the effective number of ranks of the matrix R is L, only the values of the diagonal components σ ₁₁ , σ ₂₂ , ..., Σ _LL of the singular value matrix Σ are non-zero, which is shown in FIG. like,
R = UΣV ^T
= U _{:, 1: L} Σ _{1: L, 1: L} V ^T _{1: L ,:}
= U _{:, 1: L} Σ ^0.5 _{1: L, 1: L} Σ ^0.5 _{1: L, 1} : L ^VT _{1: L ,:}
Is true. therefore,
P = U _{:, 1: L} Σ ^0.5 _{1: L, 1: L}
Q = Σ ^0.5 _{1: L, 1} : L ^VT _{1: L ,:}
By
R ≒ PQ
Will be. That is, the matrix R can be represented by the product of the n × L matrix P and the L × m matrix Q. In the singular value decomposition, since the singular value with a small value caused by the influence of noise etc. is ignored, the above R and PQ are not strictly equivalent. (The notation is that R and PQ are almost the same). Further, in FIG. 6, a singular value smaller than a predetermined value (for example, a singular value within an error range) is regarded as “0” and a singular value matrix Σ or the like is shown.

The matrix factorization processing unit 13 performs processing corresponding to the above formula on the Hankel matrix R (matrix of Ns × Nw) having an effective rank number L, and performs processing corresponding to the above equation, and the matrix P of Ns × L and the matrix P of L × Nw. Acquire the matrix Q (step S2 in FIG. 7). Then, the matrix factorization processing unit 13 outputs the acquired data including the matrices P and Q to the optimization processing unit 14.

λ：実数
μ：実数

なお、Ｒ_ｉ，ｋは、行列Ｒのｉ行ｋ列目の要素（の値）を表しており、｜｜Ａ｜｜_Ｆは、行列Ａのフロベニウスノルムを表している。また、集合Ωは、ハンケル行列Ｒの要素のうち、観測データが取得された要素のインデックス（ｉ，ｋ）の集合である。つまり、Ｒ_ｉ，ｋは、実際に観測されたデータ（観測データ（ＲＳＳＩ値））を有する要素（行列Ｒの要素）である。損失関数Ｌｏｓｓ（Ｐ，Ｑ）の第３項（μＪ_３（Ｐ，Ｑ））は、時系列において隣接するデータ（ＲＳＳＩ値）の値が近似していること（電力が大きく変化しないこと）に基づいて設定した制限項（正則化項）である。第３項（μＪ_３（Ｐ，Ｑ））を含む損失関数Ｌｏｓｓ（Ｐ，Ｑ）を用いて最適化処理を行うことで、最適化処理により取得される波形パターン（ＲＳＳＩ値の波形パターン）において、補間データが時系列で滑らかに接続された波形パターンになる（隣接するサンプル点間の変動が所定の範囲に抑えられた波形パターンになる）。 The optimization processing unit 14 performs optimization processing using the Hankel matrix R, the matrix P, and Q (matrix P and Q obtained by matrix factorizing the Hankel matrix R), and acquires the optimization matrix R_opt. Specifically, the optimization processing unit 14 sets the loss function Loss (P, Q) as shown in the following mathematical formula.

λ: real number μ: real number

Note that R _{i and k} represent the elements (values) of the i-th row and k-th column of the matrix R, and || A || _F represents the Frobenius norm of the matrix A. Further, the set Ω is a set of indexes (i, k) of the elements of the Hankel matrix R from which the observation data has been acquired. That is, R _{i and k} are elements (elements of the matrix R) having actually observed data (observation data (RSSI value)). The third term (μJ ₃ (P, Q)) of the loss function Loss (P, Q) is that the values of adjacent data (RSSI values) in the time series are close (the power does not change significantly). It is a restriction term (regularization term) set based on this. In the waveform pattern (RSSI value waveform pattern) acquired by the optimization process by performing the optimization process using the loss function Ross (P, Q) including the third term (μJ ₃ (P, Q)). , The interpolated data becomes a waveform pattern that is smoothly connected in chronological order (a waveform pattern in which the fluctuation between adjacent sample points is suppressed within a predetermined range).

行列Ｐ、Ｑの最適解Ｐ_ｏｐｔ、Ｑ_ｏｐｔは、下記数式を満たすＰ、Ｑを求めることで取得できる。

上記数式を満たす行列Ｐ、Ｑを、それぞれ、Ｐ_ｏｐｔ、Ｑ_ｏｐｔとすると、行列Ｐ_ｏｐｔ、Ｑ_ｏｐｔは、下記数式に相当する処理を行うことで取得できる。 Then, the optimization processing unit 14 acquires the optimum solutions _Popt and _Qopt of the matrices P and Q by performing the processing corresponding to the following mathematical formula.

The optimum solutions _Popt and _Qopt of the matrices P and Q can be obtained by finding P and Q satisfying the following mathematical formulas.

Assuming that the matrices P and Q satisfying the above formula are _Popt and Q _Op , respectively, the matrix _Popt and Q _Opt can be obtained by performing the processing corresponding to the following formula.

Ｉ：単位行列
（２）ｋ＝Ｎ_ｗのとき

なお、上記数式に相当する処理を行うと、計算量が多くなり、処理効率が悪くなる。そこで、最適化処理部１４は、選択行列を用いて、行列Ｒの要素のうち観測データが存在する要素（集合Ωに含まれるインデックス（ｉ，ｋ）の要素）のみを抽出して、処理を行うことで、行列Ｐ、Ｑの最適解Ｐ_ｏｐｔ、Ｑ_ｏｐｔを取得する。これについて、具体的に説明する。 Since the domain of J ₃ (P, Q) is 1 ≦ k ≦ N _w -1 (k: integer), Q _opt is divided into the following cases (1) and (2). It is required as follows.
(1) When 1 ≦ k ≦ N _w -1

I: Identity matrix (2) When k = N _w

If the processing corresponding to the above formula is performed, the amount of calculation increases and the processing efficiency deteriorates. Therefore, the optimization processing unit 14 uses the selection matrix to extract only the elements of the matrix R in which the observation data exists (elements of the index (i, k) included in the set Ω) and perform processing. By doing so, the optimum solutions _Popt and _Qopt of the matrices P and Q are obtained. This will be specifically described.

なお、上記において、行列Ｓ_ｋは、選択行列であり、ｎ×ｍのハンケル行列Ｒのｋ列において、観測データを有している要素の数がα個である場合、最適化処理部１４は、以下のようにして、α×ｎの選択行列Ｓ_ｋを生成する。 << 1: Optimization process for Q (step S4) >>
The optimization processing unit 14 extracts only the elements in which the observation data exists in the k-column (the column in which the observation data exists) of the Hankel matrix. Specifically, the optimization processing unit 14 performs a process corresponding to the following mathematical formula, and extracts only the element in which the observation data exists in the k column (the column in which the observation data exists) of the Hankel matrix R.

In the above, the matrix Sk is a selection matrix, and when the number of elements having observation data is α in the _k -column of the n × m Hankel matrix R, the optimization processing unit 14 is used. , The selection matrix Sk of α × _n is generated as follows.

When an element having observation data in column k of the Hankel matrix R is detected in ascending order with respect to the row number, the element is set as the αth element from the first element, and the qth (q: natural number, Assuming that the row number of the element of 1 ≦ q ≦ α) is row (q), the optimization processing unit 14 sets the element of the qth row of the selection matrix Sk to the value “1” only in the row ( _q ) column. , And the values of the other columns are set to be "0".

An example of the selection matrix _Sk generated in this way is shown in FIG. In FIG. 8, the elements (elements of known parts) having the observation data of the kth column of the Hankel matrix R are the elements of the first row, the sixth row, the seventh row, and the nth row (four elements). The case is shown. As shown in the lower figure of FIG. 8, the optimization processing unit 14 performs processing corresponding to Sk R _{:, k to} extract only the elements having the observation data in the k column of the Hankel matrix R. You can get the matrix x.

選択行列Ｓ_ｋにより、行列Ｐ_ｐａｒｔを取得する場合の一例を図９に示す。図９では、ハンケル行列Ｒの第ｋ列の観測データを有している要素（既知部分の要素）が第１行、第６行、第７行、第ｎ行の要素（４個の要素）である場合を示している。図９の下図に示すように、最適化処理部１４は、Ｓ_ｋＰに相当する処理を行うことで、行列Ｐにおいて、ハンケル行列Ｒのｋ列（観測データが存在する列）の観測データが存在する要素と同一行のデータ（要素）を抽出した行列Ｐ_ｐａｒｔを取得できる。 Further, the optimization processing unit 14 uses the selection matrix Sk, and in the matrix P, the data (element) in the same row as the element in which the observation data of the _k column (column in which the observation data exists) of the Hankel matrix R exists. To extract. Specifically, the optimization processing unit 14 takes the product of the selection matrix Sk and the matrix P, so that the observation data of the _k column (the column in which the observation data exists) of the Hankel matrix R exists in the matrix P. Extract the data (element) in the same row as the element to be used. That is, by executing the process corresponding to the following mathematical formula, the optimization processing unit 14 has the same row as the element in which the observation data of the k column (the column in which the observation data exists) of the Hankel matrix R exists in the matrix P. You can get the matrix P _part from which the data (elements) are extracted.

FIG. 9 shows an example of acquiring the matrix P- _part by the selection matrix _Sk . In FIG. 9, the elements (elements of the known part) having the observation data of the kth column of the Hankel matrix R are the elements of the first row, the sixth row, the seventh row, and the nth row (four elements). The case is shown. As shown in the lower figure of FIG. 9, the optimization processing unit 14 performs a process corresponding to Sk P, so that the observation data of the _k column (the column in which the observation data exists) of the Hankel matrix R can be obtained in the matrix P. It is possible to acquire a matrix _Ppart that extracts data (elements) in the same row as existing elements.

そして、最適化処理部１４は、ハンケル行列Ｒのｋ列目の観測データに注目した損失関数ＬｏｓｓＡ（Ｐ，Ｑ）を下記数式のように設定する。

そして、最適化処理部１４は、上記損失関数ＬｏｓｓＡ（Ｐ，Ｑ）の値を最小にする行列Ｑ（行列Ｑ_：，ｋ）を求める。つまり、最適化処理部１４は、下記数式を満たす行列Ｑ（行列Ｑ_：，ｋ）を求める。

上記数式を満たす行列Ｑ（行列Ｑ_：，ｋ）は、下記数式により取得されるので、最適化処理部１４は、下記数式に相当する処理を行うことで、上記の損失関数ＬｏｓｓＡ（Ｐ，Ｑ）の値を最小にする行列Ｑ_：，ｋを取得する（１≦ｋ≦Ｎ_ｗ－１の場合）。

最適化処理部１４は、上記処理により取得された行列Ｑ_：，ｋの値を行列Ｑに設定（更新）する（行列Ｑの該当する要素の値を、行列Ｑ_：，ｋで取得された値に更新する）。 The optimization processing unit 14 uses the matrix P _part acquired as described above and the matrix Q _{:, k obtained} by extracting the k-th column of the matrix Q to perform processing corresponding to the following mathematical formula, thereby performing Hankel. It is possible to efficiently (reduce the amount of calculation) the error between the RSSI value of the observation data in the kth column of the matrix R and the value acquired by the product of the matrices P and Q acquired by matrix decomposition. .. That is, the optimization processing unit 14 extracts the observation data of the k-th column of the Hankel matrix R, the matrix P _part acquired by the selection matrix Sk, and the matrix Q from which the _k -th column of the matrix Q is extracted. The error from the matrix obtained by the product of _{: and k} can be efficiently performed by performing the processing corresponding to the following mathematical formula.

Then, the optimization processing unit 14 sets the loss function LossA (P, Q) focusing on the observation data in the kth column of the Hankel matrix R as shown in the following mathematical formula.

Then, the optimization processing unit 14 obtains a matrix Q (matrix Q _{:, k} ) that minimizes the value of the loss function LossA (P, Q). That is, the optimization processing unit 14 obtains a matrix Q (matrix Q _{:, k} ) that satisfies the following mathematical formula.

Since the matrix Q (matrix Q _{:, k} ) satisfying the above formula is acquired by the following formula, the optimization processing unit 14 performs the processing corresponding to the following formula to perform the above-mentioned loss function LossA (P, Q). ) Matrix Q _{:, k} is acquired (in the case of 1 ≦ k ≦ N _w -1).

The optimization processing unit 14 sets (updates) the value of the matrix Q _{:, k} acquired by the above processing in the matrix Q (the value of the corresponding element of the matrix Q is the value acquired by the matrix Q _{::, k} ). Update to).

Then, the optimization processing unit 14 repeatedly executes the above processing for k satisfying 1 ≦ k ≦ N _w -1.

最適化処理部１４は、上記処理により取得された行列Ｑ_：，ｋの値を行列Ｑに設定（更新）する（行列Ｑの該当する要素の値を、行列Ｑ_：，ｋで取得された値に更新する）。 Then, when k = N _W , the matrix Q (matrix Q _{:, k} ) satisfying the above (mathematical expression 15) is acquired by the following mathematical expression, so that the optimization processing unit 14 performs processing corresponding to the following mathematical expression. By doing so, the matrix Q _{:, k} that minimizes the value of the loss function LossA (P, Q) is acquired.

The optimization processing unit 14 sets (updates) the value of the matrix Q _{:, k} acquired by the above processing in the matrix Q (the value of the corresponding element of the matrix Q is the value acquired by the matrix Q _{::, k} ). Update to).

That is, the optimization processing unit 14 executes the above processing (fixing the matrix P and optimizing the matrix Q) for all the columns in which the observation data exists in the Hankel matrix R.

なお、上記において、行列Ｓ_ｉは、選択行列であり、ｎ×ｍのハンケル行列Ｒのｉ行において、観測データを有している要素の数がα個である場合、最適化処理部１４は、以下のようにして、α×ｍの選択行列Ｓ_ｉを生成する。 << 2: Optimization process for P (step S5) >>
Next, the optimization processing unit 14 fixes the matrix Q and performs optimization processing on the matrix P. Specifically, the optimization processing unit 14 performs a process corresponding to the following mathematical formula, and extracts only the element in which the observation data exists in the i row (the row in which the observation data exists) of the Hankel matrix R.

In the above, the matrix S _i is a selection matrix, and when the number of elements having observation data is α in the i rows of the n × m Hankel matrix R, the optimization processing unit 14 is used. , The selection matrix S _i of α × m is generated as follows.

When an element having the observation data of row i of the Hankel matrix R is detected in ascending order with respect to the column number, the element is set as the αth element from the first element, and the qth (q: natural number, Assuming that the column number of the element of 1 ≦ q ≦ α) is col (q), the optimization processing unit 14 sets the element of the qth row of the selection matrix _Si to the value “1” only in the col (q) column. , And the values of the other columns are set to be "0".

An example of the selection matrix _Si generated in this way is shown in FIG. In FIG. 10, the elements (elements of known parts) having the observation data of the i-th row of the Hankel matrix R are the elements of the first column, the sixth column, the seventh column, and the m-th column (four elements). The case is shown. As shown in the lower figure of FIG. 10, the optimization processing unit 14 performs a process corresponding to S _i R ^T _{i, :} , so that only the element having the observation data is selected in the i row of the Hankel matrix R. The extracted matrix y can be obtained.

選択行列Ｓ_ｉにより、行列Ｑ_ｐａｒｔを取得する場合の一例を図１１に示す。図１１では、ハンケル行列Ｒの第ｉ行の観測データを有している要素（既知部分の要素）が第１列、第６列、第７列、第ｍ列の要素（４個の要素）である場合を示している。図１１の下図に示すように、最適化処理部１４は、Ｓ_ｉＱ^Ｔに相当する処理を行うことで、行列Ｑにおいて、ハンケル行列Ｒのｉ行（観測データが存在する行）の観測データが存在する要素と同一列のデータ（要素）を抽出した行列Ｑ_ｐａｒｔを取得できる。 Further, the optimization processing unit 14 uses the selection matrix S _i , and in the matrix Q, the data (element) in the same column as the element in which the observation data of the i row (the row in which the observation data exists) of the Hankel matrix R exists. To extract. Specifically, the optimization processing unit 14 obtains the observation data of the i row (the row in which the observation data exists) of the Hankel matrix R in the matrix Q by taking the product of the selection matrix S _i and the matrix Q ^T. Extract the data (element) in the same column as the existing element. That is, by executing the process corresponding to the following mathematical formula, the optimization processing unit 14 has the same column as the element in which the observation data of the i-row (the row in which the observation data exists) of the Hankel matrix R exists in the matrix Q. You can get the matrix Q _part from which the data (elements) are extracted.

FIG. 11 shows an example of acquiring the matrix Q _part by the selection matrix S _i . In FIG. 11, the elements (elements of known parts) having the observation data of the i-th row of the Hankel matrix R are the elements of the first column, the sixth column, the seventh column, and the m-th column (four elements). The case is shown. As shown in the lower figure of FIG. 11, the optimization processing unit 14 performs the processing corresponding to S iQ ^T , and in the matrix Q, the observation data of the _i row (the row in which the observation data exists) of the Hankel matrix R. You can get the matrix Q _part that extracts the data (elements) in the same column as the element in which.

そして、最適化処理部１４は、ハンケル行列Ｒのｉ行目の観測データに注目した損失関数ＬｏｓｓＢ（Ｐ，Ｑ）を下記数式のように設定する。

そして、最適化処理部１４は、上記損失関数ＬｏｓｓＢ（Ｐ，Ｑ）の値を最小にする行列Ｐ（行列Ｐ^Ｔ _ｉ，：）を求める。つまり、最適化処理部１４は、下記数式を満たす行列Ｐ（行列Ｐ^Ｔ _ｉ，：）を求める。

上記数式を満たす行列Ｐ（行列Ｐ^Ｔ _ｉ，：）は、下記数式により取得されるので、最適化処理部１４は、下記数式に相当する処理を行うことで、上記の損失関数ＬｏｓｓＢ（Ｐ，Ｑ）の値を最小にする行列Ｐ^Ｔ _ｉ，：を取得する。

最適化処理部１４は、上記処理により取得された行列Ｐ^Ｔ _ｉ，：の値を行列Ｐに設定（更新）する（行列Ｐの該当する要素の値を、行列Ｐ^Ｔ _ｉ，：で取得された値に更新する）。 The optimization processing unit 14 performs processing corresponding to the following mathematical formula using the matrix P ^T _{i ,:} extracted from the i-th row of the matrix P acquired as described above and the matrix Q _part . It is possible to efficiently (reduce the amount of calculation) the error between the RSSI value of the observation data of row i of the Hankel matrix R and the value acquired by the product of the matrices P and Q acquired by matrix decomposition. .. That is, the optimization processing unit 14 obtains by the matrix y from which the observation data of the i-th row of the Hankel matrix R is extracted, the matrix P ^T _{i ,:} from which the i-th row of the matrix P is extracted, and the selection matrix S _i . The error from the matrix obtained by the product of the matrix Q _part can be efficiently performed by performing the process corresponding to the following mathematical formula.

Then, the optimization processing unit 14 sets the loss function LossB (P, Q) focusing on the observation data in the i-th row of the Hankel matrix R as shown in the following mathematical formula.

Then, the optimization processing unit 14 obtains a matrix P (matrix P Ti _, :) that minimizes the value of the loss function ^LossB (P, Q). That is, the optimization processing unit 14 obtains a matrix P (matrix P ^Ti _{, :)} that satisfies the following mathematical formula.

Since the matrix P (matrix P Ti, :) satisfying the above formula is acquired by the following formula _, the optimization processing unit 14 performs the processing corresponding to the following formula to perform the above-mentioned loss function ^LossB (P, Acquire the matrix P ^T _{i ,:} that minimizes the value of Q).

The optimization processing unit 14 sets (updates) the value of the matrix P ^T _{i ,:} acquired by the above processing in the matrix P (the value of the corresponding element of the matrix P is acquired by the matrix P ^T _{i ,:)} . Update to the value).

Then, the optimization processing unit 14 repeatedly executes the above processing for all i. That is, in the Hankel matrix R, the above processing (fixing the matrix Q and optimizing the matrix P) is repeatedly executed for all the rows in which the observation data exists.

Then, the optimization processing unit 14 is acquired by the optimization processing for the matrix Q after performing the optimization processing for the matrix Q (step S4) and the optimization processing for the matrix P (step S5). The Hankel matrix R is updated (R = PQ) using the matrix Q and the matrix P acquired in the optimization process for the matrix P (step S6).

Then, as shown in the flowchart of FIG. 7, the above processing (steps S4 to S6) is repeated a predetermined number of times (in the flowchart of FIG. 7, the variable t is incremented by +1 and step S4 is performed while t is smaller than the predetermined number of times tmax. The process of S6 is repeated (steps S3 to S8).

The flowchart of FIG. 7 shows a case where the processes of steps S4 to S6 are repeated a predetermined number of times, but the present invention is not limited to this. For example, if the value of the loss function Loss (P, Q) does not fluctuate more than a value within a predetermined range even if the processes of steps S4 to S6 are repeatedly executed, it is determined that the optimization process of the matrix R has converged. The optimization processing unit 14 may end the processing of steps S4 to S6. Further, when the value of the loss function Loss (P, Q) becomes smaller than the predetermined value, it is determined that the optimization processing of the matrix R has converged, and the optimization processing unit 14 determines that the processing of steps S4 to S6. May be terminated.

The optimization processing unit 14 outputs the Hankel matrix R (Hankel matrix R after the optimization processing) acquired as described above to the data interpolation processing unit 15 as the optimization matrix R_opt.

<< Data interpolation processing (step S9) >>
The interpolation data acquisition unit 15 performs interpolation processing based on the optimization matrix R_opt output from the optimization processing unit 14, and acquires interpolation data. Specific processing will be described with reference to FIGS. 12 and 13.

FIG. 12 is a diagram for explaining the data interpolation process, and shows the observation data (RSSI value) intermittently acquired and the optimization matrix R_opt (matrix acquired by the optimization process for the Hankel matrix R). It is a figure. In the upper figure of FIG. 12, the horizontal axis is time and the vertical axis is RSSI value.

FIG. 13 is a diagram for explaining the data interpolation process, and is a diagram showing intermittently acquired observation data (RSSI value) and interpolation data acquired by the optimization matrix R_opt. In the upper figure of FIG. 13, the horizontal axis is time and the vertical axis is RSSI value.

In the case of FIGS. 12 and 13, the case where the optimization process is performed using the Hankel matrix R (Ns = 8, Nw = 13) of Ns × Nw and the optimization matrix R_opt of Ns × Nw is acquired is shown. ing. Further, in FIGS. 12 and 13, black circles indicate observation data (known portions).

In the case of FIGS. 12 and 13, r ₁ to r ₃ , r ₈ to r ₁₀ , r ₁₃ , r ₁₆ and r ₂₁ are data (samples) with observation data, and the other data (sample) are r ₄ to r ₇ and r. ₁₁ to r ₁₂ , r ₁₄ to r ₁₅ , and r ₁₇ to r ₂₀ are parts (samples) without observation data (data missing parts). In the optimization matrix R_opt shown in FIGS. 12 and 13, the elements to which the black circles are connected by solid lines indicate that they have the same value (same RSSI value).

In this case, as described above, in the radio condition prediction device 100, the Hankel matrix R (Ns = 8, Nw = 13) of Ns × Nw is generated (as an initial value, the element of the data missing portion is set to The optimization matrix R_opt is acquired by performing the above processing (processing of steps S2 to S8 in FIG. 7) with the value "0" inserted).

Then, as shown in FIG. 13, the interpolation data acquisition unit 15 of the radio condition prediction device 100 acquires the average value of the components (elements) in the opposite angle direction, which are the elements corresponding to the data (sample) of the data missing portion. Then, the acquired average value is used as the data (interpolated data) of the missing data. For example, in the case of FIG. 13, assuming that the elements of the i-by-j column of the optimization matrix R_opt are x _{i and j} , r ₄ to r ₇ , r ₁₁ to r ₁₂ , r ₁₄ to r ₁₅ , and r ₁₇ to r ₂₀ . Interpolated data of rh ₄ to rh ₇ , rh ₁₁ to rh ₁₂ , rh ₁₄ to rh ₁₅ , and rh ₁₇ to rh ₂₀ are as follows.
rh ₄ = Ave (x 1, ₄ , x ₂ , 3, x 3, ₂ , x 4, ₁ )
rh ₅ = Ave (x ₁ , 5, x _{2, 4} , x ₃ , 3, x ₄ , 2, x ₅ , 1)
rh ₆ = Ave (x _1,6 , x ₂ , 5, x ₃ , 4, x 4, ₃ , x 5, ₂ , x 6, ₁ )
rh ₇ = Ave (x _1,7 , x _2,6 , x _3,5 , x _4,4 , x _5,3 , x _6,2 , x ₇ , 1)
rh ₁₁ = Ave (x _1,11 , x _2,10 , x _3,9 , x _4,8 , x _5,7 , x _6,6 , x _7,5 , _x8,4 , _x9,3 )
rh ₁₂ = Ave (x _1,12 , x _2,11 , x _3,10 , x _4,9 , x _5,8 , x _6,7 , x _7,6 , x ₈ , 5, x 9, ₄ )
rh ₁₄ = Ave (x _2,13 , x _3,12 , x _4,11 , x _5,10 , x _6,9 , x _7,8 , _x8,7 , _x9,6 )
rh ₁₅ = Ave (x _3,13 , x _4,12 , x _5,11 , x _6,10 , x _7,9 , _x8,8 , _x9,7 )
rh ₁₇ = Ave (x _5,13 , x _6,12 , x _7,11 , _x8,10 , _x9,9 )
rh ₁₈ = Ave (x _6,13 , _x7,12 , _x8,11 , _x9,10 )
rh ₁₉ = Ave (x ₇ , 13, x ₈ , 12, x 9, ₁₁ )
rh ₂₀ = Ave (x ₈ , 13, x ₉ , 12)
Ave (): Function to acquire the average value of the elements In FIG. 13, the interpolated data rh ₄ to rh ₇ , rh ₁₁ to rh ₁₂ , rh ₁₄ to rh ₁₅ , and rh ₁₇ to rh ₂₀ obtained by the above processing are shown in FIG. In the upper figure of 13, it is indicated by a white circle. By performing the above processing in the data interpolation processing unit 1 of the wireless condition prediction device 100, appropriate interpolation data is acquired as shown in the upper figure of FIG.

In the above, the case of acquiring the average value of the components (elements) in the opposite angle direction of the optimization matrix R_opt using the function Ave () has been described, but the present invention is not limited to this, and for example, the optimum. The weighted average value of the components (elements) in the opposite angle direction of the conversion matrix R_opt may be acquired.

Then, the interpolation data acquisition unit 15 outputs the data including the interpolation data acquired in the above processing to the prediction processing unit 2 as data D1_intpl.

The prediction processing unit 2 executes a learning process (for example, a learning process (training process) of a learning model using a PNN model or a neural network model) using the data D1_intpl output from the data interpolation processing unit 1.

In the wireless condition prediction device 100, when the observation data is intermittently acquired and the data interpolation processing is performed on the same waveform pattern regardless of where the observation data acquisition portion (missing data portion) is. , Data interpolation processing is performed so that substantially the same waveform pattern (waveform pattern after interpolation processing) is acquired. That is, as described above, the radio condition prediction device 100 generates the Hankel matrix R from the observation data, performs the optimization process using the Hankel matrix R, and acquires the acquired optimization matrix R_opt. Then, in the radio condition prediction device 100, the data of the data missing portion is interpolated by the acquired optimization matrix R_opt.

Therefore, in the wireless condition prediction device 100, an appropriate waveform pattern (waveform pattern after interpolation processing) can be acquired, and the PNN model for future value prediction mounted on the prediction processing unit 2 can be obtained by using the waveform pattern. By performing the learning process, it is possible to perform a highly accurate and efficient learning process (learning process such as a PNN model for predicting future values).

(1.2.2: Prediction processing (operation in prediction processing execution mode))
Next, the prediction process (operation in the prediction process execution mode) will be described.

In the wireless condition prediction device 100, in the prediction processing execution mode, data interpolation processing is performed in the same manner as the processing in the learning processing mode, and the data D1_inputl after the interpolation processing is input to the prediction processing unit 2.

Then, in the prediction processing unit 2, a learned model (for example, a PNN model for predicting future values) acquired by executing a learning process using the data D1_input (wave pattern) after the interpolation processing is constructed. Therefore, the data D1_input (wave pattern) after the interpolation processing is input to the trained model, and for example, the data of the future value prediction result is acquired based on the output from the trained model. Then, the prediction processing unit 2 outputs, for example, the future value prediction result data acquired as described above as data Dout.

In the prediction processing by the prediction processing unit 2, when the processing using the PNN model is performed, for example, the techniques disclosed in Japanese Patent Application No. 2017-232442 and Japanese Patent Application No. 2018-042747 may be used.

In the wireless condition prediction device 100, when the observation data is acquired intermittently, substantially the same waveform pattern (wave pattern after interpolation processing) can be obtained regardless of where the observation data acquisition portion (missing data portion) is. Acquired data Interpolation processing is performed. Training processing is performed using the data D1_intpl after interpolation processing, and prediction processing is executed using the acquired trained model. Therefore, even if the observation data can be acquired only intermittently, the radio condition prediction device 100 performs the data interpolation processing using the observation data and the prediction processing using the data after the data interpolation processing. Therefore, highly accurate prediction processing (for example, future value prediction processing of RSSI value) can be performed.

≪Summary≫
As described above, in the radio condition prediction device 100, when the observation data is intermittently acquired, data interpolation processing is performed for the same waveform pattern regardless of where the observation data acquisition portion (missing data portion) is. When the above is performed, data interpolation processing is performed so that substantially the same waveform pattern (wave pattern after interpolation processing) is acquired. That is, as described above, the radio condition prediction device 100 generates the Hankel matrix R from the observation data, performs the optimization process using the Hankel matrix R, and acquires the acquired optimization matrix R_opt. The Hankel matrix R generated by the wireless condition prediction device 100 is a matrix acquired by stacking the data holding unit 11 of the data interpolation processing unit 1 while shifting the samples one by one. In a wireless application such as an AGV, since the wireless terminal (for example, the wireless terminal mounted on the AGV) repeatedly moves on a fixed route, the communication quality information to be interpolated also changes periodically. Therefore, the Hankel matrix generated by the radio condition prediction device 100 under such a situation has a low rank. Therefore, by decomposing the Hankel matrix into singular values, the number of non-zero singular values is reduced (the number of non-zero singular values is approximately the same as the number of effective ranks of the Hankel matrix R). Therefore, it can be decomposed into low-ranked matrices P and Q. Then, by performing the optimization process using the matrices P and Q obtained by decomposing the Hankel matrix R, it is possible to perform the optimization process with high accuracy while suppressing the amount of calculation.

Then, in the radio condition prediction device 100, the data of the missing portion can be interpolated with high accuracy by using the optimization matrix R_opt (matrix obtained by performing optimization processing on the Hankel matrix) acquired as described above. can.

As a result, the wireless condition prediction device 100 can acquire an appropriate waveform pattern (waveform pattern after interpolation processing), and using the waveform pattern, a PNN model for predicting future values mounted on the prediction processing unit 2 or the like. By performing the learning process of, it is possible to perform a highly accurate and efficient learning process (learning process such as a PNN model for predicting future values).

Further, in the wireless condition prediction device 100, a trained model (for example, a PNN model for predicting future values) acquired by the learning process is applied to an appropriate waveform pattern acquired by the data interpolation processing. Highly accurate prediction processing can be performed by performing the prediction processing used.

FIG. 14 shows, as an example, an RSSI value (intermittent acquisition) of an acquired radio signal at an access point installed at a predetermined position in an environment in which an AGV controlled by wireless communication circulates a predetermined route in a warehouse. The data obtained by interpolating the data to be obtained) is shown. In FIG. 14, the horizontal axis is the sample number (time series data number (corresponding to time)), and the vertical axis is the RSSI value. In FIG. 14, the data acquired by the interpolation by the data interpolation processing (interpolation processing executed by the radio condition prediction device 100) is shown as "interpolation by the matrix decomposition MFS", and further, the loss function is shown for comparison. The result data by data interpolation when Ross (P, Q) = J ₁ (P, Q) + λJ ₂ (P, Q) is shown as "interpolation by matrix decomposition MF".

As can be seen from FIG. 14, even when the observation data is intermittently acquired, the accuracy of the data acquired by the interpolation by the data interpolation processing (interpolation processing executed by the radio condition prediction device 100) (interpolation accuracy). ) Is higher than the data obtained by interpolation or linear interpolation based on the average value of the observed data. Further, it can be seen from FIG. 14 that the data acquired by the interpolation by the data interpolation processing (interpolation processing executed by the radio condition prediction device 100) is better than the data by the "interpolation by the matrix factorization MF". In "interpolation by matrix decomposition MF", the loss does not include the regularization term (third term (μJ ₃ (P, Q)) of the loss function Loss (P, Q)) that limits the smoothness of the waveform pattern. Since the optimization process is performed by the function, when the observation data is acquired at substantially equal intervals as shown in FIG. 14, it is interpolated by the high frequency component close to the period in which the observation data is acquired. Therefore, it becomes a state where overfitting is performed, and good interpolation data cannot be acquired.

On the other hand, in interpolation by data interpolation processing (interpolation processing executed by the radio condition prediction device 100) (“interpolation by matrix decomposition MFS”), a regularization term (loss function) that limits the smoothness of the waveform pattern is added. Since the optimization process is performed by the loss function including the third term (μJ ₃ (P, Q)) of Ross (P, Q), the observation data are acquired at approximately equal intervals as shown in FIG. Even in this case, it is possible to appropriately prevent a state in which over-learning has been performed and acquire appropriate interpolation data.

Further, as shown in FIG. 15, as an example, in an environment in which an AGV controlled by wireless communication circulates a predetermined route in a warehouse, an RSSI value (intermittently) of a wireless signal acquired at an access point installed at a predetermined position. The prediction result data when the prediction processing (prediction of RSSI value 10 seconds ahead) is performed by the PNN model using the data acquired by interpolating the data acquired in the above is shown.

As can be seen from FIG. 15, even when the observation data is intermittently acquired, the prediction process using the data acquired by the interpolation by the data interpolation process (interpolation process executed by the radio condition prediction device 100). The accuracy (interpolation accuracy) of is higher than the accuracy of the prediction processing using the data acquired by interpolation or linear interpolation based on the average value of the observed data.

In this way, by performing processing using the interpolation data acquired by executing the data interpolation processing in the wireless condition prediction device 100, the prediction processing can be performed with high accuracy even when the observation data is acquired only intermittently. Can be done.

[Other embodiments]
In the above embodiment, the case where the Hankel matrix R is decomposed into singular values when the data interpolation processing is performed in the data interpolation processing unit 1 has been described, but the redundancy of the Hankel matrix R is compressed without limitation. Matrix decomposition may be performed using another method as long as it is a method having possible characteristics (a method that can effectively utilize the low rank of the Hankel matrix R). For example, the Hankel matrix R may be matrix-decomposed by a method such as eigenvalue decomposition.

Further, in the above embodiment, the case where the second term of the loss function Loss (P, Q) is the L2 regularization term has been described, but the present invention is not limited to this, and the loss function Loss (P, Q) is not limited to this. The second term may be an L1 regularization term, or may be a term that can appropriately prevent other overfitting.

Further, in the above embodiment, the case where the processing is performed with the value of the element of the portion where the observation data of the Hankel matrix R does not exist is set to the value “0” has been described, but the process is not limited to this, and the observation of the Hankel matrix R is performed. Another value (for example, a value using a random number) may be set for the value of the element in the portion where there is no data, and the optimization process may be executed as the initial value of the Hankel matrix R.

Further, in the wireless condition prediction device 100 described in the above embodiment, each block may be individually integrated into one chip by a semiconductor device such as an LSI, or may be integrated into one chip so as to include a part or all of the blocks. good.

Although it is referred to as LSI here, it may be referred to as IC, system LSI, super LSI, or ultra LSI depending on the degree of integration.

Further, the method of making an integrated circuit is not limited to the LSI, and may be realized by a dedicated circuit or a general-purpose processor. An FPGA (Field Programmable Gate Array) that can be programmed after the LSI is manufactured, or a reconfigurable processor that can reconfigure the connection and settings of the circuit cells inside the LSI may be used.

Further, a part or all of the processing of each functional block of each of the above embodiments may be realized by a program. Then, a part or all of the processing of each functional block of each of the above embodiments is performed by the central processing unit (CPU) in the computer. Further, the program for performing each process is stored in a storage device such as a hard disk or a ROM, and is read and executed in the ROM or in the RAM.

Further, each process of the above embodiment may be realized by hardware, or may be realized by software (including the case where it is realized together with an OS (operating system), middleware, or a predetermined library). Further, it may be realized by mixed processing of software and hardware.

Further, for example, when each functional unit of the above embodiment is realized by software, the hardware configuration shown in FIG. 16 (for example, CPU (may be GPU), ROM, RAM, input unit, output unit, etc.) (Hardware configuration) connected by a bus Bus) may be used to realize each functional unit by software processing.

Further, when each functional unit of the above embodiment is realized by software, the software may be realized by using a single computer having the hardware configuration shown in FIG. 16, or a plurality of computers. It may be realized by the distributed processing using.

Further, the execution order of the processing methods in the above-described embodiment is not necessarily limited to the description of the above-mentioned embodiment, and the execution order can be changed without departing from the gist of the invention.

A computer program that causes a computer to perform the above-mentioned method and a computer-readable recording medium that records the program are included in the scope of the present invention. Here, examples of computer-readable recording media include flexible disks, hard disks, CD-ROMs, MOs, DVDs, DVD-ROMs, DVD-RAMs, large-capacity DVDs, next-generation DVDs, and semiconductor memories. ..

The computer program is not limited to the one recorded on the recording medium, and may be transmitted via a telecommunication line, a wireless or wired communication line, a network represented by the Internet, or the like.

The specific configuration of the present invention is not limited to the above-described embodiment, and various changes and modifications can be made without departing from the gist of the invention.

100 Wireless situation prediction device FE1 Observation data acquisition unit 1 Data interpolation processing unit 11 Data retention unit 12 Matrix generation unit 13 Matrix factorization processing unit 14 Optimization processing unit 15 Interpretation data acquisition unit 2 Prediction processing unit (prediction processing device, learning processing device) )

Claims (9)

It is a data interpolation processing method for performing interpolation processing on intermittently acquired observation data.
Observation data acquisition step to acquire observation data of communication quality data from wireless signals,
A data retention step that stores and retains the observation data acquired by the observation data acquisition step for a predetermined period of time, and a data retention step.
When the window corresponding to a predetermined unit period is shifted in the time direction by the first hour, which is a predetermined period, the Hankel matrix R is set so that the data group included in the period corresponding to the window becomes an element of one row. In the matrix generation step to be generated, (1) when the data corresponding to the element of the Hankel matrix R is the observation data stored and retained in the data retention step, the data corresponding to the element is used as the observation data. (2) When the data corresponding to the element of the Hankel matrix R is not stored and held in the data holding step, the data corresponding to the element is set to a value indicating that it is the data of the missing portion. Then, in the matrix generation step of generating the Hankel matrix R,
A matrix factorization processing step of performing a matrix factorization on the Hankel matrix R generated by the matrix generation step and acquiring a factorization matrix, and a matrix factorization processing step.
Based on the value of the element obtained by the product of the matrix decomposed by the matrix factorization processing step and the value of the element of the Hankel matrix, the difference between the adjacent values in the time series is within a predetermined range. The optimization processing step to acquire the optimization matrix by performing the optimization processing based on the evaluation formula indicating that it will be entered, and
An interpolation data processing step that interpolates the data of the portion where the observation data is missing based on the optimization matrix, and
A data interpolation processing method comprising. The matrix factorization processing step is
The decomposition matrix is obtained by performing a singular value decomposition on the Hankel matrix R.
The data interpolation processing method according to claim 1. The optimization processing step is
First extraction process for extracting only the element R _ij (i, j: natural number, R _ij : element of the Hankel matrix R in row i and column j), which is an element in which the observation data exists, among the elements of the Hankel matrix R. And run
Only the element _Aij (A _ij : the element of the i-by-j column of the product of the matrix decomposed by the matrix factorization processing step) corresponding to the element, which is the element of the product of the matrix decomposed by the matrix factorization processing step. Execute the second extraction process to extract
The optimization process is performed so that the error between the extracted element R _ij and the element A _ij is reduced.
The data interpolation processing method according to claim 1 or 2. The optimization processing step is
The first extraction process and / or the second Execute the extraction process,
The data interpolation processing method according to claim 3. The interpolation data processing step is
The average value or weighted average value of the elements corresponding to the part where the observation data is missing and arranged in the opposite angle direction of the optimization matrix is acquired, and the acquired average value or weighted average value is acquired. Interpolates the data of the part where the observation data is missing based on the value.
The data interpolation processing method according to any one of claims 1 to 4. A data interpolation processing device for performing interpolation processing on intermittently acquired observation data.
An observation data acquisition unit that acquires observation data related to communication quality from wireless signals,
A data holding unit that stores and holds the observation data acquired by the observation data acquisition unit for a predetermined period of time, and a data holding unit.
When the window corresponding to a predetermined unit period is shifted in the time direction by the first hour, which is a predetermined period, the Hankel matrix R is set so that the data group included in the period corresponding to the window becomes an element of one row. In the matrix generation unit to be generated, (1) when the data corresponding to the element of the Hankel matrix R is the observation data stored and held in the data holding unit, the data corresponding to the element is the observation data. (2) When the data corresponding to the element of the Hankel matrix R is not stored and held in the data holding unit, the data corresponding to the element is set to a value indicating that the data is the missing portion. As a result, the matrix generation unit that generates the Hankel matrix R and
A matrix factorization processing unit that performs matrix factorization on the Hankel matrix R generated by the matrix generation unit and acquires a decomposition matrix, and a matrix factorization processing unit.
Based on the value of the element obtained by the product of the matrix decomposed by the matrix factorization processing unit and the value of the element of the Hankel matrix, the difference between the adjacent values in the time series is within a predetermined range. An optimization processing unit that acquires an optimization matrix by performing optimization processing based on an evaluation formula that indicates that it will be entered.
An interpolation data processing unit that interpolates the data of the portion where the observation data is missing based on the optimization matrix, and
A data interpolation processing device comprising. A program for causing a computer to execute the data interpolation processing method according to any one of claims 1 to 5. A learning processing device that performs learning processing of a model for predicting future values of observation data using the interpolation data acquired by the data interpolation processing method according to any one of claims 1 to 5. The trained model acquired by performing the learning process of the model for predicting the future value of the observation data by using the interpolation data acquired by the data interpolation processing method according to any one of claims 1 to 5 is mounted. ,
A prediction processing device that predicts the future value of the observation data by inputting the interpolation data acquired by the data interpolation processing method according to any one of claims 1 to 5 into the trained model.

Images