Mesh value estimation device, mesh value estimation method, and program

Abstract

A mesh value estimation device according to the present invention comprises: an input unit that inputs the position of a mesh to be estimated, an observed value of a block, and a mesh set belonging to the block; a theoretical variogram estimation unit that estimates a model and parameters for a theoretical variogram necessary for estimating a mesh value; a mesh value estimation unit that estimates the mesh value using the model and parameters for the theoretical variogram estimated by the theoretical variogram estimation unit and an accommodation rate of blocks with respect to the mesh; and an output unit that outputs a final estimated value after the process of the theoretical variogram estimation unit and the process of the mesh value estimation unit have been repeatedly implemented until a preset objective function is optimized.

Description

Technical Field

[0001] The present invention relates to a technique for estimating mesh values based on observed values of blocks.

Background Art

[0002] Conventionally, a technique related to a spatial interpolation method for estimating a value at an estimation point using observed values obtained at a plurality of observation points existing in a target area has been known. Here, the observation point and the estimation point are the points where the observed value and the estimated value are obtained, and for example, they are position coordinates or a small area (hereinafter, mesh) centered on the position coordinates. The observed value and the estimated value are, for example, the number of users, the amount of underground resources, and the amount of precipitation. As a technique related to a spatial interpolation method for estimating a value at an estimation point using observed values obtained at a plurality of observation points existing in a target area as described above, for example, kriging is known as a typical technique.

[0003] Generally, kriging creates an empirical variogram from observed values obtained at a plurality of observation points, fits a theoretical variogram to the empirical variogram using a constrained nonlinear least squares method or the like, and estimates the value at the estimation point using the fitted theoretical variogram.

[0004] Here, the empirical variogram is a graph representing the relationship between the distance between observation points and the average dissimilarity with respect to that distance, and the theoretical variogram is a function representing the spatial characteristics between data. Kriging is classified into several methods such as simple kriging, ordinary kriging, universal kriging, and block kriging according to the assumed conditions and the type of observed values obtained. For example, Non-Patent Document 1 proposes a method using block kriging to create a distribution of an index related to the wheat yield.

[0005] While ordinary kriging is a method of estimating the value at an estimation point using the observed values obtained at the observation points, block kriging estimates the value at the estimation point using the observed values of blocks, which are a wider range than the observation points, or estimates the value of an unobserved block using the observed values of the blocks, or estimates the value of an unobserved block using the observed values obtained at the observation points.

[0006] Here, the observed value of a block is the average value of the values distributed within the block. For example, when N users are distributed within a block with an area S on a two-dimensional plane, the observed value of the block is N / S. Also, when the block is a 50[m] square mesh and the observation point or the estimation point is a 10[m] square mesh, the observed value of the block may be the average value of the values in the 25 meshes existing within the block.

Prior Art Documents

Non-Patent Documents

[0007]

Non-Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0008] However, while block kriging can estimate the value at an estimation point using the observed values obtained from a plurality of blocks existing within a target area, when part or all of a block overlaps with other blocks and the values in the overlapping areas are observed dispersed according to the accommodation rate for each of the overlapping blocks, the observed value of the block becomes smaller than the value that should originally be observed, so it cannot always be estimated correctly.

[0009] When part or all of a block overlaps with other blocks and the values in the overlapping area are observed to be distributed according to the accommodation rate for each of the overlapping blocks, for example, it is the case where part or all of the coverage ranges of multiple eci (E-UTRAN Cell ID) included in a mobile base station overlap, and multiple users existing in the overlapping range are accommodated in different eci respectively. Here, the coverage range of eci corresponds to the block, and the number of users existing in the overlapping range corresponds to the value in the overlapping area. The accommodation rate of a certain block is the ratio of the number of users observed in that block to the number of users existing in the area of that block.

[0010] For example, when the coverage ranges of two blocks B1 and B2 are equal and cover only one mesh, if the number of users existing in that mesh is 10, and the accommodation rates for blocks B1 and B2 are 0.4 and 0.6 respectively, the observed value of B1 is 4 and the observed value of B2 is 6. When B1 does not overlap with B2, the observed value of B1 is 10. Therefore, the observed value decreases due to the overlap of the coverage range with other blocks.

[0011] Generally, the coverage range of eci is different for each eci, and its coverage range overlaps with the coverage ranges of other eci existing in the same base station or the coverage ranges of eci existing in surrounding base stations.

[0012] Also, while block kriging can estimate the value of a point to be estimated using a theoretical variogram fitted to an empirical variogram, when a sufficient number of observations cannot be ensured, a highly reliable empirical variogram cannot be obtained, so it is not always possible to estimate correctly. The case where a sufficient number of observations cannot be ensured is, for example, the case where eci existing in the target area is regarded as a block and the number of users obtained for each eci is regarded as the observed value.

[0013] The present invention has been made in view of the above points, and aims to estimate the value of a mesh in a target area from the observed values of blocks, taking into account the influence of the accommodation rate for overlapping blocks and even under conditions where a sufficient number of observations cannot be obtained.

Means for Solving the Problem

[0014] According to the disclosed technique, an input unit that inputs the position of the mesh to be estimated, the observed values of the blocks, and the set of meshes belonging to the blocks, a theoretical variogram estimation unit that estimates the model and parameters of the theoretical variogram necessary for estimating the mesh value, a mesh value estimation unit that estimates the mesh value using the model and parameters of the theoretical variogram estimated by the theoretical variogram estimation unit and the accommodation rate of the blocks for the meshes, an output unit that outputs the final estimated value after repeatedly performing the processing of the theoretical variogram estimation unit and the processing of the mesh value estimation unit until a preset objective function is optimized, A mesh value estimation device having the above is provided.

Advantages of the Invention

[0015] According to the disclosed technique, it is possible to estimate the value of a mesh in a target area from the observed values of blocks, taking into account the influence of the accommodation rate for overlapping blocks and even under conditions where a sufficient number of observations cannot be obtained.

Brief Description of the Drawings

[0016]

Figure 1

Figure 2

Figure 3

Figure 4

[0017] Hereinafter, an embodiment of the present invention (the present embodiment) will be described with reference to the drawings. The embodiment described below is merely an example, and the embodiment to which the present invention is applied is not limited to the following embodiment.

[0018] In this embodiment, we will explain a mesh value estimation device 100 that takes into account the effect of the storage rate for overlapping blocks and is able to estimate mesh values within a target area from the observed values of blocks even under conditions where a sufficient number of observations cannot be obtained.

[0019] In this embodiment, it is assumed that multiple base stations exist within a target area, and multiple users (terminals performing wireless communication) exist in the target area. Each base station provides one or more cells, and each user in a cell communicates with the base station that provides that cell. Through this communication, the user is observed. The ID of a cell is eci. The coverage area of eci is called a block.

[0020] For convenience in describing the text of the specification, a hat "^" indicating that a certain character is an estimated value is written before the character instead of at the beginning of the character, for example, "^z".

[0021] In the following, as an example, Block B k (k=1,2,...,N B ) observed value z(B k ) represents the number of users observed at the base station eci, and mesh u i (i=1,2,...,N U ) true value z(u i ) and the estimated value ^z(u i ) represents the number of users present in the mesh. Here, the number of users represents the number of users observed as communicating via eci.

[0022] The mesh value estimation device 100 calculates the mesh value of eciB, which is a block of eci.k The number of users z(B k ) observed, the mesh u i of the number of users z(u i ) is estimated. Hereinafter, the configuration and operation of the mesh value estimation device 100 will be described in detail.

[0023] (Example of device configuration) First, the functional configuration of the mesh value estimation device 100 according to the present embodiment will be described with reference to FIG. 1. FIG. 1 is a diagram showing an example of the functional configuration of the mesh value estimation device 100 according to the present embodiment.

[0024] As shown in FIG. 1, the mesh value estimation device 100 according to the present embodiment includes an input unit 110, a theoretical variogram estimation unit 120, a mesh value estimation unit 130, and an output unit 140.

[0025] (Example of device operation) FIG. 2 is a flowchart showing the operation of the mesh value estimation device 100. The operations of the respective units constituting the mesh value estimation device 100 will be described according to the procedure shown in FIG. 2.

[0026] <S101: Input> In S101, the input unit 110 inputs the positions (x i (i = 1, 2,..., N U ), y i ) of the mesh u i which is the estimation target of the number of users, the observed value z(B k )(k = 1, 2,..., N B ) of the block B k ), and the mesh set U k belonging to the block B k . Here, let the mesh set be U = {u i │i = 1, 2,…, N U}, the block set be B = {B k │k = 1, 2,…, N B}, and let N U and N B represent the number of meshes and the number of blocks existing in the target area, respectively.

[0027] Note that the input unit 110 may input the above data from any input source. For example, the input unit 110 may input the position (x i , y i ) of the mesh u i by dividing the target area into N[m] square mesh units and inputting the center position of each, or may input the observed value z(B k ) of the block B k by obtaining a log related to eci, or may input the mesh set U k belonging to the block B k by mapping the coverage range of the block B k to the distribution of the meshes in the target area and using the meshes overlapping with the coverage range as the mesh set U k . Further, the data may be input by reading the data stored in an auxiliary storage device or the like provided in the mesh value estimation device 100.

[0028] <S102: Estimation of Theoretical Variogram> In S102, the theoretical variogram estimation unit 120 estimates the model parameters of the theoretical variogram necessary for estimating the mesh value and the accommodation rate α i of the block B k with respect to the mesh u i,k . Here, the model and parameters of the theoretical variogram may be estimated from a previously given list of theoretical variogram models and the search space of the parameters. The model of the theoretical variogram is, for example, a spherical function model, an exponential model, a Gaussian model, a nugget model, a power model, or a Hall effect model, and the parameters are the parameters included in these models. Further, the estimation of the model parameters and the accommodation rate of the theoretical variogram may be estimated (set) manually or may be estimated using an arbitrary optimization solver.

[0029] Note that when estimating using an optimization solver, the objective function to be optimized is the observed value z(B k ) of the block B k and the mesh u k belonging to the block Bi ∈U k The mean absolute error, mean square error, square root of the mean square error, mean square logarithmic error, square root of the mean square logarithmic error, mean absolute percentage error, and square root of the mean square percentage error with respect to the estimated value z(u i ) may be used, or a function obtained by adding a penalty term to these errors may be used. The penalty term may be a term including the difference between the empirical variogram calculated from the estimated value and the estimated theoretical variogram.

[0030] More specifically, when manually setting the model parameters and accommodation rate of the theoretical variogram, for example, the theoretical variogram model is a spherical function model, the parameters are a = 8, b = 0, c = 20, and the accommodation rate is α i,k = 1 / (|B i |). Here, the parameters a, b, and c are the parameters included in the spherical function model, and |B i | represents the number of blocks covering the mesh u i .

[0031] Also, when estimating using an optimization solver, for example, the search space of the model may be [spherical function model, exponential model, Gaussian model, nugget model, power model, hole effect model], and the search spaces of the parameters a, b, and c of each model may be [0, R max , [0, 10], [0, z(B) max , respectively, and the search space of the accommodation rate may be [0, 1].

[0032] Here, R max is the maximum distance between any two meshes within the target area, and z(B max ) represents the maximum value of the observed value z(B k ), respectively.

[0033] Note that the model and parameters of the theoretical variogram may be estimated using an optimization solver, and the accommodation rate may be manually set (for example, input from the input unit 110).

[0034] When manually setting the model parameters and accommodation rate of the theoretical variogram, the theoretical variogram estimation unit 120 has a function of, for example, inputting the model parameters and accommodation rate of the theoretical variogram and passing the input data to the mesh value estimation unit 130.

[0035] When estimating the model parameters and accommodation rate of the theoretical variogram with an optimization solver, the theoretical variogram estimation unit 120 includes the optimization solver.

[0036] <S103: Estimation of Mesh Values> In S103, the mesh value estimation unit 130 estimates the value of each mesh using an equation formulated in consideration of the theoretical variogram estimated in S102 and the influence of the accommodation rate on overlapping blocks. Details of the estimation method will be described later.

[0037] <S104: End Judgment> When estimating the model parameters and accommodation rate of the theoretical variogram using an optimization solver in S102, for example, the mesh u i estimated value ^z(u i ) of the block B k calculated from the and the error term related to the observed value z(B k ) of the block B k and the penalty term including the difference between the theoretical variogram calculated from the estimated value ^z(u k ) and the estimated theoretical variogram, steps S102 and S103 may be repeated until the objective function is optimized. If the optimization is completed, proceed to S105. Note that the objective function may include the error term and not include the penalty term.

[0038] <S105: Output> In S105, the output unit 140 outputs the estimated value of the mesh finally estimated by the theoretical variogram estimation unit 120 and the mesh value estimation unit 130. Note that the output unit 140 may output the estimated value of the mesh to any output destination. For example, the output unit 140 may output the estimated value of the mesh to a server device or the like via a communication network, may output the estimated value of the mesh to a display or the like, or may output the estimated value of the mesh to an auxiliary storage device or the like.

[0039] (Details of Mesh Value Estimation Process) Hereinafter, the mesh value estimation process by the mesh value estimation unit 130 in S103 will be described in detail.

[0040] The mesh value estimation unit 130 uses the formula formulated considering the accommodation rate and the theoretical variogram estimated in S102 described above to estimate the estimated value ^z(u i ) of the mesh u i . In the present embodiment, the estimated value ^z(u i ) is formulated as follows.

[0041] [Equation] Here, w i,k is the kriging coefficient and represents the weight of the block B i for the mesh u k . Also, the second term in the numerator on the right side is a correction term considering the influence of the accommodation rate and serves to correct the value of the observed value z(B k ) affected by the accommodation rate. However, the above correction term includes the true value z(u i ) of the mesh.

[0042] Hereinafter, with reference to FIG. 3, the process of the mesh value estimation unit 130 for calculating the estimated value from the above formula will be described. FIG. 3 is a flowchart showing an example of the process of the mesh value estimation unit 130 according to the present embodiment.

[0043] <S201: Calculation of Kriging Coefficient> In S201, the mesh value estimator 130 first calculates the Kriging coefficients. The Kriging coefficients are obtained by solving the following Kriging equation.

[0044]

Equation

[0045]

Equation

[0046] <H

Equation

[0047]

Equation

[0048]

Equation

[0049] <S202: Initial Value Setting> In S202, the mesh value estimator 130 gives an initial value of the estimated value ^z = (^z(u1), ^z(u2), …, ^z(u N_U )) T and sets ^z prev = ^z. The initial value may be, for example, a uniform value or a different value for each ^z(u i ). Also, the correction term is for block B kSince it is calculated for each, block B k The observed value z(B k ) may be used as an initial value by dividing it by the number of meshes |U k |.

[0050] <S203, S204: Estimated value calculation> In S203, the mesh value estimator 130 replaces the true value part of the formulation with the elements of the estimated value ^z prev and, in S204, by using the kriging coefficient w i,k calculated in S201 described above, the estimated value ^z(u i ) is calculated. That is, the following equation is solved.

[0051]

Equation

[0052] <S206: Update> In S206 when the estimated value ^z does not satisfy the condition, ^z prev is updated as ^z = ^z and then the process returns to S204. prev

[0053] <S207: Output> ​In S207, the mesh value estimation unit 130 outputs the ^z that satisfied the conditions in the aforementioned S205 as the estimated value of the mesh with respect to the model parameters and accommodation rate of the estimated theoretical variogram.

[0054] (Hardware configuration example) The mesh value estimation device 100 can be realized, for example, by causing a computer to execute a program. This computer may be a physical computer or a virtual machine on the cloud.

[0055] That is, the mesh value estimation device 100 can be realized by using hardware resources such as a CPU and a memory built in the computer to execute a program corresponding to the processing performed by the mesh value estimation device 100. The above program can be recorded on a computer-readable recording medium (such as a portable memory), saved, distributed, etc. Also, it is possible to provide the above program through a network such as the Internet or e-mail.

[0056] FIG. 4 is a diagram showing a hardware configuration example of the above computer. The computer in FIG. 4 includes a drive device 1000, an auxiliary storage device 1002, a memory device 1003, a CPU 1004, an interface device 1005, a display device 1006, an input device 1007, an output device 1008, etc., which are mutually connected by a bus BS.

[0057] A program for realizing the processing on the computer is provided by a recording medium 1001 such as a CD-ROM or a memory card, for example. When the recording medium 1001 storing the program is set in the drive device 1000, the program is installed from the recording medium 1001 via the drive device 1000 into the auxiliary storage device 1002. However, the installation of the program does not necessarily have to be performed from the recording medium 1001, and it may be downloaded from another computer via a network. The auxiliary storage device 1002 stores the installed program and also stores necessary files, data, and the like.

[0058] When an instruction to start the program is given, the memory device 1003 reads out and stores the program from the auxiliary storage device 1002. Also, the input data is stored in the memory device 1003 or the auxiliary storage device 1002. The CPU 1004 realizes the functions related to the mesh value estimator 100 according to the program stored in the memory device 1003. For example, the CPU 1004 reads out the input data stored in the memory device 1003 or the auxiliary storage device 1002 and executes the arithmetic processing described with reference to FIGS. 2 and 3. The interface device 1005 is used as an interface for connecting to a network or the like. The display device 1006 displays a GUI (Graphical User Interface) or the like by the program. The input device 1007 is composed of a keyboard, a mouse, buttons, or a touch panel, etc., and is used to input various operation instructions. The output device 1008 outputs the arithmetic result.

[0059] (Effects of the Embodiment) According to the technology of this embodiment, considering the influence of the accommodation rate on overlapping blocks, even under the condition that a sufficient number of observations cannot be obtained, the value of the mesh in the target area can be estimated from the observed values of the blocks.

[0060] In the present embodiment, estimation is performed using candidate theoretical variograms prepared in advance, without using an empirical variogram as in conventional block kriging, and the estimated value when using the theoretical variogram that minimizes the objective function is set as the final solution. Therefore, mesh values can be estimated even when a sufficient number of observations cannot be obtained.

[0061] Also, since estimation is performed by using a correction term that takes into account the accommodation rate in the estimation formula of the mesh value, and giving an initial value to the correction term and repeatedly estimating, it is possible to perform estimation considering the influence of the accommodation rate on overlapping blocks.

[0062] (Summary of the embodiment) This specification discloses at least a mesh value estimation device, a mesh value estimation method, and a program according to the following respective items. (Item 1) An input unit that inputs the position of a mesh to be estimated, the observed values of blocks, and the set of meshes belonging to the blocks, A theoretical variogram estimation unit that estimates the model and parameters of the theoretical variogram required for estimating the mesh value, A mesh value estimation unit that estimates the mesh value using the model and parameters of the theoretical variogram estimated by the theoretical variogram estimation unit and the accommodation rate of the block with respect to the mesh, An output unit that outputs the final estimated value after repeatedly performing the processing of the theoretical variogram estimation unit and the processing of the mesh value estimation unit until a preset objective function is optimized, A mesh value estimation device having the above. (Item 2) The objective function preset when repeatedly performing the theoretical variogram estimation unit and the mesh value estimation unit is An objective function based on the difference between the estimated value of the block calculated from the estimated value of the mesh and the observed value of the block, or An objective function having a term including the difference between the estimated value of the block calculated from the estimated value of the mesh and the observed value of the block, and a penalty term including the difference between the theoretical variogram calculated from the estimated value of the mesh and the estimated theoretical variogram The mesh value estimation device according to claim 1. (Claim 3) An input unit that inputs the position of the mesh to be estimated, the observed value of the block, and the set of meshes belonging to the block, A mesh value estimation unit that repeatedly executes a process of calculating an estimated value of a mesh based on an observed value corrected using the accommodation rate of the block with respect to the mesh and the mesh value, and a kriging coefficient calculated from a theoretical variogram, until an end condition is satisfied while updating the mesh value with the estimated value, An output unit that outputs the final estimated value calculated by the mesh value estimation unit, A mesh value estimation device having the above. (Claim 4) A mesh value estimation method executed by a mesh value estimation device, An input step of inputting the position of the mesh to be estimated, the observed value of the block, and the set of meshes belonging to the block, A theoretical variogram estimation step of estimating a model and parameters of a theoretical variogram required for estimating a mesh value, A mesh value estimation step of estimating a mesh value using the model and parameters of the theoretical variogram estimated in the theoretical variogram estimation step and the accommodation rate of the block with respect to the mesh, An output step of outputting the final estimated value after repeatedly performing the process of the theoretical variogram estimation step and the process of the mesh value estimation step until a preset objective function is optimized, A mesh value estimation method having the above. (Claim 5) A program for causing a computer to function as the mesh value estimation device according to any one of claims 1 to 3.

[0063] As described above, the present embodiment has been described, but the present invention is not limited to such a specific embodiment, and various modifications and changes are possible within the scope of the gist of the present invention described in the claims.

Explanation of Signs

[0064] 100 Mesh Value Estimation Device 110 Input Unit 120 Theoretical Variogram Estimation Unit 130 Mesh Value Estimation Unit 140 Output Unit 1000 Drive Device 1001 Recording Medium 1002 Auxiliary Storage Device 1003 Memory Device 1004 CPU 1005 Interface Device 1006 Display Device 1007 Input Device 1008 Output Device

Claims

1. An input unit that inputs the position of the mesh to be estimated, the observed value of the block, and the set of meshes belonging to the block; A theoretical variogram estimation unit that estimates the model and parameters of the theoretical variogram required for estimating the mesh value; A mesh value estimation unit that estimates the mesh value using the model and parameters of the theoretical variogram estimated by the theoretical variogram estimation unit and the accommodation rate of the block with respect to the mesh; An output unit that outputs the final estimated value after repeatedly performing the processing of the theoretical variogram estimation unit and the processing of the mesh value estimation unit until a preset objective function is optimized; A mesh value estimation device having the above.

2. The objective function preset when repeatedly performing the theoretical variogram estimation unit and the mesh value estimation unit is An objective function based on the difference between the estimated value of the block calculated from the estimated value of the mesh and the observed value of the block, or An objective function having a term including the difference between the estimated value of the block calculated from the estimated value of the mesh and the observed value of the block, and a penalty term including the difference between the theoretical variogram calculated from the estimated value of the mesh and the estimated theoretical variogram The mesh value estimation device according to Claim 1.

3. An input unit that inputs the position of the mesh to be estimated, the observed value of the block, and the set of meshes belonging to the block; A mesh value estimation unit that repeatedly executes a process of calculating an estimated value of the mesh based on the observed value corrected using the accommodation rate of the block with respect to the mesh and the mesh value, and the kriging coefficient calculated from the theoretical variogram, while updating the mesh value with the estimated value until an end condition is satisfied; An output unit that outputs the final estimated value calculated by the mesh value estimation unit; A mesh value estimation device having the above.

4. A mesh value estimation method executed by a mesh value estimation device, comprising: An input step of inputting the position of the mesh to be estimated, the observed value of the block, and the set of meshes belonging to the block; A theoretical variogram estimation step of estimating the model and parameters of the theoretical variogram required for estimating the mesh value; A mesh value estimation step of estimating the mesh value using the model and parameters of the theoretical variogram estimated in the theoretical variogram estimation step and the accommodation rate of the block with respect to the mesh; An output step of outputting a final estimated value after repeatedly performing the process of the theoretical variogram estimation step and the process of the mesh value estimation step until an initially set objective function is optimized; A mesh value estimation method having the above.

5. A program for causing a computer to function as the mesh value estimation device according to any one of claims 1 to 3.

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