WO2023026365A1

WO2023026365A1 - Mesh value estimation device, mesh value estimation method, and program

Info

Publication number: WO2023026365A1
Application number: PCT/JP2021/031012
Authority: WO
Inventors: 英朗金正; 大介池上
Original assignee: 日本電信電話株式会社
Priority date: 2021-08-24
Filing date: 2021-08-24
Publication date: 2023-03-02
Also published as: JPWO2023026365A1

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

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

The present invention relates to techniques for estimating mesh values based on block observations.

A technique related to a spatial interpolation method for estimating a value at an estimation point using observation values obtained at a plurality of observation points existing within a certain target area has been conventionally known. Here, the observation point and the estimation point are points at which the observation value and the estimation value are obtained, and are, for example, positional coordinates or a small area centered on the positional coordinates (hereinafter referred to as a mesh). Observed values and estimated values are, for example, the number of users, the amount of underground resources, and the amount of precipitation. Kriging, for example, is known as a typical technique related to the spatial interpolation method for estimating a value at an estimation point using observed values obtained at a plurality of observation points existing within a given target area. ing.

In general, kriging involves creating an empirical variogram from observations obtained at multiple observation points, fitting a theoretical variogram to the empirical variogram using a constrained nonlinear least-squares method, and using the fitted theoretical variogram. to estimate the value at the estimation point.

Here, the empirical variogram is a graph that shows the relationship between the distance between observation points and the average dissimilarity for that distance, and the theoretical variogram is a function that expresses the spatial characteristics between data. Kriging is classified into simple kriging, ordinary kriging, universal kriging, and block kriging, depending on the conditions assumed and the types of observations obtained. For example, Non-Patent Document 1 proposes a method using block kriging to create a distribution of indices related to wheat yield.

In general kriging, observation values obtained at observation points are used to estimate values at estimation points. or estimating the value of an unobserved block using the observed value of the block, or estimating the value of an unobserved block using the observed value obtained at the observation point. There is

Here, the observed value of the block is the average value of the values distributed within the block. is N/S. In addition, when a block is a 50 [m] square mesh and an observation point or an estimation point is a 10 [m] square mesh, the observed value of the block is the average value of the 25 meshes existing in the block. good too.

However, while block kriging can estimate the value at the estimation point using observations obtained from multiple blocks within a certain region of interest, some or all of the blocks overlap with other blocks, resulting in overlapping If the values of the area are observed dispersedly according to the accommodation rate for each of the overlapping blocks, the observed value of the block will be smaller than the value that should be observed, so it cannot always be estimated correctly.

A case where a part or all of a block overlaps with another block, and the value of the overlapping area is observed dispersedly according to the accommodation rate for each of the overlapping blocks is, for example, a plurality of eci ( E-UTRAN Cell ID) overlaps partially or entirely, and multiple users existing in the overlapped range are each accommodated in separate eci. Here, the eci coverage range corresponds to a block, and the number of users existing in the overlapping range corresponds to the value of the overlapping region. 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.

For example, if two blocks B ₁ and B ₂ have the same coverage area and cover only one mesh, the number of users existing in that mesh is 10, and the accommodation rate for each of blocks B ₁ and B ₂ is 0. .4 and 0.6, the observed value for _B1 is 4 and the observed value for _B2 is 6. If B ₁ does not overlap with B ₂ , the observed value for B ₁ is 10, so the overlapping coverage with other blocks reduces the observed value.

In general, the eci cover range differs for each eci, and the cover range overlaps with the cover range of other eci existing in the same base station and the cover range of eci existing in surrounding base stations.

In addition, while block kriging can estimate the value of the estimation point using the theoretical variogram fitted to the empirical variogram, it can be estimated correctly if a sufficient number of observations cannot be secured, because a highly reliable empirical variogram cannot be obtained. Not necessarily. A case where a sufficient number of observations cannot be secured is, for example, a case where the eci existing in the target region are set as blocks and the number of users obtained in each eci is set as an observation value.

The present invention has been made in view of the above points, and considering the effect of the accommodation rate on overlapping blocks, even under conditions where a sufficient number of observations cannot be obtained, from the observation value of the block, We aim to estimate the mesh values in

According to the disclosed technology, an input unit for inputting a position of a mesh to be estimated, an observed value of a block, and a set of meshes belonging to the block;
A theoretical variogram estimating unit that estimates a theoretical variogram model and parameters necessary for estimating mesh values;
a mesh value estimating unit that estimates a mesh value using the model and parameters of the theoretical variogram estimated by the theoretical variogram estimating unit, and the accommodation rate of the block with respect to the mesh;
an output unit that outputs a final estimated value after repeatedly performing the processing of the theoretical variogram estimating unit and the processing of the mesh value estimating unit until a preset objective function is optimized;
A mesh value estimator is provided having:

According to the disclosed technique, it is possible to estimate the mesh value in the target area from the block observation value even under the condition that a sufficient number of observations cannot be obtained, considering the influence of the accommodation rate for overlapping blocks. It becomes possible.

1 is a functional configuration diagram of a mesh value estimating device according to an embodiment of the present invention; FIG. 4 is a flowchart for explaining the operation of the mesh value estimating device; 4 is a flowchart for explaining the operation of the mesh value estimating device; It is a figure which shows the hardware structural example of a mesh value estimation apparatus.

An embodiment (this embodiment) of the present invention will be described below with reference to the drawings. The embodiments described below are merely examples, and embodiments to which the present invention is applied are not limited to the following embodiments.

In this embodiment, it is possible to estimate the mesh value in the target area from the observed value of the block, considering the effect of the accommodation rate for overlapping blocks, even under the condition that sufficient number of observations cannot be obtained. The mesh value estimating device 100 will be described.

In this embodiment, it is assumed that multiple base stations exist within a target area, and multiple users (terminals that perform wireless communication) exist within the target area. Each base station serves one or more cells, and each user residing in a cell communicates with the base station serving that cell. This communication allows the user to be observed. The ID of the cell is eci. The eci coverage is called a block.

In addition, for the convenience of describing the text of the specification, a hat "^" indicating that a certain character is an estimated value is described in front of the character instead of the head of the character, such as "^z". ing.

In the following, as an example, the observed value z( _B _k ) of block B _k (k=1 _, 2, . = 1, 2, ..., N _U ) and the estimated value z(u _i ₎ denote the number of users present in the mesh. Here, the number of users represents the number of users observed as users who communicate via eci.

The mesh value estimation device 100 estimates the number of users z(u _i ) of the mesh u _i from the number of users z(B _k ) observed in eciB _k which is a block of eci. The configuration and operation of the mesh value estimation device 100 will be described in detail below.

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

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

(Device operation example)
FIG. 2 is a flow chart showing the operation of the mesh value estimation device 100. As shown in FIG. The operation of each unit constituting the mesh value estimation device 100 will be described along the procedure shown in FIG.

<S101: Input>
In S101, the _input unit 110 inputs the position (x _i , _{y i} ₎ of the mesh u _i (i=1, 2, . ₂ _, _. _{_} Here, let the mesh set be U={u _i | _i =1 _, ₂ , _. Let _B denote the number of meshes and the number of blocks that exist in the region of interest, respectively.

Note that the input unit 110 may input the above data from any input source. For example, with respect to the position (x _i , y _i ) of the mesh u _i , the input unit 110 may divide the target region into N [m] square mesh units and input the respective center positions. The observation value z(B _k ) of B _k may be input by obtaining a log of eci, and the mesh set U _k belonging to block B _k may be input by obtaining the distribution of meshes in the target region The coverage of block B _k may be mapped and the meshes overlapping the coverage may be input as mesh set U _k . Alternatively, the data may be input by reading data stored in an auxiliary storage device or the like included in the mesh value estimation device 100 .

<S102: Estimation of theoretical variogram>
In S102, the theoretical variogram estimating unit 120 estimates the model parameters of the theoretical variogram necessary for estimating the mesh value and the accommodation rate α _i,k of the block B _k with respect to the mesh u _i . Here, the model and parameters of the theoretical variogram may be estimated from a list of models of the theoretical variogram given in advance and a parameter search space. A model of a 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 a parameter is a parameter contained in these models. Also, the estimation of the model parameters and capacity of the theoretical variogram may be manually estimated (set) or estimated using any optimization solver.

Note that the objective function to be optimized when estimating using the optimization solver is the observed value z(B _k ) of the block B _k and the estimated value z(u _i ) of the mesh u _i εU _k belonging to the block B _k . Mean absolute error, mean squared error, square root of mean squared error, mean squared logarithmic error, square root of mean squared logarithmic error, mean absolute percent error, square root of mean squared percent error may be used and penalties on these errors A function with additional terms may also be used. The penalty term may be a term that includes the difference between the empirical variogram calculated from the estimated values and the estimated theoretical variogram.

More specifically, when manually setting the model parameters and the capacity 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 capacity is α Let _i,k = 1/(|B _i |). where the parameters a, b, and c are parameters included in the spherical function model, and |B _i | represents the number of blocks covering the mesh u _i .

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, Hall effect model], and the parameters of each model The search space for a, b, and c may be set to [0, R _max ], [0, 10], and [0, z(B) _max ], respectively, and the search space for the accommodation rate may be set to [0, 1]. good.

Here, R _max represents the maximum distance between any two meshes in the target region, and z(B) _max represents the maximum observed value z(B _k ).

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).

The theoretical variogram estimation unit 120 in the case of manually setting the model parameters and the accommodation rate of the theoretical variogram, for example, inputs the model parameters and the accommodation rate of the theoretical variogram, and passes the input data to the mesh value estimation unit 130. have a function.

The theoretical variogram estimating unit 120 in the case of estimating the model parameters and accommodation rate of the theoretical variogram with the optimization solver is equipped with the optimization solver.

<S103: Estimation of Mesh Value>
In S103, the mesh value estimator 130 estimates the value of each mesh using the theoretical variogram estimated in S102 and the formula formulated in consideration of the influence of the accommodation rate on overlapping blocks. Details of the estimation method will be described later.

<S104: End determination>
When estimating the model parameters and accommodation rate of the theoretical variogram using the optimization solver in S102, for example, the estimation of the block B _k calculated from the estimated value ^z( _ui ) of the mesh u _i estimated in S103 and the error term for 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. You may repeat S102 and step S103 until it optimizes. After the optimization is completed, the process proceeds to S105. Note that the objective function may include the error term and not include the penalty term.

<S105: Output>
In S<b>105 , the output unit 140 outputs the mesh estimated values finally estimated by the theoretical variogram estimating unit 120 and the mesh value estimating unit 130 . Note that the output unit 140 may output the estimated value of the mesh to an arbitrary output destination. For example, the output unit 140 may output the mesh estimated value to a server device or the like via a communication network, may output the mesh estimated value to a display or the like, or may output the mesh estimated value to an auxiliary storage device or the like. Estimates may be output.

(Details of mesh value estimation processing)
The mesh value estimation processing by the mesh value estimation unit 130 in S103 will be described in detail below.

The mesh value estimating unit 130 estimates the estimated value ̂z(u _i ) of the mesh u _i using the formula formulated in consideration of the accommodation rate and the theoretical variogram estimated in S102 described above. In this embodiment, the estimated value ̂z(u _i ) is formulated as follows.

where w _i,k are the Kriging coefficients and represent the weight of block B _k with respect to mesh u _i . In addition, the second numerator term on the right side is a correction term considering the influence of the accommodation rate, and plays a role of correcting the value of the observed value z(B _k ) affected by the accommodation rate. However, the above correction term includes the mesh true value z(u _i ).

The processing of the mesh value estimating unit 130 that calculates the estimated value from the above equation will be described below with reference to FIG. FIG. 3 is a flow chart showing an example of processing of the mesh value estimation unit 130 according to this embodiment.

<S201: Kriging coefficient calculation>
In S201, the mesh value estimation unit 130 first calculates a Kriging coefficient. The Kriging coefficients are obtained by solving the following Kriging equations.

note that,

is the average variogram between blocks,

represents the block-to-mesh average variogram and is represented by the following equations.

where ν(u _i , u _j ) represents the inter-mesh variogram. Since the values of ν(u _i , u _j ) can be calculated from the theoretical variogram estimated in S102, the Kriging coefficients can be calculated using these values.

<S202: Initial value setting>
In S202, the mesh value estimation unit 130 gives an ^initial value of the estimated value ^z=(^z(u ₁ ), ^z(u ₂ ), ..., ^z(u _{N_U} )) T, and ^z _prev = Let be z. For the initial value, for example, an arbitrary value may be uniformly given, or a different value may be given for each ^z(u _i ). Also, since the correction term is calculated for each block B _k , a value obtained by dividing the observed value z(B _k ) of the block B _k by the number of meshes |U _k | may be used as the initial value.

<S203, S204: Estimated Value Calculation>
In S203, the mesh value estimating unit 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 coefficients w _i,k calculated in S201 described above, the estimated value ̂ Calculate z(u _i ). That is, solve the following equation.

<S205: End determination>
In step S205, the mesh value estimation unit 130 determines whether the estimated value ^z calculated in S204 described above satisfies the condition. The condition may be, for example, that the absolute error between ^z and ^z _prev is below a threshold or minimum, that the relative error between ^z and ^z _prev is below a threshold or minimum, or that ^z and The error of z(B _k ) (B _k εB) and the difference between the error of z _prev and z(B _k ) (B _k εB) may be below a threshold or minimal. If the estimated value ̂z does not satisfy the condition, proceed to S206; if the condition is satisfied, proceed to S207.

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

<S207: Output>
In S207, the mesh value estimator 130 outputs ̂z, which satisfies the condition in S205, as the mesh estimated value for the model parameters and accommodation rate of the estimated theoretical variogram.

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

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

FIG. 4 is a diagram showing a hardware configuration example of the computer. The computer of FIG. 4 has 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 interconnected by a bus BS.

A program that implements the processing in the computer is provided by a recording medium 1001 such as a CD-ROM or 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 to the auxiliary storage device 1002 via the drive device 1000 . However, the program does not necessarily need to be installed from the recording medium 1001, and may be downloaded from another computer via the network. The auxiliary storage device 1002 stores installed programs, as well as necessary files and data.

The memory device 1003 reads and stores the program from the auxiliary storage device 1002 when a program activation instruction is received. Input data is stored in the memory device 1003 or the auxiliary storage device 1002 . The CPU 1004 implements functions related to the mesh value estimation device 100 according to programs stored in the memory device 1003 . For example, the CPU 1004 reads input data stored in the memory device 1003 or the auxiliary storage device 1002, and executes the arithmetic processing described with reference to FIGS. The interface device 1005 is used as an interface for connecting to a network or the like. A display device 1006 displays a GUI (Graphical User Interface) or the like by a program. An input device 1007 is composed of a keyboard, a mouse, buttons, a touch panel, or the like, and is used to input various operational instructions. The output device 1008 outputs the calculation result.

(Effect of Embodiment)
With the technology according to the present embodiment, the mesh value in the target area can be estimated from the observed values of the blocks, even under the condition that a sufficient number of observations cannot be obtained, considering the influence of the accommodation rate for overlapping blocks. be able to.

In this embodiment, unlike conventional block kriging, empirical variograms are not used, but theoretical variogram candidates prepared in advance are used for estimation. Since it is the final solution, the mesh values can be estimated even if there are not enough observations.

In addition, a correction term that takes into account the storage rate is used in the mesh value estimation formula, and the initial value is given to the correction term and estimation is performed by repeatedly estimating, so the influence of the storage rate on overlapping blocks is considered. Estimates can be made.

(Summary of embodiment)
This specification discloses at least a mesh value estimation device, a mesh value estimation method, and a program for each of the following items.
(Section 1)
an input unit for inputting the position of the mesh to be estimated, the observation value of the block, and the mesh set belonging to the block;
A theoretical variogram estimating unit that estimates a theoretical variogram model and parameters necessary for estimating mesh values;
a mesh value estimating unit that estimates a mesh value using the model and parameters of the theoretical variogram estimated by the theoretical variogram estimating unit, and the accommodation rate of the block with respect to the mesh;
an output unit that outputs a final estimated value after repeatedly performing the processing of the theoretical variogram estimating unit and the processing of the mesh value estimating unit until a preset objective function is optimized;
A mesh value estimator having
(Section 2)
The objective function preset for repeatedly performing the theoretical variogram estimator and the mesh value estimator is
an objective function based on the difference between the block estimate calculated from the mesh estimate and the block observed value, or
An objective function with a term containing the difference between the block estimate computed from the mesh estimate and the block observed and a penalty term containing the difference between the theoretical variogram computed from the mesh estimate and the estimated theoretical variogram The mesh value estimation device according to claim 1.
(Section 3)
an input unit for inputting the position of the mesh to be estimated, the observation value of the block, and the mesh set belonging to the block;
While updating the mesh value with the estimated value, the process of calculating the estimated value of the mesh based on the observed value corrected using the block accommodation rate and mesh value for the mesh and the Kriging coefficient calculated from the theoretical variogram is performed. a mesh value estimator that repeatedly executes until a termination condition is satisfied;
an output unit that outputs the final estimated value calculated by the mesh value estimating unit;
A mesh value estimator having
(Section 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 mesh set belonging to the block;
A theoretical variogram estimation step of estimating the model and parameters of the theoretical variogram necessary for estimating the 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 housing ratio of blocks to the mesh;
an output step of outputting a final estimated value after repeatedly performing the theoretical variogram estimation step and the mesh value estimation step until a preset objective function is optimized;
A mesh value estimation method with
(Section 5)
A program for causing a computer to function as the mesh value estimation device according to any one of items 1 to 3.

Although the present embodiment has been described above, the present invention is not limited to such a specific embodiment, and various modifications and changes can be made within the scope of the gist of the present invention described in the claims. It is possible.

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

an input unit for inputting the position of the mesh to be estimated, the observation value of the block, and the mesh set belonging to the block;
A theoretical variogram estimating unit that estimates a theoretical variogram model and parameters necessary for estimating mesh values;
a mesh value estimating unit that estimates a mesh value using the model and parameters of the theoretical variogram estimated by the theoretical variogram estimating unit, and the accommodation rate of the block with respect to the mesh;
an output unit that outputs a final estimated value after repeatedly performing the processing of the theoretical variogram estimating unit and the processing of the mesh value estimating unit until a preset objective function is optimized;
A mesh value estimator having
The objective function preset for repeatedly performing the theoretical variogram estimator and the mesh value estimator is
an objective function based on the difference between the block estimate calculated from the mesh estimate and the block observed value, or
An objective function with a term containing the difference between the block estimate computed from the mesh estimate and the block observed and a penalty term containing the difference between the theoretical variogram computed from the mesh estimate and the estimated theoretical variogram The mesh value estimation device according to claim 1.
an input unit for inputting the position of the mesh to be estimated, the observation value of the block, and the mesh set belonging to the block;
While updating the mesh value with the estimated value, the process of calculating the estimated value of the mesh based on the observed value corrected using the block accommodation rate and mesh value for the mesh and the Kriging coefficient calculated from the theoretical variogram is performed. a mesh value estimator that repeatedly executes until a termination condition is satisfied;
an output unit that outputs the final estimated value calculated by the mesh value estimating unit;
A mesh value estimator having
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 mesh set belonging to the block;
A theoretical variogram estimation step of estimating the model and parameters of the theoretical variogram necessary for estimating the 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 housing ratio of blocks to the mesh;
an output step of outputting a final estimated value after repeatedly performing the theoretical variogram estimation step and the mesh value estimation step until a preset objective function is optimized;
A mesh value estimation method with
A program for causing a computer to function as the mesh value estimation device according to any one of claims 1 to 3.