Analysis device

Abstract

To enhance the accuracy of state estimation while reducing calculation cost.SOLUTION: An analysis device comprises: an estimation unit that obtains a current term state variable by performing state estimation using a Kalman filter based on first time series data generated by applying a first conversion to observation data, a state space model obtained from modeling time series fluctuations of each element of the first time series data, and a state variable for each element; an observation unit that generates second time series data by applying, to the current term state variable, observation processing using an observation matrix of the state space model; and a generation unit that generates estimated observation data by implementing a refining process for correcting, with a predetermined condition, each element included in the second time series data, in order to prevent the value of each cell of the estimated observation data from becoming a negative value, and to suppress the number of cells having a non-zero value included in the estimated observation data, and second conversion which is the inverse of the first conversion.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present disclosure relates to an analysis device. [Background technology]

[0002] Advances in information and communication technology and other technologies have made it possible to obtain big data, which is observational data obtained by observing real-world phenomena over a large scale and over a wide area, and the utilization of big data is expected. To utilize big data, it is necessary to reduce the noise contained in the observation data and to carry out a data assimilation process to estimate the state of the real-world phenomenon being observed from the obtained observation data. Modeling real-world phenomena using a state space model and performing state estimation using a Kalman filter is one of the most commonly used methods in data assimilation.

[0003] However, when applying the Kalman filter to data with a very large number of dimensions, such as big data, i.e., data with a very large number of cells, it is difficult to perform actual calculations in terms of calculation costs. One example of big data is mobile spatial statistics, which estimates attribute-specific populations across Japan by time period from mobile phone operation data. If population distribution across Japan at a certain time is observed by gender, age group in 5-year age brackets, and city, ward, town, and village of residence in 1 / 2 area mesh units, which are the basic units of the census, the number of 1 / 2 area meshes across Japan is about 1.5 million, the number of age groups is about 20, and the number of cities, ward, towns, and villages is about 2000. Therefore, the number of logical cells is about 120 billion. It is difficult to apply the Kalman filter to such high-dimensional big data by preparing state variables corresponding to all the cells.

[0004] Non-Patent Document 1 proposes a method called the ensemble Kalman filter as a method of applying the Kalman filter to high-dimensional data. The ensemble Kalman filter uses a method of estimating the state using an ensemble forecast by sampling. In other words, it is based on the idea that the state variables of each cell of high-dimensional data are all collected together and treated as the overall state variable, and the whole is estimated using estimates from a portion of the samples. The ensemble Kalman filter is used in estimating atmospheric states, etc. [Prior art documents] [Non-patent literature]

[0005] [Non-Patent Document 1] Evensen Geir. Sequential data assimilation with a nonlinearquasi-geostrophic model using Monte Carlo methods to forecast error statistics.Journal of Geophysical Research: Oceans. Vol.99, pp.10143-10162. 1994. Summary of the Invention [Problem to be solved by the invention]

[0006] The state variables assigned to each cell may be zero, but may not be zero, and may instead be a very small positive value such as 0.01, resulting in a "positive bias" problem. The larger the total number of cells, the greater the positive bias. In addition, the state estimation may swing to negative values, resulting in a "non-negative constraint deviation" problem, in which a cell value that cannot be negative in the original observation data becomes negative. Furthermore, as time progresses, the number of cells that have become non-zero at least once increases, which may result in an "increase in the number of non-zero cells" problem, which increases the computational cost. The method described in Non-Patent Document 1 cannot avoid these problems, so the computational cost may increase and the accuracy of state estimation may decrease.

[0007] The present disclosure describes an analysis device that can improve the accuracy of state estimation while reducing computational costs. [Means for solving the problem]

[0008] An analysis device according to one aspect of the present disclosure is a device that receives observation data related to an observation target and outputs estimated observation data. The analysis device includes an input unit that receives the observation data, a first conversion unit that generates first sequence data by applying a first conversion to the observation data, an estimation unit that obtains a current state variable by state estimation using a Kalman filter based on the first sequence data, a state space model that models the time series fluctuation of each element of the first sequence data, and a state variable generated for each element included in the first sequence data based on the state space model, an observation unit that generates second sequence data by applying an observation process using an observation matrix of the state space model to the current state variable, a refinement unit that generates third sequence data by performing a refinement process that corrects each element included in the second sequence data under a predetermined condition so that the value of each cell in the estimated observation data does not become a negative value and the number of cells having a value other than zero included in the estimated observation data is reduced, a second conversion unit that generates estimated observation data by applying a second conversion, which is an inverse conversion of the first conversion, to the third sequence data, and an output unit that outputs the estimated observation data.

[0009] In this analysis device, modeling using a state space model and state estimation using a Kalman filter are performed not on the observation data itself but on the first sequence data generated by performing a first transformation on the observation data. Since the first sequence data can take either a positive value or a negative value, if an element that is originally zero is not zero, it takes either a positive value or a negative value. Since these can be naturally offset, the occurrence of the "positive bias" problem can be avoided and the current state variable can be obtained. In the above analysis device, each element included in the second sequence data is corrected under a predetermined condition so that the value of each cell in the estimated observation data does not become a negative value and the number of cells having a value other than zero included in the estimated observation data is suppressed. Therefore, the estimated observation data can satisfy the non-negative constraint and an increase in the number of cells having a non-zero (non-zero) value in the estimated observation data can be suppressed. As a result, it is possible to improve the accuracy of state estimation while reducing calculation costs. Effect of the Invention

[0010] According to the present disclosure, it is possible to improve the accuracy of state estimation while reducing calculation costs. [Brief description of the drawings]

[0011] [Figure 1] FIG. 1 is a diagram illustrating a schematic configuration of an analysis device according to an embodiment. [Diagram 2] FIG. 2 is a flowchart showing a series of steps of an analysis method performed by the analysis device shown in FIG. [Diagram 3] FIG. 3 is a diagram illustrating a hardware configuration of the analysis device illustrated in FIG. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0012] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings. In the description of the drawings, the same elements are given the same reference numerals and duplicated description will be omitted.

[0013] 1 is a diagram showing a schematic configuration of an analysis device according to an embodiment. The analysis device 10 shown in FIG. 1 receives observation data O t Input the estimated observation data O t K The analysis device 10 is configured, for example, by an information processing device such as a server device. The time t is, for example, an integer value starting from 1. The time t increases by 1 every time a unit time (for example, 3600 seconds) passes. In other words, the time t is also a period that lasts for the unit time, and the period from the start to the end of the time t is sometimes called a period (this period). In order to promote the use of big data, which is large-scale observational data obtained by observing real-world phenomena, the analysis device 10 analyzes the observation data O t is modeled using a state space model and state estimation is performed using a Kalman filter. Details of the state space model and the Kalman filter will be described later.

[0014] Observation data O t is data about the observed object. Observation data O t is obtained by observing an object. An example of an object is a real-world event. Observation data O t is a target of state estimation by the analysis device 10, and is a set of values ​​(hereinafter referred to as "cells") obtained by counting the number of records corresponding to a certain attribute or combination of attributes in data consisting of a set of records having one or more attributes. t is generated, for example, from a database relating to the distribution of people at a certain time t. t K The analysis device 10 analyzes the observation data O t More specifically, the estimated observation data O t K is the observation data t The time series fluctuations of each cell in are modeled by a state space model and state estimation is performed by a Kalman filter. Here, the observed data O t O t=(о1,о2, ,о n ) and the estimated observation data O t K O t K =(о1 K ,о2 K ,...,о n K ) where n is the observation data O t The total number of logical cells in k (k is a natural number). For convenience of explanation, a one-dimensional data series is used, but a multidimensional data series may be used. For example, a data series can be easily expanded to a multidimensional data series by applying standard decomposition of a wavelet transform.

[0015] Observation data O t , and estimated observation data O t K Each value in is called a "cell", and the first sequence data W t , the second series data W t K , and the third series data W t K+ Each value in is called an "element." t The value of and observed data O t The estimated observation data O has the same meaning as the value of t K The value of is called a "cell" and the observation data O t The data values ​​obtained by converting are called "elements."

[0016] Functionally, the analysis device 10 comprises an input unit 11, a first conversion unit 12, a state space model memory unit 13, a state variable memory unit 14, an estimation unit 15, an observation unit 16, a refinement unit 17, a second conversion unit 18, and an output unit 19.

[0017] The input unit 11 receives observation data O t The input unit 11 receives the observation data O from the outside of the analysis device 10. t Receive the received observation data O t to the first conversion unit 12.

[0018] The first conversion unit 12 converts the observation data O t The first sequence data W is obtained by applying the first transformation to t Here, the first transformation generates the first sequence data W t Each element of can be expressed as a tree structure, and the first sequence data W t The condition that the value of each element of affects only the partial sum of its descendants in the tree is satisfied. Examples of such first transforms include multiresolution analysis using Haar wavelets, multiresolution analysis using nominal wavelets, Fourier transforms, and sum-and-difference decomposition.

[0019] As the first transformation, we will explain using multi-resolution analysis (hereinafter referred to as "multi-resolution analysis HW") with the Haar function as the mother wavelet. The Haar function is a type of step function. This multi-resolution analysis HW is an inverse transformation function, -1 Any observation data O t About O t =HW -1 (HW(O t The first transformation unit 12 transforms the observed data O, which is a vector sequence of length n, into t The first sequence data W t =(w1,w2, ,w n ) The multiresolution analysis HW is performed by recursively applying the Haar decomposition H1 k times. This Haar decomposition H1 is a vector of length 2 p A sequence of vectors Z=(z1,z2,...,z q ) with length 2 p-1 Decompose it into vector sequences cA and cD.

number

number

number

[0020] The vector sequence cA is a vector of the average of two adjacent values ​​in the vector sequence Z. The vector sequence cD is a vector of the difference of two adjacent values ​​in the vector sequence Z. The vector sequence cA is called the approximation coefficient vector. The vector sequence cD is called the detailed coefficient vector. When the generated approximation coefficient vector cA is subjected to the Haar decomposition H1 again, a vector of length 2 p-2 Approximation coefficient vector of length 2 p-2 In this way, the first conversion unit 12 converts the observed data O t Using the initial input, the Haar decomposition H1 is recursively repeated k times to finally obtain one approximate coefficient vector and k detailed coefficient vectors.

number

number

[0021] Here, i takes integer values ​​from 2 to k. Approximation coefficient vector cA i and the detailed coefficient vector cD i is the output obtained by the i-th Haar decomposition H1, which is called the coefficient vector of level i. i The x-th coefficient (hereinafter referred to as "element") of i,x and the detail coefficient vector cD i The xth coefficient (hereinafter referred to as "element") of i,x The first conversion unit 12 performs concatenation as shown in the following equation (6) to generate the first sequence data W t Configure.

number

[0022] Note that the approximate coefficient vector cA k has length 1, and the detail coefficient vector cD i The length of k-i Therefore, as shown in the following equation (7), the first sequence data W t The length of the observation data O t is equal to the length of

number

[0023] The state space model storage unit 13 stores (holds) model parameters of the state space model. t The state space model includes a system model shown in equation (8) and an observation model shown in equation (9).

number

number

[0024] Here, state x t is an m-dimensional vector that represents the state of a system that cannot be directly observed from the outside. t are also called state variables. The system noise d is an s-dimensional normal white noise with a mean vector of 0 and a variance-covariance matrix Q. The observation noise e is a b-dimensional normal white noise with a mean vector of 0 and a variance-covariance matrix R. Note that when the observation value of each element is a scalar, b=1. The state transition matrix F is an m×m matrix. The variance matrix G is an m×s matrix. The observation matrix H is a b×m matrix.

[0025] That is, the state space model storage unit 13 stores a state transition matrix F, a variance matrix G, an observation matrix H, a variance-covariance matrix Q of the system noise d, and a variance-covariance matrix R of the observation noise e. In this embodiment, these parameters are fixed values ​​that do not vary depending on the time t.

[0026] The state variable storage unit 14 stores the first sequence data W t The state variable storage unit 14 stores (holds) the state variables for each element that may exist in the first sequence data W t The state variable storage unit 14 may store state variables for all elements that can logically exist in the time series. The state variable storage unit 14 may store state variables only for elements that have appeared at least once between time 0 and time t. The state variable storage unit 14 may store state variables only for elements whose number of appearances or magnitude of value satisfy a predetermined condition. By adjusting the condition, the number of elements for which the state variable storage unit 14 stores state variables can be increased or decreased. By adjusting the number of elements, it is possible to adjust the calculation cost.

[0027] The number of state variables at time t is q t Let these q t By arranging the vectors of state variables in a column direction, we obtain m×q t The state variable matrix X t K is obtained.

[0028] At the start of time t, the state variable storage unit 14 stores the state variable matrix X t-1 K At time t=1, the state variable storage unit 14 stores (holds) the state variable matrix X0 K The state variable matrix X0 K can be obtained by, for example, generating an m-dimensional zero vector for each element present in the first sequence data W1 at time 1 and arranging the zero vectors in the column direction. K For example, the first sequence data W for a certain period tIt may be generated in advance by analysis.

[0029] Based on the state space model and state variables, the estimation unit 15 generates the state variable (current period state variable) at time t by performing state estimation using a Kalman filter. Here, the state estimation using the Kalman filter will be described. In the state space model, the time series of observation values Y t ={y1, y2, ···, y t} is used to estimate the state variable x j at time j. This problem is called prediction when estimating the state in the future (j > t), filtering when estimating the current state (j = t), and smoothing when estimating the past state (j < t). However, in the Kalman filter, only the prediction (j = t + 1) and filtering for the next period (one time step) are handled.

[0030] To perform these state estimations, the conditional distribution E(x t | Y j ) regarding the state x j given the observation value Y t needs to be obtained. When considering a linear Gaussian model, the conditional distribution is defined by the mean vector and the variance-covariance matrix. Here, the mean vector x j and the variance-covariance matrix V t that define the conditional distribution E(x j|t | Y j|t ) are represented by the following equations (10) and (11), respectively.

Equation

Equation

[0031] The prediction for the next period (one time step) is represented as a series of processes by equations (12) and (13). In equations (12) and (13), the state x t-1Based on this, a prediction for one period ahead (time t) is made.

number

number

[0032] The filter has a Kalman gain of K t This is expressed as a series of processes using equations (14) to (16).

number

number

number

[0033] The state estimation process performed by the estimation unit 15 will be described in detail. t Each element of is the observed value y at time t in the state estimation by the Kalman filter for each element. t The estimation unit 15 acquires each parameter of the state space model from the state space model storage unit 13, and acquires the state variable matrix X t-1 K The estimation unit 15 executes a series of calculation processes shown in equations (12) to (16) to obtain the state variable matrix X t K (current period state variable).

[0034] Of the series of calculations, only the calculation of equation (15) is performed to obtain the observed value y t That is, the observed value y t The state variable x t is only an estimate of the variance-covariance matrix V t and Kalman gain K t The calculation is done for the observed value y tTherefore, by using the state space model in common for all elements, the variance-covariance matrix V t However, the observation data t It is an m×l dimensional matrix that is independent of the number of dimensions of . Similarly, the Kalman gain K t However, the observation data t It is an m × m matrix that is independent of the number of dimensions of . Furthermore, the variance-covariance matrix V t After determining the initial value (t=1), the variance-covariance matrix V t and Kalman gain K t The value of can be calculated in advance. Therefore, the estimator 15 calculates the variance-covariance matrix V t After determining the initial value (t=1), the variance-covariance matrix V t and Kalman gain K t In this case, the estimation unit 15 calculates the variance-covariance matrix V t and Kalman gain K t The calculation of can be omitted.

[0035] When a common state space model is used for all elements, the calculations of formulas (12) and (15) need to be performed sequentially every time the time t increases by 1. The estimation unit 15 may calculate formulas (12) and (15) at once using the following formulas (17) and (18), respectively.

number

number

[0036] As described above, the estimation unit 15 estimates the first sequence data W t The state variable matrix X is a summary of the results of one period (one time) ahead prediction of the state variables while reflecting the value of each element of in the state estimation of the corresponding state variables. t|t-1 K and the state variable matrix X that summarizes the results of the filter t|t KThe subsequent processing is to obtain the state variable matrix X t|t-1 K and the state variable matrix X t|t K Since it is common to all, the explanation is "X t K In the subsequent processing, which result is used depends on the purpose of use, but both results may be used. The estimation unit 15 estimates the state variable matrix X t-1 K Let us consider the generated state variable matrix X t K The state variable matrix X t|t-1 K and the state variable matrix X t|t K When both are used, the state variable storage unit 14 stores the state variable matrix X t|t-1 K and the state variable matrix X t|t K Each of the above is stored.

[0037] The observation unit 16 calculates the current state variable matrix X t K By applying observation processing using the observation matrix H to the second sequence data W t K This observation process is performed by the following equation (19).

number

[0038] The refinement unit 17 performs the refinement process to obtain the third sequence data W t K+ The refinement process generates the estimated observation data O t K The second sequence data W is calculated so that each cell of the second sequence data W has a value equal to or greater than zero and the number of cells having a value other than zero is suppressed. t K Here, the third sequence data W tK+ satisfies the non-negativity constraint. The refinement unit 17, for example, t K =(cA k K |cD k K |cD k-1 K |···|cD1 K ) and verify the estimated wavelet coefficients contained in t K If there is an element that increases the number of cells having a value other than zero in the estimated observation data O, the element is corrected. Then, the refinement unit 17 performs verification and correction for all elements from level k to level 1 to ensure that the non-negativity constraint is satisfied and the estimated observation data O t K The third sequence data W is a refined wavelet coefficient sequence that can suppress the number of cells having non-zero values ​​contained in t K+ =(cA k K+ |cD k K+ |cD k-1 K+ |···|cD1 K+ ) is obtained.

[0039] The function of the refinement unit 17 will be specifically described. In the description of the refinement unit 17, i is an integer value from 0 to k. In this case, the estimated observation data O t K =cA0 K+ The refinement unit 17 refines the approximate coefficient vector cA i K+ All elements of are non-negative and the refined approximate coefficient vector cA i+1,x K+ Among the elements of cA0 K+ The estimated detailed coefficient vector cD at level (i+1) is pruned to remove elements that have no substantial effect on i+1 KRefine the values of each element. Note that pruning an element means stopping the processing of the element.

[0040] First, at i = k, the refinement unit 17 executes the following equation (20) so that the refined approximation coefficient vector cA at level k k K+ satisfies the non-negativity constraint.

Equation

[0041] At i < k, each element cA of the refined approximation coefficient vector cA at level i i K+ is recursively defined as shown in equation (21) using the element cA of the refined approximation coefficient vector cA at level i + 1, which is one level above, i,x K+ and the element cD of the refined detail coefficient vector cD i+1 K+ . i+1 , ceil(x / 2) K+ and the element cD of the refined detail coefficient vector cD i+1 K+ . i+1,ceil(x / 2) K+ That is, according to equation (21), if the following equation (23) can be satisfied, equation (24) holds.

Equation

[0042] Here, ceil(x) is the ceiling function and represents the smallest integer not less than x (i.e., rounding up the decimal part). g(x) is the sign function and takes the value shown in the following equation (22).

Equation

[0043] That is, according to equation (21), if the following equation (23) can be satisfied, equation (24) holds.

Equation

number

[0044] And the estimated observation data O t K =cA0 K+ Therefore, the refined approximate coefficient vector cA k K+ is equal to or greater than 0, and the third sequence data W t K+ If equation (23) holds for all elements of the estimated observation data O t K does not violate the non-negativity constraint.

[0045] Next, the estimated observation data O t K The process of suppressing the number of cells having non-zero values ​​in the refined approximate coefficient vector cA i K+ Each element of cA i , x K+ is the estimated observation data O t K 2 in i Since it is the average of a set of cell values, the estimated observed data O t K Each element cA i , x K+ The magnitude of the influence value Ef(cA i , x K+ ) is given by the following equation (25).

number

[0046] Here, in particular, Ef(cA i,x K+ ) ≦ 0.5 i,x K+In this case, even if the process of the subtree with the value 0 is pruned (stopped) by pruning the subtree with the value 0, the estimated observation data O t K There is no substantial difference in Ef(cA i,x K+ ) is less than or equal to 0.5, the partial sum of the region is preserved even if the tree is moved to any of the subtrees.

number

number

[0047] Here, rand(x, y) is a function that randomly selects x or y.

[0048] Therefore, the refinement unit 17 obtains the refined detailed coefficient vector cD i K+ Each element of cD i,x K+ is calculated using the following equation (28).

number

[0049] As described above, the refinement unit 17 refines the element numbers x=1 to 2 in descending order from k to 1 for i. k-i Element cA i,x K+ and element cD i,x K+ Using equations (20), (21), and (28), the refinement unit 17 calculates the estimated observation data O t K does not violate the non-negativity constraint, and the estimated observation data O t K The third series data W is calculated so that the number of cells having a value other than zero in t K+ =(cA k K+ |cDk K+ |cD k-1 K+ |···|cD1 K+ ) is obtained.

[0050] The second conversion unit 18 converts the third sequence data W t K+ The estimated observation data O is obtained by applying the second transformation, which is the inverse transformation of the first transformation, to t K When the multi-resolution analysis using the Haar function as the mother wavelet is used as the first transformation, the second transformation unit 18 generates an inverse transformation hardware for the multi-resolution analysis using the Haar function as the mother wavelet as the second transformation. -1 The second conversion unit 18 converts the third sequence data W t K+ Estimate the observed data O by applying a second transformation to t K That is, the second conversion unit 18 generates O t K =HW -1 (W t K+ ) is calculated.

[0051] The above calculation is generally known, but as an example, the second conversion unit 18 converts the third sequence data W t K+ The refined approximate coefficient vector cA is calculated by recursively calculating (21) from k-1 to 0 for i. i K+ Calculate the estimated observation data O t K =cA0 K+ Therefore, the second conversion unit 18 converts the refined approximation coefficient vector cA0 K+ By obtaining the estimated observation data O t K get.

[0052] The output unit 19 outputs the estimated observation data O t K The output unit 19 outputs the estimated observation data O tK Receive the estimated observation data O t K is output to the outside of the analysis device 10.

[0053] Next, an analysis method performed by the analysis device 10 at time t will be described with reference to Fig. 2. Fig. 2 is a flow chart showing a series of processes of the analysis method performed by the analysis device shown in Fig. 1. The series of processes shown in Fig. 2 may be performed, for example, by receiving observation data O t The process starts when the observation data O t is repeatedly input every time a unit time elapses.

[0054] As shown in FIG. 2, first, the input unit 11 inputs observation data O from outside the analysis device 10. t (Step S11). Then, the input unit 11 receives the observation data O t to the first conversion unit 12.

[0055] Next, the first conversion unit 12 receives the observation data O from the input unit 11. t When the observation data O t The first sequence data W is obtained by applying the first transformation to t (Step S12). Here, examples of the first transformation include multi-resolution analysis using Haar wavelets, multi-resolution analysis using nominal wavelets, Fourier transform, and sum-and-difference decomposition. Then, the first transformation unit 12 generates the first sequence data W t is output to the estimation unit 15.

[0056] Next, the estimation unit 15 receives the first sequence data W t When the state space model is received, each parameter of the state space model is obtained from the state space model storage unit 13, and the state variable matrix X t-1 K Then, the estimation unit 15 obtains the first sequence data W t , each parameter of the state space model, and the state variable matrix X t-1 KBy using the state estimation by the Kalman filter, the state variable matrix X t K (Step S13).

[0057] Next, the estimation unit 15 estimates the state variable matrix X t-1 K Let X be the state variable matrix for this period. t K (Step S14). Then, the estimation unit 15 updates the state variable matrix X t K is output to the observation unit 16.

[0058] Next, the observation unit 16 receives the current state variable matrix X t K Upon receiving the state space model, the observation unit 16 obtains the observation matrix H from the state space model storage unit 13. Then, the observation unit 16 obtains the state variable matrix X t K The second sequence data W is obtained by applying the observation process using the observation matrix H to t K (Step S15). Then, the observation unit 16 generates the second sequence data W t K is output to the refinement unit 17.

[0059] Next, the refinement unit 17 receives the second sequence data W t K Upon receiving the third sequence data W t K+ (Step S16). The refinement process generates the estimated observation data O t K Each cell of is not allowed to have a negative value, and the estimated observation data O t K The second sequence data W is calculated so that the number of cells having a value other than zero contained in t K The refinement unit 17 corrects each of the elements included in the third sequence data W t K+to the second conversion unit 18.

[0060] Next, the second conversion unit 18 receives the third sequence data W t K+ When the third series data W t K+ Estimate the observed data by applying a second transformation to t K (Step S17). Then, the second conversion unit 18 generates the estimated observation data O t K is output to the output unit 19.

[0061] Next, the output unit 19 outputs the estimated observation data O t K Upon receiving the estimated observation data O t K is output to the outside of analysis device 10 (step S18). With the above, a series of processes of the analysis method at time t is completed.

[0062] Note that step S14 may be performed at any timing in the series of processes at time t, so long as it is performed after step S13.

[0063] Next, the effects of the analysis device 10 will be described. t If is a natural number, when a cell that should have a zero value does not become zero, it takes a positive value. Observed data O in which multiple cells have positive values ​​even though they should have zero t When modeling is performed using a state space model and state estimation is performed using a Kalman filter, a "positive bias" problem occurs. t Not the data itself, but the observation data t The first sequence data W generated by performing the first transformation on t The first sequence data W is modeled using a state space model and subjected to state estimation using a Kalman filter. tSince can take either positive or negative values, if an element that is originally zero is not zero, it takes either positive or negative values. If multiple elements are originally zero, the values ​​of these elements may naturally cancel each other out. Therefore, it is possible to avoid the "positive bias" problem and to make the state variable matrix X t K can be obtained.

[0064] In the analysis device 10, the estimated observation data O t K The values ​​of each cell in are not negative, and the estimated observation data O t K The second sequence data W is calculated so as to suppress the number of cells having a value other than zero contained in t K Each element included in is corrected under predetermined conditions. Therefore, the estimated observation data O t K can satisfy the non-negativity constraint, and the estimated observation data O t K It is possible to suppress an increase in the number of cells having a non-zero value in . As a result, it is possible to improve the accuracy of state estimation while reducing the calculation cost.

[0065] In order to avoid the "positive bias" problem, the "violation of non-negative constraint" problem, and the "increase in the number of non-zero cells" problem, a method of deleting state variable vectors for cells below a threshold value is considered. However, since state variable vectors of cells that actually have very small values ​​are deleted, the "under-bias" problem of degrading the partial sum accuracy of the region may occur. t K Element cA contained in i , x K+ ,Estimated observation data O t K The magnitude of the effect on Ef(cA i , x K+ ) is small, the element cA i , xK+ is applied to one of the subtrees. In this case, the partial sum of the region is preserved, so that it is possible to suppress an increase in the number of non-zero cells and to avoid deterioration of the partial sum accuracy due to under-bias.

[0066] The first transformation may be a multi-resolution analysis using a Haar function as a mother wavelet. In this case, the first sequence data W generated by applying the first transformation may be t Each element of can be expressed as a tree structure, and the first sequence data W t The value of each element of affects only the partial sums of its descendants in the tree. Therefore, by simply tracing the tree from the top of the tree to the bottom of the tree and refining each element so that it satisfies the non-negativity constraint, it is guaranteed that all elements will satisfy the non-negativity constraint. This simplifies the calculations in the refinement process.

[0067] The estimation unit 15 estimates the state variable matrix X t-1 K Let X be the state variable matrix for this period. t K According to this configuration, the state variable matrix is ​​updated every time state estimation is performed. Therefore, since state estimation is performed using the latest state variable matrix, it is possible to improve the accuracy of state estimation.

[0068] Although the embodiments of the present disclosure have been described above, the present disclosure is not limited to the above embodiments.

[0069] The analysis device 10 may be configured by one device that is physically or logically combined, or may be configured by multiple devices that are physically or logically separated from each other. For example, the analysis device 10 may be realized by multiple computers distributed on a network, such as in cloud computing. As described above, the configuration of the analysis device 10 may include any configuration that can realize the functions of the analysis device 10.

[0070] Analysis device 10 may not include state space model storage unit 13. That is, state space model storage unit 13 may be provided outside analysis device 10. Analysis device 10 may not include state variable storage unit 14. That is, state variable storage unit 14 may be provided outside analysis device 10.

[0071] The first conversion unit 12 converts the observation data O t , and the first series data W t In other words, the first conversion unit 12 converts the observation data O t is expressed in a sparse data format, and the observation data O t The first series data W is obtained by applying the first transformation to the cells that have non-zero values ​​among the cells in t The first conversion unit 12 may generate the observation data O in a sparse data format that can efficiently express a sparse matrix. t and the first series data W t Examples of such sparse data formats include the COO (Coordinate) format and formats that do not explicitly represent elements that have a value of zero. In this case, the first transformation, state estimation, observation processing, refinement processing, and application of the second transformation to cells that have a value of zero are omitted, making it possible to reduce the amount of calculations.

[0072] The first conversion unit 12 converts the observation data O t The first sequence data W t The adjustment process may generate the observation data O t This is a process of correcting each value under predetermined conditions so that the scale of the magnitude of the value of each element of the data generated by applying the first transformation to the data is unified to the same level.

[0073] For example, when a multiresolution analysis using a Haar function as a mother wavelet is used as the first transformation, the generated wavelet coefficient sequence is the difference between the averages of adjacent or neighboring cells.t If is sparse, then as the level of decomposition increases, the approximate coefficient vector cA i Therefore, the first conversion unit 12 obtains adjusted wavelet coefficients by performing the calculations shown in the following equations (29) and (30), and converts the first sequence data W t get.

number

number

[0074] Furthermore, the observation unit 16 detects the current state variable X t K The second sequence data W t K The reverse adjustment process generates the current state variable X t K This is a process of correcting each value under predetermined conditions so as to return the scale of the magnitude of the value of each element of the data generated by applying an observation process using the observation matrix H to the state before the adjustment process.

[0075] For example, after applying equation (19), the observation unit 16 performs the calculations shown in the following equations (31) and (32) to obtain the inverse adjusted wavelet coefficients, and concatenates them as shown in equation (6) to obtain the second sequence data W t K get.

number

number

[0076] In the above configuration, the observation data Ot Even if the data is sparse and contains many cells with zero values, the first series data W t Since the scale of the magnitude of the values ​​of the elements of is adjusted to the same level, it is possible to improve the accuracy of state estimation by the Kalman filter.

[0077] The block diagrams used to explain the above embodiments show functional blocks. These functional blocks (components) are realized by any combination of at least one of hardware and software. The method of realizing each functional block is not particularly limited. That is, each functional block may be realized by using one device that is physically or logically combined, or may be realized by using two or more devices that are physically or logically separated and directly or indirectly connected (for example, by wire, wirelessly, etc.). The functional block may be realized by combining the one device or the multiple devices with software.

[0078] Functions include, but are not limited to, judgment, determination, judgement, calculation, computation, processing, derivation, investigation, search, confirmation, reception, transmission, output, access, resolution, selection, selection, establishment, comparison, assumption, expectation, consideration, broadcasting, notifying, communicating, forwarding, configuring, reconfiguring, allocating, mapping, and assignment. For example, a functional block (component) that performs the function of transmission is called a transmitting unit or a transmitter. In either case, as described above, there is no particular limitation on the method of realization.

[0079] For example, the analysis device 10 according to an embodiment of the present disclosure may function as a computer that performs the processing of the present disclosure. Fig. 3 is a diagram illustrating an example of a hardware configuration of the analysis device 10 according to an embodiment of the present disclosure. The above-described analysis device 10 may be physically configured as a computer device including a processor 1001, a memory 1002, a storage 1003, a communication device 1004, an input device 1005, an output device 1006, and a bus 1007.

[0080] In the following description, the term "apparatus" may be interpreted as a circuit, a device, a unit, etc. The hardware configuration of the analysis apparatus 10 may be configured to include one or more of the devices shown in the drawings, or may be configured to exclude some of the devices.

[0081] Each function in the analysis device 10 is realized by loading a specific software (program) onto hardware such as the processor 1001 and memory 1002, causing the processor 1001 to perform calculations, control communications via the communication device 1004, and control at least one of the reading and writing of data in the memory 1002 and storage 1003.

[0082] The processor 1001, for example, operates an operating system to control the entire computer. The processor 1001 may be configured with a central processing unit (CPU) including an interface with peripheral devices, a control device, an arithmetic unit, and a register. For example, each function of the above-mentioned analysis device 10 may be realized by the processor 1001.

[0083] The processor 1001 reads out a program (program code), software modules, data, etc. from at least one of the storage 1003 and the communication device 1004 into the memory 1002, and executes various processes according to the programs. As the program, a program that causes a computer to execute at least a part of the operations described in the above-mentioned embodiment is used. For example, each function of the analysis device 10 may be realized by a control program stored in the memory 1002 and operated in the processor 1001. Although the above-mentioned various processes have been described as being executed by one processor 1001, they may be executed simultaneously or sequentially by two or more processors 1001. The processor 1001 may be implemented by one or more chips. The program may be transmitted from a network via a telecommunication line.

[0084] The memory 1002 is a computer-readable recording medium, and may be configured by at least one of, for example, a Read Only Memory (ROM), an Erasable Programmable ROM (EPROM), an Electrically Erasable Programmable ROM (EEPROM), and a Random Access Memory (RAM). The memory 1002 may be called a register, a cache, a main memory (primary storage device), or the like. The memory 1002 can store an executable program (program code), software modules, and the like for implementing an analysis method according to an embodiment of the present disclosure.

[0085] Storage 1003 is a computer-readable recording medium, and may be composed of at least one of an optical disk such as a CD-ROM (Compact Disc ROM), a hard disk drive, a flexible disk, a magneto-optical disk (e.g., a compact disk, a digital versatile disk, a Blu-ray (registered trademark) disk), a smart card, a flash memory (e.g., a card, a stick, a key drive), a floppy (registered trademark) disk, and a magnetic strip. Storage 1003 may be called an auxiliary storage device. The above-mentioned storage medium may be, for example, a database, a server, or other suitable medium including at least one of memory 1002 and storage 1003.

[0086] The communication device 1004 is hardware (transmission / reception device) for performing communication between computers via at least one of a wired network and a wireless network, and is also called, for example, a network device, a network controller, a network card, or a communication module. The communication device 1004 may be configured to include a high-frequency switch, a duplexer, a filter, and a frequency synthesizer to realize, for example, at least one of Frequency Division Duplex (FDD) and Time Division Duplex (TDD). For example, the above-mentioned input unit 11 and output unit 19 may be realized by the communication device 1004.

[0087] The input device 1005 is an input device (e.g., a keyboard, a mouse, a microphone, a switch, a button, a sensor, etc.) that receives input from the outside. The output device 1006 is an output device (e.g., a display, a speaker, an LED lamp, etc.) that performs output to the outside. The input device 1005 and the output device 1006 may be integrated into one device (e.g., a touch panel).

[0088] Each device such as the processor 1001 and the memory 1002 is connected by a bus 1007 for communicating information. The bus 1007 may be configured using a single bus, or may be configured using different buses between each device.

[0089] The analysis device 10 may be configured to include hardware such as a microprocessor, a digital signal processor (DSP), an application specific integrated circuit (ASIC), a programmable logic device (PLD), a field programmable gate array (FPGA), etc., and some or all of the functional blocks may be realized by the hardware. For example, the processor 1001 may be implemented using at least one of these pieces of hardware.

[0090] Notification of information is not limited to the aspects / embodiments described in this disclosure and may be performed using other methods.

[0091] In the process steps, sequences, flow charts, etc. of each aspect / embodiment described in this disclosure, the order may be changed unless inconsistent. For example, the methods described in this disclosure present elements of various steps using an example order, and are not limited to the particular order presented.

[0092] The information may be output from a higher layer to a lower layer, or may be output from a lower layer to a higher layer. The information may be input / output via a plurality of network nodes.

[0093] The input and output information may be stored in a specific location (e.g., memory) or may be managed using a management table. The input and output information may be overwritten, updated, or added to. The output information may be deleted. The input information may be transmitted to another device.

[0094] The determination may be based on a value represented by a single bit (0 or 1), a Boolean value (true or false), or a numerical comparison (e.g., comparison with a predetermined value).

[0095] Each aspect / embodiment described in this disclosure may be used alone, in combination, or switched according to execution. Notification of predetermined information (e.g., notification of "X") is not limited to explicit notification, and may be performed implicitly (e.g., by not notifying the predetermined information).

[0096] Although the present disclosure has been described in detail above, it is clear to those skilled in the art that the present disclosure is not limited to the embodiments described in the present disclosure. The present disclosure can be implemented as modified and altered forms without departing from the spirit and scope of the present disclosure as defined by the claims. Therefore, the description of the present disclosure is for illustrative purposes only and does not have any limiting meaning on the present disclosure.

[0097] Software shall be construed broadly to mean instructions, instruction sets, code, code segments, program code, programs, subprograms, software modules, applications, software applications, software packages, routines, subroutines, objects, executable files, threads of execution, procedures, functions, etc., whether referred to as software, firmware, middleware, microcode, hardware description language, or otherwise.

[0098] Software, instructions, information, and the like may be transmitted and received over a transmission medium. For example, if the software is transmitted from a website, server, or other remote source using wired technologies (such as coaxial cable, fiber optic cable, twisted pair, Digital Subscriber Line (DSL)), and / or wireless technologies (such as infrared, microwave), then these wired and / or wireless technologies are included within the definition of transmission media.

[0099] The information, signals, etc. described in this disclosure may be represented using any of a variety of different technologies. For example, the data, instructions, commands, information, signals, bits, symbols, chips, etc. that may be referred to throughout the above description may be represented by voltages, currents, electromagnetic waves, magnetic fields or magnetic particles, optical fields or photons, or any combination thereof.

[0100] In addition, terms explained in this disclosure and terms necessary for understanding this disclosure may be replaced with terms having the same or similar meanings.

[0101] As used in this disclosure, the terms "system" and "network" are used interchangeably.

[0102] The information, parameters, etc. described in this disclosure may be expressed using absolute values, may be expressed using relative values ​​from a predetermined value, or may be expressed using corresponding other information.

[0103] The names used for the above parameters are not limiting in any way, and the formulas etc. using these parameters may differ from the formulas etc. explicitly disclosed in this disclosure.

[0104] The terms "determining" and "determining" as used in this disclosure may encompass a wide variety of actions. "Determining" and "determining" may include, for example, judging, calculating, computing, processing, deriving, investigating, looking up, search, inquiry (e.g., searching in a table, database, or other data structure), ascertaining, and the like. "Determining" and "determining" may include receiving (e.g., receiving information), transmitting (e.g., sending information), input, output, accessing (e.g., accessing data in a memory), and the like. "Judgment" and "decision" may include the deeming of resolving, selecting, choosing, establishing, comparing, etc. as having been "judged" or "decided." In other words, "judgment" and "decision" may include the deeming of some action as having been "judged" or "decided." "Judgment" may be interpreted as "assuming," "expecting," or "considering," etc.

[0105] The terms "connected," "coupled," or any variation thereof, refer to any direct or indirect connection or coupling between two or more elements, and may include the presence of one or more intermediate elements between two elements that are "connected" or "coupled" to each other. The coupling or connection between elements may be physical, logical, or a combination thereof. For example, "connected" may be read as "access." As used in this disclosure, two elements may be considered to be "connected" or "coupled" to each other using at least one of one or more wires, cables, and printed electrical connections, as well as electromagnetic energy having wavelengths in the radio frequency range, microwave range, and optical (both visible and invisible) range, as some non-limiting and non-exhaustive examples.

[0106] As used in this disclosure, the phrase "based on" does not mean "based only on," unless expressly stated otherwise. In other words, the phrase "based on" means both "based only on" and "based at least on."

[0107] Any reference to an element using designations such as "first" and "second" used in this disclosure does not generally limit the quantity or order of those elements. These designations may be used in this disclosure as a convenient way to distinguish between two or more elements. Thus, a reference to a first and a second element does not imply that only two elements may be employed or that the first element must precede the second element in some way.

[0108] The "parts" in the configuration of each of the above devices may be replaced with "circuits" or "devices", etc.

[0109] When the terms "include," "including," and variations thereof are used in this disclosure, these terms are intended to be inclusive, similar to the term "comprising." Further, when used in this disclosure, the term "or" is not intended to be an exclusive or.

[0110] In this disclosure, where articles are added by translation, such as "a," "an," and "the" in English, the disclosure may include that the nouns following these articles are in the plural form.

[0111] In the present disclosure, the term "A and B are different" may mean "A and B are different from each other." The term may also mean "A and B are each different from C." Terms such as "separate" and "coupled" may also be interpreted in the same way as "different." [Explanation of symbols]

[0112] 10...analysis device, 11...input section, 12...first conversion section, 13...state space model memory section, 14...state variable memory section, 15...estimation section, 16...observation section, 17...refinement section, 18...second conversion section, 19...output section, 1001...processor, 1002...memory, 1003...storage, 1004...communication device, 1005...input device, 1006...output device, 1007...bus.

Claims

1. An analysis device that receives observation data relating to an observation target and outputs estimated observation data, an input unit for inputting the observation data; a first conversion unit that generates first sequence data by applying a first conversion to the observation data; an estimator that performs state estimation using a Kalman filter based on the first sequence data, a state space model that models time-series fluctuations of each element of the first sequence data, and state variables generated for each element included in the first sequence data based on the state space model to obtain a current state variable; an observation unit that generates second sequence data by applying an observation process using an observation matrix of the state space model to the current state variables; a generation unit that generates the estimated observation data by performing a refinement process that corrects each element included in the second sequence data under predetermined conditions so as to prevent each cell value of the estimated observation data from becoming negative and to reduce the number of cells having values ​​other than zero included in the estimated observation data, and a second transformation that is an inverse transformation of the first transformation; an output unit that outputs the estimated observation data; An analysis device comprising:

2. The analysis device according to claim 1 , wherein the first transformation is a multiresolution analysis using a Haar function as a mother wavelet.

3. 3. The analysis device according to claim 1, wherein the first conversion unit generates the first sequence data by expressing the observation data in a sparse data format and applying the first conversion to cells having values ​​other than zero included in the observation data.

4. the first conversion unit generates the first sequence data by performing an adjustment process for performing correction under predetermined conditions so that the scale of magnitude of values ​​of elements of data generated by applying the first conversion to the observation data is adjusted to a uniform level; The analysis device according to any one of claims 1 to 3, wherein the observation unit generates the second sequence data by performing an inverse adjustment process that corrects, under predetermined conditions, a scale of a magnitude of a value of each element of data generated by applying an observation process using the observation matrix to the current state variables, so as to return the scale to before the adjustment process.

5. A state variable storage unit that stores the state variables, 5. The analysis device according to claim 1, wherein the estimation unit updates the state variable stored in the state variable storage unit to the current state variable.

6. The generation unit is a refinement unit that generates third sequence data by performing the refinement process; a second conversion unit that applies the second conversion to the third sequence data to generate the estimated observation data; The analysis device according to any one of claims 1 to 5, comprising:

Images