JP5990449B2 - Estimation system, estimation device, estimation method, and program - Google Patents

Description

  In the present invention, shape parameters such as size and outer circumference length are appropriately dispersed for an object whose shape parameters such as size and outer circumference length can change with time (or many third parties The present invention relates to a technique for estimating from a sensing result of a binary sensor that does not have a positioning function. Here, as the estimation target, there are special gas, a region in a specific weather condition, an aggregate made up of many individuals such as a group of animals.

  Research and development of sensor networks that can be used for various purposes by dispersing sensors (referred to as sensor nodes) having wireless communication functions. As an application field thereof, there are estimation of the size and shape of a target object, classification identification by them, and the like. For example, grasping the size and shape of a vehicle entering a certain area, observing and estimating the spread of a toxic gas, and the like correspond to this. In such a sensor network, it is assumed that the position of each sensor node is grasped by GPS or the like, or the installation position is designed in advance and the sensor node is installed in accordance with the design.

JP 2010-60319 A JP 2011-164084 A H. Saito, S. Tanaka, and S. Shioda, Estimating Size and Shape of Non-convex Target Object Using Networked Binary Sensors, IEEE SUTC 2010, Newport Beach, California, USA. Hiroshi Saito, Sadaharu Tanaka, and Shigeo Shioda, Stochastic Geometric Filter and Its Application to Shape Estimation for Target Objects, IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 59, NO. 10, OCTOBER 2011

  However, when a large number of sensors are used, designing and deploying a myriad of sensor positions in advance is a design / deployment cost, and attaching a positioning function to each sensor is a sensor cost. It is not desirable because it becomes enormous.

  Estimated based on the sensing results of a binary sensor that does not have a positioning function in which the size and circumference of the object with a fixed size and circumference are appropriately distributed (or installed by many third parties) This is proposed by Patent Document 1 (Japanese Patent Laid-Open No. 2010-60319). In addition, a composite sensor node that does not have a positioning function that is properly distributed (or installed by many third parties without permission) (each sensor is a binary sensor, and multiple sensors are arranged in a certain layout) The estimation of the angle of the vertex of the object based on the sensing result of the node is proposed in Patent Document 2 (Japanese Patent Application Laid-Open No. 2011-164084).

  It is realistic that the size and shape do not change over time when the target object is a special gas, an area in a specific weather condition, or an aggregate consisting of many individuals such as a group of animals. This is not an assumption. For such time-varying objects, there has been no prior art for estimating the size and shape while suppressing the design / deployment cost and the sensor cost.

  The present invention has been made in view of the above points, and uses time-varying changes in size and shape by using sensing results from a plurality of sensor nodes arranged in a distributed manner without specifying installation locations. An object of the present invention is to provide a technique for estimating the size and shape of a target while suppressing design / deployment cost and sensor cost.

In order to solve the above problems, the present invention is an estimation system that includes a plurality of sensor nodes and one center server, and estimates parameters related to the size and shape of an object that can change from time to time.
The sensor nodes are divided into classes, randomly deployed,
Sensing means for the object;
A communication means for transmitting a sensing result by the sensing means and information capable of specifying a class number to the center server,
The center server is
Storage means for storing a parameter relating to the sensor node, a parameter relating to a time variation model of a parameter relating to the size and shape of the object, and a parameter relating to an initial condition of estimation;
Communication means for receiving the sensing results from the plurality of sensor nodes;
Data processing means for performing calculation using the sensing results from the plurality of sensor nodes and parameters read from the storage means, and estimating parameters relating to the size and shape of the object, and
The data processing means includes a state equation based on a time variable model of a state variable including parameters relating to the size and shape of the object, an observation equation describing a relationship between an observed value based on a sensing result for each class and the state variable, Based on the above, the estimation system is configured to include estimation means for estimating parameters related to the size and shape of the object.

  The parameter relating to the shape is, for example, the outer peripheral length of the object, and the sensing result of the sensor node is whether or not the object is detected. Moreover, the estimation means for performing estimation based on the state equation of the state variable including parameters related to the size and shape of the object and the observation equation using the observation value based on the sensing result for each class is, for example, a Kalman filter.

  Moreover, the structure which uses the outer periphery length of a target object and another characteristic quantity as a parameter regarding the said shape is also possible.

  Further, the sensor node may be a composite sensor node configured by arranging the sensors in two rows at equal intervals, and the configuration may be configured to use the outer peripheral length of the object and the angle of each vertex as the parameters relating to the shape. .

  The present invention can also be configured as an estimation device in the above estimation system and an estimation method executed by the estimation device. Furthermore, the present invention can also be configured as a program for causing a computer including a storage unit and a communication unit to function as a data processing unit of an estimation device in the estimation system.

  According to the present invention, by arranging a large number of sensors and collecting the sensing results, even if the position of the sensor is unknown or the size and shape of the object changes with time, , Estimation of them becomes possible. This greatly increases the usage scene.

It is a block diagram of the time-varying shape estimation system which concerns on 1st Embodiment. It is a flowchart of a process of the time-varying shape estimation system according to the first embodiment. It is a figure which shows arrangement | positioning of a sensor. It is a figure for demonstrating the object area | region which arrange | positions and monitors a sensor node in related technology. It is a figure for demonstrating the range which a sensor node of a class 4 detects a target object in related technology. It is a schematic block diagram of the data processing part 302 in embodiment of this invention and related technology. It is a figure which shows the example of the data processing part 302 in the case of applying the technique of this invention to a related technique. It is a flowchart of the process of the time-varying system shape estimation system which concerns on 3rd Embodiment.

  Embodiments of the present invention will be described below with reference to the drawings. The embodiment described below is only an example, and the embodiment to which the present invention is applied is not limited to the following embodiment.

[First Embodiment]
<System configuration>
FIG. 1 shows a configuration diagram of a time-varying shape estimation system according to the first embodiment of the present invention. FIG. 2 shows a flowchart of processing of the time-varying shape estimation system. As shown in FIG. 1, the time-varying shape estimation system according to the present embodiment includes a plurality of sensor nodes 201 and one center server 401. In the present embodiment, each sensor node is randomly deployed and does not have a positioning function, so its deployment location is not specified. In FIG. 1, two sensor nodes 201 are shown as an example, but a large number of sensor nodes 201 are actually provided.

  The sensor node 201 includes a detection unit 101 that is a sensor that detects the presence or absence of an object, and a wireless communication unit 102 that transmits information that can specify a sensing result (whether or not an object is detected) and a class number to the center server 401. And a power supply unit 103 for supplying power. The detection unit 101 that is a sensor is classified into two or more types of classes according to the sensing area size and the like. The object in the present embodiment is an object that can change from moment to moment. The detection unit 101 detects the target object even when the target object is within the detection area, but the detection power increases as the target object is closer to the sensor. Here, the sensing area of the jth type sensor is

の形に検出確率で段階分けされ、Α_j,i-1にかからないがΑ_j,iにかかる対象物についてはα_j,iの検出確率であるとする（図３）。

It is assumed that the detection probability of α _{j, i} for an object related to Α _{j, i} is not applied to 段 階_{j, i-1} (FIG. 3).

  As shown in FIG. 1, the center server 401 includes a wireless communication unit 301 for receiving a sensing result from the sensor node 201, and a data processing unit for estimating the size and shape of the object based on the received sensing result. 302, a storage unit 303 for storing known parameter values used in data processing, an input / output unit 304 for inputting results and execution instructions, and inputting known parameter values, and a power source unit 305 for supplying power. The center server 401 may be referred to as an estimation device.

  The center server 401 can be realized, for example, by causing a computer having a communication function to execute a program describing the processing contents of the data processing unit 302 described in each embodiment. That is, the data processing unit 302 can be realized by executing a program corresponding to the processing content using hardware resources such as a CPU, a memory, and a hard disk built in a computer constituting the center server 401. is there. This program can be recorded on a computer-readable recording medium (portable memory or the like), stored, or distributed. It is also possible to provide the program through a network such as the Internet or electronic mail. The center server 401 can also be configured by realizing the data processing unit 302 described in each embodiment as a hardware circuit and mounting the hardware circuit.

<System operation>
Next, the processing operation of the time-varying shape estimation system according to the present embodiment having the configuration shown in FIG. 1 will be described in detail along the procedure of the flowchart of FIG.

Steps S201 and S202) A person who intends to execute size or shape estimation uses sensor information (parameters related to sensor nodes) and time-varying model information of objects (parameters related to time-varying models of parameters related to the size and shape of objects). ) And parameters related to the initial condition for estimation are input from the input / output unit 304 and stored in the storage unit 303. The sensor information includes the sensor (node) average density λ _j , the size of Α _{j, i} and the outer peripheral length of the sensor having the j-th type sensing area size (j = 1, 2,..., I = 1,2, ..., k _j ). In addition, the time-varying model information of the object is the object size at time t expressed as || T (t) || and the perimeter as | T (t) |

のモデルであり、具体的には、m_a, m_bと(e_s(t), e_l(t))の分散行列V_x(t)である。なお、上記の式において、e_s(t)、e_l(t)は誤差項、a_k、b_kは推定すべき定数項、||T(t)||、|T(t)|は推定すべき変数、m_a、m_bはモデルの一部として与えられる定数である。

Specifically, m _a , m _b and a dispersion matrix V _x (t) of (e _s (t), e _l (t)). In the above equation, e _s (t) and e _l (t) are error terms, a _k and b _k are constant terms to be estimated, and || T (t) || and | T (t) | The variables to be estimated, m _a and m _b are constants given as part of the model.

  The storage unit 303 stores and holds the individual identification number of each sensor of the target object and which type of sensor the sensor is.

Step S203) Based on the above information, the following quantities are calculated and held in advance. However, 0 _{i, j} is a zero matrix of i rows and j columns.

ステップＳ２０４）そして、入出力部３０４から実行指示を入力する。

Step S204) Then, an execution instruction is input from the input / output unit 304.

  Step S205) Each sensor node 201 performs detection (sensing) of an object at each time t by the detection unit 101.

  Step S206) Each sensor node 201 transmits the sensing result together with the sensor number to the center server 401.

  Step S207) The communication unit 301 receives the information transmitted from each sensor node 201.

  Step S208) The data processing unit 302 of the center server 401 that has obtained the information separates the received information for each sensor type from the type information for each sensor number stored in the storage unit 303. The number of sensors in which the object is detected by the i-th type sensor at time t is expressed as n (i; t). For each i, calculate n (i; t). A vertical vector in which n (i; t) is arranged is expressed as n (t).

  State variable vector x (t)

で定義する。すると、

Defined in Then

但し、I_nはn行n列の単位行列、

Where I _n is an n-by-n identity matrix,

のシステムとなることが示せるから、既知の技術であるカルマンフィルタにより状態変数の推定予測が可能となる。

Therefore, it is possible to estimate and predict state variables using a Kalman filter that is a known technique.

  That is, the data processing unit 302 has a state equation (Equation 1) based on a time variable model of a state variable including parameters related to the size and shape of an object, and an observed value and a state based on a sensing result for each sensor class (sensor type). An estimator for estimating and predicting a state variable by a Kalman filter is provided based on an observation equation describing the relationship between variables.

  Steps S209 and S210) The data processing unit 302 reads necessary information stored in the storage unit 303 and executes a Kalman filter.

  Step 211) By outputting the execution result of the Kalman filter at the input / output unit 304, information on the size and shape of the object can be obtained.

<Related application technology>
There is Japanese Patent Application No. 2012-246677 as an application related to the present application. The technology according to the present invention can be applied to the technology of the related application (hereinafter referred to as “related technology”). First, an embodiment of this related technique will be described below.

  The system configuration in the related art is the same as the system configuration according to the embodiment of the present invention, as shown in FIG.

  FIG. 4 is a diagram for explaining a target area where a sensor node is deployed and monitored in the related art. As shown in FIG. 4, in the related technology, a rectangular area composed of integers with an x-axis of 1,..., 2n_x and a y-axis of 1,. Further, it is assumed that the sensor node is arranged and the object takes a point on the grid.

  In related technology, sensor nodes are classified into a plurality of types of classes. When a sensor node of class k is deployed at a point (i, j), the sensing area is a square area with 2L_k + 1 lattice points per side centered at (i, j), that is, the x axis is The area from i-L_k to i + L_k and the y-axis from j-L_k to j + L_k. N_s (k) is the number of deployed sensor nodes of class k, p_ {k, (i, j)} is the probability that a class k sensor will be deployed at (i, j) (location-dependent probability), and each sensor Assume that the position of each node is determined independently.

In the following, for the sake of simplicity, a case where the number of sensor node classes is 4, L_1 = L_2 = L_3 = 0, and L_4 = L (L is an integer of 1 or more) will be described as an example. Also,
p_ {1, (i, j)} = d_1N_s (1) / (4n_x * n_y) (if i = 1 ,,, n_x),
p_ {1, (i, j)} = (2-d_1) N_s (1) / (4n_x * n_y) (when i = n_x + 1 ,,, 2n_x)
And In the above formula, d_1 (0 ≦ d_1 ≦ 2) is set to d_1 ≠ 1, and the sensor deployment density is changed with n_x as a boundary on the x axis in the monitoring region. Similarly,
p_ {2, (i, j)} = d_2N_s (2) / (4n_x * n_y) (when j = 1 ,,, n_x)
p_ {2, (i, j)} = (2-d_2) N_s (2) / (4n_x * n_y) (when j = n_y + 1 ,,, 2n_y)
And In the above formula, d_2 (0 ≦ d_2 ≦ 2) is set to d_2 ≠ 1, and the sensor deployment density is changed with n_y as a boundary on the y axis in the monitoring region. On the other hand, p_ {k, (i, j)} = N_s (k) / (4n_x * n_y), (k = 3,4), that is, classes 3 and 4 are deployed at each lattice point with equal probability.

  Assume that the object T is located somewhere in the monitoring area. The object is moving in the monitoring area. The size, shape, position, moving speed, and moving direction of the object are unknown. However, it is assumed that the object has a shape without a hole or a recess having a width L or less.

If S (T) is the size of the object T (area in this embodiment) and | T | is the outer peripheral length of the object T, the range in which the sensor node of class 4 detects the object is shown in FIG. Since it is a range indicated by a dotted line, its size (area in this embodiment) is
S (T) + | T | * L + ((number of convex vertices) − (number of concave vertices)) * L * L
It is represented by Since the object has vertices at points on the grid, the number of convex vertices minus the number of concave vertices is always 4. Therefore, the number n_4 (t) of class 4 sensors that detect an object at time t is
n_4 (t) = (S (T) + | T | * L + 4 * L * L) N_s (4) / (4n_x * n_y) + e_4 (t)
It can be expressed. Here, e_k (t) is an error term from the expected value (E [e_k (t)] = 0, k = 1,..., 4). The number of class 3 sensors n_3 (t) for detecting an object is
n_3 (t) = S (T) * N_s (3) / (4n_x * n_y) + e_3 (t)
It can be expressed.

On the other hand, the number of sensors n_k (t) of class k (k = 1, 2) for detecting an object is c_1 (t) of T, and the value of the x-axis enters 1, .., n_x at time t. The ratio, c_2 (t), is the ratio of the y-axis value entering 1, .., n_y at time t.
n_1 (t) = Σ_ {i = 1,…, n_x} Σ_ {j = 1,…, 2n_y} p_ {1, (i, j)} * IF ((i, j) in T)
+ Σ_ {i = n_x + 1,…, 2n_x} Σ_ {j = 1,…, 2n_y} p_ {1, (i, j)} * IF ((i, j) in T) + e_1 (t)
= (c_1 (t) * S (T) * d_1N_s (1) + (1-c_1 (t)) * S (T) * (2-d_1) N_s (1)) / (4n_x * n_y) + e_1 ( t)
n_2 (t) = Σ_ {i = 1,…, 2n_x} Σ_ {j = 1,…, n_y} p_ {2, (i, j)} * IF ((i, j) in T)
+ Σ_ {i = 1,…, 2n_x} Σ_ {j = n_y + 1,…, 2n_y} p_ {2, (i, j)} * IF ((i, j) in T) + e_2 (t)
= (c_2 (t) * S (T) * d_2N_s (2) + (1-c_2 (t)) * S (T) * (2-d_2) N_s (2)) / (4n_x * n_y) + e_2 ( t)
It becomes. Note that IF ((i, j) in T) is 1 when (i, j) is in the range of T, and is 0 when (i, j) is not in the range of T.

Less than,
c_k (t) = c_k (t-1) + e'_k (t)
E [e'_k (t)] = 0
And e′_k (t) is an independent normality random variable with known variance.

  At each time t, the center server 401 receives the sensing result from each sensor node 201 together with the class number by the wireless communication unit 301 and sends it to the data processing unit 302. The data processing unit 302 determines the size of the object, Peripheral length and position are estimated.

  FIG. 6 shows a schematic configuration of the data processing unit 302 in the related technology. The configuration of the data processing unit 302 illustrated in FIG. 6 is also an example of the configuration of the data processing unit 302 in the embodiment of the present invention. As shown in FIG. 6, the data processing unit 302 includes an adder 312 and an estimator 322 for each sensor class.

Each adder 312 receives the sensing result of the sensor node of the corresponding class (1 in the case of detection, 0 if not detected), and outputs the result of adding these to the estimator 322. The output of the adder 312 corresponds to an actual value of n_k (t). (Hereafter, this is expressed as n_k (t).)
As can be seen from the above-described expression n_k (t) (k = 1, 2, 3, 4), the unknown variables are S (T), | T |, c_1 (t), and c_2 (t). Parameters stored in the storage unit 303 and sent to the data processing unit 302 are N_s (k), L, n_x, n_y, d_k, and e_k (t) and e′_k (t) distributions and initial conditions. . The estimator 322 estimates and outputs S (T), | T |, c_1 (t), and c_2 (t) based on these parameters and the realized value of n_k (t). For example, the estimator 322 may be composed of an extended Kalman filter or the like, and S (T), | T |, c_1 (t), and c_2 (t) can be estimated using the extended Kalman filter or the like.

  The estimator 322 can be configured as shown in FIG. 7, which is simpler than an extended Kalman filter or the like. Note that k in FIG. In the configuration illustrated in FIG. 7, the estimator 322 includes an estimator 322-1 and an estimator 322-2. In the configuration of FIG. 7, n_3 (t) and n_4 (t) are input to the estimator 322-1, and the estimator 322-1 sets the object size S (T) and the perimeter length | T | to n_3 (t ) And n_4 (t) only, and the estimation result is given to the estimator 322-2. The estimator 322-2 includes S (T), outer circumference length | T |, n_1 (t), n_2 (t) Is used to estimate c_1 (t) and c_2 (t) as position information. More details are as follows.

For n_3 (t) and n_4 (t), for sufficiently large m,
Σ_ {t = 1,…, m} n_4 (t) / m = (S (T) + | T | * L + 4 * L * L) N_s (4) / (4n_x * n_y)
Σ_ {t = 1,…, m} n_3 (t) / m = S (T) * N_s (3) / (4n_x * n_y)
Holds. Therefore,
S (T) = 4n_x * n_yΣ_ {t = 1,…, m} n_3 (t) / (m * N_s (3))
| T | = (4n_x * n_y / L) {Σ_ {t = 1,…, m} (n_4 (t) / (m * N_s (4)) − n_3 (t) / (m * N_s (3)) ) −4L * L}
It becomes. The estimator 322-1 estimates S (T) and | T | by performing the above calculation using n_3 (t) and n_4 (t) sequentially input and the parameters acquired from the storage unit 303. .

  The S (T) and | T | are given as true values to the estimator 322-2. As a result, n_k (t) (k = 1, 2) becomes a linear function of c_k (t). Therefore, by configuring the estimator 322-2 with a Kalman filter, c_k (t) is estimated by the Kalman filter.

  These estimation results (S (T), | T |, c_k (t)) are sent to the input / output unit 304 every moment and displayed.

  According to this related technology, by using a binary sensor whose installation position is unknown, it is possible to estimate the location of the object in addition to the size and the outer peripheral length of the object. In addition, in the related technology, in order to make the explanation easy to understand, an example was given in which the region was divided into two along the x axis and divided into two along the y axis. However, it is easy to estimate the location by dividing more finely. It can be inferred. In this related technique, the number of sensor types is four, but the number of sensor types is not limited to four, and any other number of types can be applied. Moreover, although two types of sensors are used for position estimation, it is not necessary that these are also two types. Generally, if the position is specified in detail, more sensor types are required.

<Application of the present invention to related technologies>
The object size and the outer peripheral length are estimated in the dotted line and the upper half in the data processing unit 302 in FIG. 7, and the technique of the present invention can be applied to this portion.

  In the related art, the estimator 322-1 is the estimator for estimating the size and the outer perimeter for a time-invariant system. Position estimation is also possible for time-varying objects. That is, the center server 401 provided with the data processing part 302 which comprised the dotted line of FIG. 7, and the upper half using the estimator which concerns on this invention is one of the embodiments of the estimation apparatus of this invention. In the related art, the detection power of the sensor is not divided into stages, but this is not an essential problem in combination with the present invention.

<Relationship between this application and related technologies>
If the position does not change, it is possible to estimate the size and outer peripheral length of the time-varying object only with the technique of the present application. In addition, if the sensors are evenly spread over the monitoring area, the size and the outer peripheral length of the time-varying object can be estimated only by the technique of the present application even if the position changes. However, position estimation is not possible. When the average density of the sensors sown in the monitoring area is shaded and the estimator knows this, combine the technology of this application and related technology, and estimate the size and circumference length of the time-varying object. Can be estimated.

[Second Embodiment]
The first embodiment is an example of estimating and predicting the size and outer peripheral length of an object when the object is convex. In many cases, estimation is successful even with non-convex objects, but in the second embodiment, a more complicated model is used for estimating and predicting the size and outer circumference of an object that is not necessarily convex. An example of expanding the application range by introducing the system will be described. In the second embodiment, the range of application is widened, but the state variables increase, the influence of the change in the size of the inner angle of the target is affected by the estimation and prediction of the size and outer circumference of the target, and the like. It is necessary to keep in mind.

  Hereinafter, differences in the second embodiment from the first embodiment will be described. Except as described below, the second embodiment is the same as the first embodiment.

The interior angles of the object are smaller than π, ν ₁ , ν ₂ ..., Ν = Σ _i ν _i , and the i-th interior angle function larger than π is β _i , β = Σ _i β _i . ν and β are added to the elements of the state variable vector, and the state variable vector is

とする。

And

  In step S203 of FIG.

を加える。

Add

  Then the new equation of state is

新たな観測方程式は、

The new observation equation is

となることが、非特許文献１の近似式（式４）を用いることで示せる。ここで、

This can be shown by using the approximate expression (Expression 4) of Non-Patent Document 1. here,

である。

It is.

In step S210 of FIG. 2, state variables are estimated and predicted using the Kalman filter. If an appropriate value cannot be set for the distribution of e _x '(t), an appropriate existing technique such as an adaptive Kalman filter is used.

[Third Embodiment]
In the first and second embodiments, the sensor reports only the presence or absence of an object. However, in many sensors, the characteristic amount in the sensing area can be used as a sensing result. In the present embodiment, when the reference point of the object is (x ₀ , y ₀ ) and the reference angle is θ ₀ , the characteristic quantity at (x, y) is represented by h ((x, y) | x ₀ , y ₀ , θ ₀ ), and the sensing value q _j (t) of the type j sensor is

と書ける場合を発明の対象とする。ただし、h((x,y)|x₀, y₀, θ₀）>0、w_j,k>0である。ここで、T(t)は、時刻tにおいて、対象物が占める２次元空間上の領域である。特性量h((x,y)|x₀, y₀, θ₀）とは、対象物の(x,y)での高さや、対象物が微細物の集合体の場合は密度など、が考えられる。

Is the subject of the invention. However, h ((x, y) | x ₀ , y ₀ , θ ₀ )> 0 and w _{j, k} > 0. Here, T (t) is an area on the two-dimensional space occupied by the object at time t. The characteristic quantity h ((x, y) | x ₀ , y ₀ , θ ₀ ) is the height of the object at (x, y) or the density if the object is an aggregate of fine objects. Conceivable.

In the present embodiment, an object in which the average value h _m (t) of h ((x, y) |.) At a certain point (x, y) on the object is estimated in the first and second embodiments. A method for estimation based on the size and outer circumference of an object will be described.

Q _j (t) in the above definition can be regarded as a weighted average of the characteristic quantities in the sensing area. As can be seen from the above definition formula, when the object is not in the sensing area, it takes 0, and when it has a positive value, the sensor includes a binary sensor.

  FIG. 8 shows a flowchart of processing in the present embodiment.

As shown in step S401 in FIG. 8, first, the above-described steps S201 to S207 are executed, but there are some modifications. First, w _{j, k} (j = 1, 2,..., K = 1,..., K _j ) is added as sensor information to be stored in step S201. The sensing result transmitted by the j-th type sensor in step S205 and transmitted in step S206 is q _j (t).

Next, in step S402, the arithmetic average of the sensor values q _j (t) is taken for each type,

を計算する。

Calculate

  In step S403, information in the storage unit 303 is read, and in step S404, state variable vectors are estimated and predicted by a method such as a Kalman filter. Since the state variable vector includes the size of the object at the time t and the outer perimeter, its estimated value

を得ることができるので、この値を読み出す（ステップＳ４０５）。

This value is read out (step S405).

  It can be seen that the following equation holds when the geometric probability is used.

このことから、ステップＳ４０６において、h_m(t)の推定値を次の式で計算する。

Therefore, in step S406, an estimated value of h _m (t) is calculated by the following equation.

そして、ステップＳ４０７において、その結果を入出力部３０４にて出力する。

In step S407, the input / output unit 304 outputs the result.

[Fourth Embodiment]
About the size of the time-varying object, the outer peripheral length, and the angle of the apex by a composite sensor proposed by Patent Document 2 (Japanese Patent Application Laid-Open No. 2011-164084), in which the sensors are arranged in two rows at equal intervals. A case of estimation will be described. That is, in the present embodiment, the shape-related parameters include the outer peripheral length of the object and the angle of each vertex, and the sensor node is a complex sensor node configured by arranging the sensors in two rows at equal intervals. Different from the previous embodiments. The sensing result of each sensor of the composite sensor node is the presence or absence of detection of an object.

In this case as well, basically, as described in the previous embodiments,
1) Assuming a time-varying model of parameters to be estimated, a state equation based on the model is constructed. The state variable includes an estimation target parameter.

  2) Derive the relationship between the observed value and the state variable, and construct the observation equation based on it.

3) An appropriate estimator is constructed from the state equation from the observation equation.
Estimate according to the procedure.

As for 1), the same configuration as that of the embodiments described so far can be configured. In particular, assuming that the number of vertices is unchanged, the angle of the i-th vertex at time t is ξ _i (t), and the time variation model is

と仮定する。すると、状態変数を

Assume that Then the state variable

とすれば、式１と同様の線形の状態方程式が構成可能である。
これに対して、観測方程式は、式２とは大きく異なる。非特許文献２に示されているように、頂点の角度と、センシング結果との関係は、非常に複雑な非線形関係となる。このため、観測方程式は、非線形方程式となる。上記非特許文献２の結果を用いれば、当該非線形観測方程式を導出することは容易である。観測方程式が非線形であることから、状態推定器は、通常、非線形となる。非線形ではあるが、状態方程式、観測方程式が導出されていることから、従来技術で推定器は構成可能であり、複合センサにより、時変対象物の大きさ、外周長、頂点の角度を推定することができる。

Then, a linear equation of state similar to Equation 1 can be constructed.
On the other hand, the observation equation is greatly different from Equation 2. As shown in Non-Patent Document 2, the relationship between the vertex angle and the sensing result is a very complicated non-linear relationship. For this reason, the observation equation is a nonlinear equation. If the result of the said nonpatent literature 2 is used, it will be easy to derive | lead-out the said nonlinear observation equation. Since the observation equation is nonlinear, the state estimator is usually nonlinear. Although it is non-linear, the state equation and observation equation are derived, so the estimator can be configured with the conventional technology, and the size, outer circumference length, and vertex angle of the time-varying object are estimated by the composite sensor. be able to.

  The present invention is not limited to the above-described embodiments, and various modifications and applications are possible within the scope of the claims. For example, the sensor itself may be deployed by a third party and the sensing results collected by the operator.

201 sensor node 101 detection unit 102 wireless communication unit 103, 305 power supply unit 301 wireless communication unit 302 data processing unit 303 storage unit 304 input / output unit 312 adder 322, 322-1, 322-2 estimator 401 center server

Claims (8)

An estimation system that includes a plurality of sensor nodes and a center server, and estimates parameters related to the size and shape of an object that can change from moment to moment,
The sensor node is
Divided into classes, randomly deployed,
Sensing means for the object;
A communication means for transmitting a sensing result by the sensing means and information capable of specifying a class number to the center server,
The center server is
Storage means for storing a parameter relating to the sensor node, a parameter relating to a time variation model of a parameter relating to the size and shape of the object, and a parameter relating to an initial condition of estimation;
Communication means for receiving the sensing results from the plurality of sensor nodes;
Data processing means for performing calculation using the sensing results from the plurality of sensor nodes and parameters read from the storage means, and estimating parameters relating to the size and shape of the object, and
The data processing means includes a state equation based on a time variable model of a state variable including parameters relating to the size and shape of the object, an observation equation describing a relationship between an observed value based on a sensing result for each class and the state variable, An estimation system comprising: estimation means for estimating parameters related to the size and shape of the object based on the above. The estimation system according to claim 1, wherein the parameter relating to the shape is an outer peripheral length of an object, and a sensing result of the sensor node is presence or absence of detection of the object. The estimation means for performing estimation based on a state equation of a state variable including parameters related to the size and shape of the object and an observation equation using an observation value based on a sensing result for each class is a Kalman filter. The estimation system according to claim 1. The estimation system according to claim 1, wherein the parameter relating to the shape is an outer peripheral length of the object and another characteristic amount, and a sensing result of the sensor node is whether or not the object is detected. The parameter relating to the shape is the outer peripheral length of the object and the angle of each vertex, and the sensor node is a composite sensor node configured by arranging the sensors in two rows at equal intervals, and sensing of each sensor of the composite sensor node The estimation system according to claim 1, wherein the result is presence or absence of detection of an object. An estimation device for estimating parameters related to the size and shape of an object based on sensing results of the object that can be changed from moment to moment by a plurality of sensor nodes that are randomly divided into classes,
Storage means for storing a parameter relating to the sensor node, a parameter relating to a time variation model of a parameter relating to the size and shape of the object, and a parameter relating to an initial condition of estimation;
Communication means for receiving the sensing results from the plurality of sensor nodes;
Data processing means for performing calculation using the sensing results from the plurality of sensor nodes and parameters read from the storage means, and estimating parameters relating to the size and shape of the object, and
The data processing means includes a state equation based on a time variable model of a state variable including parameters relating to the size and shape of the object, an observation equation describing a relationship between an observed value based on a sensing result for each class and the state variable, An estimation device comprising: estimation means for estimating parameters related to the size and shape of the object based on the above. An estimation method executed by an estimation device that estimates parameters related to the size and shape of an object based on the sensing result of the object that can be changed from time to time by a plurality of sensor nodes that are randomly divided into classes. Because
The estimation device includes:
Storage means for storing a parameter relating to the sensor node, a parameter relating to a time variation model of a parameter relating to the size and shape of the object, and a parameter relating to an initial condition of estimation;
Communication means for receiving the sensing results from the plurality of sensor nodes,
The estimation method is:
A data processing step of performing calculation using the sensing results from the plurality of sensor nodes and parameters read from the storage means, and estimating parameters relating to the size and shape of the object,
In the data processing step, a state equation based on a time variable model of a state variable including parameters related to the size and shape of the object, an observation equation describing a relationship between an observed value based on a sensing result for each class and the state variable, An estimation method characterized by estimating parameters related to the size and shape of the object based on the above.   The program for functioning a computer provided with a memory | storage means and a communication means as a data processing means of the estimation apparatus in the estimation system of any one of Claims 1 thru | or 5.

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