JP7105447B2 - Shape estimation device, shape estimation method and program - Google Patents

Description

The present invention relates to a shape estimation device, a shape estimation method and a program.

In recent years, attempts have been made to scatter small sensors with wireless functions over a monitoring target area, network them, and use them for various applications. In particular, it is desirable to assume a situation where a low-cost, low-power-consumption, low-function sensor that does not require prior design or registration of the sensor position and does not have a positioning function such as GPS is used.

Under such conditions, methods for estimating the size and shape of an object have been proposed. Patent Document 1 discloses an invention that uses multiple classes of distance sensors to estimate the size and perimeter of a convex object. An invention for estimating the size and perimeter of an object has been disclosed. Furthermore, Non-Patent Document 3 proposes a method of estimating the overall shape of a polygonal object using a large number of distance sensors.

Japanese Patent No. 5371907 Japanese Patent Application Laid-Open No. 2017-156286

H. Saito and H. Ikeuchi, Estimating Shape of Target Object Moving on Unknown Trajectory by Using Location-Unknown Distance Sensors: Theoretical Framework, ArXiv 1803.04092.

However, many actual objects include curved portions, and for such objects, the conventional technique that assumes a polygonal shape cannot estimate the overall shape. In addition, the conventional technology performs statistical processing on the assumption that distance sensors are distributed according to a specific distribution such as a uniform distribution within the monitored area, and the sensor arrangement does not satisfy this assumption. In some cases, highly accurate shape estimation is difficult.

SUMMARY OF THE INVENTION It is an object of the present invention to enable estimation of the overall shape of an object using a distance sensor whose placement position does not necessarily follow a specific distribution.

Therefore, in order to solve the above problems, the shape estimation device provides an estimated sensing direction for each of the sensor terminals, based on time-series measurement results of distances between moving objects and the sensor terminals, using a plurality of sensor terminals. and a direction estimating unit that estimates a partial shape of the object based on the time-series measurement results and the sensing direction for each of the sensor terminals, and connects the partial shapes estimated for each of the sensor terminals. and a shape estimator for estimating the overall shape of the object.

A range sensor whose placement position does not necessarily follow a particular distribution can be used to allow estimation of the overall shape of the object.

It is a figure which shows the structural example of the shape estimation system in embodiment of this invention. It is a figure for demonstrating the problem setting given in embodiment of this invention. It is a figure which shows the hardware structural example of the shape estimation apparatus 10 in embodiment of this invention. It is a figure which shows the functional structural example of the shape estimation apparatus 10 in embodiment of this invention. 4 is a flowchart for explaining an example of a processing procedure executed by the shape estimation device 10; FIG. 10 is a diagram showing minute displacements from time t to t+Δt; It is a figure which shows an example of an asymmetric convex closed curve. It is a figure which shows an example of a ginkgo type|mold. It is a figure which shows an example of the situation etc. at the time of the start of an asymmetric convex closed curve. It is a figure which shows an example of the situation etc. at the time of a ginkgo-shaped start. FIG. 10 is a diagram showing a result of estimating the shape of an asymmetric convex closed curve based on the sensor terminal d1; FIG. 10 is a diagram showing the result of estimating the shape of an asymmetric convex closed curve based on the sensor terminal d2; FIG. 10 is a diagram showing the result of estimating the shape of an asymmetric convex closed curve based on the sensor terminal d3; FIG. 10 is a diagram showing a result of estimating the shape of an asymmetric convex closed curve based on the sensor terminal d4; FIG. 10 is a diagram showing a ginkgo-shaped shape estimation result based on the sensor terminal d1; FIG. 10 is a diagram showing a ginkgo-shaped shape estimation result based on the sensor terminal d2; FIG. 10 is a diagram showing a ginkgo-shaped shape estimation result based on the sensor terminal d3; FIG. 10 is a diagram showing a ginkgo-shaped shape estimation result based on the sensor terminal d4;

BEST MODE FOR CARRYING OUT THE INVENTION An embodiment of the present invention will be described below based on the drawings. FIG. 1 is a diagram showing a configuration example of a shape estimation system according to an embodiment of the present invention. The shape estimation system according to the present embodiment includes shape estimation device 10, and N ^~ (plural) sensor terminals of sensor terminal d1 ~ sensor terminal dN ^~ (hereinafter referred to as "sensor terminal d" when not distinguished). including. The shape estimation device 10 and each sensor terminal d are connected via a wired or wireless network.

Each sensor terminal d is an object that moves within the monitored area, and is a distance sensor that detects an object whose shape is to be estimated (hereinafter referred to as "target object T") and measures the distance to the target object T. is. Each sensor terminal d is a distance sensor with sharp directivity, and when the distance to the object T is r _max or less, the distance r (0≦r≦r _max ) to the object T is measured as a result ( hereinafter referred to as “sensing data”), and transmits the sensing data to the shape estimation device 10 . In this embodiment, the sensing area (the range in which the object T can be detected) of each sensor terminal d is modeled as a line segment having a specific sensing direction and a length of _rmax . The arrangement position of each sensor terminal d is random. That is, each sensor terminal d is scattered at a randomly determined arrangement position.

The shape estimation device 10 is one or more computers that estimate the overall shape of the target object T based on sensing data. The shape estimation device 10 receives sensing data from the sensor terminal d, estimates the direction of the sensor terminal d (the angle of the sensing direction with respect to the traveling direction of the object T) based on formulas (1) and (2) described later, A process of estimating the overall shape of the object T is performed. Equations (1) and (2) can be applied to a curvilinear object T and do not depend on the arrangement distribution of the sensor terminals d. Therefore, the scattered distance The sensor terminal d can be used to estimate the overall shape of the object T for objects that contain curvilinear portions and are not necessarily convex.

A shape estimation result is transmitted from the shape estimation device 10 to the user terminal 20 . The user terminal 20 is a terminal that displays the shape estimation result.

FIG. 2 is a diagram for explaining problem setting given in the embodiment of the present invention. Note that the problem setting described below is merely an example, and the applicable problem setting is not limited to this.

In FIG. 2, the object T is an area surrounded by a simple closed curve ∂T. The object T is translated in the x-axis direction at a constant speed v (v>0). In the object T, the point with the smallest y-coordinate value is called the bottom end, and the point with the largest y-coordinate value is called the top end. Below, it is assumed that there is only one lower end and one upper end. Each point of ∂T can be represented using an arc length parameter s. The starting point s=0 of the arc length parameter is the lower end of the object T, and the counterclockwise direction is the positive direction. Also, s is appropriately considered mod |∂T| (|∂T| is the perimeter of T). That is, s is considered as a remainder of the perimeter of ∂T. Also, the angle between the tangent vector pointing in the positive direction and the x-axis direction is a function of s and is denoted by ξ(s)ε[0,2π). A straight line passing through the object T and parallel to the x-axis is appropriately defined, and the area above it is called the upper half-plane, and the area below it is called the lower half-plane.

The position of the sensor terminal d, the sensing direction θε[0,2π) is unknown. The sensor number, which is the identification information of each sensor terminal d, is indicated by a subscript _i (such as θi) in each variable, but may be omitted when discussing one sensor terminal d. Each sensor terminal d obtains the distance r(t)≦r _max to the object T at each time t. However, when the distance between the sensor terminals d and T exceeds _rmax , r(t)=Φ (empty set), and when the sensor terminal d is included in T, r(t)=0. In shape estimation, only sensor terminals d whose sensing data satisfy ∀t (r(t)>0 or r(t)=Φ) and ∃t (r(t)≠Φ) are used. Such a sensor terminal d will be called a valid sensor terminal d, and the corresponding sensing data will be called valid sensing data. All the sensing data {r _i (t)} _i are transmitted to the shape estimation device 10, and the shape estimation device 10 uses them to obtain the shape of ∂T based on the shape estimation method described later.

Subsequently, important equations (1) and (2) used in shape estimation are presented. When estimating the shape, it is necessary to obtain the direction _θi of each sensor terminal d. This is made possible by using two sensing data r ₁ (t), r ₂ (t), as described below. Let r'(t), r''(t) and r'''(t) be the first, second and third derivatives of r(t). Let _{t 1} = argmin tr ₁ (t) and t ₂ = argmin tr ₂ ( _t ), and let r ₁ '(t ₁ ) and r ₂ '(t ₂ ) be simply (r ₁ )' , (r ₂ )', etc., the directions θ ₁ and θ ₂ are

の連立方程式である数式（１）（後述する［理論的背景］にて導出）を解くことで求めることができる。なお、各数式において、ｒ'は、ｒの上に・を付した記号によって表記し、ｒ''は、ｒの上に‥を付した記号によって表記し、ｒ'''は、ｒの上に…を付した記号によって表記する。

can be obtained by solving Equation (1), which is a simultaneous equation of (derived in [Theoretical background] described later). In each formula, r' is represented by a symbol above r, r'' is represented by a symbol above r, and r''' is above r. It is indicated by a symbol with … attached to it.

If (r ₁ )'=(r ₂ )'=0,

の連立方程式である数式（２）（後述する［理論的背景］にて導出）を解くことでθ_１、θ_２を求める。また、もし、ｔ_１、ｔ_２においてそれぞれｒ_１（ｔ）、ｒ_２（ｔ）が左微係数又は右微係数をもつときは、その値を用いて数式（１）を解けばよい。

θ ₁ and θ ₂ are obtained by solving Equation (2), which is a simultaneous equation of (derived in [Theoretical background] described later). Also, if r ₁ (t) and r ₂ (t) at t ₁ and t ₂ respectively have a left derivative or a right derivative, Equation (1) can be solved using that value.

The shape estimating device 10 for estimating the shape of the object T based on the above will be specifically described. FIG. 3 is a diagram showing a hardware configuration example of the shape estimation device 10 according to the embodiment of the present invention. The shape estimation device 10 of FIG. 3 has a drive device 100, an auxiliary storage device 102, a memory device 103, a CPU 104, an interface device 105, and the like, which are connected to each other via a bus B, respectively.

A program for realizing processing in the shape estimation device 10 is provided by a recording medium 101 such as a CD-ROM. When the recording medium 101 storing the program is set in the drive device 100 , the program is installed from the recording medium 101 to the auxiliary storage device 102 via the drive device 100 . However, the program does not necessarily need to be installed from the recording medium 101, and may be downloaded from another computer via the network. The auxiliary storage device 102 stores installed programs, as well as necessary files and data.

The memory device 103 reads out and stores the program from the auxiliary storage device 102 when a program activation instruction is received. The CPU 104 executes functions related to the shape estimation device 10 according to programs stored in the memory device 103 . The interface device 105 is used as an interface for connecting to a network.

FIG. 4 is a diagram showing a functional configuration example of the shape estimation device 10 according to the embodiment of the present invention. In FIG. 4, the shape estimation device 10 has a receiver 11, a direction estimator 12, a shape estimator 13, and the like. Each of these units is realized by processing that one or more programs installed in the shape estimation apparatus 10 cause the CPU 104 to execute. The shape estimation device 10 also utilizes the data storage unit 14 . The data storage unit 14 can be implemented using, for example, the auxiliary storage device 102 or a storage device that can be connected to the shape estimation device 10 via a network.

The receiving unit 11 receives sensing data from each sensor terminal d and stores the sensing data in the data storage unit 14 . The data storage unit 14 stores sensing data of each sensor terminal d in chronological order.

The direction estimating unit 12 estimates the direction θ _i of each sensor terminal d based on the time-series sensing data of each sensor terminal d stored in the data storage unit 14, Or classified into the lower half plane.

The shape estimation unit 13 estimates the overall shape of the target object T based on the time-series sensing data of each sensor terminal d and the direction _θi of each sensor terminal d. At this time, the shape estimating unit 13 estimates the upper half plane portion of the overall shape based on the direction θ _i of the sensor terminal d classified into the upper half plane, and the sensor terminal d classified into the lower half plane. A lower half-plane portion of the overall shape is estimated based on the direction _θi .

A processing procedure executed by the shape estimation device 10 will be described below. FIG. 5 is a flowchart for explaining an example of a processing procedure executed by the shape estimation device 10. As shown in FIG. At the start of FIG. 5, the sensing data {r _i (t)} _i=1 ^N are stored in time series in the data storage unit 14 (where N is the number of effective sensor terminals d). Also, in FIG. 5, it is assumed that the sensor terminal d1 belongs to the lower half-plane (θ ₁ ε[0, π)). In the present embodiment, this assumption is not essential because the top and bottom of the object T cannot be determined in the first place due to the reflection symmetry of θ with respect to the x-axis direction.

In step S101, the direction estimation unit 12 generates each pair ((r ₁ , r ₂ ), (r ₁ , r ₃ ), . , (r ₁ , r _N )), θ _{1 and} θ ₂ are calculated based on equations (1) and (2). As a result, N−1 solution sets are obtained for θ _{1 and} θ ₂ . In _each solution set, θ1 indicates the direction of the sensor terminal d1, and θ2 indicates the direction of the other sensor terminal d in the _pair with the sensor terminal d1. Now, of the N−1 solution sets, in general about half should contain nearly identical estimates θ ₁ for θ ₁ , and the rest either contain no solutions close to θ ₁ or are empty sets. be. Here, the range of "substantially the same" may be determined by a threshold or the like.

Therefore, the direction estimating unit 12 classifies the sensor terminal d associated with the solution set including the estimated value θ^ ₁ among the N−1 solution sets into the lower half plane, and classifies the other sensor terminals d into the upper half plane. (S102). The θ of the sensor terminal d that is classified into the lower _half plane and is paired with the sensor terminal d1 has already been obtained as θ2.

Subsequently, the direction estimation unit 12 determines whether or not the number of sensor terminals d classified into the upper half plane is 2 or more (S103). If the number of corresponding sensor terminals d is two or more (Yes in S103), the direction estimation unit 12 selects one of the sensor terminals d classified into the upper half plane and the sensor terminal d classified into the upper half plane. For each pair of sensor terminal d with another sensor terminal d, θ _{1 and} θ ₂ are calculated based on Equations (1) and (2) (S104). That is, the same process as S101 is executed for the corresponding sensor terminal group d. As a result, θ of each sensor terminal d classified into the upper half plane is estimated.

Subsequently, the shape estimating unit 13 estimates the shape of mainly the lower half plane portion of the simple closed curve ∂T based on the direction θ _i of each sensor terminal d classified into the lower half plane and r in the time series. (S105). Specifically, when θε[0, π) is assumed and estimation of mainly the lower half plane portion of the simple closed curve ∂T is considered, t ₀ =argmin tr( _t ), and the lower end of the object T is ^t Let (0,0)∈∂T. At this time, the following formula (3) is established.

したがって、形状推定部１３は、下半平面に分類されたセンサ端末ｄごとにｔを有効な範囲で動かして∂Ｔの部分形状を推定する。形状推定部１３は、下半平面に分類されたセンサ端末ｄごとの部分形状を、それぞれの重複部分で接続することで∂Ｔの主に下半平面部分の形状を推定する（下半平面部分の形状の推定値を計算する）。

Therefore, the shape estimator 13 estimates the partial shape of ∂T by moving t within an effective range for each sensor terminal d classified into the lower half plane. The shape estimating unit 13 connects the partial shapes of each sensor terminal d classified into the lower half plane at overlapping portions, thereby estimating the shape of the lower half plane portion of ∂T (lower half plane portion to calculate an estimate of the shape of ).

Subsequently, the shape estimating unit 13 performs the same processing as in step S105 for each sensor terminal d classified into the upper half plane, and estimates the shape of mainly the upper half plane portion of ∂T (upper half plane Calculate the estimated value of the shape of the planar portion) (S106).

Subsequently, the shape estimating unit 13 connects the lower half-plane portion estimated in step S105 and the upper half-plane portion estimated in step S106 at appropriate points, thereby obtaining the shape of the object T(∂T). Estimate the overall shape (obtain an estimated value of the overall shape) (S107).

On the other hand, when the top and bottom edges of the object T have almost the same shape, a solution set containing almost the same estimated value θ^ ₁ is obtained for almost all sensing data, and the sensor is classified into the upper half plane. The number of terminals d becomes less than two. That is, a sufficient number of sensor terminals d for estimating the shape of the upper half plane cannot be classified into the upper and lower half planes. In this case (No in S103), the shape estimating unit 13 applies θ _i of each sensor terminal d obtained in step S101 and time-series r to Equation (3), and calculates the target object for each sensor terminal d. The partial shape of T is estimated (drawn) (S108). Here, if the curved portions (the curved portion around the upper end or the curved portion around the lower end) that are commonly sensed by the two sensor terminals d match, the sensor terminals d belong to the same half plane. can be considered. Therefore, the shape estimation unit 13 classifies the sensor terminal d into an upper half plane and a lower half plane based on whether or not each partial shape has an overlapping portion (S109). If the classification is successful, that is, if the number of sensor terminals d classified into the upper half plane is one or more (Yes in S110), steps S105 to S107 are executed.

On the other hand, if the classification fails, that is, if the number of sensor terminals d classified into the upper half plane is 0 (No in S110), the shape estimating unit 13 calculates each sensor terminal d estimated for each sensor terminal d in step S108. By connecting partial shapes with overlapping portions, mainly the shape of the lower half plane portion of ∂T is estimated (an estimated value of the shape of the lower half plane portion is calculated) (S111). Subsequently, the shape estimation unit 13 estimates the upper half plane portion based on the lower half plane portion (S112). That is, in this case, the object T is considered to have reflection symmetry with respect to the x-axis direction. Therefore, the upper half plane portion is estimated based on the reflection symmetry. Subsequently, step S107 is executed.

As described above, it is possible to estimate the overall shape of the object T as long as enough sensor terminals d are scattered on the upper half plane and the lower half plane so that all the locations of the object T can be sensed. , that the sensor terminals d are seeded according to a particular distribution is not required. Further, by obtaining the direction of the sensor terminal d according to the formulas (1) and (2), it is possible to estimate the shape even if the object T has a curved shape. unnecessary.

[Theoretical background]
Next, formulas (1) and (2) are derived. These are derived by calculating the curvilinear surface information of the object T (slope of tangent, curvature, derivative of curvature).

FIG. 6 is a diagram showing minute displacements from time t to t+Δt. Note that in FIG. 6, instead of the object T, the sensor terminal d is moved.

By considering a first-order minute quantity, the following formula (4) holds from the sine theorem.

これより数式（５）が得られる。

Equation (5) is obtained from this.

この関係式は図６に示される領域のみならず、θ，ξ∈［０，２π）で成立する。ここで、ｓ（ｔ）は、時刻ｔにおけるセンシング領域（線分）と∂Ｔの交点を与える弧長パラメタｓを指す（ξ（ｔ）も同様の意味で用いる）。ｒ（ｔ）に関しては、以下の性質（＃）が重要である。
性質（＃）：ｔ_０＝ａｒｇｍｉｎ_ｔｒ（ｔ）⇔ｓ（ｔ_０）はＴの上端または下端
∂Ｔ固有の量であるξ（ｓ）、曲率κ（ｓ）＝ｄξ／ｄｓ、およびその微分ｄκ／ｄｓのセンシングデータによる表示式を求める。ξ（ｓ）は、数式（５）の上の式を変形して以下の数式（６）のようになる。

This relational expression holds not only for the region shown in FIG. 6, but also for θ, ξ∈[0, 2π). Here, s(t) indicates an arc length parameter s that gives the intersection of the sensing region (line segment) and ∂T at time t (ξ(t) is also used in the same sense). Regarding r(t), the following property (#) is important.
Property (#): t ₀ = argmin _t r(t) ⇔ s(t ₀ ) is the top or bottom of T ∂T is the intrinsic quantity ξ(s), the curvature κ(s) = dξ/ds, and its An expression for differential dκ/ds based on sensing data is obtained. ξ(s) is obtained by transforming the above formula of formula (5) into formula (6) below.

また、曲率は、以下の数式（７）で求まる。

Also, the curvature is determined by the following formula (7).

ここで、複号±は、それぞれｃｏｓξ＜０、ｃｏｓξ＞０に対応する。さらに曲率の微分ｄκ（ｓ）／ｄｓは、以下の数式（８）で求まる。

Here, the symbols ± correspond to cos ξ<0 and cos ξ>0, respectively. Further, the derivative dκ(s)/ds of curvature is obtained by the following formula (8).

数式（１）は、数式（６）と数式（７）を、数式（２）は、数式（７）と数式（８）を、性質（＃）を根拠に、異なるセンシングデータ間を等号で結ぶことで得られる。

Formula (1) is based on formulas (6) and (7), formula (2) is based on formulas (7) and (8), and based on the property (#), an equal sign is used between different sensing data. obtained by tying.

As described above, according to the present embodiment, distance sensor terminals d that are scattered without necessarily having a specific distribution are used to measure an object T that includes a curved portion and is not necessarily convex. It is possible to estimate the overall shape of T of .

Subsequently, results of a simulation according to the present embodiment will be described using (a) an asymmetric closed convex curve shown in FIG. 7 and (b) a ginkgo biloba (non-convex example) shown in FIG. 8 as objects T, respectively.

The velocity v=1 of the object is known, and the positions (x, y) and direction θ of the four sensor terminals d with respect to (a) the asymmetric convex closed curve shown in FIG. gave to

また、図８に示す（ｂ）イチョウ型に対する４つのセンサ端末ｄの位置（ｘ，ｙ）、方向θは、形状推定が可能となるよう表２のように与えた。

In addition, the positions (x, y) and directions θ of the four sensor terminals d for the ginkgo shape (b) shown in FIG. 8 are given as shown in Table 2 so that the shape can be estimated.

但し、形状推定装置１０はそれらのセンサ端末ｄの位置、方向の情報は有していない。なお、表１及び表２において、左端の列の番号は、センサ端末ｄＮのＮの部分を示す。

However, the shape estimation device 10 does not have information on the positions and directions of those sensor terminals d. In Tables 1 and 2, the number in the leftmost column indicates the N portion of the sensor terminal dN.

Each sensor terminal d sets r _max =100 and acquires sensing data r(t) at intervals of Δt=0.05. 7 or 8 is moved in parallel in the x-axis direction at v=1 from the state attached to ^t (0, 75). 9 and 10 show the situation of each object T at the start time, the number of each sensor terminal d, and the line segment indicating the sensing area (sensing direction and distance). The measurement is completed when the object exits the solid-line rectangular area (monitoring target area). Since the ginkgo biloba is vertically symmetrical, it is checked whether the shape of the lower half plane portion is correctly estimated.

Table 3 shows the result of obtaining θ for the asymmetric convex closed curve (a) shown in FIG. 7 according to the present embodiment.

また、本実施の形態に従い、図８に示す（ｂ）イチョウ型についてθを求めた結果が表４である。

Further, Table 4 shows the result of obtaining θ for the ginkgo biloba (b) shown in FIG. 8 according to the present embodiment.

（ａ）非対称凸閉曲線について形状を推定した結果が図１１～図１４である。すなわち、図１１は、センサ端末ｄ１に基づく非対称凸閉曲線の形状の推定結果を示す図である。図１２は、センサ端末ｄ２に基づく非対称凸閉曲線の形状の推定結果を示す図である。図１３は、センサ端末ｄ３に基づく非対称凸閉曲線の形状の推定結果を示す図である。図１４は、センサ端末ｄ４に基づく非対称凸閉曲線の形状の推定結果を示す図である。

(a) The results of estimating the shape of an asymmetric convex closed curve are shown in FIGS. 11 to 14. FIG. That is, FIG. 11 is a diagram showing the result of estimating the shape of the asymmetric convex closed curve based on the sensor terminal d1. FIG. 12 is a diagram showing the result of estimating the shape of an asymmetric convex closed curve based on the sensor terminal d2. FIG. 13 is a diagram showing the result of estimating the shape of an asymmetric convex closed curve based on the sensor terminal d3. FIG. 14 is a diagram showing the result of estimating the shape of an asymmetric convex closed curve based on the sensor terminal d4.

15 to 18 show the results of estimating the shape of (b) ginkgo biloba. That is, FIG. 15 is a diagram showing the result of estimating the shape of the ginkgo biloba based on the sensor terminal d1. FIG. 16 is a diagram showing the result of estimating the shape of the ginkgo biloba based on the sensor terminal d2. FIG. 17 is a diagram showing the result of estimating the shape of the ginkgo biloba based on the sensor terminal d3. FIG. 18 is a diagram showing the estimation result of the ginkgo shape based on the sensor terminal d4.

In FIGS. 11 to 18, the original shape of the asymmetric convex curve or ginkgo biloba is indicated by a broken line, and the estimated portion is indicated by a solid line.

Shape estimation of asymmetric convex closed curves is very accurate. As for the ginkgo biloba, there is a gap in the concave part that cannot be sensed by the sensor terminal d2 (Fig. 16) and the sensor terminal d4 (Fig. 18), but it can be complemented by the sensor terminal d1 and the sensor terminal d3 that can sense the part. Therefore, the shape can be estimated with high accuracy as a whole.

Although the embodiments of the present invention have been described in detail above, the present invention is not limited to such specific embodiments, and various modifications can be made within the scope of the gist of the present invention described in the claims. Transformation and change are possible.

10 shape estimation device 11 reception unit 12 direction estimation unit 13 shape estimation unit 14 data storage unit 20 user terminal 100 drive device 101 recording medium 102 auxiliary storage device 103 memory device 104 CPU
105 interface device B bus d sensor terminal

Claims (7)

a direction estimating unit that calculates an estimated value of a sensing direction for each of the sensor terminals based on time-series measurement results of distances between moving objects and the sensor terminals by a plurality of sensor terminals;
estimating a partial shape of the object based on the time-series measurement results and the sensing direction for each of the sensor terminals, and estimating the overall shape of the object by connecting the partial shapes estimated for each of the sensor terminals; a shape estimation unit that
A shape estimation device characterized by comprising: The direction estimating unit estimates the sensing direction using a formula for estimating the sensing direction of the sensor terminal based on the time-series measurement results, which is formulated based on the curved surface information of the object. do,
The shape estimation device according to claim 1, characterized in that: the curvilinear surface information is the slope of the tangent line, the curvature, and the derivative of the curvature of the object;
3. The shape estimation device according to claim 2, characterized in that: a direction estimation procedure for calculating an estimate of a sensing direction for each of said sensor terminals based on time-series measurements of distances between moving objects and said sensor terminals by a plurality of sensor terminals;
estimating a partial shape of the object based on the time-series measurement results and the sensing direction for each of the sensor terminals, and estimating the overall shape of the object by connecting the partial shapes estimated for each of the sensor terminals; a shape estimation procedure for
A shape estimation method characterized in that the computer executes The direction estimation procedure estimates the sensing direction using a formula for estimating the sensing direction of the sensor terminal based on the time-series measurement results, which is formulated based on curvilinear surface information of the object. do,
5. The shape estimation method according to claim 4, wherein: the curvilinear surface information is the slope of the tangent line, the curvature, and the derivative of the curvature of the object;
6. The shape estimation method according to claim 5, wherein: A program for causing a computer to execute the shape estimation method according to any one of claims 4 to 6.

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