JP2011174759A - Position computing device, method, and program - Google Patents

Abstract

Position coordinates calculated for each local coordinate system are accurately integrated into one coordinate system.
Means for detecting a plurality of local coordinate systems and calculating position coordinates of the plurality of transmitters in each of the local coordinate systems based on distances between the terminal and each of the plurality of transmitters; Among the two local coordinate systems, means for extracting two or more local coordinate systems sharing a number of transmitters equal to or greater than a threshold as coordinate systems that can be integrated with each other, and each of the two or more extracted local coordinate systems , The inter-transmitter distance and the reliability of the inter-transmitter distance are calculated, weighted by the reliability of the inter-transmitter distance calculated in each of two or more local coordinate systems, and the inter-transmitter distance after weighting correction The reliability of the position coordinates of each transmitter in a coordinate system integrating two or more local coordinate systems is calculated using only the corrected inter-transmitter distance of the transmitter that is higher than a certain value. Calculate in descending order A means 1932 for, including a.
[Selection] Figure 19

Description

  The present invention relates to a position calculation apparatus, method, and program.

  Conventionally, in an indoor user tracking system (user position calculation system), a method of calculating the position of a user in a space using a sensor installed in the environment, or attaching a sensor to a user or an object to determine the relative position of each user. A combination and a method of calculating the position of a user or an object in a space is used.

Non-Patent Document 1 describes a sensing room that can acquire the position of a person by placing sensors around the room. According to this technology, it is possible to accurately measure the position of a human in the sensing room.
Patent Document 1 describes a technique for calculating a relative position between a plurality of fixing devices whose positions are unknown and a moving device whose position is unknown using a relative distance between the fixing device and the moving device. This technology can be expected to reduce system installation costs.

Japanese Patent No. 4057023

Mori, “Intelligent House to Help Learn Life Patterns”, Network Robot Society, pp20-24, 2005

However, in the sensing room described in Non-Patent Document 1, 500 or more sensors are installed in one room, and not only the installation cost but also labor required for calibration is increased, and it cannot be said that it is a general-purpose system.
Moreover, in the technique described in Patent Document 1, in order to calculate the positions of all the fixed devices and the moving device on one coordinate system, it is necessary to simultaneously measure the distance between the all fixed devices and the moving device. Is difficult. Therefore, only position calculation on the coordinate system set for each combination of the fixed devices that have performed distance measurement can be realized.

  The present invention has been made in view of the above circumstances. A relative coordinate system generated based on the relative positional relationship of the fixing device (hereinafter referred to as a local coordinate system ID obtained by assigning an identification number to the relative coordinate system). It is an object of the present invention to provide a position calculation device, a position calculation method, and a position calculation program that can accurately integrate position coordinates calculated for each of them into one coordinate system.

  In order to solve the above-described problem, the position calculation apparatus of the present invention receives distance information between a terminal that can move in the environment and each of the plurality of transmitters in an environment including a plurality of transmitters. A position calculation device for calculating the position coordinates of the terminal, detecting a plurality of local coordinate systems each composed of a plurality of transmitters, and based on the distance between the terminal and each of the plurality of transmitters In each of the local coordinate systems, first coordinate calculation means for calculating position coordinates of a plurality of transmitters constituting the local coordinate system, and a number of transmitters equal to or greater than a threshold value among the plurality of local coordinate systems. In each of the two or more local coordinate systems extracted as the coordinate system that can be integrated, and an integrated coordinate system extraction unit that extracts two or more local coordinate systems sharing the same as a coordinate system that can be integrated with each other, Distance And calculating the reliability of the distance between the transmitters, calculating the distance between the transmitters after weight correction by performing weighting according to the reliability of the distance between the transmitters calculated in each of the two or more local coordinate systems, Using only the corrected inter-transmitter distance of the transmitter whose reliability is higher than a certain value, the position coordinates of each transmitter in the coordinate system in which the two or more local coordinate systems are integrated in descending order of reliability. And a second coordinate calculation means for calculating.

  According to the configuration of the present invention, the position coordinates calculated for each local coordinate system can be accurately integrated into one coordinate system.

The system configuration figure showing an example of the position calculation system concerning one embodiment of the present invention. The block diagram which shows the functional structure of the transmission / reception terminal and position calculation apparatus which concern on 1st Embodiment. The figure which shows an example of the data structure stored in the measurement distance table with which a data storage part is equipped. The figure which shows an example of the data structure stored in the local coordinate table with which a data storage part is equipped. The flowchart which shows the whole process performed in a position calculation apparatus. The flowchart of the process which a local coordinate calculation part performs. The figure for demonstrating how to determine the position coordinate in a new local coordinate system. The flowchart of the process which an integrated coordinate system extraction part performs. The flowchart of the production | generation process of the measurement sensor list which an integrated process part performs. The flowchart of the sensor matching process which an integrated process part performs. The flowchart of the position coordinate correction process which an integrated process part performs. The flowchart of the calculation process of the distance between transmitters which an integrated process part performs. The figure which shows an example of a local coordinate system. The figure for demonstrating the distance between transmitters calculated in a local coordinate system, and reliability. The figure which shows the difference in the distance between transmitters each calculated in two local coordinate systems. The figure for demonstrating the production | generation of the undirected graph by an integrated process part. The figure which represented the distance between transmitters by the weighted average distance in the above-mentioned undirected graph. The figure which shows the mode of correction of the position coordinate of a transmitter. The block diagram of the position calculation apparatus which concerns on 2nd Embodiment. The figure which shows an example of a data structure of the measurement distance table of FIG. The figure which shows an example of the data structure of the local coordinate table of FIG. FIG. 20 is a flowchart showing an example of the operation of the position calculation device of FIG. 19. FIG. The flowchart which shows an example of operation | movement of the local coordinate calculation part of FIG. The flowchart which shows an example of operation | movement of the local coordinate calculation part of FIG. The flowchart which shows an example of operation | movement of the integrable local coordinate system extraction part of FIG. The flowchart which shows an example of operation | movement of the integrable local coordinate system extraction part of FIG. 20 is a flowchart showing an example of the operation of the integration unit in FIG. 19. 20 is a flowchart showing an example of the operation of the integration unit in FIG. 19. 20 is a flowchart showing an example of the operation of the integration unit in FIG. 19.

Hereinafter, a position detection device, a position calculation method, and a position calculation program according to embodiments of the present invention will be described in detail with reference to the drawings. Note that, in the following embodiments, the same numbered portions are assumed to perform the same operation, and repeated description is omitted.
First, an outline of the embodiment will be described.
The combination of sensors (for example, transmitters) that can measure the distance to the moving object according to the position of the moving object (for example, a transmission / reception terminal possessed by the user) varies from moment to moment. The positions of these sensors and the moving object are calculated on the local relative coordinate system set one by one. Eventually, if there are more than a certain number of sensors that exist in common among the local relative coordinate systems that are formed independently of each other, the relative coordinate system can be changed to any one relative coordinate system (reference coordinate system). By projecting upward, it is possible to calculate the distance-measured sensor and the position of the moving object on the reference coordinate system. However, in general, when errors in some sensor estimation positions and sensor measurement values become large due to movement of the sensor, a decrease in sensor measurement accuracy, and the like, those influences spread throughout. In the embodiment, paying attention to the distance from the reference coordinate system and the reliability of the estimated position of the sensor, the position of the sensor and the moving object is calculated without the influence of a part of the estimation error affecting the whole.

However, it is assumed that the technology for calculating the sensor position on the local relative coordinate system uses a known technique, and the sensor position calculated by the local relative reference system is given reliability. .
(First embodiment)
FIG. 1 is a system configuration diagram showing an example of a position calculation system according to an embodiment of the present invention. As shown in FIG. 1, the user U carries the transmitting / receiving terminal 10 and carries it in the system. The (n + 1) transmitters # 0 to #n are installed at arbitrary locations in the system environment (for example, one room). However, n is 3 or more and an arbitrary positive integer.

  In this position calculation system, at least two local coordinate systems are integrated, and one local coordinate system includes at least three transmitters. Therefore, four or more transmitters are provided. ID: i is assigned to the i-th transmitter #i, and its position coordinate is, for example, X0_i = (X0i, Y0i) in the coordinate system of the local coordinate system ID0 by the transmitters # 0, # 1, and # 2. It is represented by

  The transmitters # 0 to #n are, for example, transmission terminals that generate waves such as radio waves and sound waves. The transmission / reception terminal 10 receives the radio waves and sound waves from the transmitters # 0 to #n, and transmits the transmitters. The distance di (t) from is measured. However, mediation of communication between the transmitters # 1 to #n and the transmission / reception terminal 10 is not limited to radio waves or sound waves, and any media may be used as long as conversion to distance is possible. The transmitters # 0 to #n transmit the current time (transmission time) and information on the transmitter ID unique to the transmitter by radio waves or sound waves at predetermined time intervals.

In the example illustrated in FIG. 1, a sensor system is illustrated in which a transmission / reception terminal 10 carried by the user U receives radio waves or sound waves transmitted from the transmitters # 0 to #n. May carry a transmitter and a receiver installed in the environment.
In the following, an example in which a transmitter (sensor) is fixed in the environment and the user carries the receiver (transmission / reception terminal 10) in the environment will be described based on the example of FIG. The position coordinate of the transmission / reception terminal 10 at time t is represented by X0_h (t) = (X0h (t), Y0h (t)) in the coordinate system whose local coordinate system ID is 0.

  The position calculation device 20 calculates various position coordinates such as calculation of position coordinates of each transmitter and transmission / reception terminal 10 in the reference coordinate system and calibration of the calculated position coordinates based on information from the transmission / reception terminal 10 carried by the user U. A computer system that executes processing. The position calculation device 20 includes a processor, a program memory, and a work memory (not shown), and controls various processes according to the present embodiment when the processor executes a predetermined program stored in the program memory.

FIG. 2 is a block diagram illustrating functional configurations of the transmission / reception terminal 10 and the position calculation device 20 in the position calculation system.
Transmitters # 0 to #n transmit the current time (transmission time) and transmitter ID information by radio waves or sound waves at predetermined time intervals.
The transmission / reception terminal 10 includes a reception unit 101, a distance measurement unit 102, and a transmission unit 103. The receiving unit 101 receives radio waves or sound waves transmitted from transmitters (# 0 to #n). The distance measuring unit 102 calculates the propagation time of radio waves or sound waves based on the current time (reception time or measurement time) and the transmission time from the transmitter, and between the transmission / reception terminal 10 and the transmitter based on the propagation time. The distance di (t) at the measurement time t is calculated. The transmission unit 103 transmits the calculated distance (measurement distance) to the position calculation device 20 in association with the transmitter ID and the measurement time.

  The distance calculation between the transmitter and the transmission / reception terminal 10 may be performed by combining radio waves and ultrasonic waves. In this case, a calling instruction for instructing transmission of ultrasonic waves is transmitted from the transmission / reception terminal 10 to the transmitter #i by radio waves, and the transmitter #i that has received the radio waves emits ultrasonic waves. Then, the distance di (t) between the transmitter #i and the transmission / reception terminal 10 is obtained by multiplying the time difference between the time when the transmission / reception terminal 10 receives the ultrasonic wave and the time when the transmitter #i emits the ultrasonic wave by the speed of sound. ) Is calculated.

The position calculation device 20 includes a reception unit 210, a data storage unit 220, a local coordinate calculation unit 230, and a local coordinate integration unit 240.
The receiving unit 210 receives measurement distance, transmitter ID, and measurement time data transmitted from the transmitter / receiver terminal 10 to each transmitter.
The data storage unit 220 is a storage device including a hard disk device, a flash memory, and the like. The data storage unit 220 includes a measurement distance table 221 illustrated in FIG. 3, a local coordinate table 222 illustrated in FIG. 4, and a reference coordinate system information storage unit 223. Data sent from the transmission / reception terminal 10 is held in the measurement distance table 221.

  FIG. 3 is a diagram illustrating an example of a data configuration stored in the measurement distance table 221 provided in the data storage unit 220. As illustrated in FIG. 3, the measurement distance table 221 stores the measurement time t and the measurement distance di (t) at the measurement time t, corresponding to the transmitter ID of each transmitter.

  FIG. 4 is a diagram illustrating an example of a data configuration stored in the local coordinate table 222 provided in the data storage unit 220. As shown in FIG. 4, the local coordinate table 222 includes, for each local coordinate system, a local coordinate system ID, a sensor (transmitter) included in the coordinate system, coordinates of each sensor, each sensor and the transmission / reception terminal 10. Measurement distance, reliability described later, ID of local coordinate system that can be integrated, average measurement distance, and position coordinates of the transmission / reception terminal 10 are stored.

The reference coordinate system information storage unit 223 stores information on a reference local coordinate system that provides a reference coordinate system. The reference local coordinate system may be determined in advance according to a setting operation by the user.
The local coordinate calculation unit 230 generates and updates the storage contents of the local coordinate table 222 based on the data received by the reception unit 210.

  The local coordinate integration unit 240 includes an integrated coordinate system extraction unit 241, an integration processing unit 242, and an input / output unit 243. The integrated coordinate system extraction unit 241 extracts and sets two local coordinate systems that share a predetermined number or more of transmitters as local coordinate systems that can be integrated. The integration processing unit 242 performs integration processing of the local coordinate system extracted as being able to be integrated. The input / output unit 243 includes a display device for outputting the integration result. Alternatively, the input / output unit 243 may be connected to a storage device (not shown), and the integration result may be output and stored in the storage device.

Next, the operation of the position calculation device 20 configured as described above will be described.
FIG. 5 is a flowchart showing the entire processing executed in the position calculation device 20.
The receiving unit 210 receives data including the transmitter ID, measurement time, and measurement distance of at least one transmitter (#i) from the transmission / reception terminal 10 (step S501). The reception unit 210 also outputs the received data to the measurement distance table 221 and the local coordinate calculation unit 230 of the data storage unit 220. In the measurement distance table 221, the data of the measurement time and the measurement distance are updated corresponding to the transmitter ID: i of the at least one transmitter (#i).

The local coordinate calculation unit 230 determines whether or not a new local coordinate system is created based on the transmitted transmitter ID, measurement time, and measurement distance data (step S502).
If the local coordinate system included in the received data is not stored in the local coordinate table 222, it is necessary to create a new local coordinate system (Yes in step S502). In this case, the local coordinate calculation unit 230 generates an ID that is not in the local coordinate table 222 as a new local coordinate system ID (step S503).

  If the local coordinate system included in the received data is already stored in the local coordinate table 222, a new local coordinate system is not created (No in step S502). In this case, the local coordinate calculation unit 230 selects, from the local coordinate table 222, a local coordinate system ID that is included in the received data and is to be updated (step S504).

  The local coordinate calculation unit 505 includes the local coordinate system ID newly created in step S503 or the transmitter (sensor) and the transmission / reception terminal 10 constituting the local coordinate system corresponding to the local coordinate system ID selected in step S504. Are added to the stored contents of the local coordinate table 222, the position coordinates of the transmitter (sensor) constituting the local coordinate system corresponding to the local coordinate system ID, the latest position calculation time, the reliability, and The value of the average measurement distance is calculated, and the content stored in the local coordinate table 222 is updated (step S505). When a new local coordinate system is detected, the latest measurement distance from each sensor to the transmission / reception terminal 10 is added to the stored content of the local coordinate table 222 in association with the newly created local coordinate system ID. The calculated position coordinates of the sensor, latest position calculation time, reliability, and average measurement distance are stored in the local coordinate table 222, and the stored contents are updated. The local coordinate calculation unit 230 also stores the ID of each sensor included in the new local coordinate system in the local coordinate table 222.

  On the other hand, when the local coordinate system ID to be updated is selected in step S504, the position coordinate of the sensor corresponding to the selected local coordinate system ID, the latest position calculation time, the reliability, The value of the average measurement distance is updated to the calculated value. The local coordinate calculation unit 230 also calculates a measurement distance of each sensor included in the selected local coordinate system, and corresponds to the local coordinate system ID of the selected local coordinate system in the local coordinate table 222. Add the position coordinate value of each sensor.

Next, in the local coordinate integration unit 240, the integrated coordinate system extraction unit 241 determines whether there is a coordinate system that can be integrated among the local coordinate systems stored in the local coordinate table 222 (step S506). The determination result is sent to the integration processing unit 242.
The integration processing unit 242 integrates the local coordinate system based on the determination result (step S507). The integration result may be output via the input / output unit 243.

  In addition, although the example which implements the process of the local coordinate integration part 240 after the process of the local coordinate calculation part 230 was described in FIG. 5, the process of the local coordinate calculation part 230 and the process of the local coordinate integration part 240 were isolate | separated. The local coordinate calculation unit 230 updates the stored contents of the local coordinate table 222 of the data storage unit 220 and terminates the process, and the local coordinate integration unit 240 performs a predetermined timing (for example, at a predetermined time interval). Alternatively, the process of step S506 in FIG. 5 may be started (by an activation instruction from the input / output unit).

Next, the processing executed by the local coordinate calculation unit 230 and the local coordinate integration unit 240 will be described in more detail.
FIG. 6 is a flowchart showing details of processing executed by the local coordinate calculation unit 230. The process shown in FIG. 6 corresponds to the process of steps S502 to S505 in FIG.
When the reception unit 210 stores the received data in the data storage unit 220, the local coordinate calculation unit 230 acquires information in the local coordinate table 222 of the data storage unit 220 (step S601). The local coordinate calculation unit 230 generates all combinations of three or more IDs from the transmitter ID included in the received data (step S602). The local coordinate calculation unit 230 selects one combination from the generated combinations (step S603). Here, M is the number of transmitter IDs received by the receiving unit 210.

The local coordinate calculation unit 230 determines whether or not the selected combination of IDs is a combination of representative sensors included in any of the local coordinate systems stored in the local coordinate table 222 (step S604).
If the selected ID combination is a combination of representative sensors included in any of the local coordinate systems stored in the local coordinate table 222 (Yes in step S604), the local coordinate calculation unit 230 performs the selection. The local coordinate system ID of the local coordinate system corresponding to the combination of IDs thus selected is selected as a processing target (step S605).

  If the selected combination of IDs is not a combination of representative sensors included in any of the local coordinate systems stored in the local coordinate table 222 (No in step S604), for all combinations generated in step S602, It is determined whether or not the process of step S604 has been performed (step S614). If there is a combination that has not yet been processed in step S604 (No in step S614), the process returns to step S603 to select another combination, and the subsequent processing is repeated. On the other hand, if the processing has been completed for all the combinations (Yes in step S614), a local coordinate calculation unit is assumed that a new local coordinate system is configured by the transmitter specified by the selected ID combination. 230 sets the information of the new local coordinate system in the local coordinate table 222 (step S606). The information on the new local coordinate system to be set includes the local coordinate system ID of the new local coordinate system, information on the representative transmitter of the local coordinate system, its position coordinates, and the like. The local coordinate system ID may be assigned sequentially from 0, for example.

  FIG. 7 is a diagram for explaining how to determine position coordinates in a new local coordinate system. Three representative transmitters are arbitrarily selected from the selected ID combination, and as shown in FIG. 7, one of the three representative transmitters is set as the origin, and the other is set on the x-axis. . It is determined that the remaining one representative transmitter exists in the + direction of the y axis, and a coordinate system in a new local coordinate system is set. The local coordinate table 222 stores a local coordinate system ID assigned to the new local coordinate system and a representative transmitter ID that defines the coordinate system.

  The local coordinate calculation unit 230 sets the local coordinate system ID selected in step S605 or the newly assigned local coordinate system ID in step S606 as the ID of the processing target coordinate system, and the transmitter included in the processing target coordinate system. Measurement time and measurement distance data are acquired from the measurement distance table 221 (step S607). The local coordinate calculation unit 230 detects from the measurement distance table 221 the number N of measurement times at which the measurement distances are stored for all M transmitters included in the processing target coordinate system (step S608).

  The local coordinate calculation unit 230 determines whether or not a conditional expression MN ≧ 2M + 2N indicating whether the relative distance of each transmitter can be calculated is satisfied (step S609). If the conditional expression MN ≧ 2M + 2N is not satisfied (No in step S609), the relative distance between the transmitters cannot be calculated, and the process ends.

On the other hand, when the conditional expression MN ≧ 2M + 2N is satisfied (Yes in step S609), the relative distance of each transmitter can be calculated.
For example, in the local coordinate system whose local coordinate system ID is 0, the measurement distance di (t) between the transmitter #i and the transmission / reception terminal 10 can be obtained from the following equation (1).

ここで、（Ｘ０ｉ，Ｙ０ｉ）（＝Ｘ＿０）は、局所座標系ＩＤが０である局所座標系における送信機＃ｉの位置座標を表す。また、時刻ｔにおける当該局所座標系での送受信端末１０の位置座標は、Ｘ０＿ｈ（ｔ）＝（Ｘ０ｈ（ｔ），Ｙ０ｈ（ｔ））で表される。

Here, (X0i, Y0i) (= X_0) represents the position coordinate of the transmitter #i in the local coordinate system whose local coordinate system ID is 0. Further, the position coordinates of the transmission / reception terminal 10 in the local coordinate system at time t are represented by X0_h (t) = (X0h (t), Y0h (t)).

  Accordingly, for the N measurement times selected in step S608, the relational expression (2) between the measurement distance and the position coordinates of each transmitter and the transmission / reception terminal 10 is generated by the local coordinate calculation unit 230 (step S610). .

局所座標算出部２３０は、この連立方程式（２）を解いて、各計測時刻における送信機及び送受信端末１０との相対位置座標を算出する（ステップＳ６１１）。
図７に示すように、１つの代表送信機が原点にあり、他の１つの代表送信機がｘ軸上にある場合、Ｍ個の送信機の２次元位置座標値として２Ｍ−３個（３次元位置座標の場合は３Ｍ−６個）、送受信端末１０の２次元位置座標として２Ｎ個（３次元位置座標の場合は３Ｎ個）の未知変数があることになる。また、連立方程式（２）に含まれる式の数はＭＮ個である。したがって、ステップＳ６０９で条件式ＭＮ≧２Ｍ＋２Ｎ−３（３次元座標の場合はＭＮ≧３Ｍ＋３Ｎ−６）が満足されれば、各時刻における送信機及び送受信端末１０の位置座標を算出（推定）することができる。例えば、選択された局所座標系に含まれる送信機の数が３個の場合、Ｎ≧３の場合に条件式が満足される。従って、３つの時刻以上距離情報が取得された場合に、位置座標の算出が可能となる。

The local coordinate calculation unit 230 solves the simultaneous equation (2) and calculates the relative position coordinates between the transmitter and the transmission / reception terminal 10 at each measurement time (step S611).
As shown in FIG. 7, when one representative transmitter is at the origin and the other representative transmitter is on the x-axis, 2M−3 (3 In the case of the three-dimensional position coordinates, there are 3M-6), and there are 2N (3N in the case of the three-dimensional position coordinates) unknown variables as the two-dimensional position coordinates of the transmission / reception terminal 10. The number of equations included in the simultaneous equations (2) is MN. Therefore, if the conditional expression MN ≧ 2M + 2N−3 (MN ≧ 3M + 3N−6 in the case of three-dimensional coordinates) is satisfied in step S609, the position coordinates of the transmitter and the transmission / reception terminal 10 at each time are calculated (estimated). Can do. For example, when the number of transmitters included in the selected local coordinate system is 3, the conditional expression is satisfied when N ≧ 3. Therefore, the position coordinates can be calculated when distance information is acquired for three or more times.

  Subsequently, the local coordinate calculation unit 230 calculates the reliability of the calculated position coordinates of each transmitter (step S612). As the reliability, a function including the calculated differential fluctuation amount f of the transmitter position, the norm g of the difference between the calculation result of the distance between the transmitter and the transmission / reception terminal 10 and the measurement result, and the like are used. In the local coordinate system whose local coordinate system ID is 0, the differential fluctuation amount f of the transmitter #i is expressed by the following equation (3), and the calculation result and measurement of the distance between the transmitter #i and the transmission / reception terminal 10 are measured. The norm g of the difference between the results is expressed by the following formula (4).

また、局所座標系ＩＤが０である局所座標系において、送信機iの尤度ｗ０＿ｉは、微分変動量ｆ及びノルムｇを用いて以下式（５）によって表される。

Further, in the local coordinate system whose local coordinate system ID is 0, the likelihood w0_i of the transmitter i is expressed by the following equation (5) using the differential fluctuation amount f and the norm g.

式（５）においてα、及びβは所定の重み係数であり、０以上の値を取るものとする。また、このとき局所座標系ＩＤが0である局所座標系において、算出された位置座標全体の精度指標を示す信頼度Ｗ0を算出する。信頼度Ｗ0としては、例えば局所座標系ＩＤが0である局所座標系において座標系を設定するための３つの代表送信機の算出された位置座標の尤度の積が、以下の式（６）によって求められてもよい。

In Expression (5), α and β are predetermined weighting factors, and assume values of 0 or more. At this time, in the local coordinate system whose local coordinate system ID is 0, the reliability W0 indicating the accuracy index of the entire calculated position coordinates is calculated. As the reliability W0, for example, the product of the likelihoods of the calculated position coordinates of the three representative transmitters for setting the coordinate system in the local coordinate system whose local coordinate system ID is 0 is the following equation (6). May be required.

算出された局所座標系の信頼度及び送信機位置座標の信頼度は、当該局所座標系の局所座標系ＩＤに対応付けられ、局所座標テーブル２２２に追加記憶され（ステップＳ６１３）、フローを終了する。
図１３に示す例では、局所座標系ＩＤが０である局所座標系上に、３つの送信機＃０〜＃２が図示されている。送信機ＩＤが０である送信機＃０の位置座標（Ｘ００，Ｙ００）は、式（２）の連立方程式から算出される。また、この送信機＃０の位置座標の信頼度ｗ０＿０は式（５）より算出される。同様に、送信機ＩＤが１である送信機＃１の位置座標（Ｘ０１，Ｙ０１）は、式（２）の連立方程式から算出され、この送信機＃１の位置座標の信頼度ｗ０＿１は式（５）より算出される。送信機ＩＤが２である送信機＃２の位置座標（Ｘ０２，Ｙ０２）も式（２）の連立方程式から算出され、この送信機＃２の位置座標の信頼度ｗ０＿１は式（５）より算出される。

The calculated reliability of the local coordinate system and the reliability of the transmitter position coordinates are associated with the local coordinate system ID of the local coordinate system, and are additionally stored in the local coordinate table 222 (step S613), and the flow ends. .
In the example illustrated in FIG. 13, three transmitters # 0 to # 2 are illustrated on the local coordinate system whose local coordinate system ID is 0. The position coordinates (X00, Y00) of the transmitter # 0 whose transmitter ID is 0 is calculated from the simultaneous equations of the equation (2). Further, the reliability w0_0 of the position coordinate of the transmitter # 0 is calculated from the equation (5). Similarly, the position coordinate (X01, Y01) of the transmitter # 1 whose transmitter ID is 1 is calculated from the simultaneous equations of the equation (2), and the reliability w0_1 of the position coordinate of the transmitter # 1 is expressed by the equation (2). 5) is calculated. The position coordinate (X02, Y02) of the transmitter # 2 whose transmitter ID is 2 is also calculated from the simultaneous equations of the equation (2), and the reliability w0_1 of the position coordinate of the transmitter # 2 is calculated from the equation (5). Is done.

  In the above equation, the differential fluctuation amount f and the norm g of the difference between the calculation result and the measurement result are obtained for the position coordinates of the transmitter, and the reliability of the position coordinates of the transmitter is obtained based on this. However, the differential fluctuation amount f and the norm g of the difference between the calculation result and the measurement result may be calculated for the inter-transmitter distance described later.

  In step S615, a predetermined number of data for newer measurement times are left and other data is deleted. Alternatively, an evaluation value may be assigned to each data by a predetermined method, and the data may be deleted in order from the lowest evaluation value. Moreover, you may complete | finish the process of the local coordinate calculation part 230, without deleting data.

Next, the process performed in the local coordinate integration unit 240 will be described.
FIG. 8 is a flowchart showing details of processing executed by the integrated coordinate system extraction unit 241. The process shown in FIG. 8 corresponds to the process of step S506 in FIG.
First, the integrated coordinate system extraction unit 241 acquires information of the local coordinate table 222 (step S801). The integrated coordinate system extraction unit 241 generates all combinations for selecting two local coordinate systems from the local coordinate systems stored in the local coordinate table 222 (step S802). The integrated coordinate system extraction unit 241 selects one combination (first ID and second ID) from the generated combinations (step S803).

  The integrated coordinate system extraction unit 241 calculates the number of transmitters included in both of the two selected local coordinate systems (step S804). Then, the integrated coordinate system extraction unit 241 determines whether or not the number of transmitters (sensors) shared by the two local coordinate systems is equal to or greater than a predetermined threshold (step S805). When a transmitter having a predetermined threshold value or more is shared by two local coordinate systems (Yes in step S805), it is determined that these two coordinate systems can be integrated, and the local coordinate table is a coordinate system that can be integrated with each other. 222 is set. That is, in the local coordinate table 222, the second ID is stored as the “integrable coordinate system ID” corresponding to the first ID, and conversely, the “integrable coordinate system ID” corresponding to the second ID. As the first ID is stored.

  Next, the integrated coordinate system extraction unit 241 determines whether or not the processing in steps S803 to S806 has been performed for all the combinations generated in step S802 (step S807). If there is a combination that has not yet been processed in steps S803 to S806 (No in step S807), the process returns to step S803 to select another combination, and the subsequent processing is repeated. On the other hand, if the processing has been completed for all combinations (Yes in step S807), the extraction result of the integrated coordinate system is transmitted to the local coordinate table 222, and the flow ends. Further, the integrated coordinate system extraction unit 241 generates a list of local coordinate systems (integration target list) that can be integrated with the local coordinate system for each local coordinate system, and transmits the list to the integration processing unit 242.

  When the integrated coordinate system extraction unit 241 extracts a local coordinate system that can be integrated, the integration processing unit 242 performs integration processing. The integration processing unit 242 generates a measurement sensor list for each local coordinate system that can be integrated with respect to one local coordinate system (target coordinate system) (FIG. 9), and integrates the target coordinate system and the target coordinate system. Measurement sensors included in both possible other integrated coordinate systems are detected and associated (FIG. 10), and a correction value of the position coordinates of the transmitter included in the measurement sensor list is calculated (FIG. 11).

FIG. 9 is a flowchart illustrating details of the measurement sensor list generation process executed by the integration processing unit 242.
When the integration processing unit 242 receives the extraction result of the integrated coordinate system from the integrated coordinate system extraction unit 241 (step S901), the integration processing unit 242 integrates with the target coordinate system from the integration target list for one local coordinate system (target coordinate system). A local coordinate system ID of one coordinate system is selected from the possible integrated coordinate systems (step S902).

  The integration processing unit 242 selects one measurement sensor from the measurement sensors (transmitters) included in the selected integrated coordinate system (step S903), and the ID of the selected measurement sensor is the selected target coordinate system. It is determined whether it is included in the measurement sensor list (step S904).

  If the ID of the selected measurement sensor is included in the measurement sensor list (Yes in step S904), the process proceeds to step S906. On the other hand, when the ID of the selected measurement sensor is not included in the measurement sensor list (No in step S904), the integration processing unit 242 adds the ID of the measurement sensor to the measurement sensor list (step S905).

  The integration processing unit 242 determines whether or not the processing in steps S903 to S905 has been completed for all the measurement sensors included in the selected local coordinate system (step S906). If there is a measurement sensor that has not yet been subjected to the processes of steps S903 to S905 (No in step S906), the process returns to step S903 to select a measurement sensor, and the subsequent processes are repeated. On the other hand, if the process has been completed for all measurement sensors (Yes in step S906), the integration processing unit 242 has completed the processes in steps S902 to S906 for all the integrated coordinate systems that can be integrated with the target coordinate system. It is determined whether or not (step S907).

  If there is a local coordinate system that has not been subjected to the processes of steps S903 to S906 yet (No in step S907), the process returns to step S902 to select another local coordinate system, and the subsequent processes are repeated. On the other hand, if the processing has been completed for all integrated coordinate systems that can be integrated with the target coordinate system (Yes in step S907), the flow ends.

As described above, a list (measurement sensor list) of measurement sensors (transmitters) included in the local coordinate system that can be integrated with respect to one local coordinate system is generated by the process shown in FIG.
Next, processing performed by the integration processing unit 242 will be described with reference to FIGS.
FIG. 10 is a flowchart illustrating details of the sensor association process executed by the integration processing unit 242.
When the measurement sensor list for the target coordinate system is generated, the integration processing unit 242 selects one measurement sensor (transmitter) from the measurement sensor list (step S1002).

  Next, the integration processing unit 242 selects one local coordinate system from the X local coordinate systems stored in the local coordinate system table 222 (step S1003), and the measurement sensors included in the selected local coordinate system are: It is determined whether or not it matches the measurement sensor selected in step S1002 (step S1004).

  If the measurement sensor included in the selected local coordinate system does not match the selected measurement sensor (No in step S1004), the process proceeds to step S1005. On the other hand, when the measurement sensor included in the selected local coordinate system matches the selected measurement sensor (Yes in step S1004), the measurement sensors are associated (step S1005). In association with measurement sensors, all measurement sensors included in the selected local coordinate system are assumed to be other measurement sensors in the same coordinate system as the selected measurement sensor, and transmitters of these other measurement sensors are used. The ID and the transmitter ID of the selected measurement sensor are associated with each other and stored in the local coordinate table 222.

  The integration processing unit 242 determines whether or not the processing in steps S1003 to S1005 has been completed for all X local coordinate systems included in the local coordinate table 222 (step S1006). If there is a local coordinate system that has not been subjected to the processes of steps S1003 to S1005 (No in step S1006), the process returns to step S1003 to select the local coordinate system, and the subsequent processes are repeated. On the other hand, if the processing has been completed for all local coordinate systems (Yes in step S1006), the integration processing unit 242 determines whether the processing in steps S1002 to S1006 has been completed for all transmitters included in the measurement sensor list. Is determined (step S1007).

  If there is a transmitter that has not been subjected to the processes of steps S1002 to S1006 (No in step S1007), the process returns to step S1002, selects another transmitter, and the subsequent processes are repeated. On the other hand, if the processing has been completed for all transmitters (Yes in step S1007), the flow ends.

As described above, a transmitter (measurement sensor) is associated between a plurality of local coordinate systems by the process illustrated in FIG.
FIG. 11 is a flowchart showing details of the sensor position coordinate correction process on the reference coordinate system executed by the integration processing unit 242. The initial position of each sensor is assumed to be a value calculated by the local coordinate calculation unit 230 for the sensor on the local coordinate system set as the reference coordinate system, and given by a random number for the other sensors.
The integration processing unit 242 sets a reference coordinate system from the reference local coordinates stored in the local coordinate table 222 (step S1100). The reference coordinate system may be determined in advance according to a setting operation by the user, and the setting information is stored in the reference coordinate system information storage unit 223 of the data storage unit 220. In the following, for the sake of explanation, it is assumed that the coordinate system whose local coordinate system ID is 0 is the reference coordinate system. The integration processing unit 242 selects one measurement sensor (transmitter #i) from the measurement sensor list generated for the target coordinate system constituting the reference coordinate system (step S1101). Then, the integration processing unit 242 sets a set of other transmitters (set in the process of FIG. 10) in the same local coordinate system as the selected transmitter #i as a transmitter set gi, and the following equation (7) Thus, the corrected coordinate value ΔXi of the calculation position of the selected transmitter #i is calculated.

式（７）においてＬ0__ｉｊは送信機＃ｉと送信機＃ｊとの間の送信機間距離を表す。
統合処理部２４２は、計測センサリスト内の全ての送信機についてステップＳ１１０１〜Ｓ１１０２の処理が終了したか否かを判定する（ステップＳ１１０３）。まだステップＳ１１０１〜Ｓ１１０２の処理が行われていない送信機があれば（ステップＳ１１０３でＮｏ）、ステップＳ１１０１に戻って他の送信機を選択し、以降の処理を繰り返す。

L0_ _ij in Equation (7) represents the transmitter distance between the transmitter #j transmitter #i.
The integration processing unit 242 determines whether or not the processing in steps S1101 to S1102 has been completed for all transmitters in the measurement sensor list (step S1103). If there is a transmitter that has not been subjected to the processes of steps S1101 to S1102 (No in step S1103), the process returns to step S1101 to select another transmitter, and the subsequent processes are repeated.

  When the processing is completed for all transmitters (Yes in step S1103), the integration processing unit 242 obtains the value of the evaluation formula J from the following formula (8), and determines whether the value is smaller than a predetermined threshold value. Determination is made (step S1104).

式（８）において、Ｇは後述するように、送信機間距離が求められている２つの送信機の組合せの集合を表す。
評価式Ｊの値が閾値よりも小さい場合（ステップＳ１１０４でＹｅｓ）、フローを終了する。一方、評価式Ｊの値が所定の閾値以上である場合（ステップＳ１１０４でＮｏ）、計測センサリストに含まれる全ての送信機が未選択であるとして（ステップＳ１１０５）ステップＳ１１０１に戻り、再び計測センサリストから送信機を選択して以降の処理を繰り返す。

In Expression (8), G represents a set of combinations of two transmitters for which the distance between transmitters is required, as will be described later.
If the value of the evaluation formula J is smaller than the threshold value (Yes in step S1104), the flow ends. On the other hand, if the value of the evaluation formula J is equal to or greater than the predetermined threshold (No in step S1104), it is determined that all transmitters included in the measurement sensor list are not selected (step S1105), and the process returns to step S1101 and the measurement sensor again. Select a transmitter from the list and repeat the subsequent processing.

As described above, the correction value of the position coordinate of the transmitter included in the measurement sensor list generated for the target coordinate system can be obtained by the process shown in FIG.
9 to 11 may be executed continuously for one target coordinate system, but may be executed individually for different local coordinate systems.

Further, the inter-transmitter distance calculation shown in FIG. 12 may be performed in a local coordinate system that is determined to be able to be integrated with another local coordinate system.
FIG. 12 is a flowchart showing details of the inter-transmitter distance calculation processing executed by the integration processing unit 242.
The integration processing unit 242 acquires the extraction result by the integrated coordinate system extraction unit 241 illustrated in FIG. 8 and the information of the local coordinate table 222 (step S1201). The integration processing unit 242 determines whether or not the integrated coordinate system extraction unit 241 has extracted a local coordinate system that can be integrated with another local coordinate system (step S1202). If there is no local coordinate system that can be integrated (No in step S1202), the process ends.

  On the other hand, if there is a local coordinate system that can be integrated (Yes in step S1202), the integration processing unit 242 selects one local coordinate system from unselectable coordinate systems that can be integrated (step S1203). The integration processing unit 242 determines whether there is a combination of transmitters for which the distance between the transmitters is not calculated in the selected local coordinate system (step S1204).

  If there is no combination of transmitters for which the inter-transmitter distance is not calculated (No in step S1204), the process returns to step S1202, and the subsequent processing is repeated. On the other hand, if there is a combination of transmitters for which the distance between transmitters has not been calculated (Yes in step S1204), the integration processing unit 242 selects a combination of unselected transmitters (step S1205). Then, for the selected combination of transmitters, the inter-transmitter distance and its reliability are calculated (step S1206), and the process returns to step S1204. The calculated inter-transmitter distance and its reliability are stored in the local coordinate table 222.

  The inter-transmitter distance is calculated in each local coordinate system, and is calculated using the position coordinates of the transmitter stored in the local coordinate table 222. For example, in the example shown in FIG. 13, the position coordinates and reliability of the three transmitters # 0 to # 2 included in the local coordinate system whose local coordinate system ID is 0 are calculated and stored in the local coordinate table 222. Has been. In this case, the distance L0_01 between the transmitter # 0 having the calculated position coordinates (X00, Y00) and the transmitter # 1 having the calculated position coordinates (X01, Y01) is expressed by the following equation (9). Is calculated from

また、このように算出された送信機間距離の信頼度ｗ０＿０１は、一例として、式（１０）に示すように各送信機の位置座標の信頼度ｗ０＿０とｗ０＿１の積で与えられる。

In addition, the reliability w0_01 of the distance between transmitters calculated in this way is given by a product of the reliability w0_0 and w0_1 of the position coordinates of each transmitter, as shown in Expression (10), for example.

図１３に示す３つの送信機＃０〜＃２の例では、図１４に示すように、送信機＃１と送信機＃２との間の距離Ｌ０＿１２、及び送信機＃２と送信機＃０との間の距離Ｌ０＿２０も式（９）と同様に算出される。また、送信機間距離Ｌ０＿１２の信頼度ｗ０＿１２及び送信機間距離Ｌ０＿２０の信頼度ｗ０＿２０も式（１０）と同様に算出される。

In the example of the three transmitters # 0 to # 2 shown in FIG. 13, as shown in FIG. 14, the distance L0_12 between the transmitter # 1 and the transmitter # 2, and the transmitter # 2 and the transmitter # 0 The distance L0_20 between is also calculated in the same manner as the equation (9). Further, the reliability w0_12 of the inter-transmitter distance L0_12 and the reliability w0_20 of the inter-transmitter distance L0_20 are also calculated in the same manner as in the equation (10).

As described above, according to the processing of FIG. 12, the distance between transmitters in the local coordinate system and the reliability thereof can be calculated.
9 to 12, the position coordinates of each transmitter in the local coordinate system and the reliability thereof, and the distance between the transmitters and the reliability thereof can be calculated.

  It should be noted that the calculation result of the transmission engine distance differs depending on the local coordinate system. FIG. 15 shows a local coordinate system whose local coordinate system ID is 0 and a local coordinate system whose local coordinate system ID is 1. In the example of FIG. 15, the inter-transmitter distance L0_12 between the transmitter # 1 and the transmitter # 2 calculated in the local coordinate system whose local coordinate system ID is 0, and the local coordinate system whose local coordinate system ID is 1 The calculated transmitter # 1 and transmitter-to-transmitter distance L1_12 have different sizes. Thus, it is considered that the distance between transmitters and the reliability thereof vary depending on the local coordinate system.

The distance between the transmitters may be calculated using a weighted average of the distances between the transmitters weighted by the reliability in order to reduce the influence of the distance between the transmitters having low reliability. In the example shown in FIG. 15, the transmitter distance L ₁₂ of the transmitter # 1 and transmitter # 2, which is calculated using the reliability is given by the following equation (11).

これにより、信頼度の高いデータを優先的に使用して送信機間の距離を算出することができる。
次に、統合処理部２４２は、送信機間距離の加重平均を用いて無向グラフ上の全局所座標系の基準座標系への統合を行う。すなわち、各送信機の基準座標系における位置座標を算出する。

Thereby, the distance between transmitters can be calculated using data with high reliability preferentially.
Next, the integration processing unit 242 integrates all the local coordinate systems on the undirected graph into the reference coordinate system using the weighted average of the distances between the transmitters. That is, the position coordinate in the reference coordinate system of each transmitter is calculated.

  FIG. 17 is a diagram showing the distance between the transmitters shown in FIG. 16 by the weighted average distance between the transmitters. The position coordinate X0_i of the transmitter #i on the reference coordinate system is calculated by performing an optimal calculation that minimizes the value J of the evaluation formula given by the formula (8). In equation (8), a set G represents a set of transmitter combinations for which the inter-transmitter distance is calculated. An example of an algorithm for minimizing the value J of the evaluation equation is a method of correcting the position coordinates of each transmitter using the correction value obtained from Equation (7). The integration processing unit 242 performs recursive calculation according to Expression (8) until the value J of the evaluation expression becomes equal to or less than the threshold value.

  For example, in the example shown in FIG. 17, the set g2 of transmitters for which the inter-transmitter distance is calculated with the transmitter # 2 is g2 = {0, 1, 3, 4, 5}. The integration processing unit 242 determines the position coordinates of the transmitter # 2 based on the difference between the calculated position coordinates of the transmitter # 2 and the weighted average distance between each transmitter included in the set g2 and the transmitter # 2. Correct the position coordinates of transmitter # 2.

  FIG. 18 is a diagram illustrating how the position coordinates of transmitter # 2 are corrected. For example, when the position of transmitter # 2 is corrected using the estimated calculation position of transmitter # 0, the distance between transmitters calculated from the estimated positions of both transmitters is calculated, and the value of the calculated distance between transmitters is calculated. And the difference in the distance between transmitters weighted by the reliability (hereinafter, the difference is assumed to be n). When the value of n is positive, the position coordinates of the point where the transmitter # 2 is moved by the amount of n in the opposite direction to the transmitter # 0 on the straight line connecting the estimated positions of the two transmitters are Let 2 be the corrected position coordinates. When the value of n is negative, the position coordinate of the point where the transmitter # 2 is moved by the amount n toward the transmitter # 0 on the straight line is set as the corrected position coordinate of the transmitter # 2. Similarly, the position coordinates of the transmitter # 2 are corrected using the position coordinates of the transmitter # 2 and the position coordinates of other transmitters (transmitters # 1, # 3 to # 5) that have measured the distance.

With the above processing, the position coordinates of each transmitter in the reference coordinate system are calculated.
The integration processing unit 242 also calculates the position coordinates of the transmission / reception terminal 10. The position coordinates of the transmission / reception terminal 10 are calculated by solving simultaneous equations generated by the measured distance between the calculated position coordinates of the transmitter #i and the transmission / reception terminal 10. For example, when the transmission / reception terminal 10 performs distance measurement with the transmitters # 0 to # 2, the position coordinates of the transmission / reception terminal 10 are calculated from the following simultaneous equations (12).

以上の第１の実施の形態によれば、基準座標系における各送信機及び送受信端末１０の位置座標を算出することが可能となる。また、センサの移動やセンサ計測精度の低下等により一部のセンサ推定位置やセンサ計測値の誤差が大きくなった場合でも、それらの影響を低減しながら各局所的な相対座標系を統合することが可能となる。さらに、障害物がある等の理由で、移動物体までの距離計測が困難であるセンサ位置も、局所的相対座標系の統合により、一つの相対座標系上で求めることが可能になる。

According to the first embodiment described above, it is possible to calculate the position coordinates of each transmitter and the transmission / reception terminal 10 in the reference coordinate system. Also, even if errors in some estimated sensor positions or sensor measurement values become large due to sensor movement or sensor measurement accuracy degradation, etc., integration of each local relative coordinate system while reducing those effects Is possible. Furthermore, the sensor position where it is difficult to measure the distance to the moving object due to an obstacle or the like can be obtained on one relative coordinate system by integrating the local relative coordinate system.

(Second Embodiment)
In the second embodiment, the calculation position is determined in order from the sensor with the highest reliability, and the position of the moving object is calculated using only the sensor position with the higher reliability. By setting the reference coordinate system as a local coordinate system in which a moving object always exists, the sensor position estimation error on the local coordinate system that is physically separated from the reference coordinate system increases, As the object approaches, the sensor position estimation error can be reduced.

A position calculation apparatus according to the present embodiment will be described with reference to FIG.
The position calculation apparatus 1900 according to the present embodiment includes a reception unit 210, a data recording unit 1910, a local coordinate calculation unit 1920, and a local coordinate integration unit 1930. The data recording unit 1910 records a measurement distance table 1911, a local coordinate table 1912, and a reference local coordinate system ID 1913. The local coordinate integration unit 1930 includes an integrable local coordinate system extraction unit 1931, an integration unit 1932, and an input / output unit 243.

As shown in FIG. 20, the measurement distance table 1911 includes a measurement time t and a measurement distance di (t) at the measurement time t corresponding to the transmitter ID (#i) of each transmitter.
As shown in FIG. 21, the local coordinate table 1912 includes, for each local coordinate system, a local coordinate system ID, a transmitter ID included in the coordinate system, coordinates of each transmitter, the latest position calculation time, each transmitter, It includes the distance from the reference local coordinate system in addition to the measurement distance from the transmission / reception terminal 10, the reliability described later, the ID of the local coordinate system that can be integrated, the average measurement distance, and the position coordinates of the transmission / reception terminal 10. . The measured distance between each transmitter / receiver indicates the measured distance between each transmitter and a transmitter / receiver terminal.

The reference local coordinate system ID 1913 is an ID of the reference local coordinate system.
The local coordinate calculation unit 1920 calculates a local coordinate system using a table recorded in the data recording unit 1910. Detailed operation will be described later with reference to FIGS. 23A and 23B.
The local coordinate integration unit 1930 integrates the local coordinate system stored in the local coordinate table 1912. More specifically, the local coordinate table 1912 and the reference local coordinate system ID are acquired from the data recording unit 1910, and it is determined whether each local coordinate system recorded in the local coordinate table 1912 can be integrated. The distance between the transmitters existing on the area is calculated based on the reliability, and the local coordinate system is integrated using the information in the local coordinate table 1912 and the determination result. Detailed operations of the integrable local coordinate system extraction unit 1931 included in the local coordinate integration unit 1930 will be described later with reference to FIGS. 24A and 24B. Detailed operation of the integration unit 1932 included in the local coordinate integration unit 1930 will be described later with reference to FIGS. 25A, 25B, and 25C.

Next, an example of the operation of the position calculation device 1900 will be described with reference to FIG.
The receiving unit 210 receives the transmitter ID, the measurement time, and the distance measurement result (measurement distance) from the transmission / reception terminal 10 (step S2201). The reception unit 210 adds the reception result to the measurement distance table 1911 of the data recording unit 1910 and passes it to the local coordinate calculation unit 1920.

  When the local coordinate calculation unit 1920 receives the transmitter ID, measurement time, and distance measurement result (measurement distance) from the reception unit 210, the local coordinate calculation unit 1920 extracts the local coordinate table 1912 from the data recording unit 1910 and receives the transmitter. It is determined whether or not the combination of transmitters is a new combination based on the ID (step S2202). If it is a new combination, the process proceeds to step S2203. If it is not a new combination (that is, the local coordinate system created from the received data is already included in the local coordinate table 1912), the process proceeds to step S2204. .

  The local coordinate calculation unit 1920 creates a new local coordinate system ID, selects three representative transmitters from the measured transmitter IDs, sets the local coordinate system, and proceeds to step S2205 (step S2203). On the other hand, the local coordinate calculation unit 1920 selects a local coordinate system ID to be updated from among the local coordinate system IDs recorded in the local coordinate table 1912 (that is, an ID corresponding to the transmitter ID received in step S2201). The process proceeds to step S2205 (step S2204).

  The local coordinate calculation unit 1920 uses the local coordinate system ID created in step S2203 or the transmitter coordinate value corresponding to the local coordinate system ID selected in step S2204, the latest position calculation time, the measured distance between each transceiver, The reliability, the local coordinate system ID that can be integrated, the distance from the reference local coordinate system, the average measurement distance, and the terminal position are calculated, and the information in the data recording unit 1910 is updated (step S2205). When a new local coordinate system ID is created in step S2203, the calculated transmitter coordinate value, latest position calculation time, reliability, and integration are possible in association with the newly created local coordinate system ID in the local coordinate table 1912. The local coordinate system ID, the distance from the reference local coordinate system, the average measurement distance, and the terminal position are calculated and recorded in the data recording unit 1910.

  The local coordinate system extraction unit 1931 that can be integrated acquires the local coordinate table 1912 and the reference local coordinate system ID from the data recording unit 1910 and determines whether each local coordinate system recorded in the local coordinate table 1912 can be integrated. Then, the information of the local coordinate table 1912 and the determination result are transferred to the integration unit 1932 and the process proceeds to step S2207 (step S2206).

Based on the reliability, the distance between the transmitters existing on the local area that can be integrated by the integration unit 1932 is calculated (step S2207).
The integration unit 1932 integrates the local coordinate system using the information of the local coordinate table 1912 received from step S2206 and the determination result of whether or not each local coordinate system can be integrated, and the transmission calculated on the reference local coordinate system The machine position is calculated and the process proceeds to step S2209 (step S2208).

  The transmission / reception terminal position on the reference coordinate system is calculated using the integrated transmitter position and distance measurement value, and the integration result is output via the input / output unit (step S2209). The integration result may be recorded in the data recording unit 1910 instead of being output. Further, the reference local coordinate system may be set dynamically such that it is set to a local coordinate system in which a moving object exists.

  In FIG. 22, an example in which the processing of the local coordinate integration unit 1930 is performed after the processing of the local coordinate calculation unit 1920 is described. However, the processing of the local coordinate calculation unit 1920 and the processing of the local coordinate integration unit 1930 are separated. The local coordinate calculation unit 1920 updates the local coordinate table 1912 of the data recording unit 1910 and terminates the process, and the local coordinate integration unit 1930 performs a predetermined timing (for example, at a predetermined time interval, or The process of step S2206 in FIG. 22 may be started (by an activation instruction from the input / output unit).

Next, an example of the operation of the local coordinate calculation unit 1920 will be described with reference to FIGS. 23A and 23B.
The local coordinate calculation unit 1920 acquires the local coordinate table 1912 (FIG. 21) from the data recording unit 1910 (step S601). With reference to the transmitter ID recorded for each local coordinate system ID in the acquired local coordinate table 1912, it is determined whether or not the combination of the transmitter ID acquired from the measurement result is recorded in the local coordinate table 1912 ( Step S2301). If it is recorded, the process proceeds to step S2302, and if it is not recorded, the process proceeds to step S2303.

  When it is determined that the combination of transmitter IDs previously recorded by the data recording unit 1910 is obtained, the local coordinate table 1912 shown in FIG. 21 is read from the data recording unit 1910, and the corresponding measurements measured so far The measurement distance between each transmitter / receiver on the local coordinate system and the representative transmitter ID for setting the coordinate system are acquired, and the process proceeds to S2304 (step S2302).

  On the other hand, if the combination is a new transmitter ID, a unique local coordinate system ID that is not assigned is newly assigned to the combination by referring to the local coordinate table 1912 (step S2303). At this time, the local coordinate system ID is assigned sequentially from 0. Further, three representative transmitters are arbitrarily selected from the transmitters obtained from the measurement results, and as shown in FIG. 7, two arbitrary representative transmitters are set on the x-axis, and one of them is the origin. . Furthermore, the coordinate system in the local coordinate system is set by setting the + y-axis direction as the direction in which the remaining representative transmitters exist. The local coordinate system ID newly assigned to the local coordinate table 1912 and the representative transmitter ID for setting the coordinate system are recorded in the data recording unit 1910 (updated in FIG. 21), and the process proceeds to S2304 (step S2303).

  From FIG. 21, information corresponding to the local coordinate system ID selected in S2302 or set in S2303 is acquired (step S2304). The information of the measurement distance table 1911 is acquired from the data recording unit 1910 (step S2305), and the transmitter ID acquired from the measurement result is configured using the measurement results at a plurality of times corresponding to the transmitter ID acquired from the measurement result. The relative coordinates of each transmitter in the local coordinate system are calculated (S2306 to S2309).

  Specifically, when the number of transmitters acquired from the latest measurement results is M, and the number of distance information (distance information for N times) between the corresponding transmitter and the transmission / reception terminal recorded so far is N, When the method described in Patent Document 1 is used, the relative distance of each transmitter can be calculated using a predetermined relational expression when MN ≧ 2M + 2N is satisfied. In addition, if a precondition that one transmitter is at the origin and the other one is on the X axis is added, the variable to be estimated is 2M-3 coordinates (three-dimensional) of the transmitter. In the case of position coordinates, there are 3M-6 pieces), and 2N two-dimensional position coordinates of the transmission / reception terminal (3N pieces in case of three-dimensional position coordinates). On the other hand, the number of conditional expressions is MN. Therefore, when the conditional expression MN ≧ 2M + 2N−3 (MN ≧ 3M + 3N−6 in the case of three-dimensional coordinates) is satisfied, it is possible to calculate the position estimation of the transmission / reception terminal at each time. For example, when the number of transmitters is three, N ≧ 3. Therefore, if distance information to each transmitter for three or more times can be acquired, it is possible to estimate the positions of the transmitters and the transmission / reception terminals.

  The conditional expression used for position estimation of the transmitter and the transmitting / receiving terminal in the local coordinate system ID # 0 is calculated using the above expression (2). However, the subscript i is a transmitter ID, and t, t1, and t2 are different times. Further, (x0i, y0i), (x0h (t), y0h (t)) are the position of the transmitter ID0 in the local coordinate system 0 and the position of the transmitting / receiving terminal at time t, respectively.

By solving the simultaneous equations, the positions of the transmitter and the transmitting / receiving terminal at time t can be calculated.
The reliability of each calculated transmitter position is calculated (step S2310). The reliability includes, for example, a function including a differential fluctuation amount f of the estimated position, a norm g of a difference between the distance calculated from the estimated positions of the transmitter and the transmission / reception terminal and the actual distance measurement value. For example, the likelihood w0_i of the transmitter i in the local coordinate system ID0 is indicated by changing X to x and Y to y in the above equations (3), (4), and (5). Here, α and β are weighting factors and have values of 0 or more.

  Further, the reliability Wi indicating the accuracy index of the entire estimated position calculated at this time (on the local coordinate system ID # i) is calculated using the above equation (6). As the reliability Wi, for example, the product of the likelihoods of the three representative transmitter estimated positions that set the coordinate system of the local coordinate system i is given (formula (6), S: representative transmitter ID).

  The distance between each transmitter on the corresponding local coordinate system and its reliability are calculated from the transmitter position estimated in S2310 (step S2311). For example, the estimated distance L0_01 between the estimated position (x00, y00) of the transmitter # 0 estimated on the local coordinate system # 0 and the estimated position (x01, y01) of the transmitter # 1 is expressed by the above equation (9). To calculate.

  As the reliability of the estimated distance between the transmitters, for example, the product of the reliability of the estimated transmitter position calculated in S2310 can be cited (for example, the distance reliability between the sensor IDs # 0 and # 1 on the local coordinate system # 0). Degree (formula (10)). The estimated position of the transmitter and the transmission / reception terminal in the local coordinate system, the reliability of the estimated position, and the distance between the transmitters and the reliability of the distance between the transmitters are associated with the local coordinate system ID and passed to the data recording unit 1910 (that is, 21 is updated) (step S2312).

  Then, a part of the data in the measurement distance table 1911 is deleted (step S2313). Note that the data to be deleted is, for example, data other than a predetermined number of new times, deleted only a predetermined number of data, an evaluation value is assigned to each data by some method, and the evaluation value is low There are methods such as deleting in order. Moreover, you may complete | finish the process of the local coordinate calculation part 1920, without deleting data.

  Next, an example of the operation of the integrable local coordinate system extraction unit 1931 will be described with reference to FIGS. 24A and 24B. If the local coordinate system extraction unit 1931 determines that local coordinate systems sharing a predetermined number or more of transmitters can be integrated (step S2402), the local coordinate system ID that can be integrated An integrated local coordinate system ID list in which the correspondence between each other is recorded is created (step S2408).

  First, all local coordinate tables 1912 recorded in the data recording unit 1910 are acquired from the data recording unit 1910 (step S801). The number X of local coordinate systems recorded in the acquired local coordinate table 1912 is calculated, and all combinations for selecting two local coordinate system IDs from the X local coordinate system IDs are generated (step S802). X is a number obtained by adding 1 to the latest recorded local coordinate system ID.

  It is determined whether there is an unselected combination among the combinations of selecting two from the X local coordinate systems (step S2401). If there is an unselected combination, the process proceeds to step S803. If there is no unselected combination, the process advances to step S2404. In addition, as an example of a method for determining whether a combination for selecting two of X local coordinate systems is unselected or selected, a buffer is provided, and combinations of selected local coordinate system IDs are sequentially selected. There is a method of adding to the buffer and referring to the buffer.

One unselected combination is selected from among the two combinations selected from the X local coordinate systems, and the process proceeds to step S804 (step S803).
A list of transmitter IDs included in each of the two local coordinate system IDs selected from the local coordinate table 1912 is acquired (step S804). For the sake of explanation, the selected local coordinate system IDs are assumed to be ID1 and ID2, respectively. The number of transmitter IDs included in both the list of transmitter IDs included in the local coordinate system ID1 and the list of transmitter IDs included in the local coordinate system ID2 is calculated, and the process proceeds to step S2402 (step S804).

  It is determined whether or not the calculated number of transmitters included in both transmitter ID lists is equal to or greater than a predetermined local coordinate system integration determination threshold (for example, 3) (step S2402). If the calculated number of transmitters included in both transmitter ID lists is equal to or greater than a predetermined local coordinate system integration availability determination threshold, the two local coordinate systems selected in step S803 (local coordinate system ID1, It is determined that two local coordinate systems specified by the local coordinate system ID2) can be integrated, and the process proceeds to step S2403. When the calculated number of transmitters included in both transmitter ID lists is smaller than a predetermined local coordinate system integration possibility determination threshold, the two local coordinate systems (local coordinates selected in step S803) It is determined that the two local coordinate systems specified by the system ID1 and the local coordinate system ID2) cannot be integrated, and the process returns to step S2401.

  The local coordinate system ID2 is added to the “integrable area ID” for the local coordinate system ID1 of FIG. 21 of the data recording unit 1910, and the “integrable area ID” for the local coordinate system ID2 of FIG. The local coordinate system area ID1 is additionally written (step S2403).

  A local coordinate table 1912 and a reference local coordinate system ID are acquired from the data recording unit 1910 (step S2404). Next, each local coordinate system that can be integrated is extracted from the reference local coordinate system, and an integrated local coordinate system list is created (steps S2405 to S2411). Further, the distance from the reference local coordinate system of each local coordinate system that can be integrated is calculated.

The reference local coordinate system ID is added to the integrated local coordinate system ID list, and the reference local coordinate system ID is set as the initial value of the integrated local coordinate system ID (step S2405). Further, “distance from the reference local coordinate system” corresponding to the reference local coordinate system ID in FIG. 21 is set to 0, and the initial value of the distance D from the reference local coordinate system is set to 1.
It is determined whether or not there is an unselected local coordinate system ID in the “integratable local coordinate system ID” of the integrated local coordinate system ID (step S2406). If there is an unselected local coordinate system ID, the process proceeds to S2407, and one of the unselected local coordinate system IDs is selected (step S2407). If all have been selected, the process proceeds to S2409.

  The local coordinate system ID selected in step S2407 is added to the integrated local coordinate system ID list, and the “distance from the reference local coordinate system ID” associated with the selected local coordinate system ID in FIG. The value is recorded, and the selected local coordinate system is selected (step S2408).

In the local coordinate system whose distance from the reference coordinate system is D, it is determined whether there is a local coordinate system that has not been stored in the integrated local coordinate system ID (step S2409). If there is, the process proceeds to step S2410, and if not, the process proceeds to step S2411.
One local coordinate system ID that has not been stored in the integrated local coordinate system ID is selected from the local coordinate systems whose distance from the reference coordinate system is D, and the selected local coordinate system ID is selected as a new integrated local coordinate system ID. The coordinate system ID is set (step S2410). When all the local region IDs having the distance D are stored in the integrated local coordinate system ID, one value of D is added.
The local coordinate table 1912 and the integrated local coordinate system ID list in FIG. 21 are passed to the integrating unit 1932, and the local coordinate table 1912 and the integrated local coordinate system ID list in FIG. 21 are updated (step S2411).

Next, an example of the operation of the integration unit 1932 will be described with reference to FIGS. 25A, 25B, and 25C. For the combination of all local coordinate systems that can be integrated from the reference coordinate system, the following processing is performed to calculate the positions of all transmitters and transmission / reception terminals in the reference coordinate system.
The local coordinate table 1912 and the integrated local coordinate system ID list of FIG. 21 are received from the integrable local coordinate system extraction unit 1931 (step S2501).

It is determined whether there is an unselected local coordinate system in the integrated local coordinate system ID list (step S2502). If there is an unselected local coordinate system, the process proceeds to step S2503, and if not, the process proceeds to step S2508.
One unselected local coordinate system ID is selected, and the selected local coordinate system ID is set as selected (step S2503).
It is determined whether there is a combination of unselected transmitters among the combinations of transmitter IDs constituting the “distance between transmitters” in FIG. 21 associated with the local coordinate system ID selected in step S2503. This is performed (step S2504). If there is, the process proceeds to step S2505, and if not, the process returns to step S2502.

  A combination of unselected transmitter IDs is selected (step S2505), and the local coordinate system ID stored in the integrated local region ID list is associated with each local coordinate system ID not selected in step S2503. It is determined whether there is a combination of transmitter IDs selected in step S2505 in the “inter-transmitter distance” (step S2506). If there is, the process proceeds to step S2507, and if not, the process returns to step S2504.

The transmitter-to-transmitter distance calculated in the local coordinate system other than the local coordinate system selected in step S2503 having the same combination as the transmitter ID combination selected in step S2505 is integrated by reliability, and integrated transmission is performed. The calculation result of the inter-machine distance is recorded (step S2507). The combination of transmitters integrating the distance is set as processed, and the process returns to S2504. In the example of FIG. 15 shows the method of calculating the reliability distance between the sensors L ₁₂ using the above equation (11). As a result, it is possible to estimate the distance between transmitters with priority given to those having high reliability.

The calculation result of each inter-transmitter distance using the information and reliability of the local coordinate table 1912 of FIG. 21 is received from the integrable local coordinate system extraction unit 1931 (step S2508). The initial value of the distance D from the reference local coordinate system is set to 0.
In FIG. 21, it is determined whether there is an unselected local coordinate system ID whose “distance from the reference local coordinate system” is D (step S2509). If there is an unselected local coordinate system ID, the process proceeds to step S2510; otherwise, the process proceeds to step S2516.

One local coordinate system is selected from the unselected local coordinate systems, and the selected local coordinate system is set as selected (step S2510). However, the reference local coordinate system ID is selected at the first time.
It is determined whether or not there is an unselected transmitter ID in the selected local coordinate system (step S2511). If there is, the process proceeds to step S2512; otherwise, the process returns to S2509.

The transmitter having the highest reliability is selected from the transmitter IDs of the local coordinates selected in S2510 (step S2512). Here, for the sake of explanation, it is assumed that the selected sensor ID is i.
It is determined whether there is a transmitter whose reliability is higher than a preset threshold among the transmitters that have performed the transmitter-to-transmitter distance using the transmitter i (step S2513). If there is, the process proceeds to S2514, and if not, the process returns to S2511.

Among the transmitters that performed the transmitter-to-transmitter distance using the transmitter i, select all transmitters whose reliability is higher than a preset threshold, and the above formula (7) in descending order of reliability. To the set gi (step S2514).
Δxi that is the position correction movement amount of the transmitter i is calculated using the above equation (7), and the transmitter i is set as selected (step S2515). However, the initial value of each transmitter is set as follows. Of the representative transmitters on the reference coordinate system, the representative transmitter position set at the origin is (0, 0), and the y coordinate of the representative transmitter set on the x-axis is 0. All remaining transmitter initial positions are randomly given by random numbers.

  After adding 1 to the value of D (step S2516), it is determined whether the value of D is equal to or less than the maximum value of “distance from the reference coordinate system” in FIG. 21 (step S2517). If it is equal to or smaller than the maximum value, the process returns to step S2509, and if it is larger than the maximum value, the process proceeds to step S2518.

The estimated transmitter position is evaluated by the above equation (8) (step S2518). If the evaluation value of the above equation (8) is smaller than a preset threshold value, the process proceeds to step S2520. If the evaluation value is equal to or greater than the threshold value, the process proceeds to step S2519.
The selection determination result of all the local coordinate systems and the selection determination result of the transmitter are not selected, the distance D from the reference local coordinate system is set to 0, and the process returns to step S2509 (step S2519).

  The reciprocal of the inter-transmitter distance using each transmitter position and reliability on the reference coordinate system calculated in step S2507 is cost to each node, and the cost calculation of each node (transmitter estimated position) is performed by the Dijkstra method. This is performed (step S2520). However, the transmitter position set at the origin on the reference coordinate system in the Dijkstra method is used as the start node.

A preset number (for example, three) of combinations of transmitter IDs is selected from the smallest cost among the costs of the transmitter positions calculated in step S2520 (step S2521).
The position of the transmission / reception terminal is calculated by solving simultaneous equations using the estimated positions of the three selected transmitters on the reference coordinate system and the distance measurement values to the transmission / reception terminal (step S2522). For example, the simultaneous equations when transmitter IDs 0, 1, and 2 are selected are obtained by changing X to x and Y to y in the above equation (12). However, (xi, yi), (xh (t), yh (t)) are the position of the transmitter IDi on the reference local coordinate system and the transmitting / receiving terminal position at time t, respectively.

The estimated positions of the transmitter and the transmission / reception terminal on the reference coordinate system are transmitted to the input / output unit (step S2523), and the processing of the integration unit 1932 ends.
According to the second embodiment described above, by setting the reference coordinate system as the local coordinate system in which the moving object always exists, the sensor on the local coordinate system that is physically separated from the reference coordinate system is set. Although the position estimation error is relatively large, the sensor position estimation error can be reduced as the moving object approaches. For example, in navigation of a moving object, a rough explanation is sufficient when the target landmark is far away, and it is effective when detailed navigation is required as it approaches.

The instructions shown in the processing procedure shown in the above embodiment can be executed based on a program that is software. A general-purpose computer system stores this program in advance and reads this program, so that it is possible to obtain the same effect as that obtained by the position calculation device of the above-described embodiment. The instructions described in the above-described embodiments are, as programs that can be executed by a computer, magnetic disks (flexible disks, hard disks, etc.), optical disks (CD-ROM, CD-R, CD-RW, DVD-ROM, DVD). ± R, DVD ± RW, etc.), semiconductor memory, or a similar recording medium. As long as the recording medium is readable by the computer or the embedded system, the storage format may be any form. If the computer reads the program from the recording medium and causes the CPU to execute an instruction described in the program based on the program, the same operation as that of the position calculation apparatus of the above-described embodiment can be realized. Of course, when the computer acquires or reads the program, it may be acquired or read through a network.
In addition, the OS (operating system), database management software, MW (middleware) such as a network, etc. running on the computer based on the instructions of the program installed in the computer or embedded system from the recording medium implement this embodiment. A part of each process for performing may be executed.
Furthermore, the recording medium in the present invention is not limited to a medium independent of a computer or an embedded system, but also includes a recording medium in which a program transmitted via a LAN or the Internet is downloaded and stored or temporarily stored.
Further, the number of recording media is not limited to one, and when the processing in the present embodiment is executed from a plurality of media, it is included in the recording media in the present invention, and the configuration of the media may be any configuration.

The computer or the embedded system in the present invention is for executing each process in the present embodiment based on a program stored in a recording medium, and includes a single device such as a personal computer and a microcomputer, Any configuration such as a system in which apparatuses are connected to a network may be used.
Further, the computer in the embodiment of the present invention is not limited to a personal computer, but includes an arithmetic processing device, a microcomputer, and the like included in an information processing device, and a device capable of realizing the functions in the embodiment of the present invention by a program, The device is a general term.

  Note that the present invention is not limited to the above-described embodiment as it is, and can be embodied by modifying the constituent elements without departing from the scope of the invention in the implementation stage. In addition, various inventions can be formed by appropriately combining a plurality of components disclosed in the embodiment. For example, some components may be deleted from all the components shown in the embodiment. Furthermore, constituent elements over different embodiments may be appropriately combined.

DESCRIPTION OF SYMBOLS 10 ... Transmission / reception terminal, 20 ... Position calculation apparatus, 101 ... Reception part, 102 ... Distance measurement part, 103 ... Transmission part, 210 ... Reception part, 220 ... Data storage part, 221 ... Local coordinate table, 223 ... Reference coordinate system information Storage unit 240 ... local coordinate integration unit 241 ... integrated coordinate system extraction unit 242 ... integration processing unit 243 ... input / output unit.

Claims (5)

In an environment including a plurality of transmitters, a position calculation device that receives distance information between a terminal that can move within the environment and each of the plurality of transmitters, and calculates the position coordinates of the terminal,
A plurality of local coordinate systems each composed of a plurality of transmitters are detected, and the local coordinate system is configured in each of the local coordinate systems based on the distance between the terminal and each of the plurality of transmitters. First coordinate calculating means for calculating position coordinates of a plurality of transmitters;
An integrated coordinate system extracting means for extracting two or more local coordinate systems sharing a number of transmitters equal to or greater than a threshold among the plurality of local coordinate systems as coordinate systems that can be integrated with each other;
In each of the two or more local coordinate systems extracted as a coordinate system that can be integrated, the distance between transmitters and the reliability of the distance between the transmitters are calculated, and calculated in each of the two or more local coordinate systems. Weighting is performed according to the reliability of the inter-transmitter distance to calculate the inter-transmitter distance after the weight correction, and only the corrected inter-transmitter distance of the transmitter having a reliability higher than a certain value is used. Second coordinate calculation means for calculating the position coordinates of each transmitter in a coordinate system in which two or more local coordinate systems are integrated in descending order of reliability;
A position calculation device comprising:   The integrated coordinate system extraction means is a local coordinate system composed of a plurality of transmitters, and a local coordinate system in which the position of the terminal is included in a polygonal region connecting the positions of the plurality of transmitters is 2. The position calculation according to claim 1, wherein one of a plurality of local coordinate systems is selected, and the position of any one of the transmitters constituting the selected local coordinate system is set as the origin of the relative coordinate system. apparatus. In an environment including a plurality of transmitters, a position calculation method for receiving distance information between each of the plurality of transmitters and a terminal movable in the environment, and calculating a position coordinate of the terminal,
A plurality of local coordinate systems each composed of a plurality of transmitters are detected, and the local coordinate system is configured in each of the local coordinate systems based on the distance between the terminal and each of the plurality of transmitters. Calculate the position coordinates of multiple transmitters,
Among the plurality of local coordinate systems, two or more local coordinate systems sharing a number of transmitters equal to or greater than a threshold are extracted as coordinate systems that can be integrated with each other,
In each of the two or more local coordinate systems extracted as a coordinate system that can be integrated, the distance between transmitters and the reliability of the distance between the transmitters are calculated, and calculated in each of the two or more local coordinate systems. Weighting is performed according to the reliability of the inter-transmitter distance to calculate the inter-transmitter distance after the weight correction, and only the corrected inter-transmitter distance of the transmitter having a reliability higher than a certain value is used. A position calculation method characterized by calculating position coordinates of each transmitter in a coordinate system obtained by integrating two or more local coordinate systems in descending order of reliability.   Extracting as a coordinate system that can be integrated with each other is a local coordinate system composed of a plurality of transmitters, and the position of the terminal is included in a polygonal region connecting the positions of the plurality of transmitters. 4. A local coordinate system is selected from the plurality of local coordinate systems, and the position of any one transmitter constituting the selected local coordinate system is set as the origin of the relative coordinate system. The position calculation method described in 1.   A program for causing a computer to be executed as each unit of the position calculation device according to claim 1 or 2.

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