JP2009065394A - Sensor network attenuation constant estimation system, node position estimation system, estimation method, and program thereof - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a system for estimating an attenuation constant α by using reception field intensity information received at a fixed node, and a position estimation system, or the like for estimating a mobile node position by using the system. <P>SOLUTION: The system is provided with a plurality of fixed nodes 20 for receiving a signal from a mobile node 30 within a sensor network area and measuring its reception field intensity P<SB>i</SB>, and a node position estimating device 40 for collecting the measured reception field intensity P<SB>i</SB>to estimate the position of a mobile node 30 on the basis of the reception field intensity P<SB>i</SB>, wherein the node position estimating device 40 comprises: a temporary position specifying means 81 for temporarily specifying a three-dimensional temporary position of the mobile node 30 according to the received field intensity P<SB>i</SB>; a distance function calculating means 82 for calculating a function D of the total amount about distances d<SB>i</SB>to respective fixed nodes 20 on the basis of the temporary position of the mobile node 30; and an attenuation constant operating means 83 for operating and calculating an attenuation constant α of radio wave propagation about positional environment of the mobile node 30 on the basis of the total amount of the received field intensity P<SB>i</SB>and the function D. <P>COPYRIGHT: (C)2009,JPO&INPIT

Description

  The present invention relates to an attenuation constant estimation system, a node position estimation system, and the like for estimating an attenuation constant of a propagation environment necessary for estimating a position of a target node in a sensor network. And the program.

  In recent years, sensor network technology for ubiquitous society has attracted attention. In a sensor network, small wireless terminals (called “nodes”) equipped with a large amount of sensor functions are distributed in a distributed manner, forming a network autonomously, collecting necessary information at each terminal, and collecting the collected information as information It can be sent to a processing center or a client who needs information. The application examples are various such as energy saving in the office, medical care, welfare, disaster, disaster prevention, and transportation.

Here, a wireless network used in a narrower range (several [m] to several tens [m]) than the wireless LAN is called a WPAN (Wireless Personal Area Network). Here, “ZigBee” (currently a registered trademark of Koninklijke Philips Electronics NV) is one of the standards of this WPAN (wireless communication standard IEEE 802.15.4 (radio frequency is 2.4 [GHz]). ])).
This wireless terminal has low power consumption and more than 60,000 wireless terminals form a mesh or tree type network, and ZigBee Router relays data, allowing communication even between terminals that do not receive radio waves directly It is expected to be widely used in sensor networks. Of course, a sensor network can be constructed using not only ZigBee but also various technologies such as Bluetooth.

  In such a sensor network, the node often moves, and the position information of the node (wireless terminal) is often important, and many studies on position estimation have been made so far. For example, there are position measurement systems using GPS, infrared rays, ultrasonic waves, etc., but these require hardware dedicated to measurement, and are not suitable for sensor nodes aiming at power saving, downsizing, and cost reduction. .

  On the other hand, the method of estimating the distance from the received signal strength indicator (RSSI) of the radio wave uses a received electric field strength that can be easily measured, and therefore does not require new hardware, and is required for a sensor network. It can be said that it is optimal for realizing miniaturization and cost reduction.

  Here, the principle of the position estimation method based on RSSI will be described. This position estimation method is based on the fact that there is an average relationship between the received electric field strength p and the distance d between the transmitting and receiving terminals (nodes), excluding variations due to various causes, expressed by the following equation. Is.

(Equation 1)
p = Cd− ^α (1)
Here, α is a propagation parameter representing the degree of attenuation with respect to the distance of radio wave propagation, and is usually called an attenuation constant. This attenuation constant α is known to take a different value depending on the position environment of the node due to the influence of reflected waves and the like in an indoor environment, and the value generally varies between 2 and 4. In addition, the larger the value of the attenuation constant α, the stronger the attenuation at the same distance. The symbol C in the above equation (1) indicates the reception electric field strength when d = 1, that is, the reception electric field strength at a unit distance, and is constant when the transmission power and transmission frequency of the transmission node are constant. It becomes the value of.

  Therefore, when the received electric field strength P is measured at a certain receiving node, if the attenuation constant α at the node position is known in advance, the received electric field strength C is constant based on this equation (1). The distance d can be estimated.

As described above, the position estimation method using the received electric field strength (RSSI) needs to know the attenuation constant α in advance in an environment where the node position is to be estimated.
For this purpose, the received field strength is measured in advance for various distances and environments separately from the measurement of the received field strength for position estimation at the time of communication with a wireless terminal, and the obtained measurement data is approximated. It is necessary to determine the attenuation constant α in advance. This operation is time consuming and laborious and is not easy. For this reason, it is one of the disadvantages (defects) of the RSSI (Receiving Electric Field Strength) method.

  So far, a method has been proposed in which the propagation environment is not investigated in advance, the value of the attenuation constant is changed between 2 and 4, and an infinite number of positions are estimated and outliers are excluded (non-patent document). Reference 1).

Yamada et al. “Indoor location estimation method considering local attenuation constant differences” IEICE, Type 2 Study Group Document SN 2006-38 (2006.12)

  However, the method described above certainly does not require prior investigation, but the attenuation constant at each terminal changes and estimation is performed for all patterns, which requires a huge amount of calculation and real-time performance. The questioned application has the inherent disadvantage of being difficult to use.

  As described above, the position estimation method using RSSI has the trouble of having to investigate the propagation environment (attenuation constant α) in advance in the environment where the position is to be estimated. However, there is a problem that the calculation amount is enormous and it is difficult to use for applications that require real-time performance.

(Object of invention)
In view of the above problems, the present invention provides an attenuation constant estimation system and method, program, and program for effectively obtaining the attenuation constant α by using measurement data of received electric field strength at a fixed node without prior investigation. An object of the present invention is to provide a node position estimation system, method, and program using this.

To achieve the above object, the attenuation constant estimation system sensor network according to the present invention receives a radio signal from the target node of the sensor network region and a plurality of fixed nodes for measuring the received field strength P _i, the A node position estimating device that collects the measured received electric field strength P _i and estimates the position of the target node based on the collected received electric field strength P _i, and the node position estimating device uses the target based on the received electric field strength P _i A distance function for temporarily determining a three-dimensional temporary position of a node and a function D of a summation of distances d _i between the fixed nodes based on the temporary position of the temporarily specified target node and calculating means, according to the position environment of the target node based on the sum and the calculated been function D of the received signal strength P _i Characterized by being configured by a damping constant computing means for calculating calculates the attenuation constant of the wave propagation α for each communication.

In order to achieve the above object, the node position estimation system according to the present invention, disposed in the sensor network region for measuring the received field strength P _i which receives the radio signals from the target node in the sensor network region a plurality of fixed nodes, the nodes to estimate the node location of the target node based on the collected such information to the received field strength P _i was with collecting measured the received signal strength P _i at the respective fixed node A temporary position specifying means for specifying a three-dimensional temporary position of the target node based on the collected received electric field strength _Pi , and the specified target node. seeking function D of the logarithm of the sum according to the distance d _i between the fixed node based on the temporary position of A distance function calculating means, the attenuation constant α of such radio wave propagation in the position environment of the target node for each communication based on the sum and the calculated been function D of the received signal strength P _i that is collected at each fixed node , Α = (N × P ₀ −ΣP _i ) / [10 × D (xm, ym, zm)], where P ₀ is the received electric field strength at a unit distance, N is the number of fixed nodes that can be received, xm, ym, and zm are each provided with an attenuation constant calculating means for calculating and calculating with the three-dimensional temporary position of the target node), and the position of the target node is determined for each communication based on the estimated attenuation constant α. A node position calculation means for estimation is provided.

Furthermore, in order to achieve the above object, a method for estimating an attenuation constant for a sensor network according to the present invention receives a radio signal from a target node in a sensor network area at each of a plurality of fixed nodes and sets the received electric field strength P _i thereof. A first step of measuring, a second step of collecting information of the measured received electric field strength P _i and temporarily specifying the three-dimensional temporary position of the target node based on the collected information; A third step of obtaining a function D of the sum of distances d _i between each fixed node based on the temporary position of the target node, a sum of the received electric field strengths P _i collected in the second step, and Based on the contents of the function D calculated in the third step, the attenuation constant α of radio wave propagation applied to the position environment of the target node is calculated for each communication based on an arithmetic expression specified in advance. Characterized in that a fourth step of calculated.

In order to achieve the above object, a node position estimation method according to the present invention is a method of receiving a radio signal from a target node in a sensor network region at each of a plurality of fixed nodes and measuring the received electric field strength P _i . 1 and the information on the received electric field strength P _i measured in the first step, and the three-dimensional of the target node based on the received electric field strength P _i of each of the collected fixed nodes. And a function D of the sum of logarithms over the distance d _i between each fixed node based on the provisional position of the target node provisionally identified in the second step. a third step of specifying a content, based on the contents of the function D is calculated by the sum and the third step of the received signal strength P _i collected in the second step, the target The alpha decay constants of such radio wave propagation in the position environment over _{de, α = (N × P 0} -ΣP i) / [10 × D (xm, ym, zm) ] As (where, _{P 0} is the unit distance Received electric field strength, N is the number of fixed nodes that can be received, xm, ym, zm are the three-dimensional temporary positions of the target nodes), a fourth step of calculating and calculating this for each communication, and this estimated attenuation And a fifth step of estimating the position of the target node for each communication based on a constant α.

Further, in order to achieve the above object, the attenuation constant estimation program sensor network according to the present invention receives a radio signal from the target node of the sensor network region and a plurality of fixed nodes for measuring the received field strength P _i A sensor network including a node position estimation device that collects the measured received field strength P _i and estimates the position of the target node based on the collected received field strength P _i, and the collected received field strength P _i and A temporary node position specifying function for temporarily specifying a three-dimensional temporary position of the target node based on the sum, and a distance d _i between each fixed node based on the temporary position of the temporary target node Based on the distance function calculation function for obtaining the sum function D, the sum of the received electric field strengths Pi, and the calculated function D An attenuation constant calculation function for calculating and calculating an attenuation constant α of radio wave propagation related to the position environment of the target node for each communication based on a previously specified calculation formula is executed by a computer equipped in the node position estimation device. It is characterized by that.

  Since the present invention is configured as described above, according to this, reception that is received by each fixed node at the time of communication with substantially the same accuracy without performing a laborious and time-consuming preliminary investigation when specifying the attenuation constant α. It is possible to effectively estimate the attenuation constant α in real time on the spot using the information related to the electric field strength, and as a result, it is possible to quickly identify the position of the target node.

  Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings.

  FIG. 1 is a conceptual diagram showing a schematic configuration of a node position estimation system 10 in the present embodiment. The node position estimation system 10 includes a sensor network 1 composed of a plurality of fixed nodes 20 distributed, a mobile node (target node) 30 placed in the sensor network area, and a position of the mobile node 30. And a node position estimation device 40 for estimating.

  The fixed node 20 has a sensor function and a wireless communication function, is distributed in fixed positions, and transmits radio waves (packets) emitted from a mobile node (target node) 30 that also has the sensor function and the wireless communication function. At the same time, the received electric field strength is measured at the time of receiving at 20, and the measured received electric field strength data is sent to the node position estimating device 40 for use in node position estimation.

  The node position estimation device 40 has a function of estimating the position of the mobile node based on the received electric field strength from the sensor network (fixed node) as a whole. For this reason, as shown in FIG. 2, the node position estimation device 40 controls the information transfer with the sensor network and acquires sensing data such as received field strength data from the node, and the received field strength. An attenuation constant estimation module 44 that estimates the attenuation constant α based on the data, a node position estimation module 46 that estimates the position of the mobile node (target node) using the estimated attenuation constant α, fixed node position information, etc. A storage module 48 for accumulation is provided.

Here, in FIG. 2, these modules 42, 44, 46, and 48 are displayed as being integrally configured within the frame of the node position estimation device 40, but each is configured as a separate device, The mutual communication function may be retained and distributed.
In FIG. 2, the sensor network 1 and the modules 42, 44, and 48 in the node position estimation device 40 described above constitute a sensor network attenuation constant estimation system.

Further, the node position estimation system 10 described above need not be restricted by a specific form or operation of the sensor network. For example, with respect to a method for collecting and managing received electric field strength data and the like, the IEEE. An autonomous sensor network having information transfer capability conforming to the 802.15.4 standard may be formed. Alternatively, the data management apparatus may be provided with a function of actively acting on each node to collect sensing information.
In the node position estimation system 10 according to the present embodiment, the basic content is based on data processing based on measurement data collected at each fixed node, and the measurement data is used by the node position estimation device 40 described above. The point that it is structured to obtain is important.

Next, an outline of the operation of the node position estimation system 10 according to the position estimation of the mobile node (target node) 30 described above using the attenuation constant estimated by the attenuation constant estimation system will be described. Detailed explanation will be given.
FIG. 3 is a flowchart showing a schematic operation of the node position estimation system 10.
In FIG. 3, first, transmission radio waves (packets) are transmitted in all directions from a mobile node (target node) 30 that is a position estimation target (step S101, radio wave transmission step). The radio wave transmission from the target node 30 in all directions may be performed autonomously or based on a command from the node position estimation device 40 (particularly, the interface module 42).

  The transmission radio wave (packet) from the target node 30 is received by the sensor of each fixed node 20, and at the same time, the received electric field strength is measured (step S102, electric field strength measuring step, first step). The measurement data is transferred to the information processing apparatus 40 directly or via the fixed node 20 (step S103, data transfer process).

In the node position estimation device 40, first, the attenuation constant α is estimated by the attenuation constant estimation module 44 based on the collected measurement data of the received electric field strength P _i from each fixed node 20 (step S104, attenuation). Constant estimation step). In this case, in the present embodiment, a method using a successive approximation method is also employed in order to improve the accuracy of the estimation (details will be described later). In this case, transmission of radio waves from the target node 30 and reception of radio waves at each fixed node 20, measurement of electric field strength, transfer of electric field strength measurement data, and estimation of attenuation constant are repeated. Then, this repeating process ends when it is determined that a certain number of times has been repeated, for example.

When the attenuation constant estimation process is completed, the location estimation module (node position estimating means) 46, using an attenuation constant alpha, if there is no variation in the measured values of the received power P _i at the i-th fixed node, wherein (1): Since P _i = Cd _i ^−α , since the constant C is known, the distance d _i between the target node and the i-th fixed node is obtained in principle.
Thus, the target node position can be determined from the geometric relationship using the distances d _i from each fixed node to the target node (at least three). On the other hand, in the actual field, the measured value of the received power p _i varies, and the obtained distance d _i also varies. For this purpose, there is a method of obtaining the average value of the received power P _i and obtaining the distance d _i , but here, as will be described later, generally known “estimation using a probability density function” (maximum Likelihood estimation method) is used to estimate the target node position.

Next, the configuration and operation (attenuation constant estimation step: step S104) of the attenuation constant estimation module 44 for estimating the attenuation constant α, which is a basic part of the present invention, will be described.
Here, in order to clarify the contents of the operation, first, the principle of the present attenuation constant estimation method will be described.

The decay constant estimation method, for each communication, is characterized by estimating the attenuation constant α by using only the measurement data P _i of the reception field strength at each fixed node 20.

  This received electric field strength has a property that it is uniquely determined from the attenuation constant α and the distance d as shown in the equation (1) in the average value ignoring variation (C is the transmission power). In fact, the received electric field strength has “variation” due to the influence of noise or fading at the reception point.

Therefore, the damping constant estimation method, these measured data P _i containing a "variation", estimates less attenuation constant α of errors by statistical processing based on the measurement data in a large number of fixed nodes and different time To do.
Note that variations in the received field strength P _i is commonly said to be a normal distribution, but the method is not dependent directly on the shape of the distribution, it can also be applied to a more general distribution is there.

  Here, for the convenience of future handling, the following equation (2) is obtained by replacing the equation (1), which is the basic equation of the present attenuation constant estimation method and position estimation method, with a logarithmic display.

(Equation 2)
_{P i = P 0 -10αlog 10 d} i + ε i ..................... (2)
This equation (2) takes the logarithm of both sides of the above-described equation (1) (the common logarithm of the base 10 is multiplied by 10 for decibel display), and each of the N fixed nodes (i The received field intensity at the second) is P _i [decibel display: dBm], the electric field intensity P ₀ [decibel display: dBm] at the unit distance, the attenuation constant α, the i-th fixed position node from the mobile node (position coordinates are The distance d _i to (x _i , y _i , z _i ))
d _i = [(x−x _i ) ² + (y−y _i ) ² + (z−z _i ) ² ] ^1/2
The variation from the theoretical value is ε _i .

The theoretical value of the electric field intensity P ₀ [decibel display: dBm] at a unit distance can also be obtained from the following Friis transmission formula using the following relationship.

P ₀ [dBm] = Pt + Gt + Gr−PL _{d = 1} (Fris's transmission formula)

Here, Pt is transmission power [dBm], Gt is transmission antenna gain [dBm], and Gr is reception antenna gain [dBm]. PL _{d = 1} represents a path loss [dBm] at a unit distance [1 m], and the distance d and the wavelength λ of the radio wave are generally expressed as PL = ₁₀ log ₁₀ (4πd / λ) ² . It is obtained by setting d = 1.

Then, the sum of the equation (2), i.e., when making the sum of the received signal strength P _i from N fixed location node received radio waves at a constant received signal strength level or higher from the mobile node, the next It is expressed as equation (3).

(Equation 3)
ΣP _i = ΣP ₀ −10αΣlog ₁₀ d _i + Σε _i (3)

Here, the total sum Σε _i of variations from the theoretical value can be relatively ignored by the law of large numbers (central limit theorem) in probability theory, as the number N of the sum increases, compared to the other terms. Become. Therefore, P ₀ is the known constant value, the Σlog ₁₀ d _i is found because even seen from the measured data the sum of the received signal strength P _i, so that the α decay constants from equation (3) is obtained.

That is, Σlog ₁₀ d _i = D (x, y, z)
When the distance function D (x, y, z) is assumed to be known in advance, the distance d _i is given by assuming that the position (x _i , y _i , z _i ) of the fixed node is known in advance.
Since d _i = [(x−x _i ) ² + (y−y _i ) ² + (z−z _i ) ² ] ^1/2 , the position (x, y, z) only, and the attenuation constant α is expressed by the following equation from equation (3).
Here, function D = distance function D (x, y, z), and here, the above-mentioned function D is specifically expressed as a distance function D (x, y, z) and generalized.

(Equation 4)
α = (N × P ₀ −ΣP _i ) / (10 × D (x, y, z)) (4)

Here, the value of the numerator in the above formula (4) is known by subtracting the sum ΣP _{i of} measured values from the theoretical value N × P ₀ . Therefore, if the denominator D (x, y, z) is known, the attenuation constant α can be obtained from the equation (4).

However, D (x, y, z) is a distance function D (x, y, z) representing the sum of logarithms of the distance d _i between the mobile node position (x, y, z) and each fixed node. = Σlog ₁₀ d _i ”, and the position of the mobile node (target node) 30 to be finally estimated in the node position estimation system 10 is related. For this reason, the value of D (x, y, z) is not determined as it is.

  Therefore, in this attenuation constant estimation method, a method is employed in which the position (x, y, z) of the mobile node that can be specified using the attenuation constant α after being estimated is provisionally assumed in advance. .

  One specific method assumes that when there is a fixed node having the highest received electric field strength, the mobile node position is at the fixed node position (xm, ym, zm). This is based on the assumption that the mobile node position is at a position closest to the fixed node 20 having the highest received electric field strength compared to the other fixed nodes 20, and the mobile node position is the fixed node position (xm, ym, zm). By this method, since the unknown mobile node position is fixed at (xm, ym, zm), the distance function D (xm, ym, zm) can be calculated.

  As another method, about 2 to 4 fixed nodes may be selected in descending order of the received electric field strength, and the approximate position may be determined from the ratio between the fixed node position and the electric field strength.

Here, an example showing how the value of the distance function D (x, y, z) changes is shown in FIG.
FIG. 4 shows the state of the function D (x, y, z) in the case of the sensor network 1 in which the fixed nodes are arranged in a mesh shape (4 × 4 state) at equal intervals (for example, 2 [m]). .
As shown in FIG. 4, the distance function D (x, y, z) has a small rate of change in the central portion of the sensor network 1 and increases as it goes to the peripheral portion. Therefore, the distance function D (x, y, z) has almost no change in the vicinity of the central portion of the sensor network 1 even if the position (x, y, z) of the mobile node 30 slightly changes. In other words, the value of the distance function D (x, y, z) is not so different near the center of the sensor network without knowing the position (x, y, z) of the mobile node accurately. Therefore, the attenuation constant α can be obtained relatively accurately.

  In addition, the rate of change of the function D (x, y, z) gradually increases as it moves away from the center of the sensor network 1 (see FIG. 4). For example, the distance function D within a limited area of 2 [m] square. The change in the value of (x, y, z) is not so great. In any case, once the temporary position is determined, the attenuation constant α is obtained based on the equation (4).

  In this way, the attenuation constant α obtained only from the received electric field strength is tentatively increased in accuracy by the successive approximation method because the variation in the received electric field strength and the value of the function D (x, y, z) are provisional. is doing.

  Next, a basic configuration of the attenuation constant estimation module 44 based on the principle described above will be described. FIG. 5 shows a block diagram of the attenuation constant estimation module 44.

In FIG. 5, the attenuation constant estimation module 44 receives the received electric field strength P _i from the target node 30 measured at each fixed node 20 from the front interface module 42, and the received electric field strength P _i a node position provisional identifying means 81 for temporarily identifying the node position from the information, the temporary identified node temporary position (xm, ym, zm) from the distance function D (xm, ym, zm) = Σlog calculating the ₁₀ d _i Attenuation constant calculation for calculating the attenuation constant α based on the above equation (4) using the distance function calculating means 82, the distance function D (xm, ym, zm) calculated here, and the received electric field strength P _i. A means 83 and a successive approximation means 84 for correcting α based on the calculated attenuation constant α and the previously determined attenuation constant α ₋₁ are provided.

  The attenuation constant estimation module 44 employs a successive approximation method that repeatedly measures the received electric field strength at each fixed node and repeatedly obtains the attenuation constant by using the above-described means 81, 82, 83, and 84. Including this, the control is performed by a control unit (not shown) of the node position estimation device 40 as a whole.

Here, the temporary node position specifying means 81 compares the received electric field strength P _i when each fixed node 20 receives a radio signal from the target node, and determines the fixed node 20 having the strongest received electric field strength among them. A maximum strength node extraction function is provided that identifies and extracts the position (xm, ym, zm) of the fixed node 20. The node position temporary specifying means 81 has a target node position temporary specifying function for temporarily specifying the extracted position (xm, ym, zm) of the fixed node 20 as a three-dimensional temporary position of the target node. Yes. Here, the position of the target node 30 is provisionally specified. That is, the temporary position of the target node 30 is specified as (xm, ym, zm). Note that the position data of each fixed node 20 is stored in advance in the storage module 48 of the node position estimation apparatus 40.

Metric calculating means 82, the distance function D (xm, ym, zm) = Σlog calculating the ₁₀ d _i.
Here, the symbol d _i represents the distance between the temporary position (xm, ym, zm) of the target node 30 and the i-th fixed node position,
d _i = [(xm−x _i ) ² + (ym−y _i ) ² + (zm−z _i ) ² ] ^1/2
It is. The temporary position (xm, ym, zm) and the i-th fixed node position (x _i , y _i , z _i ) are determined from the fixed node position information stored in advance, and the distance function D (xm, ym, zm) = Σlog each time the ₁₀ d _i, calculates directly.
This is an effective method when the storage function for calculating the distance function D (xm, ym, zm) in advance and making it a table is insufficient.

Damping constant computing means 83, the sum and the calculated communication the attenuation constant α of the distance function D wave propagation in accordance with the position environment of the target node based on the received signal strength P _i that is collected at each fixed node 20 Each has a function of calculating and calculating with α = f [ΣP _i , D].
In other words, the attenuation constant calculating means 83 uses the received electric field strength P _i and the distance function D (xm, ym, zm) that are already known, and calculates the attenuation constant α by the following equation:
α = f [ΣP _i , D]
= (N × P ₀ −ΣP _i ) / (10 × D (xm, ym, zm))
Calculate based on
Here, N in the numerator is the number of fixed nodes that can be received, and P ₀ is the received electric field intensity at a unit distance determined by the Friis transfer equation already described. Since both are known, N × P ₀ is also calculated. The attenuation constant α can be obtained by calculation.

Here, the above-described node position estimation device has a function of repeatedly executing n times of measurement of the received electric field strength P _i and the corresponding calculation of the attenuation constant α corresponding to the measurement. This node position estimation apparatus is further equipped in advance with the _nth attenuation constant estimated as α _n , the n−1th attenuation constant as α _n−1 , and R (0 <R ≦ 1) as a learning rate. Attenuation constant approximation calculation function (sequential approximation means) for calculating the attenuation constant α _n by successive approximation using the following equation stored in the memory: α _n = α _n-1 + R (α _n -α _n-1 ) 84).
In this case, the node position calculation means described above is configured to use the attenuation constant approximated by the attenuation constant approximation calculation function (sequential approximation means 84) instead of α _n and the attenuation constant α. .
That is, the successive approximation means 84 takes the difference between the attenuation constant α _n calculated for the nth time and the attenuation constant α _n−1 calculated immediately before, and the learning rate R (0 <R ≦ 1) is taken as the difference. ), And a new attenuation constant α _n is calculated by adding the correction term to the attenuation constant α _n−1 . When expressed by an equation, “α _n = α _n−1 + R (α _n −α _n−1 )” is obtained.

Above-mentioned node position provisional identifying means 81 further fixed node to identify the plurality of fixed nodes when a plurality there near the maximized strength or leakage of the received signal strength P _i measured at each fixed node a plurality nodes extracting function for extracting the position Te, tentatively identify the temporary position of the three-dimensional of the target node based on said plurality of received signal strength P _i corresponding to the fixed node position extracted by the plurality of nodes extractors And a target node position provisional specifying function.
That is, in the present embodiment, for example, when there are a plurality of fixed nodes that do not have a large difference in received electric field strength, the node position temporary specifying unit 81 described above calculates the plurality of fixed node positions and the received electric field strength there. And a function for determining the temporary position of the target node.

As another configuration of the distance function calculating means 82, a distance function D (x, y, z) of the sum of logarithms of the distance d _i between the target node (x, y, z) and the i-th fixed node. The
Formula “D (x, y, z) = Σlog ₁₀ d _i ”
Is stored in the distance function table in advance, and the distance function table is searched from the temporary position (xm, ym, zm) of the target node to obtain the distance function D (xm, ym, zm). You may comprise so that it may require | require.

Further, the distance function calculating means 82 calculates the distance function D (x, y, z) in advance based on D (x, y, z) = Σlog ₁₀ d _i , for example, the storage module 48. Is stored as a distance function table, and when the temporary position (xm, ym, zm) of the target node is specified, the function D (xm, ym, zm) is obtained by searching the distance function table. It may be configured. There is an advantage that the distance function D (x, y, z) need not be calculated every time, and the speed for obtaining the distance function D (x, y, z) is increased.

The successive approximation means 84 can take various methods in order to obtain the value of the attenuation constant α close to the theoretical value with a smaller number of iterations. For example, in the above-described expression “α _n = α _n−1 + R (α _n −α _n−1 )”, the learning rate R may be varied without being constant.
That is, the learning rate R used for the calculation of the attenuation constant α _n may be changed depending on the number of repetitions n.

As one of the methods, a method can be used in which the learning rate R (0 <R ≦ 1) is set to a value relatively close to 1 at the beginning of the number of repetitions, and is changed to a smaller value from the middle.
That is, the learning rate R used for the estimation calculation of the attenuation constant α _n is Ra until the repetition number n reaches a specific number M, and thereafter Rb (Ra> Rb). As a result, the follow-up speed up to the target attenuation constant α _n is increased, and stable operation can be expected.

Furthermore, aiming at the same effect, the learning rate R is set to a value relatively close to 1 at the beginning of the number of repetitions, the learning rate R is gradually reduced, and is fixed to a constant small value from the middle. Techniques can also be used. That is, the learning rate R used for the calculation of the attenuation constant α _n is decreased in proportion to a constant value a to n until the repetition number n reaches a specific number M, and the repetition number n is a specific number M. Thereafter, it is a method of setting a constant value b.

The node position estimation device described above, as described above, has a function of repeatedly executing n times repeatedly executing over time n times the measurement and estimation calculation of α the attenuation constant which corresponds to the received signal strength P _i . The node position estimation apparatus is preliminarily equipped with the learning constant as α _n , the attenuation constant estimated at the nth time as α _n-1 , the α _n−1 attenuation constant as the learning rate, and r _i (Σr _i = 1). The following formula stored in the memory
α _n = r ₀ α _n + r ₁ α _n−1 + r ₂ α _n−2 +... + r _m α _n−m
Is provided with an attenuation constant approximation calculation function (sequential approximation means 84) for calculating by successive approximation using. The node position estimation module (node position calculation means) 46 described above uses the attenuation constant approximated by the attenuation constant approximation calculation function (sequential approximation means 84) instead of α _n and the attenuation constant as α. May be.
That is, in the successive approximation means 84 described above, two values of the attenuation constant value α _n and the previous attenuation constant value α _{n−1 in} the _nth successive approximation are used. attenuation constant _{"α -1, α -2, ···,} α -m " respectively learning rate _{"r 1, r 2, ···,} r m ( _{although, Σr i = 1, i =} 0,1, .., M) "and taking the sum,
α _n = r ₀ α _n + r ₁ α _n−1 + r ₂ α _n−2 +... + r _m α _n−m It is also possible to take a method of successive approximation. Thereby, a smoother and more stable operation can be expected.

  Next, the operation of the attenuation constant estimation module 44 will be described with reference to FIG. FIG. 6 is a flowchart of this attenuation constant estimation method.

  In the flowchart shown in FIG. 6, a transmission radio wave (packet) is transmitted from the target node 30 in the sensor network area in all directions, received by each fixed node 20, and the received electric field strength is measured ( The process after 1st process) is completed is shown.

First, the received electric field strength data _Pi is collected by data transfer from each fixed node to the node position estimation device 40 (step S401, data collection step).

Then, based on the collected received signal strength data P _i, to identify the temporary position of the target node (step S402, temporary position determination step, a second step). Here, it is assumed that the target node is located at a fixed node position indicating the strongest received electric field strength data, and the position (xm, ym, zm) is searched by searching the fixed node position table of the storage module 48. Get.

The value of the distance function D (xm, ym, zm) corresponding to the specified temporary position (xm, ym, zm) of the target node is obtained (step S403, distance function value calculation step, third step). Here, the calculation is performed each time based on the formula [D (xm, ym, zm) = Σlog ₁₀ d _i ].

Then, the distance function obtained D (xm, ym, zm) , using a received signal strength _{P i,} the following equation the attenuation constant alpha,
α = f [ΣP _i , D] = (N × P ₀ −ΣP _i ) / (10 × D (xm, ym, zm))
(Step S404, attenuation constant α calculation step, fourth step). Here, N in the numerator is the number of fixed nodes that can be received, and P ₀ is the received electric field intensity at a unit distance determined by the Friis transfer equation already described. Since both are known, N × P ₀ is also calculated. The attenuation constant α can be obtained by calculation.

The difference between the calculated attenuation constant α and the previously calculated attenuation constant α ₋₁ is taken, a corrected term is created by multiplying the difference by the learning rate R, and the corrected term is added to the attenuation constant α to create a new one. The attenuation constant α is set (step S405, attenuation constant successive approximation step).

The above steps are repeated. It is determined whether a predetermined number of repetitions has been performed (step S406, determination step), and the process ends. The attenuation constant at the end is the final attenuation constant α to be estimated. Thus, the operation in the present attenuation constant estimation module 44 ends.
Next, using the attenuation constant α obtained here, the node position estimation module 46 (FIG. 2) performs the node position estimation as the fifth step, as already described in the operation outline of the node position estimation device 40. A process (step S105 of FIG. 3, a node position estimation process) is performed.
Here, as an example, position estimation by the maximum likelihood method used in the present embodiment will be described.
In the maximum likelihood method, the position is estimated by obtaining a position condition that maximizes the probability density function with the position condition.
That is, when the variation of the measured value P = [P ₁ , P ₂ ,..., P _M ] of the received power of a certain fixed node i is normally distributed around the average received power, The probability density function p (Pi | d) of Pi obtained at the fixed node i at the distance d can be expressed by the following equation.

p (P _i d)
= [1 / (2π) ^1/2 σ]] exp [− (P _i [dBm] −10 Log ₁₀ (Cd ^−α )) ² / 2σ ² ]
However, (sigma) represents the degree of dispersion | variation in a measured value, and is about 4 [dB] indoors.
Here, assuming that the position calculation is performed on a two-dimensional plane, p (Pi | d) is replaced with p (Pi | x, y).
However, there is a relationship of d = [(x _i −x) ² + (y _i −y) ² ] ^1/2 , the sensor field is divided into fine grids, and any coordinates (x, y ) To calculate p (Pi | x, y). When there are N fixed nodes used for position estimation, the combined probability density function of received power in all fixed nodes is
p (P | x, y)
= P (P ₁ , P ₂ , ..., Pn | x, y)
= (1 / (2π) ^1/2 σ) ^N exp [−Σ (P _i [dBm] −10 Log ₁₀ (C d ^−a )) ² / 2σ ² ]
The coordinates (x, y) that maximize this function are used as the final target node position estimation coordinates.

  In the above description, in the temporary position determination step of the mobile node in step S402, the method is assumed to be at the fixed node position with the strongest received electric field strength. However, as another method, for example, the received electric field strength is changed. When there are a plurality of fixed nodes that do not have a large difference, the temporary position of the target node may be determined using the plurality of fixed node positions and the received electric field intensity there.

  In addition, the distance function value calculation step of step S403 is, as another method, here, D (xm, ym, zm) is prepared in advance as a table, and the value is quickly calculated by referring to the table. May be.

  In addition, various different methods can be employed for the attenuation constant successive approximation process. For example, the learning rate R (0 <R ≦ 1) may be variable without being constant. As one of the methods, there is a method of setting a value relatively close to 1 at the beginning of the successive approximation process and switching to a smaller value from the middle. As a result, the follow-up speed to the target attenuation constant is increased, and stable operation can be expected.

  Further, in order to achieve the same effect, the learning rate R is set to a relatively large value at the beginning of the successive approximation process, the learning rate R is gradually reduced, and is fixed to a small value from the middle. Can also be used.

In the above-described attenuation constant successive approximation step, the current attenuation constant value α and the previous attenuation constant value α ₋₁ are used. For example, the past m attenuation constants “α ₋ ” are used. ₁ , α ₋₂ ,..., Α _−m ”and learning rates“ r ₁ , r ₂ ,..., R _m (where Σr _i = 1, i = 0, 1,..., M ) "And taking the sum [α _n = r ₀ α _n + r ₁ α _n-1 + r ₂ α _n-2 +... + R _m α _n−m ] It may be taken. Thereby, a smoother and more stable operation can be expected.

  Here, in the present embodiment, the first step (electric field strength measurement step), the second step (temporary position determination step), the third step (distance function value calculation step), and the fourth step (attenuation) described above. The attenuation constant estimation method including the constant α calculation step) is referred to as a sensor network attenuation constant estimation method. Further, a method in which this estimation method further includes the above-described attenuation constant successive approximation step and the fifth step (node position estimation step) is referred to as a node position estimation method.

  In addition, regarding the data collection step, the node temporary position determination step, the function value calculation step, the attenuation constant α calculation step, the attenuation constant successive approximation step, and the determination step, each processing content is programmed and executed by a computer. You may comprise. Here, in the present embodiment, this program is the attenuation constant estimation program for sensor network. As shown in FIG. 7, the computer that executes this program includes a CPU 90 that controls the operation of the entire system, a memory 91 that stores a program and necessary information necessary for the control operation of the CPU 90, and a sensor network. An information processing device (for example, a personal computer) including an input / output interface 92, an external input device 93, an external output device 94, and the like can be used. In FIG. 7, reference numeral 90A denotes a connection bus.

  Furthermore, it may be configured such that the processing content corresponding to the node position estimation step (fifth step) is added to the processing content of each of the above steps to be programmed and similarly executed by the computer. In this embodiment, this program is a node position estimation program.

(Evaluation of this damping constant estimation method by simulation)
Next, the results of evaluating the attenuation constant estimation method according to the present invention by computer simulation will be described with reference to the drawings.

First, the system specifications used for the simulation are described. The sensor field is 8 m x 8 m, the fixed nodes are 16 (4 x 4), arranged in a grid at a height of 2.8 m from the floor (see Fig. 8), and the target node is 1 m high from the floor Now, it is assumed that the distribution of the measured value of the received electric field strength is a normal distribution with a variance value σ ² = 30. Detailed specifications including these are shown in FIG. In addition, the learning rate R in the successive approximation is fixed, and the following three conditions:
Condition I: Learning rate R = 1 (no update)
Condition II: Learning rate R = 0.1
Condition III: Learning rate R = 0.01
FIG. 10 shows the result of the simulation performed under the above.

From FIG. 10, it can be seen that, for the measurement with the learning rate R = 1 (no update), by using the update program with update, results are gathered near the theoretical value, and a large error for each measurement time is suppressed. . Further, as the learning rate R becomes smaller, variations in estimation results become less noticeable.
However, as can be seen from FIG. 10, when the learning rate R becomes extremely small, if the number of trials increases, it will eventually converge near the theoretical value, but if the initial value of the measurement result contains a large error, It can be seen that a considerable number of trials are required until convergence, and the convergence speed greatly depends on the initial value.

  On the other hand, if the learning rate R is large, if the initial value contains a large error, it will be corrected immediately in the next trial. There is a case that inconvenience of not showing.

Therefore, as an improvement method, the learning rate R is made variable depending on the number of trials n as in the following condition IV.
Condition IV: Learning rate R = 0.1−0.001 × (n−1) R ≧ 0.01
: Learning rate R = 0.01 R <0.01
The learning rate R is set so as to gradually approach the parameter of the condition III and eventually become equal to the condition III from the value of the condition II as the number of trials is repeated. FIG. 11 shows the result of simulation using this learning rate and comparison with conditions I to III. It can be seen that by making the learning rate R variable, the average error is less than 0.1 at the time of 20 trials, which is an improvement of about 80% compared to the condition I without update. Also, it can be seen that the convergence speed is fast, and if the number of trials is repeated, it converges to the same error as in condition III.

  From the above simulation results, the attenuation constant estimation method according to the present embodiment can be estimated with a significant attenuation constant within a practical time by combining with the successive approximation method and appropriately selecting the learning rate. It was confirmed that it can also be used.

  In this way, in the above-described embodiment, the method disclosed in the related art described above, that is, with the same accuracy as the case of prior investigation / measurement that takes time and effort, is performed for each communication. The attenuation constant α can be determined on the spot in real time, and the node position can be specified, which is effective for the convenience of the sensor network and the expansion of the application range.

  In the present invention, the attenuation constant α can be estimated in real time on the spot for each communication with almost the same accuracy without performing a time-consuming and time-consuming preliminary investigation, and thus the position can be specified. Become. For this reason, the convenience of the sensor network is greatly improved, and the use range can be expected to be significantly expanded.

1 is a configuration block diagram of a position estimation system according to an embodiment of the present invention. FIG. 2 is a module configuration diagram of the node position estimation device disclosed in FIG. 1; FIG. 2 is a schematic diagram of an operation flowchart of the position estimation system disclosed in FIG. It is the figure which showed an example of the function D (x, y, z). FIG. 3 is a configuration block diagram of an attenuation constant estimation module disclosed in FIG. 2. FIG. 6 is a flowchart of an attenuation constant estimation operation according to the attenuation constant estimation module disclosed in FIG. 5. It is a hardware block diagram showing the information processing apparatus on which the attenuation constant estimation program for sensor networks etc. operate | move. FIGS. 8A and 8B are diagrams showing fixed nodes in the sensor field used in the computer simulation of the attenuation constant estimation method disclosed in FIG. 6. FIG. 8A is a layout diagram, and FIG. is there. FIG. 7 is a list showing specifications used in computer simulation of the attenuation constant estimation method disclosed in FIG. 6. FIG. 6 shows a simulation result of the attenuation constant estimation value using the learning rate R as a parameter in the computer simulation of the attenuation constant estimation method disclosed in FIG. 7 is a simulation result showing a difference in convergence speed due to a difference in learning rate R in a computer simulation of the attenuation constant estimation method disclosed in FIG. 6.

Explanation of symbols

1 sensor network 10 node position estimation system 20 fixed node (fixed position sensor)
30 Mobile node (target node, position estimation target node)
40 Node position estimation device 42 Interface module 44 Attenuation constant estimation module 46 Node position estimation module (node position calculation means)
48 storage module 81 node position temporary specifying means (temporary position specifying function)
82 Distance function calculating means 83 Attenuation constant calculating means 84 Successive approximation means

Claims (18)

A plurality of fixed nodes for measuring the received radio signal the reception field strength P _i from the target node of the sensor network region, of the target node based collects the said measured received signal strength P _i to A node position estimation device for estimating the position;
The node position estimation device;
A distance d between temporary position specifying means for temporarily specifying the three-dimensional temporary position of the target node based on the received electric field strength P _i and each fixed node based on the temporary position of the temporarily specified target node a distance function calculating means for obtaining the function D of the sum according to _i, the received signal strength P _i sum and the calculated by function radio propagation attenuation constant α of each communication relating to the position environment of the target node based on the D of An attenuation constant estimation system for a sensor network, characterized by comprising an attenuation constant calculation means for calculating and calculating the above. A plurality of fixed nodes arranged in the sensor network area for receiving a radio signal from a target node in the sensor network area and measuring the received electric field strength P _i , and the received electric field measured at each fixed node and a node position estimation device for estimating a node position of the target node based on the collected such information to the received field strength P _i was with collecting strength P _i,
Based on the temporary position specifying means for temporarily specifying the three-dimensional temporary position of the target node based on the collected received electric field strength P _i, and the temporary position of the temporarily specified target node. Distance function calculating means for obtaining a logarithmic sum function D of distances d _i between the fixed nodes, the sum of the received electric field strengths P _i collected at the fixed nodes, and the calculated function D And an attenuation constant calculating means for calculating and calculating the attenuation constant α of the radio wave propagation according to the position environment of the target node for each communication with α = f [ΣP _i , D] for each communication,
A node position estimation system comprising node position calculation means for estimating the position of the target node for each communication based on the estimated attenuation constant α. In the node position estimation system according to claim 2,
The above expression of the attenuation constant α in the attenuation constant calculating means, α = f [P _i , D] is expressed as α = (N × P ₀ −ΣP _i ) / [10 × D (xm, ym, zm)],
Here, P ₀ is the received electric field intensity at a unit distance,
N is the number of fixed nodes that can be received,
xm, ym, zm are the 3D temporary positions of the target node,
A node position estimation system characterized by that. In the node position estimation system according to claim 2 or 3,
Up to the temporary position specifying means the node position estimating apparatus includes, extracting the identified its position fixed node of the maximum intensity of the received electric field strength P _i of the radio signal measured at each fixed node Node position estimation comprising: an intensity node extracting function; and a target position temporary specifying function that temporarily specifies a fixed node position extracted by the maximum intensity node extracting function as a three-dimensional temporary position of the target node. system. In the node position estimation system according to claim 2 or 3,
The provisional position specifying means provided in the node position estimation device may include a plurality of fixed nodes when there are a plurality of fixed nodes close to or the maximum intensity of the received electric field intensity Pi of the radio signal measured at each fixed node. A three-dimensional provisional node of the target node based on a plurality of node extraction functions for identifying a fixed node and extracting the position thereof, and the plurality of received electric field strengths corresponding to the fixed node positions extracted by the multiple node extraction function. A node position estimation system comprising a temporary target position specifying function for temporarily specifying a position. In the node position estimation system according to claim 2, 3, 4, or 5,
The distance function calculating means calculates a numerical value relating to the function D based on a three-dimensional temporary position of the temporarily specified target node by D (xm, ym, zm) = Σlog10d _i in a memory table prepared in advance. A node position estimation system having a function of storing D in advance and specifying D stored in the memory table by searching. In the node position estimation system according to claim 2, 3, 4, or 5,
The distance function calculating means calculates a numerical value related to the function D by D (xm, ym, zm) = Σlog10d _i based on a three-dimensional temporary position of the temporarily specified target node, for each communication. A node position estimation system having a function for calculating and identifying in real time. The node position estimation system according to any one of claims 2 to 7,
The node position estimation device;
A function of repeatedly performing the measurement of the received electric field strength P _i and the estimation calculation of the attenuation constant α corresponding thereto repeatedly n times over time;
The estimation calculation damping constant n th as alpha _n, n-1 th the attenuation constant _{α n-1, R (0} <R ≦ 1) equation stored in advance equipped with memory as a learning rate,
α _n = α _n−1 + R (α _n −α _n−1 ), and a configuration including an attenuation constant approximation calculation function that sequentially calculates and calculates the attenuation constant α _n ,
A node position estimation system, wherein the node position calculation means is configured to use an attenuation constant approximated by the attenuation constant approximation calculation function in place of α _n and the attenuation constant as α. The node position estimation system according to claim 8, wherein
A node position estimation system characterized in that the learning rate R used for the calculation of the attenuation constant α _n varies depending on the number of repetitions n. The node position estimation system according to claim 8, wherein
The learning rate R used for the calculation of the attenuation constant α _n is Ra until the repetition number n reaches a specific number M, and thereafter Rb (Ra> Rb). Position estimation system. In the node position estimation system according to claim 9 or 10,
The learning rate R used for the calculation of the attenuation constant α _n is decreased in proportion to a constant value a to n until the repetition number n reaches a specific number M, and the repetition number n is a specific number M. A node position estimation system characterized by a constant value b thereafter. The node position estimation system according to any one of claims 2 to 8,
The node position estimation device comprises:
A function of repeatedly performing the measurement of the received electric field strength P _i and the estimation calculation of the attenuation constant α corresponding thereto repeatedly n times over time;
The following equation stored in a memory equipped in advance as a learning rate, where α _{n is} the attenuation constant estimated for the nth time, α _n-1 is the _n− 1th attenuation constant, and r _i (Σr _i = 1) is:
α _n = r ₀ α _n + r ₁ α _n−1 + r ₂ α _n−2 +... + r _m α _n−m
It has a decay constant approximation calculation function that performs successive approximation using
A node position estimation system, wherein the node position calculation means is configured to use an attenuation constant approximated by the attenuation constant approximation calculation function by using α _n instead of the attenuation constant α. In the node position estimation system according to any one of claims 2 to 12,
The node position calculation means is configured to estimate and calculate the target node position by a maximum likelihood method based on the estimated and calculated attenuation constant α and the received electric field strength P _i at each fixed node. Node location estimation system. A first step of receiving a radio signal from a target node in a sensor network area at each of a plurality of fixed nodes and measuring the received electric field strength P _i ;
Collecting information of the measured received signal strength P _i, a second step of temporarily identifying a temporary position of the three-dimensional of the target node based on this,
A third step of obtaining a summation function D for the distance di between each fixed node based on the provisional position of the provisionally identified target node;
Based on the contents of the function D is calculated by the sum and the third step of the reception field strength P _i that is collected in this second step, pre-attenuation constant of such radio wave propagation in the position environment of the target node α And a fourth step of calculating and calculating for each communication based on the specified arithmetic expression. A first step of receiving a radio signal from a target node in a sensor network area at each of a plurality of fixed nodes and measuring the received electric field strength P _i ;
Information related to the received electric field strength P _i measured in the first step is collected, and the three-dimensional temporary position of the target node is temporarily calculated based on the collected received electric field strength P _i of each fixed node. A second step to identify;
A third step of specifying the content of a logarithmic summation function D for the distance di between each fixed node based on the temporary position of the target node temporarily specified in the second step;
Based on the sum of the received electric field strengths P _i collected in the second step and the contents of the function D calculated in the third step, the attenuation constant α of radio wave propagation over the position environment of the target node is a fourth step of calculating and calculating for each communication from α = f [ΣP _i , D];
A node position estimation method comprising a fifth step of estimating the position of the target node for each communication based on the estimated attenuation constant α. A plurality of fixed nodes for measuring the received radio signal the reception field strength P _i from the target node of the sensor network region, of the target node based collects the said measured received signal strength P _i to In a sensor network comprising a node position estimation device for estimating a position,
A node position provisional specification function for provisionally specifying a three-dimensional provisional position of the target node based on the collected received electric field strength _Pi and the sum thereof;
A distance function calculation function for obtaining a function D of the sum of the distances d _i between the fixed nodes based on the provisionally specified temporary positions of the target nodes;
Attenuation computed for each communication to calculate on the basis of the radio wave propagation prespecified computing equation the attenuation constant α of according to the position environment of the target node based on the sum and the calculated been function D of the received signal strength P _i Constant operation function,
Is executed by a computer equipped in the node position estimation apparatus. A damping constant estimation program for a sensor network. In the sensor network attenuation constant estimation program according to claim 16,
An arithmetic expression specified in advance for the attenuation constant α is:
α = (N × P ₀ −ΣP _i ) / (10 × D),
Here, P ₀ is the received electric field intensity at a unit distance,
N is the number of fixed nodes that can be received,
xm, ym, zm are the 3D temporary positions of the target node,
An attenuation constant estimation program for a sensor network. The target node position is estimated by a maximum likelihood method based on the attenuation constant α estimated by the attenuation constant estimation program for sensor network according to claim 16 and the received electric field strength P _i at each of the fixed nodes. A node position estimation program comprising a node position calculation function for calculation and causing the computer to execute the function.

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