CN102608570B - Wireless sensor node ranging and positioning methods for tunnels - Google Patents

Abstract

Translated fromChinese

本发明提出一种坑道无线传感器节点测距方法，该方法通过测量报文在两节点之间的传输时间来获得节点之间的测量距离以及对测量距离的合理筛选，有效克服了坑道环境中无线电信号多径效应、衰减、畸变等对测距精度的影响，对测距过程中出现的瞬时故障有良好的抑制效果。本发明还提供了传感器节点定位方法，首先按照上述测距方法获取移动节点与参考节点的测量距离，再采用迭代法计算移动节点坐标，该方法在极大似然估计法的基础上加上了迭代求精的过程，大幅度提高了移动节点定位计算的精度。

The present invention proposes a tunnel wireless sensor node distance measurement method, which obtains the measurement distance between the nodes by measuring the transmission time of the message between the two nodes and reasonably screens the measurement distance, effectively overcoming the problem of wireless sensor nodes in the tunnel environment. The impact of signal multipath effect, attenuation, distortion, etc. on the ranging accuracy has a good suppression effect on the instantaneous faults that occur during the ranging process. The present invention also provides a sensor node positioning method. First, obtain the measurement distance between the mobile node and the reference node according to the distance measuring method above, and then use an iterative method to calculate the coordinates of the mobile node. This method adds the maximum likelihood estimation method on the basis of The process of iterative refinement greatly improves the accuracy of mobile node location calculation.

Description

The wireless sensor node range finding of a kind of tunnel and localization method

Technical field

The present invention relates to wireless sensor network technology field, particularly relate to a kind of range finding and localization method of the wireless sensor network tunnel based on the radio frequency transmission time.

Background technology

Tunnel refers to railway or the vcehicular tunnel in Construction State, or coal mining tunnel.Its common feature is that structure is long and narrow space, and among continuous variation; Electric power and the communications infrastructure are incomplete, there is no reliable wired or wireless communication link; Ventilation and pumping equipment are not studied carefully standby, and air humidity is large; Workmen and preparation of construction comparatively dense, construction environment is more severe.China is coal mining big country, and in the high-speed development period of capital construction, construction safety accident in above-mentioned tunnel happens occasionally, cause great personnel and property loss, therefore in the urgent need to adapting to the monitoring means of this type of environment, can carry out Real-Time Monitoring to construction environment, workmen is positioned, set up advanced disaster early warning system, ensure the safety of workmen and equipment.

Wireless sensor network has following characteristics, makes it be particularly suitable for the monitoring to tunnel environment:

(1) most node low-power consumption in network, can adopt powered battery, require very low to electric power facility;

(2) network uses and exempts from license wireless channel communication (Industrial Scientific Medical, ISM), without wiring;

(3) network using network, message can multi-hop transmission, node flexible arrangement, network topology capable of dynamic changes;

(4) network size is large, and redundance is high, and part of nodes damages the normal operation that does not affect whole system;

(5) adopt direct-sequence spread-spectrum modulation (Direct Sequence Spread Spectrum, DSSS) technology, antijamming capability is strong.

Location is one of most important application of wireless sensor network with following the tracks of.In a lot of application cases, only have its data that gather of location aware of sensor just meaningful; Positional information is for geographical routing algorithm also particular importance; Sometimes position itself is exactly to need the data that gather, as the tracking of the location of goods, target etc.Traditional localization method often can not meet the requirement of wireless sensor network, and reason is as follows:

(1) traditional wireless location technology is as ultra broadband (Ultra Wide Band, UWB), GPS (Global Position System, etc. GPS) power consumption is higher, is difficult in battery powered situation continuous firing some months even several years;

(2) traditional position location techniques need to be used distinctive signal to find range, and equipment cost is high, and data processing complex is difficult to realize on the serious limited wireless sensor node of resource;

(3) traditional position location techniques is often higher to environmental requirement, as GPS can only be in outdoor application, and can not in indoor or tunnel, use.

(4) traditional location algorithm time complexity is high, and computational accuracy is low, is not suitable on radio node, moving in electric weight and computing power is limited and requirement of real-time is high tunnel.

Wireless sensor network (Wireless Sensor Network, WSN) node positioning method can be divided into based on measurement and the two large classes based on non-measurement.It is large that method based on non-measurement is applicable to WSN node density, orientation range circlet border.Its principle is the location of realizing mobile node according to the efficient communication scope of mobile node and graphic method.The method does not have extra hardware requirement to node, but communication overhead is large, and location algorithm complexity adopts centralized location algorithm more, and positioning precision is not high.Localization method based on measuring in two-dimensional space mainly contains three kinds:

(1) according to distance and the direction of destination node and a known location node;

(2) according to the direction of destination node and two known location nodes;

(3) according to the distance of destination node and three known location nodes.

First two method needs user to type antenna, and this is to be difficult to realize for wireless sensor node, and therefore the third method is widely used in WSN location.Hence one can see that, and the distance between Obtaining Accurate destination node and reference mode is the key of location.But the localization method based on range finding at present, precision is low, is not suitable for the location of wireless sensor node in tunnel.

Summary of the invention

The object of the invention is to propose a kind of tunnel wireless sensor node distance-finding method, the method is the relative distance between the transmission time computing node between two nodes by measured message, improves the distance accuracy in tunnel environment.

A kind of tunnel wireless sensor node distance-finding method, comprises the following steps:

Mobile node broadcast Location Request;

Receive the beaconing nodes feedback acknowledgment signal of Location Request;

Mobile node from the beaconing nodes of feedback acknowledgment signal selected part as with reference to node;

Mobile node and reference mode are carried out to forward direction range finding and oppositely range finding, and the mean value that calculates forward direction range finding result and the result of oppositely finding range is the measuring distance between mobile node and reference mode;

The implementation of described forward direction range finding is: mobile node sends inquiry frame to reference mode, calculates the flight time of inquiry frame from mobile node to reference mode, is multiplied by the light velocity obtains forward direction range finding result by the flight time;

The implementation of described reverse range finding is: reference mode sends inquiry frame to mobile node, calculates the inquiry flight time of frame from reference mode to mobile node, is multiplied by the light velocity result of oppositely being found range by the flight time.

Further, if negative value appears in forward direction range finding result or the result of oppositely finding range, this negative value is replaced with to the measuring distance adopting between mobile node and the reference mode calculating based on radio transmission signal intensity (RSSI) decay distance-finding method.

Further, the range finding of described forward direction and oppositely range finding number of times for once or once.

Further, before the mean value that calculates forward direction range finding result and reverse range finding result, also comprise measuring distance screening step:

For each forward direction range finding result, calculate respectively the absolute difference of the each forward direction range finding result beyond itself and its, if certain absolute difference is greater than predetermined failure threshold value, remember that this absolute difference is fault difference, if the fault difference number of certain forward direction range finding result is greater than the half of forward direction range finding overall measurement number of times, screen out this forward direction range finding result;

For each reverse range finding result, calculate respectively the absolute difference of the each reverse range finding result beyond itself and its, if certain absolute difference is greater than predetermined failure threshold value, remember that this absolute difference is fault difference, if certain is oppositely found range, the fault difference number of result is greater than the half of reverse range finding overall measurement number of times, screens out this oppositely range finding result.

Further, the reference mode of choosing described in is not entirely in the same side in tunnel.

Further, described in the half of the reference mode chosen derive from the beaconing nodes signal intensity that is arranged in tunnel one side compared with powerhouse, second half derives from the beaconing nodes signal intensity that is arranged in tunnel opposite side compared with powerhouse.

The localization method of the tunnel wireless sensor node distance-finding method described in application, first obtains the measuring distance between mobile node and each reference mode, then calculates in the following manner mobile node coordinate:

Estimate the initial position of mobile node;

The middle estimated position of iterative computation mobile node; Wherein

Iterative formula is

$\left\{\begin{array}{c}{x}^{(k+1)}=x^{\left(k\right)}+\frac{f(x^{\left(k\right)},y^{\left(k\right)})g_y(x^{\left(k\right)},y^{\left(k\right)})-g(x^{\left(k\right)},y^{\left(k\right)})f_y(x^{\left(k\right)},y^{\left(k\right)})}{g_x(x^{\left(k\right)},y^{\left(k\right)})f_y(x^{\left(k\right)},y^{\left(k\right)})-f_x(x^{\left(k\right)},y^{\left(k\right)})g_y(x^{\left(k\right)},y^{\left(k\right)})}\\ y^{(k+1)}=y^{\left(k\right)}+\frac{g(x^{\left(k\right)},y^{\left(k\right)})f_x(x^{\left(k\right)},y^{\left(k\right)})-f(x^{\left(k\right)},y^{\left(k\right)})g_x(x^{\left(k\right)},y^{\left(k\right)})}{g_x(x^{\left(k\right)},y^{\left(k\right)})f_y(x^{\left(k\right)},y^{\left(k\right)})-f_x(x^{\left(k\right)},y^{\left(k\right)})g_y(x^{\left(k\right)},y^{\left(k\right)})}\end{array}\right.$

(x⁽⁰⁾, y⁽⁰⁾) be the initial estimated location of mobile node;

(x^(k), y^(k)) be the k time iteration result, wherein k=0,1,2,3,

$f(x^{\left(k\right)},y^{\left(k\right)})=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}[x^{\left(k\right)}-x_i-\frac{d_i(x^{\left(k\right)}-x_i)}{\sqrt{{(x^{\left(k\right)}-x_i)}^2+{(y^{\left(k\right)}-y_i)}^2}}];$

$g(x^{\left(k\right)},y^{\left(k\right)})=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}[y^{\left(k\right)}-y_i-\frac{d_i(y^{\left(k\right)}-y_i)}{\sqrt{{(x^{\left(k\right)}-x_i)}^2+{(y^{\left(k\right)}-y_i)}^2}}];$

$f_x(x^{\left(k\right)},y^{\left(k\right)})=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}[1-\frac{d_i{(y^{\left(k\right)}-y_i)}^2}{{[{(x^{\left(k\right)}-x_i)}^2+{(y^{\left(k\right)}-y_i)}^2]}^{\frac{3}{2}}}];$

$f_y(x^{\left(k\right)},y^{\left(k\right)})=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{d_i(x^{\left(k\right)}-x_i)(y^{\left(k\right)}-y_i)}{{[{(x^{\left(k\right)}-x_i)}^2+{(y^{\left(k\right)}-y_i)}^2]}^{\frac{3}{2}}};$

$g_x(x^{\left(k\right)},y^{\left(k\right)})=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}\frac{d_i(x^{\left(k\right)}-x_i)(y^{\left(k\right)}-y_i)}{{[{(x^{\left(k\right)}-x_i)}^2+{(y^{\left(k\right)}-y_i)}^2]}^{\frac{3}{2}}};$

$g_y(x^{\left(k\right)},y^{\left(k\right)})=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}[1-\frac{d_i{(x^{\left(k\right)}-x_i)}^2}{{[{(x^{\left(k\right)}-x_i)}^2+{(y^{\left(k\right)}-y_i)}^2]}^{\frac{3}{2}}}];$

(x_i, y_i) be the coordinate of i reference mode;

D_ifor mobile node is to the measuring distance of i reference mode;

N is the number of reference mode;

When

or iterations exceedes in limited time, stops iteration, the middle estimated position (x of mobile node^m, y^m) be the iteration result of last iteration, EPS is computational accuracy;

By mobile node initial position (x⁽⁰⁾, y⁽⁰⁾) and middle estimated position (x^m, y^m) difference substitution evaluation function$S(x,y)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{(\sqrt{{(x-x_i)}^2+{(y-y_i)}^2}-d_i)}^2;$

If S is (x⁽⁰⁾, y⁽⁰⁾)) < S (x^m, y^m), choose (x⁽⁰⁾, y⁽⁰⁾) as the optimal estimation position of mobile node, otherwise choose (x^m, y^m) as the optimal estimation position of mobile node.

Further, adopt Maximum Likelihood Estimation Method to estimate the initial position (x of mobile node⁽⁰⁾, y⁽⁰⁾).

The present invention, according to the feature of tunnel environment, proposes the above-mentioned WSN tunnel localization method based on the range finding of radio frequency transmission time.Compared with more existing sensor localization technology, the present invention has following several advantage:

(1) distance-finding method based on the radio frequency transmission time (Radio Frequency Time Of Flight, RF TOF) is suitable for this special applied environment in tunnel.Signal intensity instruction (the Received Signal Strength Indication receiving, RSSI) affected by environment very large, particularly in narrow and small tunnel environment, the multipath effect of radiofrequency signal is serious, ponding in tunnel and wall also make radiowave decay speed serious, and these factors make the hurried increase of error of finding range with RSSI in tunnel.And the RF TOF range finding time is short, can adopt the mode of frequency hopping, reduce and produce the probability that multipath disturbs and is detected, in tunnel, signal attenuation is very little on the velocity of propagation impact of radio frequency signal, therefore in long distance (the more than 3 meters) range finding of RF TOF in tunnel, shown good adaptability.

(2) based on RF TOF range finding aspect by rational fault threshold is set, ranging data is repeatedly carried out to difference calculating, and by difference and fault threshold comparison, rejects the abnormal data that difference exceedes fault threshold.The method has effectively solved range finding failure and positioning system locate failure that transient fault causes, make distance accuracy and wireless system be positioned with efficiency and obtain raising by a relatively large margin, the locator data missing rate that effectively reduces range finding mortality and system, has promoted positioning system performance.

(3) on the basis of traditional maximum likelihood estimation algorithm, added the repeatedly process of iteration Stepwise Refinement, this location algorithm has the features such as time complexity is low, precision is high, good stability, is adapted at long-time running on radio node in electric weight and computing power are limited and requirement of real-time is high tunnel.

(4) location algorithm that the present invention proposes has good economic benefit.Location and the tracking of traditional wireless sensor network to mobile node is very difficult, and cost is high.The present invention utilizes the localization method that the transmission time of wireless signal is realized WSN node both can reduce costs, and can in this rugged environment in tunnel, realize easily again the location of workmen and equipment is followed the tracks of, and can extensively promote, and economic and social profit is good.

Brief description of the drawings

Fig. 1 is position system device overall construction drawing;

Fig. 2 is mobile node positioning flow figure;

Fig. 3 comes and goes range measurement principle figure based on RF TOF.

Embodiment

Below in conjunction with accompanying drawing, the present invention is described in detail, be to be noted that described embodiment is only intended to be convenient to the understanding of the present invention, and it is not played to any restriction effect.

In the present invention, main controlled node (as in accompanying drawing 1 1.) receive the self-position information that mobile node calculates and report host computer by cable network by wireless sensor network; Beaconing nodes (as in accompanying drawing 1 2.) refer to known position information and there is the wireless sensor node of radio frequency transmission function; Reference mode refers to the beaconing nodes that participates in location Calculation; Mobile node (as in accompanying drawing 1 3.) refer to the node that need to position it that has mobile behavior in wireless sensor network.

The above-mentioned wireless sensor network tunnel localization method based on the radio frequency transmission time, beaconing nodes along tunnel wall with homonymy uniformly-spaced, bilateral alternative arrangement, to ensure that in tunnel, chain-shaped network structure has certain communication redundancy degree, and at least three beaconing nodes can be found in mobile node arbitrary position in tunnel within the scope of its efficient communication.Beaconing nodes carries out network numbering according to the following rules: the beaconing nodes that is set in phase the same side, tunnel is odd-numbered, opposite side be even-numbered.

As shown in Figure 2, concrete steps are as follows for wireless sensor network tunnel localization method flow process based on the radio frequency transmission time:

Step (1) mobile node broadcast Location Request;

Step (2) is received the beaconing nodes feedback acknowledgment signal of Location Request;

Step (3) mobile node from the beaconing nodes of feedback acknowledgment signal selected part as with reference to node:

This example is evenly distributed on both sides, tunnel as reference mode selection criterion taking signal energy height and reference mode as far as possible.Be specially:

Mobile node is monitored the beacon that sends of beaconing nodes, and by the individual beaconing nodes of following rules selection n (n >=3) as the needed reference mode in location: the beaconing nodes that (1) is close to position according to the received signal strength indicator (RSSI) that receives beacon sorts; (2) choose each [n/2] the individual conduct of the beaconing nodes of odd number that received signal strength indicator value is the highest and the beaconing nodes of even number with reference to node, if 2 × [n/2] < n, then choose point that in all the other beaconing nodes, received signal strength indicator value is the highest as with reference to node ([n/2] represents to be no more than the maximum integer of n/2).

Step (4) is calculated the measuring distance of mobile node and each reference mode and result is carried out to fault-tolerant processing:

(4.1) measuring distance of calculating mobile node and each reference mode:

RF TOF refers to that message node from WSN is sent to the needed time of another node by less radio-frequency.Because the aerial velocity of propagation of radiofrequency signal is constant, be c=3 × 10⁸(m/s) distance that, therefore can calculate between two nodes is Distance=c × T_tOF, wherein T_tOFrepresent the transmission time of radiofrequency signal between two nodes.Range measurement system based on RF TOF is utilized the radio-frequency (RF) transceiver for data communication in WSN, carries out simple signal processing, without add extra hardware on node, can in complex environment, obtain the distance accuracy of meter level; Short based on the RF TOF range finding time, can adopt the mode of frequency hopping, reduce and produced the probability that disturbs and be detected.

Based on RF TOF, range finding has two schemes.The first is unidirectional measurement, require two nodes that participate in measuring to have high precision, synchronous clock, the node of known location sends message to another one node, the positional information that message comprises node and transmission time information, another one node deducts the transmitting time that message comprises by message after receiving message time of arrival, gets final product to obtain the flight time.This scheme is very high to node hardware requirement, will greatly increase cost and the power consumption of WSN network.First scheme is called to come and go to be measured, and as shown in Figure 3, A node sends a query message POLL to B node, and B node automatically replies a response message ACK.A node can be measured from query message and be sent to and receive response message T.T. used, is denoted as T_tOT; B node measurement is replied required time of query message, i.e. response time T_tAT.From T.T., deduct response time, get final product to obtain message fl transmission and reverse transfer time sum, be denoted as T_rTT.Suppose the transmission time T of both direction message_tOFequate T_tOFbe half of the round-trip transmission time,

T_TOF＝T_RTT/2＝(T_TOT-T_TAT)/2 (1)

The present invention adopts two-way round measuring method, reduces due to the caused measuring error of clock jitter that participates in two nodes measuring.Sent and inquire about frame to reference mode by mobile node, the scheme of calculating the flight time (Time of Flight, TOF) according to message time of return is called forward direction measurement, and is referred to as reverse measurement by the scheme of reference mode transmission inquiry frame calculating TOF.When the present invention measures TOF, carry out m forward direction and measure, oppositely measure for m time, then calculate the mean value of 2m TOF measurement result as the actual value of message transfer time between two nodes, improve measuring accuracy.M generally gets 5～10.

The message transfer time unit measuring based on RF TOF distance-finding method is psec, 10^-12second, the transmission speed that is multiplied by radiowave with it, can obtain the distance between two nodes,

Distance＝T_ToF×3×10^-4(m) (2)

In addition, the clock frequency of considering reference mode and mobile node has error and other factors to cause T_tOT≤ T_tATtime, adopting based on RSSI decay range finding and replace the range finding based on RF TOF, the logarithm normal distribution model tormulation formula based on RSSI decay range finding is

$\mathrm{RSSI}\left(d_i\right)=\mathrm{RSSI}\left(d_0\right)-10\mathrm{\&lambda;lg}\left(\frac{d_i}{d_0}\right)+{\mathrm{\&zeta;}}_{\mathrm{\&sigma;}}---\left(3\right)$

Wherein:

D_ifor mobile node and i, (i=1,2 ... n) distance between individual reference mode (rice);

D₀for reference distance (rice), generally get 1 meter;

RSSI (d_i) be that distance is d_itime receiving end received signal power (dBm);

RSSI (d₀) be reference distance d₀the received signal power (dBm) that point is corresponding;

ζ_σbe the Gaussian random variable (dBm) that a mean value is 0, reflected when distance one timing, the variation of received signal power;

λ is path loss index, be one with the value of environmental correclation.

Make P=RSSI (d₀)+10 λ lg (d₀)+ζ_σ, Q=10 λ, is organized into expression formula (3)

RSSI(d_i)＝P-Qlg(d_i) (4)

Therefore in definite localizing environment, the value of P and Q can be according to many groups RSSI (d of test_i) and d_ivalue utilize logarithm matching (with reference to " computing method " Shen Yuantong, sealwort China, publishing house of Li Shaohua volume-China University of Geosciences, 2004.2:53～57) to obtain.

(42) range finding result fault-tolerant processing:

In 2m the measured value for each reference mode in (4.1) and mobile node relative distance, calculate the wherein absolute difference of each measured value and other 2m-1 measured value, if certain absolute difference is greater than predetermined failure threshold value (predetermined failure threshold value is generally got 5～10 times of expectation measuring accuracy), remember that this absolute difference is fault difference, if the fault difference number of this measured value is greater than m, screen out this measured value;

Step (5) is estimated mobile node initial position:

The method of estimating mobile node initial position is a lot, and synthesis precision height, programming difficulty or ease, complexity height many factors, preferentially adopt Maximum Likelihood Estimation Method.

If

$\left\{\begin{array}{c}A=\left[\begin{array}{cc}2(x_1-x_n)& 2(y_1-y_n)\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ \&CenterDot;& \&CenterDot;\\ 2(x_{n-1}-x_n)& 2(y_{n-1}-y_n)\end{array}\right]\\ X=\left[\begin{array}{c}{x}^{\left(0\right)}\\ y^{\left(0\right)}\end{array}\right]\\ b=\left[\begin{array}{c}{x}_1^2-x_n^2+y_1^2-y_n^2+d_n^2-d_1^2\\ \&CenterDot;\\ \&CenterDot;\\ \&CenterDot;\\ x_{n-1}^2-x_n^2+y_{n-1}^2-y_n^2+d_n^2-d_{n-1}^2\end{array}\right]\end{array}\right.---\left(5\right)$

Wherein

(x_i, y_i) be the coordinate of i reference mode;

D_ifor mobile node is to the measuring distance of i reference mode;

(x⁽⁰⁾, y⁽⁰⁾) be the mobile node initial position of estimating.

By formula

X＝(A^TA)^-1A^Tb (6)

Can obtain initial position (x⁽⁰⁾, y⁽⁰⁾).

The middle estimated position of step (6) iterative computation mobile node:

By the initial estimated location (x obtaining in step (5)⁽⁰⁾, y⁽⁰⁾) being updated to iterative formula, iteration expression formula is as follows

$\left\{\begin{array}{c}{x}^{(k+1)}=x^{\left(k\right)}+\frac{f(x^{\left(k\right)},y^{\left(k\right)})g_y(x^{\left(k\right)},y^{\left(k\right)})-g(x^{\left(k\right)},y^{\left(k\right)})f_y(x^{\left(k\right)},y^{\left(k\right)})}{g_x(x^{\left(k\right)},y^{\left(k\right)})f_y(x^{\left(k\right)},y^{\left(k\right)})-f_x(x^{\left(k\right)},y^{\left(k\right)})g_y(x^{\left(k\right)},y^{\left(k\right)})}\\ y^{(k+1)}=y^{\left(k\right)}+\frac{g(x^{\left(k\right)},y^{\left(k\right)})f_x(x^{\left(k\right)},y^{\left(k\right)})-f(x^{\left(k\right)},y^{\left(k\right)})g_x(x^{\left(k\right)},y^{\left(k\right)})}{g_x(x^{\left(k\right)},y^{\left(k\right)})f_y(x^{\left(k\right)},y^{\left(k\right)})-f_x(x^{\left(k\right)},y^{\left(k\right)})g_y(x^{\left(k\right)},y^{\left(k\right)})}\end{array}\right.---\left(7\right)$

Wherein

(x⁽⁰⁾, y⁽⁰⁾) be the mobile node initial estimated location of utilizing Maximum Likelihood Estimation Method to obtain;

(x^(k), y^(k)) be the k time iteration result, wherein k=1,2,3,

$f(x^{\left(k\right)},y^{\left(k\right)})=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}[x^{\left(k\right)}-x_i-\frac{d_i(x^{\left(k\right)}-x_i)}{\sqrt{{(x^{\left(k\right)}-x_i)}^2+{(y^{\left(k\right)}-y_i)}^2}}];$

$g(x^{\left(k\right)},y^{\left(k\right)})=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}[y^{\left(k\right)}-y_i-\frac{d_i(y^{\left(k\right)}-y_i)}{\sqrt{{(x^{\left(k\right)}-x_i)}^2+{(y^{\left(k\right)}-y_i)}^2}}];$

$f_x(x^{\left(k\right)},y^{\left(k\right)})=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}[1-\frac{d_i{(y^{\left(k\right)}-y_i)}^2}{{[{(x^{\left(k\right)}-x_i)}^2+{(y^{\left(k\right)}-y_i)}^2]}^{\frac{3}{2}}}];$

$f_y(x^{\left(k\right)},y^{\left(k\right)})=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{d_i(x^{\left(k\right)}-x_i)(y^{\left(k\right)}-y_i)}{{[{(x^{\left(k\right)}-x_i)}^2+{(y^{\left(k\right)}-y_i)}^2]}^{\frac{3}{2}}};$

$g_x(x^{\left(k\right)},y^{\left(k\right)})=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\frac{d_i(x^{\left(k\right)}-x_i)(y^{\left(k\right)}-y_i)}{{[{(x^{\left(k\right)}-x_i)}^2+{(y^{\left(k\right)}-y_i)}^2]}^{\frac{3}{2}}};$

$g_y(x^{\left(k\right)},y^{\left(k\right)})=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}[1-\frac{d_i{(x^{\left(k\right)}-x_i)}^2}{{[{(x^{\left(k\right)}-x_i)}^2+{(y^{\left(k\right)}-y_i)}^2]}^{\frac{3}{2}}}];$

N is the number of reference mode.

When

or iterations exceedes in limited time, stops iteration, the middle estimated position (x of mobile node^m, y^m) be the iteration result of last iteration.Wherein EPS is computational accuracy, if iteration precision will reach one decimal place, EPS=0.1; If reach after radix point 4, and EPS=0.0001, the rest may be inferred.The iterations upper limit is generally got 5～10 times.

Step (7.0) is by mobile node initial position (x⁽⁰⁾, y⁽⁰⁾) and middle estimated position (x^m, y^m) distinguish in substitution evaluation function, the expression formula of evaluation function is

$S(x,y)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{(\sqrt{{(x-x_i)}^2+{(y-y_i)}^2}-d_i)}^2---\left(8\right)$

If S is (x⁽⁰⁾, y⁽⁰⁾) < S (x^m, y^m), choose (x⁽⁰⁾, y⁽⁰⁾) as the optimal estimation position of mobile node, otherwise choose (x^m, y^m) as the optimal estimation position of mobile node.Mobile node reports main controlled node by wireless sensor network by the elements of a fix.

The present invention is not only confined to above-mentioned embodiment; persons skilled in the art are according to content disclosed by the invention; can adopt other multiple embodiment to implement the present invention; therefore; every employing project organization of the present invention and thinking; do some simple designs that change or change, all fall into the scope of protection of the invention.

Claims (7)

Translated fromChinese

1.一种坑道无线传感器节点的定位方法，1. A positioning method for tunnel wireless sensor nodes,首先获取移动节点与各参考节点间的测量距离其过程为：Firstly, the process of obtaining the measurement distance between the mobile node and each reference node is as follows:移动节点广播定位请求；The mobile node broadcasts a positioning request;收到定位请求的信标节点反馈确认信号；The beacon node receiving the positioning request feeds back an acknowledgment signal;移动节点从反馈确认信号的信标节点中选取部分作为参考节点；The mobile node selects some of the beacon nodes that feed back the confirmation signal as reference nodes;对移动节点与参考节点进行前向测距和反向测距，计算前向测距结果和反向测距结果的平均值即为移动节点与参考节点间的测量距离；Carry out forward ranging and reverse ranging for the mobile node and the reference node, and calculate the average value of the forward ranging result and the reverse ranging result as the measurement distance between the mobile node and the reference node;所述前向测距的实现方式为：移动节点向参考节点发送查询帧，计算查询帧从移动节点到参考节点的飞行时间，由飞行时间乘以光速得到前向测距结果；The implementation of the forward distance measurement is: the mobile node sends a query frame to the reference node, calculates the flight time of the query frame from the mobile node to the reference node, and obtains the forward distance measurement result by multiplying the flight time by the speed of light;所述反向测距的实现方式为：参考节点向移动节点发送查询帧，计算查询帧从参考节点到移动节点的飞行时间，由飞行时间乘以光速得到反向测距结果；The implementation of the reverse distance measurement is: the reference node sends a query frame to the mobile node, calculates the flight time of the query frame from the reference node to the mobile node, and obtains the reverse distance measurement result by multiplying the flight time by the speed of light;移动节点利用定位算法计算自身坐标，其过程为：The mobile node uses the positioning algorithm to calculate its own coordinates, and the process is as follows:预估移动节点的初始位置；Estimate the initial position of the mobile node;迭代计算移动节点的中间估计位置；其中Iteratively calculate the intermediate estimated position of the mobile node; where迭代公式为The iterative formula is$\left\{\begin{array}{c}{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}<span><span>=</span>=</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>+</span>+</span>\frac{\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>-</span>-</span>\mathrm{<span><span>g</span>g</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>}{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>-</span>-</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>}\\ {\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>+</span>+</span>\mathrm{<span><span>1</span>1</span>}<span><span>)</span>)</span>}<span><span>=</span>=</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>+</span>+</span>\frac{\mathrm{<span><span>g</span>g</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>-</span>-</span>\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>}{{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>-</span>-</span>{\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>{\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span>}\end{array}\right.$(x⁽⁰⁾,y⁽⁰⁾)为移动节点的初始估计位置；(x⁽⁰⁾ , y⁽⁰⁾ ) is the initial estimated position of the mobile node;(x^(k),y^(k))为第k次迭代结果，其中k=0,1,2,3,...；(x^(k) ,y^(k) ) is the kth iteration result, where k=0,1,2,3,...;$\mathrm{<span><span>f</span>f</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>-</span>-</span>\frac{{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}{\sqrt{{<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>]</span>]</span><span><span>;</span>;</span>$$\mathrm{<span><span>g</span>g</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>-</span>-</span>\frac{{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}{\sqrt{{<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}}<span><span>]</span>]</span><span><span>;</span>;</span>$${\mathrm{<span><span>f</span>f</span>}}_{<span><span>(</span>(</span>\mathrm{<span><span>x</span>x</span>}<span><span>)</span>)</span>}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\frac{{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>i</span>i</span>}}{<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{<span><span>[</span>[</span>{<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>]</span>]</span>}^{\frac{\mathrm{<span><span>3</span>3</span>}}{\mathrm{<span><span>2</span>2</span>}}}}<span><span>]</span>]</span><span><span>;</span>;</span>$${\mathrm{<span><span>f</span>f</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span><span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}{{<span><span>[</span>[</span>{<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>]</span>]</span>}^{\frac{\mathrm{<span><span>3</span>3</span>}}{\mathrm{<span><span>2</span>2</span>}}}}<span><span>;</span>;</span>$${\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>x</span>x</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}\frac{{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span><span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}{{<span><span>[</span>[</span>{<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>]</span>]</span>}^{\frac{\mathrm{<span><span>3</span>3</span>}}{\mathrm{<span><span>2</span>2</span>}}}}<span><span>;</span>;</span>$${\mathrm{<span><span>g</span>g</span>}}_{\mathrm{<span><span>y</span>the\; y</span>}}<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>,</span>,</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>)</span>)</span><span><span>=</span>=</span>\underset{\mathrm{<span><span>i</span>i</span>}<span><span>=</span>=</span>\mathrm{<span><span>1</span>1</span>}}{\overset{\mathrm{<span><span>n</span>no</span>}}{\mathrm{<span><span>\&Sigma;</span>\&Sigma;</span>}}}<span><span>[</span>[</span>\mathrm{<span><span>1</span>1</span>}<span><span>-</span>-</span>\frac{{\mathrm{<span><span>d</span>d</span>}}_{\mathrm{<span><span>i</span>i</span>}}{<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}}{{<span><span>[</span>[</span>{<span><span>(</span>(</span>{\mathrm{<span><span>x</span>x</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>x</span>x</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>+</span>+</span>{<span><span>(</span>(</span>{\mathrm{<span><span>y</span>the\; y</span>}}^{<span><span>(</span>(</span>\mathrm{<span><span>k</span>k</span>}<span><span>)</span>)</span>}<span><span>-</span>-</span>{\mathrm{<span><span>y</span>the\; y</span>}}_{\mathrm{<span><span>i</span>i</span>}}<span><span>)</span>)</span>}^{\mathrm{<span><span>2</span>2</span>}}<span><span>]</span>]</span>}^{\frac{\mathrm{<span><span>3</span>3</span>}}{\mathrm{<span><span>2</span>2</span>}}}}<span><span>]</span>]</span><span><span>;</span>;</span>$(x_i,y_i)为第i个参考节点的坐标；(x_i , y_i ) is the coordinates of the i-th reference node;d_i为移动节点到第i个参考节点的测量距离；d_i is the measured distance from the mobile node to the i-th reference node;n为参考节点的个数；n is the number of reference nodes;当$\sqrt{{(x^{\left(k\right)}-x^{(k+1)})}^2+{(y^{\left(k\right)}-y^{(k+1)})}^2}<\mathrm{EPS}$或者迭代次数超过上限时，停止迭代，移动节点的中间估计位置(x^M,y^M)为最后一次迭代的迭代结果，EPS是计算精度；when$\sqrt{{(x^{\left(k\right)}-x^{(k+1)})}^2+{({\mathrm{the\; y}}^{\left(k\right)}-{\mathrm{the\; y}}^{(k+1)})}^2}<\mathrm{EPS}$ Or when the number of iterations exceeds the upper limit, the iteration is stopped, and the estimated intermediate position (x^M , y^M ) of the mobile node is the iteration result of the last iteration, and EPS is the calculation accuracy;将移动节点初始位置(x⁽⁰⁾,y⁽⁰⁾)和中间估计位置(x^M,y^M)分别代入评价函数$S(x,y)=\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\sqrt{{\left({x-x}_i\right)}^2+{\left({y-y}_i\right)}^2}-d_i}^2;$Substitute the initial position (x⁽⁰⁾ , y⁽⁰⁾ ) and intermediate estimated position (x^M , y^M ) of the mobile node into the evaluation function$S(x,\mathrm{the\; y})=\underset{i=1}{\overset{\mathrm{no}}{\mathrm{\&Sigma;}}}{\sqrt{{\left({x-x}_i\right)}^2+{\left({\mathrm{the\; y}-\mathrm{the\; y}}_i\right)}^2}-d_i}^2;$如果S(x⁽⁰⁾,y⁽⁰⁾)＜S(x^M,y^M)，选取(x⁽⁰⁾,y⁽⁰⁾)作为移动节点的最优估计位置，否则选取(x^M,y^M)作为移动节点的最优估计位置。If S(x⁽⁰⁾ ,y⁽⁰⁾ )<S(x^M ,y^M ), select (x⁽⁰⁾ ,y⁽⁰⁾ ) as the best estimated position of the mobile node, otherwise select (x^M , y^M ) as the optimal estimated position of the mobile node.2.根据权利要求1所述的坑道无线传感器节点定位方法，其特征在于，若前向测距结果或反向测距结果出现负值，则将该负值替换为采用基于无线传播信号强度(RSSI)衰减测距方法计算的移动节点与参考节点间的测量距离。2. tunnel wireless sensor node localization method according to claim 1, it is characterized in that, if negative value occurs in forward distance measurement result or reverse distance measurement result, then this negative value is replaced by adopting based on wireless propagation signal strength ( The measurement distance between the mobile node and the reference node calculated by RSSI) attenuation ranging method.3.根据权利要求1所述的坑道无线传感器节点定位方法，其特征在于所述前向测距和反向测距次数为一次或一次以上。3. The tunnel wireless sensor node positioning method according to claim 1, characterized in that the times of the forward ranging and reverse ranging are one or more times.4.根据权利要求3所述的坑道无线传感器节点定位方法，其特征在于，在计算前向测距结果和反向测距结果的平均值前还包括测量距离筛选步骤：4. tunnel wireless sensor node positioning method according to claim 3, is characterized in that, before calculating the average value of forward distance measurement result and reverse distance measurement result, also comprises measurement distance screening step:对于每个前向测距结果，分别计算其与它以外的各前向测距结果的差值绝对值，若某差值绝对值大于预定故障阈值，则记该差值绝对值为故障差值，若某前向测距结果的故障差值个数大于前向测距总测量次数的一半，则筛除该前向测距结果；For each forward ranging result, calculate the absolute value of the difference between it and other forward ranging results, if the absolute value of a certain difference is greater than the predetermined fault threshold, record the absolute value of the difference as the fault difference , if the number of fault differences of a certain forward distance measurement result is greater than half of the total measurement times of the forward distance measurement, then the forward distance measurement result is screened out;对于每个反向测距结果，分别计算其与它以外的各反向测距结果的差值绝对值，若某差值绝对值大于预定故障阈值，则记该差值绝对值为故障差值，若某反向测距结果的故障差值个数大于反向测距总测量次数的一半，则筛除该反向测距结果。For each reverse ranging result, calculate the absolute value of the difference between it and other reverse ranging results, if the absolute value of a certain difference is greater than the predetermined fault threshold, record the absolute value of the difference as the fault difference , if the number of fault differences of a certain reverse ranging result is greater than half of the total number of reverse ranging measurements, then the reverse ranging result is screened out.5.根据权利要求1所述的坑道无线传感器节点定位方法，其特征在于，所述选取的参考节点不全在坑道的同一侧。5. The tunnel wireless sensor node positioning method according to claim 1, wherein the selected reference nodes are not all on the same side of the tunnel.6.根据权利要求5所述的坑道无线传感器节点定位方法，其特征在于，所述选取的参考节点的一半来源于位于坑道一侧的信标节点中信号强度较强者，另一半来源于位于坑道另一侧的信标节点中信号强度较强者。6. The tunnel wireless sensor node positioning method according to claim 5, characterized in that half of the selected reference nodes come from beacon nodes located on one side of the tunnel with stronger signal strengths, and the other half come from beacon nodes located on one side of the tunnel. The one with the stronger signal strength among the beacon nodes on the other side of the tunnel.7.根据权利要求1所述的坑道无线传感器节点定位方法，其特征在于，采用极大似然估计法预估移动节点的初始位置(x⁽⁰⁾,y⁽⁰⁾)。7. The tunnel wireless sensor node positioning method according to claim 1, characterized in that the initial position (x⁽⁰⁾ , y⁽⁰⁾ ) of the mobile node is estimated by using the maximum likelihood estimation method.

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