CN112051545A - Underground mine correction positioning method based on Bluetooth ranging - Google Patents

Underground mine correction positioning method based on Bluetooth ranging Download PDF

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CN112051545A
CN112051545A CN202010948968.2A CN202010948968A CN112051545A CN 112051545 A CN112051545 A CN 112051545A CN 202010948968 A CN202010948968 A CN 202010948968A CN 112051545 A CN112051545 A CN 112051545A
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bluetooth
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CN112051545B (en
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程森林
武雅迪
杨金玉
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Chongqing University
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    • GPHYSICS
    • G01MEASURING; TESTING
    • G01SRADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
    • G01S5/00Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
    • G01S5/02Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
    • G01S5/14Determining absolute distances from a plurality of spaced points of known location
    • EFIXED CONSTRUCTIONS
    • E21EARTH DRILLING; MINING
    • E21FSAFETY DEVICES, TRANSPORT, FILLING-UP, RESCUE, VENTILATION, OR DRAINING IN OR OF MINES OR TUNNELS
    • E21F17/00Methods or devices for use in mines or tunnels, not covered elsewhere
    • E21F17/18Special adaptations of signalling or alarm devices
    • YGENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02DCLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
    • Y02D30/00Reducing energy consumption in communication networks
    • Y02D30/70Reducing energy consumption in communication networks in wireless communication networks

Abstract

The invention relates to an underground mine correcting and positioning method based on Bluetooth ranging, and belongs to the technical field of ranging. The method comprises the following steps: s1: secondary filtering processing of RSSI data; s2: establishing a segmented path loss model based on a sliding window; s3: determining a triangle centroid positioning intersection point; s4: optimized by integrating the Bluetooth position information. Aiming at the problem that the logarithmic path loss model cannot accurately fit the relationship between the distances along with the increase of the distances, the invention provides a segmented path loss model based on a sliding window to reduce errors caused by a channel propagation model. According to the particularity of the mine environment, the invention provides the method for correcting the triangle centroid positioning intersection point by integrating the Bluetooth position information, so that the positioning precision is further improved.

Description

Underground mine correction positioning method based on Bluetooth ranging
Technical Field
The invention belongs to the technical field of distance measurement, and relates to an underground mine correction positioning method based on Bluetooth distance measurement.
Background
In recent years, mine safety accidents happen frequently, and accurate positioning under a mine environment becomes a key technical hotspot in order to safely and efficiently mine a mine, ensure the safety of workers and effectively rescue underground trapped personnel. Currently, indoor positioning technologies are mainly classified into 2 types: the first type is an indoor positioning technology based on an external information source, and the realization of the technology depends on the external information source and mainly comprises ultrasonic waves, WiFi, Bluetooth, ultra wide band and the like; the second type is an indoor positioning technology based on natural information sources, which only relies on the sensors of the terminal, including inertial navigation, geomagnetism, and the like. The Bluetooth technology is more and more widely applied to mine environment positioning by virtue of the advantages of low power consumption, low cost, easiness in deployment and the like.
When the Bluetooth technology is adopted for positioning in an actual environment, the whole positioning precision is low because Bluetooth signals are easily influenced by multipath effect and environmental noise in the process of propagation, and RSSI sampling data needs to be preprocessed before positioning.
At present, the most common theoretical model in wireless signal transmission is a logarithmic path loss model, but when the signal propagation distance increases, the error and uncertainty also increase, and it is difficult to establish a signal propagation model conforming to practical application. Based on the method, the segmented path loss model based on the sliding window is provided, and the signal propagation condition is more accurately described.
The triangular positioning algorithm is one of the commonly used positioning algorithms in the RSSI ranging positioning algorithm, the traditional weighted triangular centroid positioning algorithm has certain problems in weight selection, the influence of different Bluetooth beacons on unknown nodes cannot be accurately reflected, and in order to better highlight the action of the closer Bluetooth beacons, the invention optimizes the weight coefficient. Meanwhile, the method provides the additional Bluetooth position information by utilizing the particularity of the mine environment, and adds a screening step before the triangle centroid positioning intersection point is determined, so that the problem of inaccurate positioning caused by interference is solved again.
Based on the fact that the application of the Bluetooth positioning technology in a corridor type mine environment is researched, aiming at the characteristic that a mine tunnel is long and narrow, the invention provides an RSSII correction positioning improvement algorithm based on Bluetooth position information, the algorithm implements multiple optimization in the positioning process, the positioning accuracy and stability can be effectively improved, and the RSSII correction positioning improvement algorithm has research and practical application significance for positioning under a mine.
Disclosure of Invention
In view of the above, the present invention provides a method for correcting and positioning an underground mine based on bluetooth ranging.
In order to achieve the purpose, the invention provides the following technical scheme:
an underground mine correction positioning method based on Bluetooth ranging comprises the following steps:
s1: secondary filtering processing of RSSI data;
s2: establishing a segmented path loss model based on a sliding window;
s3: determining a triangle centroid positioning intersection point;
s4: optimized by integrating the Bluetooth position information.
Optionally, the S1 specifically includes:
and performing secondary filtering processing on RS5I sampling data before Bluetooth positioning: adopting Gaussian filtering as primary filtering to remove gross errors in the data; kalman filtering is selected as secondary filtering, so that the influence of random errors on positioning in the measurement process is reduced.
And (4) randomly and continuously acquiring the Bluetooth signal strength value for 150 times at a certain point, and processing the RSSI sampling data by respectively using Gaussian filtering, Kalman filtering and secondary filtering.
Optionally, the S2 specifically includes:
when the RSSI ranging principle is that the distance from the target node to the bluetooth beacon is calculated according to the RSSI value received by the bluetooth terminal and the propagation model of the wireless signal in the space, the Shadowing model, i.e. the logarithmic path loss model, is shown as the formula (1).
Figure BDA0002676277200000021
Wherein, P (d)0) And P (d) indicates the distance of the Bluetooth terminal from the Bluetooth beacon d0And d, the received signal strength value is in dBm; d0D is the actual distance from the receiving end to the Bluetooth beacon; n is the path loss exponent, and the magnitude of n reflects the rate at which the signal strength varies with propagation distanceMainly related to the propagation environment; x sigma is a masking factor and is a normal random variable with a mean value of 0 and a standard deviation of sigma.
And setting a segmentation fitting point according to the RSSI parameter aiming at the propagation characteristic of the Bluetooth signal. Assuming that the effective range of the fitting model is [0, a ], searching a segmentation fitting point through a sliding window, and calculating a discrete coefficient in the sliding window. When the discrete coefficient has a sudden change, the distance corresponding to the median value of the sliding window is used as a piecewise fitting point, and then curve fitting is performed on each segment to obtain a fitted path loss model, as shown in formula (2).
Figure BDA0002676277200000022
Wherein the RSSI0(d),RSSI1(d),...,RSSIn(d) For each segment path loss model, d ∈ [0, a ]]。
And establishing a signal transmission model by adopting actually measured data, then calculating the distance corresponding to the data required for establishing the ranging model, and calculating the corresponding error.
Optionally, the S3 specifically includes:
the intersection point of two circles is defined, wherein the position relation of the two circles has 4 cases in total, and the approximate point is taken as the reference intersection point.
Let a, B, C be coordinates of 3 bluetooth beacons, where circles a, B, C are circles with 3 bluetooth beacons as centers, and A, B are two circles as examples, and their distances to unknown nodes are r1、r2、r3,LabIs the distance between the circle centers of a and b. Selecting an approximation point (x)1,y1) Representing the reference intersection point, and then using the reference intersection point to calculate the coordinates of the final unknown node.
Lab=r1+r2The unique intersection point P of the two circles is used as an approximate point of the reference intersection point.
Lab>r1+r2When the approximate point is reached, the centers of circles a and b are connected to intersect two circles respectively at two points E and F, and the midpoint P of EF is taken as the approximate point.
Lab<r1+r2When two circles intersect at two points E and F, the point closer to the center of the third circle is taken as an approximate point.
r1=Lab+r2When the approximate point is reached, the circle centers of a and b are connected and extended to intersect with two circles respectively at two points E and F, and the midpoint P of EF is taken as the approximate point.
Optionally, the S4 specifically includes:
in the rectangle mine, when utilizing bluetooth beacon to fix a position, bluetooth beacon deploys in the wall both sides mostly, fuses into bluetooth positional information by this special condition, increases one step of screening step when confirming triangle-shaped barycenter location is nodical to reduce the inaccurate problem in location because of disturbing and bring once more. When positioning is carried out by using Bluetooth in a mine environment, most Bluetooth beacons are arranged in a staggered mode, and sequence numbers are compiled for the corresponding Bluetooth beacons.
Assuming that coordinates of an unknown node O are (x, y), RSSI values of n Bluetooth beacons are received at the point, wherein the selection mode of the RSSI selects a selection mode based on RSSI power, collected RSSI data are arranged in a descending order, and RSSI is ═ RSSI1、RSSI2...RSSIn]And acquiring the serial number and the coordinate of the corresponding Bluetooth beacon;
in addition, when the coordinates of the intersection point of the two circles are calculated, the intersection point is outside the mine wall, a perpendicular line is drawn towards the selected triangle, and the intersection point is taken as an approximate point of the selected triangle.
Two more reference intersections are obtained between circle B, C and circle A, C to reference intersection P1、P2、P3A triangle is formed for the vertex, and the centroid of the triangle is used as the final position coordinate of the unknown node O (x, y).
The invention has the beneficial effects that:
1. aiming at the problem that the logarithmic path loss model cannot accurately fit the relationship between the distances along with the increase of the distances, the invention provides a segmented path loss model based on a sliding window to reduce errors caused by a channel propagation model.
2. According to the particularity of the mine environment, the invention provides the method for correcting the triangle centroid positioning intersection point by integrating the Bluetooth position information, so that the positioning precision is further improved.
Additional advantages, objects, and features of the invention will be set forth in part in the description which follows and in part will become apparent to those having ordinary skill in the art upon examination of the following or may be learned from practice of the invention. The objectives and other advantages of the invention may be realized and attained by the means of the instrumentalities and combinations particularly pointed out hereinafter.
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For the purposes of promoting a better understanding of the objects, aspects and advantages of the invention, reference will now be made to the following detailed description taken in conjunction with the accompanying drawings in which:
FIG. 1 is a comparison graph of RSSI data before and after filtering;
FIG. 2 is a graph of a sliding window based fit path loss model;
FIG. 3 is a comparison of model curve fitting errors;
FIG. 4 is a schematic diagram of a point position of intersection of two circles;
FIG. 5 is a mine Bluetooth beacon deployment diagram;
FIG. 6 is a triangular Bluetooth location information algorithm;
fig. 7 shows the intersection outside the mine wall.
Detailed Description
The embodiments of the present invention are described below with reference to specific embodiments, and other advantages and effects of the present invention will be easily understood by those skilled in the art from the disclosure of the present specification. The invention is capable of other and different embodiments and of being practiced or of being carried out in various ways, and its several details are capable of modification in various respects, all without departing from the spirit and scope of the present invention. It should be noted that the drawings provided in the following embodiments are only for illustrating the basic idea of the present invention in a schematic way, and the features in the following embodiments and examples may be combined with each other without conflict.
Wherein the showings are for the purpose of illustrating the invention only and not for the purpose of limiting the same, and in which there is shown by way of illustration only and not in the drawings in which there is no intention to limit the invention thereto; to better illustrate the embodiments of the present invention, some parts of the drawings may be omitted, enlarged or reduced, and do not represent the size of an actual product; it will be understood by those skilled in the art that certain well-known structures in the drawings and descriptions thereof may be omitted.
The same or similar reference numerals in the drawings of the embodiments of the present invention correspond to the same or similar components; in the description of the present invention, it should be understood that if there is an orientation or positional relationship indicated by terms such as "upper", "lower", "left", "right", "front", "rear", etc., based on the orientation or positional relationship shown in the drawings, it is only for convenience of description and simplification of description, but it is not an indication or suggestion that the referred device or element must have a specific orientation, be constructed in a specific orientation, and be operated, and therefore, the terms describing the positional relationship in the drawings are only used for illustrative purposes, and are not to be construed as limiting the present invention, and the specific meaning of the terms may be understood by those skilled in the art according to specific situations.
1 RSSI data secondary filtering process
The bluetooth signal has nonlinear time-varying characteristics, but the signal strength value is always stable within a certain range, so the RSSI sampling data is subjected to secondary filtering processing before positioning: adopting Gaussian filtering as primary filtering to remove gross errors in the data; kalman filtering is selected as secondary filtering, so that the influence of random errors on positioning in the measurement process is reduced.
The method comprises the steps of randomly and continuously collecting 150 times of Bluetooth signal strength values at a certain point, and processing RSSI sampling data by respectively using Gaussian filtering, Kalman filtering and secondary filtering, wherein effect graphs before and after filtering are shown in figure 1.
It can be seen from fig. 1 that the data fluctuation after the second filtering is relatively small, and the data fluctuation can be effectively controlled. Therefore, the invention adopts secondary filtering to preprocess the sampling data so as to improve the positioning stability and accuracy.
Sliding window based segmented path loss model
When the RSSI ranging principle is that the distance from a target node to a bluetooth beacon is calculated according to an RSSI value received by a bluetooth terminal and a propagation model of a wireless signal in a space, a Shadowing model (i.e., a logarithmic path loss model) is the most common theoretical model in wireless signal transmission, as shown in formula (1).
Figure BDA0002676277200000051
Wherein, P (d)0) And P (d) indicates the distance of the Bluetooth terminal from the Bluetooth beacon d0And d, the received signal strength value is in dBm; d0D is the actual distance from the receiving end to the Bluetooth beacon; n is a path loss index, and the magnitude of n reflects the rate of the signal intensity changing along with the propagation distance and is mainly related to the propagation environment; x sigma is a masking factor and is a normal random variable with a mean value of 0 and a standard deviation of sigma.
Since the error of the log path loss model gradually increases as the signal propagation distance increases, and the uncertainty also increases accordingly, in order to more accurately fit the relationship between the distance and the RSSI, a segmented path loss model based on a sliding window is proposed herein, as shown in fig. 2.
And setting a segmentation fitting point according to the RSSI parameter aiming at the propagation characteristic of the Bluetooth signal. Assuming that the effective range of the fitting model is [0, a ], searching a segmentation fitting point through a sliding window, and calculating a discrete coefficient in the sliding window. When the discrete coefficient has a sudden change, the distance corresponding to the median value of the sliding window is used as a piecewise fitting point, and then curve fitting is performed on each segment to obtain a fitted path loss model, as shown in formula (2).
Figure BDA0002676277200000052
Wherein the RSSI0(d),RSSI1(d) ,., RSSIn (d) for each segment path loss model, d ∈ [0, a ·]。
A signal transmission model is established by using actually measured data, then a distance corresponding to data required for establishing a ranging model is calculated, and a corresponding error is calculated, as shown in fig. 3.
The logarithmic path loss model has the characteristic of common use, but is somewhat insufficient in accuracy, and the segmented path loss model based on the sliding window can reduce errors caused by the RSSI channel propagation model, more accurately describes the signal propagation condition and has more advantages in accuracy.
3 determination of triangle centroid locating intersection point
The triangle positioning algorithm is one of the positioning algorithms commonly used in the RSSI ranging positioning algorithm. In practical circumstances, since the existence of the deviation makes it possible that 3 circles do not intersect at one point, it is necessary to define the intersection point of two circles, wherein the positional relationship between the two circles is 4 cases, and the approximate point is taken as the reference intersection point.
Let a, B, C be coordinates of 3 bluetooth beacons, where circles a, B, C are circles with 3 bluetooth beacons as centers, and we will take A, B two circles as an example below, and their distances to unknown nodes are r respectively1、r2、r3,LabIs the distance between the circle centers of a and b. Selecting an approximation point (x)1,y1) Representing the reference intersection point, and then using the reference intersection point to calculate the coordinates of the final unknown node. The intersection of the two circles is chosen as shown in figure 4.
1.Lab=r1+r2The unique intersection point P of the two circles is used as an approximate point of the reference intersection point.
2.Lab>r1+r2When the approximate point is reached, the centers of circles a and b are connected to intersect two circles respectively at two points E and F, and the midpoint P of EF is taken as the approximate point.
3.Lab<r1+r2When two circles intersect at two points E and F, the point closer to the center of the third circle is taken as an approximate point.
4.r1=Lab+r2When the approximate point is reached, the circle centers of a and b are connected and extended to intersect with two circles respectively at two points E and F, and the midpoint P of EF is taken as the approximate point.
4 incorporating bluetooth location information for optimization
In an actual scene, because the propagation of the bluetooth signal is easily interfered, the unknown node coordinate obtained by the optimization method may have a certain deviation with the actual coordinate, so that a positioning algorithm blended into the bluetooth position coordinate is provided on the original basis. Taking a rectangular mine environment as an example, when utilizing the bluetooth beacon to fix a position, the bluetooth beacon is mostly deployed on both sides of the wall, and the bluetooth position information is merged into by this special condition, and one step of screening step is added when confirming triangle-shaped barycenter location intersection point, thereby reducing the inaccurate problem of location brought because of interfering once more. When positioning is performed by using bluetooth in a mine environment, most bluetooth beacons are deployed in a staggered manner, and sequence numbers of the corresponding bluetooth beacons are compiled as shown in fig. 5.
Assuming that coordinates of an unknown node O are (x, y), RSSI values of n Bluetooth beacons are received at the point, wherein the selection mode of the RSSI selects a selection mode based on RSSI power, collected RSSI data are arranged in a descending order, and RSSI is ═ RSSI1、RSSI2...RSSIn]And acquiring the serial number and the coordinates of the corresponding Bluetooth beacon. The addition of the bluetooth location information algorithm is shown in fig. 6.
In addition, when the coordinates of the intersection point of the two circles are calculated, if the situation shown in fig. 7 occurs, namely, the intersection point is outside the mine wall, a perpendicular line is drawn to the selected triangle, and the intersection point is taken as the approximate point.
Two more reference intersections can be obtained between B, C and A, C according to the above rule, so as to obtain a reference intersection P1、P2、P3A triangle is formed for the vertex with the triangle centroid as the final position coordinate of the unknown node O (x, y).
The algorithm makes full use of the position information of the Bluetooth beacon, and the positioning precision is further improved by combining with the actual environment.
Finally, the above embodiments are only intended to illustrate the technical solutions of the present invention and not to limit the present invention, and although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that modifications or equivalent substitutions may be made on the technical solutions of the present invention without departing from the spirit and scope of the technical solutions, and all of them should be covered by the claims of the present invention.

Claims (5)

1. The underground mine correction positioning method based on the Bluetooth ranging is characterized by comprising the following steps: the method comprises the following steps:
s1: secondary filtering processing of RSSI data;
s2: establishing a segmented path loss model based on a sliding window;
s3: determining a triangle centroid positioning intersection point;
s4: optimized by integrating the Bluetooth position information.
2. The underground mine correcting and positioning method based on Bluetooth ranging according to claim 1, characterized in that: the S1 specifically includes:
and (3) performing secondary filtering processing on the RSSI sampling data before Bluetooth positioning: adopting Gaussian filtering as primary filtering to remove gross errors in the data; kalman filtering is selected as secondary filtering, so that the influence of random errors on positioning in the measurement process is reduced;
and (4) continuously acquiring the Bluetooth signal strength value for 150 times at a certain point randomly, and processing the RSSI sampling data by using Gaussian filtering, Kalman filtering and secondary filtering respectively.
3. The underground mine correcting and positioning method based on Bluetooth ranging according to claim 1, characterized in that: the S2 specifically includes:
when the RSSI ranging principle is that the distance from a target node to a Bluetooth beacon is calculated according to an RSSI value received by a Bluetooth terminal and a propagation model of a wireless signal in a space, a Shadowing model, namely a logarithmic path loss model, is shown as a formula (1);
Figure FDA0002676277190000011
wherein, P (d)0) And P (d) indicates the distance of the Bluetooth terminal from the Bluetooth beacon d0And the received signal strength value at d, in dBm;d0D is the actual distance from the receiving end to the Bluetooth beacon; n is a path loss index, and the magnitude of n reflects the rate of the signal intensity changing along with the propagation distance and is mainly related to the propagation environment; x sigma is a masking factor and is a normal random variable with the mean value of 0 and the standard deviation of sigma;
setting a segmentation fitting point according to the RSSI parameter aiming at the propagation characteristic of the Bluetooth signal; assuming that the effective range of the fitting model is [0, a ], searching a segmentation fitting point through a sliding window, and calculating a discrete coefficient in the sliding window; when the discrete coefficient has a sudden change, taking the distance corresponding to the median value of the sliding window as a segmentation fitting point, and then carrying out curve fitting on each segment to obtain a fitting path loss model as shown in a formula (2);
Figure FDA0002676277190000012
wherein the RSSI0(d),RSSI1(d),…,RSSIn(d) For each segment path loss model, d ∈ [0, a ]];
And establishing a signal transmission model by adopting actually measured data, then calculating the distance corresponding to the data required for establishing the ranging model, and calculating the corresponding error.
4. The underground mine correcting and positioning method based on Bluetooth ranging according to claim 1, characterized in that: the S3 specifically includes:
defining the intersection point of two circles, wherein the position relation of the two circles has 4 conditions in total, and taking the approximate point of the two circles as a reference intersection point;
let a, B, C be coordinates of 3 bluetooth beacons, where circles a, B, C are circles with 3 bluetooth beacons as centers, and A, B are set as two circles, and their distances to unknown nodes are r1、r2、r3,LabThe distance between the circle centers of a and b is shown; selecting an approximation point (x)1,y1) Representing the reference intersection point, and then calculating the coordinates of the final unknown node by using the reference intersection point;
Lab=r1+r2then, the unique intersection point P of the two circles is used as an approximate point of the reference intersection point;
Lab>r1+r2connecting the centers of a and b to intersect two circles at two points E and F respectively, and taking the midpoint P of EF as an approximate point;
Lab<r1+r2then, two circles intersect at two points E and F, and at the moment, a point closer to the center of a third circle is used as an approximate point;
r1=Lab+r2when the approximate point is reached, the circle centers of a and b are connected and extended to intersect with two circles respectively at two points E and F, and the midpoint P of EF is taken as the approximate point.
5. The underground mine correcting and positioning method based on Bluetooth ranging according to claim 1, characterized in that: the S4 specifically includes:
in a rectangular mine, when positioning is carried out by using Bluetooth beacons, the Bluetooth beacons are mostly arranged on two sides of a wall, Bluetooth position information is integrated by the special condition, and a screening step is added when a triangle centroid positioning intersection point is determined, so that the problem of inaccurate positioning caused by interference is reduced again; when positioning is carried out by using Bluetooth in a mine environment, most Bluetooth beacons are arranged in a staggered mode, and serial numbers are compiled for the corresponding Bluetooth beacons;
assuming that coordinates of an unknown node O are (x, y), RSSI values of n Bluetooth beacons are received at the point, wherein the selection mode of the RSSI selects a selection mode based on RSSI power, collected RSSI data are arranged in a descending order, and RSSI is ═ RSSI1、RSSI2...RSSIn]And acquiring the serial number and the coordinate of the corresponding Bluetooth beacon;
in addition, when the coordinates of the intersection points of the two circles are calculated, if the intersection points are outside the mine wall, a perpendicular line is drawn to the selected triangle, and the intersection points are taken as approximate points of the selected triangle;
two more reference intersections are obtained between circle B, C and circle A, C to reference intersection P1、P2、P3Forming a triangle for the vertex, and using the triangle centroid as the final unknown node O (x, y)The position coordinates.
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