CN113253200B - Mobile anchor node RSSI value positioning method based on regular triangle motion path - Google Patents
Mobile anchor node RSSI value positioning method based on regular triangle motion path Download PDFInfo
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO 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
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-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
- G01S5/14—Determining absolute distances from a plurality of spaced points of known location
- G01S5/145—Using a supplementary range measurement, e.g. based on pseudo-range measurements
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO 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
- G01S19/00—Satellite radio beacon positioning systems; Determining position, velocity or attitude using signals transmitted by such systems
- G01S19/38—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system
- G01S19/39—Determining a navigation solution using signals transmitted by a satellite radio beacon positioning system the satellite radio beacon positioning system transmitting time-stamped messages, e.g. GPS [Global Positioning System], GLONASS [Global Orbiting Navigation Satellite System] or GALILEO
- G01S19/42—Determining position
- G01S19/45—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement
- G01S19/46—Determining position by combining measurements of signals from the satellite radio beacon positioning system with a supplementary measurement the supplementary measurement being of a radio-wave signal type
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- G01S—RADIO 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
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-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
- G01S5/0257—Hybrid positioning
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- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
- H04W4/02—Services making use of location information
- H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
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- H04W4/38—Services specially adapted for particular environments, situations or purposes for collecting sensor information
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Abstract
The invention discloses a mobile anchor node RSSI value positioning method based on a regular triangle motion path, which comprises the steps of determining the communication radius of a mobile anchor node according to a monitoring area, dividing the monitoring area into a layer number and a layer height, and dividing each layer into a right-angled triangle area unit and an inverted regular triangle area unit which are alternately connected; anchor nodes with GNSS positioning function continuously traverse the boundaries of regular triangle area units of the monitoring area layer by layer, layer by layer in an end-to-end manner, periodically broadcast own position information in the moving process, and the unknown nodes receive the position information broadcast by the anchor nodes and RSSI values at the position and obtain the positioning of the unknown nodes through calculation. According to the invention, the unknown node in the whole monitoring area can be positioned by only one mobile anchor node, the hardware cost is low, the positioning accuracy is high, and the method is suitable for the open outdoor wireless sensor network monitoring environment; the method has the advantages of being not easily affected by RSSI ranging errors and GNSS positioning errors, not having collinear beacon points, being capable of effectively positioning boundary points, and the like.
Description
Technical Field
The present invention relates to a wireless communication positioning method, and in particular, to a positioning method for RSSI values.
Background
With the rapid development of microprocessor technology, embedded technology, sensor technology and wireless communication technology, wireless sensor networks are widely used in the fields of military investigation, smart home, biological medicine, environmental monitoring, internet of things and the like. The position information of the nodes is a premise and a foundation for effective deployment and application of the wireless sensor network. In practical use, GNSS (Global Navigation SATELLITE SYSTEM ) devices cannot be installed for each node in the network due to the limitation of network cost, energy consumption, node volume and other factors. Therefore, the node positioning technology of the wireless sensor network is researched, the anchor node with the positioning function is used for positioning the node with unknown network position, and the method has important significance for promoting further application and progress of the wireless sensor network technology.
The node location algorithm may be classified into a location algorithm based on ranging and a location algorithm without ranging. The node positioning algorithm without distance measurement can only generally position the unknown node on the mass center of a certain area, the positioning accuracy is low, and the practical application range is limited. The positioning algorithm based on distance measurement measures the distance from an unknown node to a plurality of anchor nodes with known positions (more than three) by using a certain technical means, and then calculates the position of the unknown node by using a trilateration or maximum likelihood estimation positioning method. Node technologies based on ranging are generally divided into: TOA (Time of Arrival), TDOA (TIME DIFFERENCE of Arrival Time difference), AOA (Angle of Arrival), RSSI (received signal strength index), wherein an additional measuring component is required to be added based on TOA, TDOA, AOA positioning technology, the positioning cost is relatively high, and the method is not suitable for a large-scale wireless sensor network; the positioning technology based on the RSSI does not need additional hardware, has the advantages of low communication cost, low hardware cost, simple realization, strong expansibility and the like, is widely applied, and becomes a focus and a hot spot of research.
Relevant literature currently studied for an anchor node positioning algorithm based on RSSI values is as follows:
1. Wang Zhenchao, zhang Qi et al in the paper "improved weighted centroid positioning algorithm based on RSSI ranging" published in 2014 adopt a weighted value to correct the RSSI ranging value, thus effectively improving the positioning accuracy of the traditional weighted centroid algorithm, and the algorithm has the following defects: (1) Three or more anchor nodes are measured to realize the calculation of the coordinates of the unknown node, and three or more anchor nodes are kept to be small probability events in the communication range of the unknown node at the actual use moment; (2) The positioning accuracy of the algorithm is in direct proportion to the number and distribution density of the anchor nodes, a large number of static anchor nodes are required to be distributed on a network with high requirements on the positioning accuracy of unknown nodes, and the positioning cost is high.
2. Han Guangjie, zhang Chenyu et al invent a wireless sensor network node positioning method adopting a single mobile anchor node in a regular hexagon-based mobile anchor node path planning method (an authorized bulletin number: CN 1036077726B) in a wireless sensor network of a national patent granted in 2016, greatly reduce the number of anchor nodes, effectively reduce the positioning cost, and the method has the following defects: (1) The three-side positioning method based on RSSI ranging is adopted to realize the coordinate calculation of the unknown node in the monitoring area, and the positioning deviation of the unknown node is greatly influenced because the ranging of the RSSI value is inaccurate; (2) The round path compensation algorithm is adopted to realize the positioning of boundary nodes of a monitoring area, and the existing research results show that when the network coverage area is large, the radius of the round track of the boundary is quite large, and a plurality of similar beacon points on the same local circular arc are similar to collineation, so that larger error is introduced to the calculation of the unknown node coordinates.
3. The invention patent 'a sensor node positioning method based on RSSI of a mobile anchor node' (application publication number: CN 107770861A) applied by Xu Juan, zhao Yakun and the like in 2018 proposes a positioning scheme for measuring an unknown node by adopting an RSSI intensity value.
In summary, the research of the anchor node positioning algorithm based on the RSSI value has been greatly advanced at present, but the defects still exist:
(1) In the conventional RSSI value ranging and positioning algorithm based on the static anchor nodes, coordinate calculation can be performed only by obtaining the distances from the unknown nodes to more than three anchor nodes in the communication range of the unknown nodes, when the number of anchor nodes in the communication range of the unknown nodes is small (less than 3), the solution cannot be realized, and the limitation of the algorithm is obvious; and the positioning precision of the unknown nodes is in direct proportion to the number and distribution density of the anchor nodes, so that the arrangement and use cost of the anchor nodes can be greatly increased for a large-scale wireless sensor network with high positioning precision requirements.
(2) In the existing positioning algorithm based on the RSSI value of the mobile anchor node, the problems of collineation of the beacon points on the moving path and low positioning precision of the boundary points of the monitoring area exist.
(3) The existing positioning algorithm based on the mobile anchor node does not consider the influence of the positioning error of the GNSS system, and when the error is larger, the positioning data is directly provided to participate in the coordinate calculation of the unknown node, so that the great deviation is introduced.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provides a wireless sensor node positioning method based on a single mobile anchor node. In order to achieve the above purpose, the technical scheme adopted by the invention is as follows:
A mobile anchor node RSSI value positioning method based on a regular triangle motion path comprises the following steps:
S1, determining a proper mobile anchor node communication radius R according to the size and positioning timeliness requirements of a monitoring area of a wireless ad hoc network, wherein the number of layers n and the layer height h of the monitoring area are divided into alternately connected right-angled and inverted right-angled triangle area units, as shown in figure 1.
S2, continuously traversing the boundaries of all regular triangle area units of the monitoring area layer by layer and layer by layer in an end-to-end mode by a mobile anchor node with a GNSS positioning function, and periodically broadcasting own position information in the moving process as shown in fig. 1, wherein an unknown node receives the position information broadcast by the mobile anchor node and an RSSI value at the position.
S3, receiving three position data values forming a linear relation and RSSI values at the positions by unknown nodes in any regular triangle area unit, carrying out least square processing on the three groups of position data values to respectively obtain linear track equations of three boundaries of the regular triangle area unit, taking the intersection point of the linear track equations, namely the vertex of the regular triangle area unit as a reference node, broadcasting information position points of the anchor node, namely the relative distance d between a beacon point and the reference node as an independent variable, carrying out curve fitting on the RSSI values and the relative distance d to respectively obtain track equations of an RSSI value increasing trend section and an RSSI value reducing trend section on each boundary of the regular triangle area unit, and calculating intersection points of two RSSI value polynomial equations to obtain RSSI peak point coordinates of the unknown node on three boundaries of the regular triangle area unit.
S4, obtaining coordinates of the unknown node through mathematical calculation according to the coordinates of the RSSI peak points of the unknown node on three sides of the regular triangle area unit.
Further, in order to ensure that the unknown node in the boundary area of the wireless sensor network can receive enough mobile anchor node information to realize the calculation of the self position information, and simultaneously, in order to ensure that the unknown node in each layer can effectively receive the position information and the RSSI value broadcast by the mobile anchor node, the motion area of the mobile anchor node covers and is slightly larger than the monitoring area, and the relationship between the communication radius R of the mobile anchor node and the side length L of the regular triangle area unit is as follows: R.gtoreq.L.
Further, the step S3 comprises the following steps and calculation methods,
S31, respectively obtaining linear track equations of three boundaries of the regular triangle area unit according to a least square method, wherein the specific calculation method comprises the following steps:
when the mobile anchor node moves on three boundaries of the regular triangle area unit, the unknown node respectively obtains three geographic position coordinate sets of linear relations broadcasted by the mobile anchor node on the three boundaries, the position data set received on one boundary is (x i,yi), and a linear track equation is set as follows:
y＝k1x+b1 (1)
According to the least squares criterion, the optimal estimates of parameters k 1 and b 1 can be derived from the following equation:
Wherein,
And solving the linear track equation of the mobile anchor node on the other two boundaries by the same method: y=k 2x+b2 (3)
y＝k3x+b3 (4)
S32, solving the intersection points of the three linear track equations obtained in the step S31 to obtain the coordinates of the three vertexes of the regular triangle area unit.
S33, in the moving process of the mobile anchor node, the RSSI value of the anchor node received by the unknown node shows a change trend of gradually increasing and gradually decreasing after reaching the peak point; the radio signal attenuation model can know that the closest point to the unknown node has the largest RSSI value; calculating the relative distances d m1,dm2 and d m3 of the RSSI peak point of the mobile anchor node by using d as an independent variable and the RSSI value as an independent variable in the motion process of each boundary of the mobile anchor node; the specific calculation method comprises the following steps:
Curve fitting is carried out on the relative distances d and the RSSI values of all the beacon points of the RSSI value increasing trend section and the RSSI value decreasing trend section on the same boundary respectively, and polynomial equations F (x) and P (x) of the RSSI value increasing trend section and the RSSI value decreasing trend section are obtained as shown in fig. 3;
F(x)＝c0+c1x+c2x2+···+cjxj (5)
P(x)＝c0′+c1′x+c2′x2+···+cj′xj (6)
The intersection point of F (x) and P (x) is the peak point of the RSSI value acquired by the unknown node, namely the point of the mobile anchor node closest to the unknown node on the linear track; solving simultaneous equations F (x) and P (x) to obtain an intersection point, and obtaining a relative distance value d m1 of the peak point M 1; the relative distances d m2 and d m3 of the RSSI peak points M 2 and M 3 on the other two boundaries are obtained in the same way.
S34, calculating the coordinates of peak points M 1,M2 and M 3 through linear algebra and trigonometric functions according to the values of d m1,dm2 and d m3 and the coordinates of three vertexes of the regular triangle area unit.
Further, the step S4 comprises the following specific steps,
S41, obtaining a linear equation of the vertical lines L 1,L2 and L 3 taking the peak points M 1,M2 and M 3 as vertical points through linear algebraic calculation; the three perpendicular lines theoretically intersect at a point, the point is an unknown node to be solved, as shown in fig. 4, in actual use, because the GNSS positioning system has deviation, and the RSSI value received by the unknown node is interfered by environmental factors and has certain error, the three perpendicular lines obtained by solving deviate from the theoretical value to a certain extent, that is, intersection points of the three perpendicular lines intersecting each other are not coincident, and the specific intersecting situation is shown in fig. 5.
S42, calculating coordinates of intersection points C 1,C2 and C 3 of the perpendicular lines L 1,L2 and L 3 through linear algebra.
S43, obtaining a mean value of coordinate values of the intersection points C 1,C2 and C 3, and taking the mean value as the coordinate of the unknown node.
The beneficial effects of the invention are as follows: compared with the prior art, the invention has the following advantages:
(1) Aiming at the problem that GNSS positioning deviation influences the calculation of unknown node coordinates in the traditional anchor node positioning algorithm, the invention adopts a least square method to process the anchor node position data set with linear relation, calculates to obtain the optimal linear track equation of the mobile anchor node, obtains the vertical point coordinates of the anchor node participating in the calculation of the unknown node coordinates by solving the RSSI value change trend of the mobile anchor node received by the optimal linear track equation and the unknown node, and effectively reduces the influence of the GNSS positioning deviation on the solving precision of the unknown node compared with the situation that the unknown node coordinates are calculated by directly adopting the position coordinates provided by a GNSS system in the traditional mobile anchor node positioning algorithm.
(2) According to the invention, the intersection point of the anchor node optimal trajectory equation is skillfully used as a reference node, the RSSI peak point coordinate is obtained by solving the polynomial equation of the RSSI value, the unknown node coordinate calculation is realized according to the relative position relation between the RSSI peak point and the unknown node, the algorithm does not need to use RSSI value distance measurement, and the influence of the RSSI distance measurement error on the unknown node coordinate calculation precision is effectively avoided. (3) In the invention, in order to ensure the nodes in the boundary area of the wireless sensor network, the node information of the beacon node broadcasted by enough mobile anchor nodes can be obtained, and the track motion strategy that the coverage area of the mobile anchor nodes is slightly larger than the monitoring area of the wireless sensor is adopted, so that the boundary area of the monitoring area is usually not covered enough by the existing mobile anchor node positioning algorithm, the positioning precision of the boundary node is not high, and the actual use of the wireless sensor network is affected.
(4) According to the invention, a single anchor node is adopted to make regular triangle track movement layer by layer in a monitoring area, and the positioning of all nodes to be detected in the area is realized through RSSI value peak points on three boundaries of the regular triangle area, so that the problem of collineation of beacon points in a traditional mobile anchor node algorithm is effectively avoided, and the algorithm does not need additional hardware, and has the advantages of low positioning cost, simplicity and easiness in implementation.
The invention can locate the unknown node in the whole monitoring area by only one mobile anchor node, has low hardware cost and high positioning precision, and is suitable for the open outdoor wireless sensor network monitoring environment. Typical application scenarios are as follows: (1) The environment monitoring system adopts unmanned aerial vehicle or ground mobile equipment, and can position wireless sensor nodes in a monitoring environment, thereby ensuring real-time monitoring and collecting environment data of all position points in a monitoring area. (2) In military application, a micro mobile robot or a military aircraft is used as a mobile anchor node, so that own sensing nodes in a relevant area can be positioned, information of appointed geographic position points is collected, and an interested target is monitored and tracked. The method has the advantages of low use cost, high positioning accuracy, insusceptibility to RSSI ranging errors and GNSS positioning errors, no signal point collineation, effective positioning of boundary points and the like.
Drawings
FIG. 1 is a schematic diagram of a regular triangle motion path;
FIG. 2 is a schematic diagram of relative distances;
fig. 3 is an RSSI change trend graph;
FIG. 4 is a diagram of an RSSI peak point coordinate solution model;
FIG. 5 is a schematic diagram of unknown node coordinate solution.
Detailed Description
The invention is further described in detail below with reference to the embodiments, and a method for positioning an RSSI value of a mobile anchor node based on a regular triangle motion path, the method comprising the steps of:
S1, determining a proper mobile anchor node communication radius R according to the size and positioning timeliness requirements of a monitoring area of a wireless ad hoc network, wherein the number of layers n and the layer height h of the monitoring area are divided into alternately connected right-angled and inverted right-angled triangle area units, as shown in figure 1.
S2, continuously traversing the boundaries of all regular triangle area units of the monitoring area layer by layer and layer by layer in an end-to-end manner by a mobile anchor node with a GNSS positioning function, periodically broadcasting own position information in the moving process, and receiving the position information broadcast by the mobile anchor node and an RSSI value at the position by an unknown node; as shown in FIG. 1, the thick dotted line is a monitoring area of the wireless sensor network, the mobile anchor node starts to move from the point A to the point B along an angle of 120 degrees with the horizontal line according to the direction indicated by the arrow, then moves from the point B to the point C along the horizontal line after reaching the point B, moves from the point C to the point A along an angle of-60 degrees with the horizontal line according to the arrow after reaching the point A, moves from the point A to the point D along the direction of the horizontal line according to the arrow after reaching the point A, and circulates in this way, the anchor node moves from left to right to the point E, and the first layer traversal of the monitoring area is completed. After the anchor node moves to the point E, the anchor node moves from the point E to the point F along an angle of 60 degrees with a horizontal line according to the direction of a graphic drawing, moves from the point F to the point G along an angle of 180 degrees with the horizontal line according to the direction of a graphic arrow after the anchor node reaches the point F, moves from the point F to the point G to the point E along an angle of-60 degrees with the horizontal line after the anchor node reaches the point E, moves to the point H along an angle of 180 degrees with the horizontal line according to the direction of the graphic drawing after the anchor node reaches the point E, and circulates in this way until the second layer of traversal is completed. And the mobile anchor node walks along the route until the whole monitoring area is covered. In order to ensure that unknown nodes in a boundary area of a wireless sensor network can receive enough mobile anchor node information to realize self position information calculation, and simultaneously ensure that the unknown nodes in each layer can effectively receive the position information and RSSI value of the broadcast of the mobile anchor node, a movement area of the mobile anchor node covers and is slightly larger than a monitoring area, and the relation between a communication radius R of the mobile anchor node and a side length L of a regular triangle area unit is as follows: R.gtoreq.L.
S3, receiving three position data values forming a linear relation and RSSI values at the positions by unknown nodes in any regular triangle area unit, carrying out least square processing on the three groups of position data values to respectively obtain linear track equations of three boundaries of the regular triangle area unit, taking the intersection point of the linear track equations, namely the vertex of the regular triangle area unit as a reference node, broadcasting information position points of anchor nodes, namely the relative distance d between a beacon point and the reference node as an independent variable, carrying out curve fitting on the RSSI values and the relative distance d to respectively obtain track equations of an RSSI value increasing trend section and an RSSI value reducing trend section on each boundary of the regular triangle area unit, and calculating intersection points of two RSSI value polynomial equations to obtain RSSI peak point coordinates of the unknown nodes on three boundaries of the regular triangle area unit;
s31, as shown in FIG. 2, a point W is a node to be positioned in the regular triangle area unit EHG, and when an anchor node moves on the regular triangle boundaries EH, HG and GE, unknown nodes respectively obtain three geographic position coordinate sets of a linear relation broadcasted by the anchor node on the three boundaries; according to the least square method, the linear track equations of the three boundaries of the regular triangle area unit are respectively obtained, and the specific calculation method comprises the following steps: when the mobile anchor node moves on three boundaries of the regular triangle area unit, the unknown node respectively obtains geographic position coordinate sets of three linear relations broadcasted by the mobile anchor node on the three boundaries, and assuming that a position data set received on a boundary HG is (x i,yi), a HG linear track equation is set as follows:
y＝k1x+b1 (1)
According to the least squares criterion, the optimal estimates of parameters k 1 and b 1 can be derived from the following equation:
Wherein,
And solving the linear track equation of the mobile anchor node on the boundaries GE and EH by the same method: y=k 2x+b2 (3)
y＝k3x+b3 (4)
S32, solving intersection points of the three linear track equations obtained in the step S31 to obtain coordinates of three vertexes E, H and G of the regular triangle area unit;
S33, as shown in fig. 2, in the process that the mobile anchor node moves from the point H to the point G, the RSSI value of the mobile anchor node received by the unknown node shows a change trend of gradually increasing and gradually decreasing after reaching the peak point, as shown in fig. 3; the radio signal attenuation model can know that the closest point to the unknown node has the largest RSSI value; the method for calculating the relative distance d m1 of the RSSI peak point of the mobile anchor node by the unknown node in the motion process of the mobile anchor node by taking the vertex H as an origin and taking d as an independent variable and the RSSI value as an independent variable comprises the following steps of:
curve fitting is carried out on the relative distances d and the RSSI values of all the beacon points of the RSSI value increasing trend section and the RSSI value decreasing trend section on the boundary, and polynomial equations F (x) and P (x) of the RSSI value increasing trend section and the RSSI value decreasing trend section are obtained;
F(x)＝c0+c1x+c2x2+···+cjxj (5)
P(x)＝c0′+c1′x+c2′x2+···+cj′xj (6)
The intersection point of F (x) and P (x) is the peak point of the RSSI value acquired by the unknown node, namely the point of the mobile anchor node closest to the unknown node on the linear track; solving simultaneous equations F (x) and P (x) to obtain an intersection point, and obtaining a relative distance value d m1 of the peak point M 1; the relative distances d m2 and d m3 of the RSSI peak points M 2 and M 3 on the other two boundaries GE and EH are found in the same manner.
S34, calculating the coordinates of peak points M 1,M2 and M 3 through linear algebra and trigonometric functions according to the values of d m1,dm2 and d m3 and the coordinates of three vertexes E, H and G of the regular triangle area unit.
S4, obtaining coordinates of the unknown node W through mathematical calculation according to the coordinates of the RSSI peak points of the unknown node on three sides of the regular triangle area unit. The step S4 comprises the following specific steps, S41, obtaining a linear equation of the perpendicular lines L 1,L2 and L 3 taking the peak points M 1,M2 and M 3 as the vertical points through linear algebraic calculation; s42, calculating coordinates of intersection points C 1,C2 and C 3 of the perpendicular lines L 1,L2 and L 3 through linear algebra; s43, obtaining a mean value of coordinate values of the intersection points C 1,C2 and C 3, and taking the mean value as the coordinate of the unknown node W.
The foregoing is merely illustrative of the present invention, and simple modifications and equivalents may be made thereto by those skilled in the art without departing from the spirit and scope of the present invention.
Claims (1)
1. A mobile anchor node RSSI value positioning method based on a regular triangle motion path is characterized by comprising the following steps of: the method comprises the following steps:
S1, determining a proper mobile anchor node communication radius R according to the size and positioning timeliness requirements of a monitoring area of a wireless ad hoc network, wherein the number of layers n and the layer height h of the monitoring area are divided into a right-angled and an inverted right-angled triangle area unit which are alternately connected;
S2, continuously traversing the boundaries of all regular triangle area units of the monitoring area layer by layer and layer by layer in an end-to-end manner by a mobile anchor node with a GNSS positioning function, periodically broadcasting own position information in the moving process, and receiving the position information broadcast by the mobile anchor node and an RSSI value at the position by an unknown node;
S3, receiving three position data values forming a linear relation and RSSI values at the positions by unknown nodes in any regular triangle area unit, carrying out least square processing on the three groups of position data values to respectively obtain linear track equations of three boundaries of the regular triangle area unit, taking the intersection point of the linear track equations, namely the vertex of the regular triangle area unit as a reference node, broadcasting information position points of anchor nodes, namely the relative distance d between a beacon point and the reference node as an independent variable, carrying out curve fitting on the RSSI values and the relative distance d to respectively obtain track equations of an RSSI value increasing trend section and an RSSI value reducing trend section on each boundary of the regular triangle area unit, and calculating intersection points of two RSSI value polynomial equations to obtain RSSI peak point coordinates of the unknown nodes on three boundaries of the regular triangle area unit;
S4, obtaining coordinates of the unknown node through mathematical calculation according to the coordinates of the RSSI peak points of the unknown node on three sides of the regular triangle area unit;
the motion area of the mobile anchor node covers and is slightly larger than the monitoring area, and the relation between the communication radius R of the mobile anchor node and the side length L of the regular triangle area unit is as follows: r is larger than or equal to L;
The step S3 includes the following steps and calculation methods,
S31, respectively obtaining linear track equations of three boundaries of the regular triangle area unit according to a least square method, wherein the specific calculation method comprises the following steps:
when the mobile anchor node moves on three boundaries of the regular triangle area unit, the unknown node respectively obtains three geographic position coordinate sets of linear relations broadcasted by the mobile anchor node on the three boundaries, the position data set received on one boundary is (x i,yi), and a linear track equation is set as follows:
y＝k1x+b1 (1)
According to the least squares criterion, the optimal estimates of parameters k 1 and b 1 can be derived from the following equation:
Wherein,
And solving the linear track equation of the mobile anchor node on the other two boundaries by the same method: y=k 2x+b2 (3)
y＝k3x+b3 (4)
S32, solving intersection points of the three linear track equations obtained in the step S31 to obtain coordinates of three vertexes of the regular triangle area unit;
S33, calculating the relative distances d m1,dm2 and d m3 between the RSSI peak points of the mobile anchor nodes obtained by the unknown nodes in the motion process of each boundary of the mobile anchor nodes; the specific calculation method comprises the following steps:
Curve fitting is carried out on the relative distances d and the RSSI values of all the beacon points of the RSSI value increasing trend section and the RSSI value decreasing trend section on the same boundary respectively to obtain polynomial equations F (x) and P (x) of the RSSI value increasing trend section and the RSSI value decreasing trend section;
F(x)＝c0+c1x+c2x2+···+cjxj (5)
P(x)＝c0′+c1′x+c2′x2+···+cj′xj (6)
Solving simultaneous equations F (x) and P (x) to obtain an intersection point, and obtaining a relative distance value d m1 of the peak point M 1; the relative distances d m2 and d m3 of the RSSI peak points M 2 and M 3 on the other two boundaries are obtained by the same method;
S34, calculating coordinates of peak points M 1,M2 and M 3 through linear algebra and trigonometric functions according to the values of d m1,dm2 and d m3 and coordinates of three vertexes of the regular triangle area unit;
The step S4 comprises the following specific steps,
S41, obtaining a linear equation of the vertical lines L 1,L2 and L 3 taking the peak points M 1,M2 and M 3 as vertical points through linear algebraic calculation;
S42, calculating coordinates of intersection points C 1,C2 and C 3 of the perpendicular lines L 1,L2 and L 3 through linear algebra;
S43, obtaining a mean value of coordinate values of the intersection points C 1,C2 and C 3, and taking the mean value as the coordinate of the unknown node.
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