CN108769996B - Beacon node layout method for positioning and positioning method - Google Patents

Beacon node layout method for positioning and positioning method Download PDF

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CN108769996B
CN108769996B CN201810347500.0A CN201810347500A CN108769996B CN 108769996 B CN108769996 B CN 108769996B CN 201810347500 A CN201810347500 A CN 201810347500A CN 108769996 B CN108769996 B CN 108769996B
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beacon
nodes
positioning
beacon node
node
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CN108769996A (en
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赵宇
刘海伟
丛林
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Hangzhou Yixian Advanced Technology Co., Ltd.
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Hangzhou Yixian Advanced Technology Co ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/18—Network planning tools
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W16/00—Network planning, e.g. coverage or traffic planning tools; Network deployment, e.g. resource partitioning or cells structures
    • H04W16/22—Traffic simulation tools or models
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
    • H04W84/00—Network topologies
    • H04W84/18—Self-organising networks, e.g. ad-hoc networks or sensor networks

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  • Computer Networks & Wireless Communication (AREA)
  • Signal Processing (AREA)
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Abstract

The embodiment of the invention provides a beacon node layout method for positioning. The method comprises the following steps: pre-laying out beacon nodes in an area to be positioned, and modeling the signal coverage range of the beacon nodes; based on all sampling position points in the area to be positioned, adopting an integer linear programming method to approximately solve the minimum coverage problem of the beacon nodes, and obtaining the final layout of the beacon nodes with the minimum quantity and meeting the positioning requirement; and setting beacon nodes according to the final layout. By converting the layout problem of the minimum coverage beacon nodes into the integer linear programming problem, the method of the invention enables the obtained final layout of the beacon nodes to be in optimal distribution, thereby obviously reducing the layout cost of the beacon nodes, bringing better experience to users and reducing invalid calculation processes. In addition, the embodiment of the invention provides a positioning method.

Description

Beacon node layout method for positioning and positioning method
Technical Field
The embodiment of the invention relates to the field of beacon node layout, in particular to a beacon node layout method and a positioning method for positioning.
Background
This section is intended to provide a background or context to the embodiments of the invention that are recited in the claims. The description herein is not admitted to be prior art by inclusion in this section.
The minimum coverage problem, also called set coverage problem, can be described as, given a non-empty set U, and a set S consisting of subsets of n U, with the union of these n subsets being U, it is required to find a minimum subset C of S, such that the union of all sets in C is U. In an indoor positioning scenario, the problem may be changed to that many beacon nodes (e.g., iBeacon) are arranged in a three-dimensional space, a minimum of nodes are reserved, and meanwhile, a receiving end can receive signals of at least 3 (or other constants greater than 3) different beacon nodes at any position in the space, so that indoor positioning can be achieved by using 3-edge positioning (or multi-edge positioning).
Such a problem is usually an NP-Hard problem, which is difficult to solve, and a common method is often a greedy algorithm, as described in the paper, "greedy approximation algorithm for minimum coverage set of wireless sensor network", which can be described simply as selecting a sensor located at the center of a map from all sensors, calculating a coverage area, and then continuously adding new sensors to increase the coverage area to the maximum until the entire map is covered. The method cannot guarantee that the obtained result is optimal, the final result is greatly influenced by the selection of the initial sensor, and the algorithm in the method is only used for two-dimensional conditions and is ideal.
Meanwhile, the algorithm in the text is not suitable for the positioning problem because it cannot guarantee that the receiving end can receive the signals of more than 3 beacon nodes at any (or most) positions in the map. The beacon nodes positioned indoors are distributed in a three-dimensional space, and when the indoor area is large, the structure is complex, and the beacon nodes are distributed unevenly, a more efficient simulation method is needed to realize the optimal layout of the beacon nodes.
Disclosure of Invention
However, due to the problem of difficulty in solving the minimum coverage, the prior art cannot solve the problem of obtaining the optimal distribution of the beacon nodes.
Therefore, in the prior art, since no effective arrangement rule can be followed, the arrangement cost is increased due to unreasonable distribution of the positions of the beacons, and the arrangement efficiency of the beacons is affected, which is a very annoying process.
For this reason, an improved method for arranging beacons for positioning is needed, so that the beacons can meet the requirement of positioning at any position in the area to be positioned on the basis of the approximate optimal arrangement.
In this context, embodiments of the present invention are intended to provide a beacon node layout method and a positioning method for positioning.
In a first aspect of embodiments of the present invention, there is provided a beacon node layout method for positioning, including: pre-laying out beacon nodes in an area to be positioned, and modeling the signal coverage range of the beacon nodes; based on all sampling position points in the area to be positioned, adopting an integer linear programming method to approximately solve the minimum coverage problem of the beacon nodes, and obtaining the final layout of the beacon nodes with the minimum quantity and meeting the positioning requirement; and setting beacon nodes according to the final layout.
In another embodiment of the invention, the beacon nodes are pre-laid out based on a map of the area to be located.
In yet another embodiment of the invention, the map comprises a two-dimensional map or a three-dimensional map.
In yet another embodiment of the present invention, the pre-arrangement of the beacon nodes includes manual arrangement according to a predetermined rule.
In yet another embodiment of the present invention, the pre-arrangement of the beacon nodes includes randomly arranging the beacon nodes in a computer.
In yet another embodiment of the invention, said modeling of the signal coverage of the beacon comprises modeling based on signal attenuation characteristics of the beacon.
In yet another embodiment of the invention, modeling the signal coverage of the beacon nodes includes establishing a semi-circular signal coverage model for each beacon node with a first predetermined distance as a radius and towards an open area, in the case of a two-dimensional map.
In a further embodiment of the invention, modelling the signal coverage of the beacon nodes comprises establishing a hemispherical signal coverage model with a radius of the second predetermined distance for each beacon node and towards the open area, in the case of a three-dimensional map.
In a further embodiment of the invention, the sampling location points are obtained by means of random sampling.
In a second aspect of embodiments of the present invention, there is provided a positioning method, comprising:
setting the beacon nodes in the area to be positioned according to the beacon node layout method for positioning in advance;
and obtaining the positions of at least a predetermined number of beacon nodes according to the signals of the predetermined number of beacon nodes received by the position point to be positioned, and further determining the position of the position point to be positioned.
According to the beacon node layout method and the beacon node positioning method for positioning, provided by the embodiment of the invention, the beacon nodes can be pre-laid out, and then the integral linear programming method is adopted to solve the layout of the beacon nodes which is minimum in quantity and meets the positioning requirement. On the basis of pre-layout of the beacon nodes, the minimum coverage problem is solved, so that the calculation rule for selecting the layout position points of the beacon nodes can be followed, the sensor layout which cannot be guaranteed to be optimized is obtained through the overlapping calculation of the coverage areas of the beacon nodes on the basis of artificially selecting the basic beacon nodes, the layout cost of the beacon nodes is remarkably reduced, the invalid calculation process is reduced, the beacon nodes can be efficiently and reasonably arranged, the accurate positioning of any position point in an area to be positioned can be realized on the basis, and better experience is brought to users.
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The above and other objects, features and advantages of exemplary embodiments of the present invention will become readily apparent from the following detailed description read in conjunction with the accompanying drawings. Several embodiments of the invention are illustrated by way of example, and not by way of limitation, in the figures of the accompanying drawings and in which:
fig. 1 schematically illustrates a flowchart of an exemplary process of a beacon node placement method for positioning according to an embodiment of the present invention;
fig. 2 schematically illustrates a schematic diagram of manual or random placement of beacons on a known indoor map, according to one embodiment of the invention; wherein, the ellipses distributed on the outer contour of the indoor object model represent beacon nodes;
fig. 3 schematically illustrates a signal coverage model of a beacon node according to another embodiment of the invention;
fig. 4 schematically shows a flowchart of an exemplary process of a beacon node placement method for positioning according to another embodiment of the present invention;
fig. 5 schematically shows a flow chart of an exemplary process of a positioning method according to an embodiment of the present invention.
Detailed Description
The principles and spirit of the present invention will be described with reference to a number of exemplary embodiments. It is understood that these embodiments are given solely for the purpose of enabling those skilled in the art to better understand and to practice the invention, and are not intended to limit the scope of the invention in any way. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.
According to the embodiment of the invention, a beacon node layout method and a positioning method for positioning are provided.
In this document, it is to be understood that any number of elements in the figures are provided by way of illustration and not limitation, and any nomenclature is used for differentiation only and not in any limiting sense.
The principles and spirit of the present invention are explained in detail below with reference to several representative embodiments of the invention.
Summary of The Invention
The inventor finds that in the trilateration or multilateration field, the minimum coverage problem used is difficult to solve, and therefore a greedy algorithm is often adopted to determine the layout of the beacon nodes. For example, a beacon node is manually selected, the coverage area of the beacon node is calculated, and new beacon nodes are sequentially added until the area of the whole area to be located is covered. This approach is generally only applicable to positioning in two dimensions. However, due to the influence of the selected position of the initial beacon node, on one hand, the optimal layout of the beacon node (the minimum number of beacon nodes) cannot be guaranteed, and on the other hand, trilateral or multilateral positioning of any position point in the space cannot be guaranteed. Therefore, the positioning accuracy of the area to be positioned is affected and the positioning cost is increased.
The invention provides a beacon node layout method and a beacon node positioning method for positioning aiming at the positioning problem of spatial position points, which convert the layout problem of the beacon nodes with minimum coverage into an integer linear programming problem, thereby being capable of approximately obtaining the optimal distribution of the beacon nodes. The invention ensures that the beacon nodes are more reasonable in layout on the basis of meeting the positioning requirement, reduces the layout cost and improves the stability of space positioning.
Having described the general principles of the invention, various non-limiting embodiments of the invention are described in detail below.
Exemplary method
A beacon node placement method for positioning according to an exemplary embodiment of the present invention is described below with reference to fig. 1. It should be noted that the embodiments of the present invention are not limited by any application scenarios. Rather, embodiments of the present invention may be applied to any scenario where applicable.
Fig. 1 schematically illustrates an exemplary process flow 100 of a method for beacon node placement for positioning in accordance with an embodiment of the disclosure.
As shown in fig. 1, process flow 100 begins at S110 and then proceeds to step S120.
In step S120, the beacons may be first pre-laid out in the area to be located and the signal coverage of the beacons is modeled.
A beacon Node (Anchor Node) is a static set of nodes whose global or local locations are known. For example, a communication device (such as a smartphone or other device) using the iBeacon protocol, which is located at a plurality of known locations, may be used as the plurality of beacons. In the method, the positioning of any position point in an area to be positioned can be realized, and the positions of all the distributed beacon nodes are known; regarding how to arrange the beacon nodes so that the signals of the beacon nodes can fully cover the area to be positioned, the method is related to the type of the signals transmitted by the beacon nodes; therefore, a coverage model is established based on the type of signal transmitted by the beacon to provide a basis for subsequent determination of the topology of the beacon.
As an example, the area to be located may be any two-dimensional or three-dimensional space whose boundaries can be determined, including indoor spaces as well as outdoor spaces.
As an example, the beacon nodes may be pre-laid out based on a map of the area to be located. Compared with the method that the beacon nodes are directly distributed in the actual area to be positioned, the method has the advantage that the efficiency of solving the minimum coverage problem can be greatly improved by taking the map of the area to be positioned as a medium for determining the layout of the beacon nodes.
As an example, the map may be a construction map that can be directly acquired; or may be a map obtained by three-dimensional reconstruction of a building using means such as laser scanning. For maps constructed and obtained in different modes, as long as the calculated layout of the beacon nodes is not unreliable due to low precision, the construction mode of the maps does not influence the layout of the beacon nodes.
The map may comprise, as an example, a two-dimensional map or a three-dimensional map. That is, the layout method of the present disclosure is applicable to the layout of beacon nodes in any two-dimensional space or three-dimensional space where a boundary can be determined; even for the space with large area and complex structure, the beacon nodes can still be reasonably distributed by adopting the method of the invention.
In fact, the pre-arrangement of the beacon nodes is not always a completely non-principle arrangement, and generally needs to be performed based on the signal characteristics of the beacon nodes so as to at least meet the requirement of full signal coverage in the space to be located. In the pre-layout, the number of the beacon nodes can be relatively large, namely, on the basis of meeting the requirement that the signal fully covers the area to be positioned, the area covered by the signal superposition exists, and on the basis, redundant beacon nodes are removed through post-sequence calculation, so that the approximate optimal layout of the beacon nodes is favorably obtained. And the positioning requirement cannot be met due to the insufficient number of beacon nodes in the pre-layout.
As an example, the pre-arrangement of the beacon nodes comprises manual arrangement according to a predetermined rule. The beacon nodes in a manual mode are pre-arranged according to the signal coverage characteristics on the basis of the signal types of the beacon nodes, and the arrangement density of the beacon nodes is to enable signals to be at least partially overlapped in an area to be positioned.
As an example, the pre-arrangement of the beacon nodes further includes randomly arranging the beacon nodes by using a computer. The beacon nodes randomly arranged by the computer are generally realized based on the relevant distribution principle under the control of the relevant programs.
As an example, the above mentioned pre-placement of the beacons according to the characteristics of the signal coverage includes modeling the signal coverage of the beacons, and further includes modeling based on the signal attenuation characteristics of the beacons.
The signal coverage model of the beacon is determined by the type of beacon signal actually used, and the model closest to its actual signal coverage is preferably selected.
As an example, the signal transmitted by the beacon node may be an electromagnetic wave signal, and modeling the signal coverage of the signal may need to take into account the attenuation of the signal strength of the electromagnetic wave during transmission.
Since the beacon node layout method of the present disclosure is applicable to a two-dimensional or three-dimensional space, therefore:
as an example, modeling the signal coverage of a beacon includes establishing a semi-circular signal coverage model for each beacon, with a first predetermined distance as a radius, towards an open area, in the case of a two-dimensional map. Wherein the radius is selected based on the attenuation characteristics of the signal.
Similarly, as an example, modeling the signal coverage of the beacon nodes includes establishing a hemispherical signal coverage model with a radius of the second predetermined distance and toward the open area for each beacon node in the case of a three-dimensional map. Wherein the radius is also selected based on the attenuation characteristics of the signal.
It should be noted that the first predetermined distance and/or the second predetermined distance may also be set according to an empirical value, or may also be determined through an experimental method, which is not described herein again.
In addition, besides the semi-circle signal coverage model and the semi-sphere signal coverage model, the signal coverage model of the beacon node may also adopt other types of models, such as a sector signal coverage model or a rectangular signal coverage model.
Due to the fact that the two-dimensional space and the three-dimensional space are different in positioning dimension, the correspondingly established signal coverage model is also presented in a planar or stereoscopic form, such as a semicircular signal coverage model or a hemispherical signal coverage model.
As an example, as shown in connection with fig. 2, an indoor two-dimensional map of a building may first be obtained, which may be, but is not limited to, obtained by a CAD modeling method. In a two-dimensional indoor map, the indoor object 21 may be represented as a rectangle, a circle, or an irregular polygon (not all labeled in the figure). Then, arranging a large number of beacon nodes 22 (not all marked in the drawing) on the outline of the object 21 of the two-dimensional indoor map in a manual or computer random mode, wherein small ellipses on the outline of the object 21 in the drawing in FIG. 2 all represent the beacon nodes 22; assuming that the signal of the beacon 22 is an electromagnetic wave signal, the signal coverage of the beacon is modeled as a semicircle (a hemisphere in the case of three dimensions) having a radius r and facing an open area (a non-wall surface direction) in consideration of the intensity attenuation characteristic of the electromagnetic wave signal, as shown in fig. 3. Here, if the beacon transmits other types of signals, the other types of signal coverage models that match are considered.
After the signal coverage model of the beacon node is determined, step S130 may be performed next.
In step S130, an integer linear programming method may be adopted based on all sampling location points in the area to be located, to approximately solve the minimum coverage problem of the beacon node, and the solution result needs to satisfy the minimum number of the beacon nodes in the obtained final layout, and also can satisfy the location requirement at the same time.
In step S130, the minimum coverage problem is solved by using some selected sampling position points as the basis; the related integer linear programming method is an optimization algorithm in operation research, and optimized variables are integer variables.
Solving the problem of minimal coverage in this disclosure is also an NP-Hard problem, which is one of the most important complexity classes in computational complexity theory, referring to a problem that the correctness of a solution may not necessarily be verified in polynomial time. Therefore, the final layout solving problem of the beacon nodes is converted into the integer linear programming problem, so that the reliability of the calculation process is improved, and the solving efficiency is improved.
In the disclosure, the sampling position point is used as a reference for testing whether the beacon node can fully cover signals in the area to be positioned, and therefore, the determination of the sampling position point is also involved.
As an example, the sampling location points are obtained by means of random sampling. The sampling position points acquired by the random sampling mode have the opportunity of being selected because no artificial will is exerted, so that whether the coverage area of the beacon node signal meets the requirement or not can be judged relatively objectively.
As an example, the randomly sampling comprises randomly selecting a sampling location point on a map of the area to be located. Because the beacon node pre-layout of the present disclosure may be implemented on a map, the sampling location points may also be determined from the map as a basis for subsequent calculations.
As an example, the random sampling may include randomly selecting a sampling location point on a predetermined path or area. For example, the path or area where the sampling location point is located is defined according to the area where the receiving end, such as a person, often walks, within the area to be located; the sampling position points are determined in a targeted manner, so that the determined beacon node layout can meet the positioning requirement of a specific area, and the data processing efficiency is improved.
As an example, assuming that positioning at an arbitrary position in a space of 5 meters or more from the ground is to be achieved in a single three-dimensional space, since the layout of the beacon nodes in a determination area to be positioned in the single determination space is only required to satisfy the positioning in the determination area, the sampling position points may be selected entirely in a space of 5 meters or more from the ground.
After the pre-layout of the beacon nodes is completed and the sampling position points are determined, the solution of the minimum coverage problem of the beacon nodes is performed next.
As an example, a beacon may be represented by means of an indicator variable, each element of which represents the state of the respective beacon. This is a mathematical form of the beacon representation method used to participate in subsequent mathematical operations. Since the determination process of the final layout of the beacon nodes in the present disclosure is, in fact, a process of determining whether each beacon node is reserved or not by solving one by one, each element representation included in the indicator variable should be able to represent whether the corresponding beacon node is reserved or removed.
For the indicator variable, its initial value can be customized. Because the optimization problem of the indicating variable is a convex optimization problem, the selection of the initial value expression form does not influence the final solution result.
As an example, the initial value of all elements in the indicator variable may be selected to be 1. At the initial moment, all the pre-laid beacon nodes are used as solving objects of the minimum coverage problem, the initial value of an element in the selection indication variable is 1, and all the beacon nodes are in a reserved state at the moment. Accordingly, the beacon node determined to be deleted in the solving process will be modified to 0 in the indicator variable.
As an example, the indicator variable may be a multidimensional vector, and the dimension of the indicator variable is the same as the number of beacons. Since the positioning of the present disclosure requires at least three beacon nodes for trilateration, the number of dimensions of the indicator variable is at least three. If multilateration is required, the dimension of the indicator variable will change accordingly, and the number of beacon nodes to be set will also change accordingly.
Based on the specific mathematical representation form of the indicator variable, the solution of the beacon node minimum coverage problem can be further developed.
As an example, the approximating a minimum coverage problem for a beacon comprises approximating a minimum coverage problem for a beacon using iterative computations. In the present disclosure, since the layout condition of the beacon nodes is determined by the reception condition of the signals by a series of sampling location points, the process of determining the beacon nodes one by one is actually an iterative calculation process.
As an example, the approximating a minimum coverage problem for a beacon node using iterative computation includes approximating a solution indicator variable using iterative computation. That is, the determination process of the final layout of the beacon node is the change process of each element in the indication variable, and the final value of each element in the indication variable is determined, that is, the final layout of the beacon node is determined.
The result of the solution to the indicator variable is related to the reception of the beacon signal at each sampling location. As an example, the approximating a minimum coverage problem for a beacon includes observing signals of the beacon at all sampling locations, forming an observable matrix. In the process of forming the observable matrix, if the corresponding sampling position points are too few, it cannot be ensured that the obtained beacon node layout can meet the requirement of signal coverage in most areas, and too many sampling position points cause large calculation amount. The number of sampling points is therefore chosen on a case-by-case basis, and can be set empirically, for example, by a skilled person.
As an example, the method for representing the signal reception results of the beacons in the observable matrix includes representing that the corresponding beacon is an unobservable node for the current sampling location point by 0, and representing that the corresponding beacon is an observable node for the current sampling location point by 1.
And judging whether the signal of each beacon node of a certain sampling position point is receivable or not receivable, and in the iterative calculation for solving the indicating variable, determining the signal according to the position relation of the sampling position point relative to the certain beacon node.
As an example, the observable nodes include beacon nodes that have sampled location points within their signal coverage model. The receiving conditions of the sampling position points to the beacon node signals are represented as observable nodes and unobservable nodes in an observable matrix, so that subsequent further calculation is facilitated; if the current sampling position point is within the signal coverage range of the target beacon node, the beacon node is considered to be observable and is represented by 1; otherwise, the beacon node is considered to be unobservable for the current sampling location point, and is represented by 0.
As an example, based on the foregoing settings, a method for obtaining a final layout of a beacon node through a complete iterative solution may include:
firstly, the approximate solving of the indicator variable by adopting the iterative computation comprises the following steps:
presetting a weight vector corresponding to a beacon node, wherein each element in the weight vector represents the weight of the corresponding beacon node;
then, the dot product of the weight vector and the indicating variable is made as small as possible by iterative calculation, and the following conditions are made during the iterative calculation: making the number of observable nodes corresponding to each sampling position point greater than or equal to a predetermined number; and enabling the value of each element in the indication variable to be 0 or 1, wherein the element with the value of 1 represents that the beacon node corresponding to the element is reserved, and the element with the value of 0 represents that the beacon node corresponding to the element is deleted.
In the iterative calculation process, a concept of a weight vector is further introduced, and each element in the weight vector represents the weight of a corresponding beacon node, so that a nonzero value is taken; if the weight vector is zero, the corresponding beacon node is available or not, and the significance of setting the weight vector is lost.
It should be understood that the various vectors or matrices involved in the embodiments of the present invention are in the form only for explaining and describing the embodiments, and the specific forms of the various vectors or matrices are not limited to the forms mentioned in the embodiments.
As an example, to calculate the dot product of a weight vector and an indicator variable, the weight vector may take the form of a row vector, for example, and the indicator variable may take the form of a column vector; and vice versa. In addition, the weight vector and the indication variable may both be represented by column vectors or row vectors, and one of the column vectors or the row vectors (e.g., the weight vector or the indication variable) may be inverted before the dot product is calculated, and then the dot product is calculated.
The solution of the indicator variables is described below in a specific embodiment:
assuming that n beacon nodes are arranged on a map of a certain area to be positioned, and x represents an indication variable, x is a vector comprising n elements. For example, if n is 10,the final value of x may be: x ═ 1, 0, 0, 0, 0, 1, 0, 0, 1, 0)TThis means that only the beacon nodes No. 1, 6 and 9 are reserved in the final layout, which can satisfy the requirement of making the signals of the area to be positioned fully covered and the number is minimum, and satisfy the positioning requirement.
Taking a certain sampling position point P as an example, the receiving end is used to observe the beacon node signal at the point P, and for all beacon nodes around the sampling position point P, the beacon node whose distance between the two is less than the stable signal transmission range can be used as an observable node. For example, taking a beacon node of a semicircular signal coverage model as an example, a beacon node with a distance smaller than the radius r of the model is taken as an observable node. Assuming that there are m sampling location points and a denotes an observable matrix, a may be a matrix of m rows and n columns, where each row records observations of one sampling location point on n beacons, 1 denotes observable, 0 denotes unobservable, e.g., one of the elements aij1 may indicate that the ith sampling point receives the signal of the jth beacon. After m times of sampling is completed, the observable matrix A is completely constructed, and then the problem of optimizing the beacon node layout can be converted into an integer linear programming problem:
min qTx，
s.t.Ax≥b，
x∈{0，1}n，
where q represents a weight vector, which is also an n-dimensional vector (e.g., an n-dimensional column vector), and each element represents the weight of the corresponding beacon node, if not specifically required, it may be assumed that all elements in q are equal to 1. b is a predetermined multi-dimensional vector, and each element in b is a non-negative integer, and the dimension of b is equal to the number of all sampling location points, i.e. b is an m-dimensional vector (e.g. an m-dimensional column vector), each element represents at least the number of beacons that need to be received per sampling, and all elements in b can be generally set to 3.
Thus, min qTx represents such that qTThe dot product with x is as small as possible. Ax ≧ b denotes a value at which each element in the dot product of A and x is made greater than or equal to a predetermined number, e.g., as indicated in bWhen there are all 3 elements, Ax ≧ b means that the value of each element in the dot product of A and x is made greater than or equal to 3. x is formed by {0, 1}nRepresenting that each element in x takes a value of 1 or 0.
And solving the optimization problem to obtain a solution of the indicator variable x, and if one element is 0, deleting the corresponding preset beacon node in the map, wherein the rest beacon nodes are the optimal distribution in the map and the sampling mode. Step S140 may be performed next.
In step S140, according to the obtained solution of the indicator variable, the beacon nodes are arranged at the corresponding positions of the area to be located, i.e. the final layout of the beacon nodes is completed. Then, step S150 is performed.
Process flow 100 ends at S150.
For the pre-arranged beacon nodes, in some cases, the final arrangement of the beacon nodes meeting the minimum number and positioning requirements cannot be obtained under the current pre-arrangement situation due to the arrangement mode problem. I.e., the initial distribution of beacons may not satisfy the requirement for a certain sampling location point to receive 3 or more beacon signals, which results in the above-mentioned optimization problem being solved, and in order to solve this problem, a relaxation variable is introduced below.
As an example, in the optimization process of the minimum coverage problem, a slack variable may be introduced, and the slack variable may be an m-dimensional vector for guiding to increase the beacon nodes to be arranged when the pre-arranged beacon nodes cannot meet the positioning requirement of the partial sampling location points. In the process of participating in the solution of optimization through the relaxation variables, the beacon nodes can be additionally arranged under the condition that the pre-arrangement of the beacon nodes is unreasonable and the guidance of directivity is provided.
As an example, the directing of incremental placement of beacons includes directing of incremental placement of a number of beacons. The number of the beacon nodes needing to be added is determined by the corresponding value of the slack variable obtained by solving.
As an example, the guided augmentation arrangement beacon includes a beacon location of a guided augmentation arrangement. The positions of the beacon nodes which need to be additionally arranged cannot be accurately determined, but an approximate range is determined by sampling position points corresponding to corresponding values of the relaxation variables, and then the approximate range is determined by combining a signal coverage range model of the beacon nodes.
For example, the value of the first row element in the slack variable is calculated to be 2, which means that in the vicinity of the sampling position point corresponding to the first row of the observable matrix a, 2 more beacons need to be added to meet the positioning requirement, i.e. the later mentioned requirement greater than or equal to b is met. The distance between the 2 beacons is determined by a signal coverage range model, and if the coverage radius is r, the distance between the 2 beacons needs to be smaller than or equal to r.
As an example, a method of beacon node placement including a slack variable may include:
firstly, the approximate solving of the indicator variable by using the iterative computation includes:
presetting a weight vector corresponding to the beacon node, wherein each element of the weight vector represents the weight of the corresponding beacon node;
the sum of the dot product of the weight vector and the indication variable and the dot product of the preset constant vector and the relaxation variable is made as small as possible through iterative calculation, and the following conditions are satisfied during the iterative calculation: the sum of the number of observable nodes corresponding to each sampling position point and the corresponding element value in the relaxation variable is larger than or equal to a preset number; making the value of each element in the indicator variable be 0 or 1, wherein the element with the value of 1 represents that the beacon node corresponding to the element is reserved, and the element with the value of 0 represents that the beacon node corresponding to the element is deleted; and making the value of each element in the relaxation variable a non-negative integer;
the relaxation variable is a multidimensional vector, and the dimension of the relaxation variable is equal to the number of all sampling position points, namely the number of rows of the observable matrix.
Here, compared to the previously mentioned beacon placement method, the deployment of beacons determined by slack variables is added, which will be combined with the deployed beacons to meet the signal reception requirements at each sampling location point.
For example, a dot product of the weight vector and the indicator variable is defined as a first dot product, a dot product of the predetermined constant vector and the relaxation variable is defined as a second dot product, and the sum of the first dot product and the second dot product is defined as a sum of the dot products of the weight vector and the indicator variable and the dot products of the predetermined constant vector and the relaxation variable.
As an example, to calculate the dot product of a weight vector and an indicator variable, the weight vector may take the form of a row vector, for example, and the indicator variable may take the form of a column vector; and vice versa. Similarly, to calculate the dot product of the predetermined constant vector and the slack variable, the predetermined constant vector may take the form of a row vector, for example, and the slack variable may take the form of a column vector; and vice versa.
For example, the weight vector, the indication variable, the predetermined constant vector and the relaxation variable may all be expressed in a column vector or a row vector, and before the first dot product and the second dot product are calculated, the first dot product is calculated after the weight vector and one of the indication variables (such as the weight vector or the indication variable) are rotated, and the second dot product is calculated after the predetermined constant vector and one of the relaxation variables (such as the predetermined constant vector or the relaxation variable) are rotated. The following describes a specific embodiment of the solution method of the indicating variable with the slack variable added:
firstly, approximate solving of indicator variables by iterative computation comprises the following steps:
based on an observable matrix, converting the pre-layout beacon node optimization problem into an integer linear programming problem, wherein an optimization equation is as follows:
min qTx+∈1Tγ，
s.t.Ax+γ≥b，
x∈{0，1}n，
γ∈{Z+∪{0}}m，
wherein γ represents a relaxation variable; e is a constant scalar coefficient, and can be set according to an empirical value or determined through experiments; 1TRepresenting the transpose of a vector whose elements are all 1 (a vector whose elements are all 1 as an example of a preset constant vector), for example, 1 when γ is an m-dimensional column vectorTFor exampleA transpose of an m-dimensional column vector representing one element all as 1; z+Represents a positive integer; n represents the number of all beacon nodes; m represents the number of all sampled location points.
Thus, min qTx+∈1TGamma denotes such that qTDot product with x (equivalent to the first dot product described above) and 1TThe sum obtained by adding the dot product of γ (corresponding to the second dot product described above) is as small as possible. Ax + γ ≧ b denotes that the sum of the value of each element in the dot product of A and x and the value of the corresponding element in γ is greater than or equal to a predetermined number, for example, when all the elements in b are 3, Ax + γ ≧ b denotes that the sum of the value of each element in the dot product of A and x and the value of the corresponding element in γ is greater than or equal to 3. x is formed by {0, 1}nRepresenting that each element in x takes a value of 1 or 0. Gamma e { Z ∈+∪{0}}mThe value of each element in gamma is expressed as a non-negative integer. Therefore, when some sampling points cannot meet the requirement of the minimum receiving number, the corresponding element in the gamma is larger than 0, and the approximate position and the number of the beacon nodes needing to be added can be approximately determined according to the guidance of the position and the number of the sampling position points corresponding to the element in the gamma.
And further combining the actual positioning requirement, determining whether the layout of the beacon nodes meets the application requirement according to the proportion of the sampling position points capable of normally receiving the beacon node signals to all the sampling position points.
As an example, the positioning requirements include: enabling at least a first threshold percentage of the sampling location points within the area to be located to receive signals from at least a predetermined number of beacon nodes. For example, in a place where the use requirement can be satisfied only by approximate positioning, a relatively low first threshold value can be set, and the first threshold value is a ratio of sampling position points where signals can be normally received to the number of all sampling position points; otherwise, a relatively high first threshold value needs to be set.
As an example, the first threshold may range from 80% to 100%. This range is defined in accordance with the actual usage requirement, and may be, for example, 80%, 85%, 90%, 95%, or 100%.
It should be noted that the predetermined number may be a non-negative integer, such as 0, 1, 2, 3, 4, or 5. For example, when the positioning in the present disclosure is based on a trilateral positioning or more, the value of the element in b is at least 3, in which case the predetermined number may be at least 3 (i.e., an integer greater than or equal to 3) to satisfy the above positioning requirement.
Since the positioning in the present disclosure is based on trilateral positioning or multilateral positioning, the value of the element in b is at least 3, i.e. the predetermined number is at least 3 to meet the positioning requirement.
Considering that in the actual positioning process, it is possible that the pre-arranged beacons cannot meet the positioning requirement, this situation is solved by adding the slack variable mentioned above, and it may also be tried to re-arrange the beacons; in another case, after the slack variable is increased, the placement of the beacons may still not meet the positioning requirement, and the placement of the beacons may be tried again.
Fig. 4 schematically illustrates a process flow 200 of another example of a beacon node placement method for positioning according to an embodiment of the disclosure.
As shown in fig. 4, process flow 200 begins at S210 and then proceeds to step S220.
The processing of step S220 may be the same as the processing corresponding to step S120 in the processing flow 100 described above with reference to fig. 1, and similar functions and effects can be achieved, which is not described again here. And then S230 is performed.
The process of step S230 may also be the same as the process of corresponding step S130 in the process flow 100 described above in connection with fig. 1, and similar functions and effects can be achieved. Step S230 is different from step S130 in that step S230 determines the processing result of step S130, determines whether the final layout of the beacon nodes satisfying the positioning requirement with the minimum number can be obtained after the processing means of step S130, if so, step S250 is executed, and the processing flow 200 ends at step S260; the processing of step S250 may also be the same as the processing of step S140 in the processing flow 100 described above with reference to fig. 1, and is not repeated here.
Otherwise, step S240 is executed: and when the pre-layout of the current beacon nodes cannot meet the positioning requirements of part of the sampling position points, re-layout is carried out on the beacon nodes, and then the minimum coverage problem of the re-laid beacon nodes is solved based on all the sampling position points until the final layout of the beacon nodes with the minimum quantity and meeting the positioning requirements of all the sampling position points is obtained. Step S240 is to solve the indication variable by the same technical means as the processing flow 100 described above after the beacon nodes are rearranged for the remedy means under the condition that the beacon nodes are not rationally arranged until the reasonable final arrangement of the beacon nodes is obtained; step S250 may then be performed and the final process flow 200 ends at step S260.
As an example, the step of rearranging the beacon nodes may include one of the following three ways:
changing the position of at least part of the current beacon nodes; adding one or more beacon nodes; one or more beacons are removed.
When the three modes are used independently and cannot meet the requirement of the rearrangement of the beacon nodes, any two modes can be combined to realize the rearrangement of the beacon nodes; or combine the three approaches together to implement the re-arrangement of the beacon node.
In one example, assume that the original beacon includes P1、P2、P3And P4When the beacon nodes need to be rearranged, for example, a new beacon node P may be added5Or may change the beacon node P3And P4Or a new beacon node P may be added5While changing the beacon node P3And P4Or a new beacon node P may be added5And change the beacon node P3And P4While removing the beacon P1And so on.
The method efficiently and approximately solves the problem of minimum coverage of beacon nodes in three-dimensional and two-dimensional spaces by modeling the signal range of the beacon nodes and adopting a random sampling and integer linear programming method, so that the finally obtained beacon node layout can meet the requirement of positioning while meeting the minimum quantity, and a receiving end can be ensured to receive signals of three or more different beacon nodes at most positions of an area to be positioned.
Fig. 5 schematically illustrates an exemplary process flow 300 of a positioning method according to an embodiment of the disclosure.
The process flow 300 begins at step S310, where step S310 is substantially equivalent to the process flow 100 of the method for beacon node placement for positioning, and then step S320 is performed.
In step S320, positioning of an arbitrary position point in the region to be positioned can be achieved. Positioning any position point in the space according to the principle of trilateral positioning or multilateral positioning, and calculating the position of the beacon node to obtain the position of the beacon node; therefore, the beacon nodes corresponding to at least a predetermined number of beacon node signals received by the current to-be-positioned point are determined, and then calculation is performed according to the position information of the corresponding beacon nodes to determine the position of the current to-be-positioned point. Taking trilateral positioning as an example, for a position point to be positioned, signals of at least three beacon nodes can be received, and since the positions of the three beacon nodes are known, the coordinate position of the position point to be positioned can be obtained through calculation after the distances between the position point to be positioned and the three beacon nodes are respectively obtained. Step S330 is performed next.
Process flow 300 ends at step S330.
According to the method, after reasonable beacon node layout is obtained, the beacon nodes can be actually arranged in the area to be positioned according to the calculation result, and the positioning stability of any position point in a definable space is realized on the basis of reducing the beacon node arrangement cost.
Although the processes of the method of the present invention are depicted in the drawings in a particular order, this does not require or imply that all of the operations must be performed in this particular order to achieve desirable results. Additionally or alternatively, certain steps may be omitted, multiple steps combined into one step execution, and/or one step broken down into multiple step executions.
While the spirit and principles of the invention have been described with reference to several particular embodiments, it is to be understood that the invention is not limited to the disclosed embodiments, nor is the division of aspects, which is for convenience only as the features in such aspects may not be combined to benefit. The invention is intended to cover various modifications and equivalent arrangements included within the spirit and scope of the appended claims.
In summary, in the embodiments according to the present disclosure, the present disclosure provides the following solutions, but is not limited thereto:
scheme 1. a beacon node placement method for positioning, comprising:
pre-laying out beacon nodes in an area to be positioned, and modeling the signal coverage range of the beacon nodes; and
based on all sampling position points in the area to be positioned, an integer linear programming method is adopted to approximately solve the minimum coverage problem of the beacon nodes, and the final layout of the beacon nodes with the minimum quantity and meeting the positioning requirement is obtained;
and finally, setting the beacon nodes according to the final layout.
Scheme 2. according to the beacon node layout method for positioning in scheme 1, the beacon nodes are pre-laid based on a map of an area to be positioned.
Scheme 3. the beacon node layout method for positioning according to scheme 2, wherein the map comprises a two-dimensional map or a three-dimensional map.
Scheme 4. according to the beacon node layout method for positioning in any one of schemes 1 to 3, the pre-layout manner of the beacon nodes comprises manual arrangement according to a predetermined rule.
Scheme 5. according to the beacon node layout method for positioning of any one of schemes 1 to 3, the pre-layout manner of the beacon nodes includes random arrangement by a computer.
Scheme 6. the beacon node placement method for positioning according to any of the schemes 1 to 5, wherein the modeling of the signal coverage of the beacon node comprises modeling based on signal attenuation characteristics of the beacon node.
Scheme 7. according to the beacon node layout method for positioning of any one of schemes 3 to 6, modeling the signal coverage of the beacon nodes includes establishing a semicircular signal coverage model with a first predetermined distance as a radius and towards an open area for each beacon node in the case of a two-dimensional map.
Scheme 8. according to the beacon node layout method for positioning of any one of schemes 3 to 6, modeling the signal coverage of the beacon nodes includes establishing a hemispherical signal coverage model with a radius of the second predetermined distance as a radius and toward an open area for each beacon node in the case of a three-dimensional map.
Scheme 9. according to the beacon node layout method for positioning in any one of schemes 1 to 8, the sampling position points are obtained by means of random sampling.
Scheme 10. according to the beacon node layout method for positioning in scheme 9, the random sampling includes randomly selecting a sampling location point on a map of the area to be positioned.
Scheme 11. the beacon node placement method for positioning according to scheme 10, wherein the random sampling includes randomly selecting a sampling location point on a predetermined path or area.
Scheme 12. the beacon node placement method for positioning according to any one of schemes 1 to 11, the beacon nodes are represented by indicator variables, each element of the indicator variables representing a state of the corresponding beacon node.
Scheme 13. according to the beacon node layout method for positioning in scheme 12, the initial value of all elements in the indicator variable is 1.
Scheme 14. according to the beacon node placement method for positioning in scheme 12 or 13, the indicator variable is a multidimensional vector, and the number of dimensions of the indicator variable is the same as the number of beacon nodes.
Scheme 15. the method for arranging beacons according to any of schemes 12 to 14, wherein the approximately solving the minimum coverage problem of the beacons includes approximately solving the minimum coverage problem of the beacons by iterative computation.
Scheme 16. according to the beacon node layout method for positioning in scheme 15, the approximating a minimum coverage problem for a beacon node using iterative computation includes approximating a solution indicator variable using iterative computation.
Scheme 17. according to the beacon node layout method for positioning in scheme 15 or 16, the approximate solution of the minimum coverage problem of the beacon node includes observing signals of the beacon node at all sampling positions to form an observable matrix.
Scheme 18. according to the beacon node layout method for positioning in scheme 17, the elements in the observable matrix represent beacon node signal reception results observed by all sampling location points.
Scheme 19. according to the beacon node layout method for positioning according to scheme 18, the method for representing the signal reception results of the beacon nodes in the observable matrix includes that a corresponding beacon node is an unobservable node for the current sampling location point by 0, and a corresponding beacon node is an observable node for the current sampling location point by 1.
Scheme 20. according to the beacon node layout method for positioning of scheme 19, the observable nodes include beacon nodes having sampling location points within their signal coverage model.
Scheme 21. the beacon node placement method for positioning according to any one of schemes 16 to 20,
the approximate solution of the indicator variable by adopting iterative computation comprises the following steps:
presetting a weight vector corresponding to a beacon node, wherein each element in the weight vector represents the weight of the corresponding beacon node;
the dot product of the weight vector and the indicator variable is made as small as possible by iterative calculation, and the following conditions are made during the iterative calculation: making the number of observable nodes corresponding to each sampling position point greater than or equal to a predetermined number; and enabling the value of each element in the indication variable to be 0 or 1, wherein the element with the value of 1 represents that the beacon node corresponding to the element is reserved, and the element with the value of 0 represents that the beacon node corresponding to the element is deleted.
Scheme 22. according to the beacon node placement method for positioning of scheme 21,
the approximate solution of the indicator variable by adopting iterative computation comprises the following steps:
based on an observable matrix, converting the pre-layout beacon node optimization problem into an integer linear programming problem:
min qTx，
s.t.Ax≥b，
x∈{0，1}n，
wherein q represents a weight vector, x represents an indicator variable, a represents an observable matrix, b is a preset multi-dimensional vector, each element in b is a non-negative integer, and the dimension of b is equal to the number of all sampling position points; n represents the number of all beacons.
Scheme 23. the beacon node placement method for positioning according to any one of schemes 16 to 20,
and the relaxation variable is used for guiding the increase of the arranged beacon nodes when the pre-arranged beacon nodes cannot meet the positioning requirement of the partial sampling position points.
Scheme 24. according to the beacon node placement method for positioning of scheme 23,
the directing incremental placement of beacons includes directing incremental placement of a number of beacons.
Scheme 25. according to the beacon node placement method for positioning described in scheme 23 or 24,
the guided incremental placement beacons include guided incremental placement beacon locations.
Scheme 26. the beacon node placement method for positioning according to any one of schemes 23 to 25,
the approximate solution of the indicator variable by adopting iterative computation comprises the following steps:
presetting a weight vector corresponding to the beacon node, wherein each element of the weight vector represents the weight of the corresponding beacon node;
the sum of the dot product of the weight vector and the indication variable and the dot product of the preset constant vector and the relaxation variable is made as small as possible through iterative calculation, and the following conditions are satisfied during the iterative calculation: the sum of the number of observable nodes corresponding to each sampling position point and the corresponding element value in the relaxation variable is larger than or equal to a preset number; making the value of each element in the indicator variable be 0 or 1, wherein the element with the value of 1 represents that the beacon node corresponding to the element is reserved, and the element with the value of 0 represents that the beacon node corresponding to the element is deleted; and making the value of each element in the relaxation variable a non-negative integer;
wherein, the relaxation variable is a multidimensional vector, and the dimension of the relaxation variable is equal to the number of all sampling position points.
Scheme 27, the beacon node placement method for positioning according to scheme 26,
the approximate solution of the indicator variable by adopting iterative computation comprises the following steps:
based on an observable matrix, converting the pre-layout beacon node optimization problem into an integer linear programming problem:
min qTx+∈1Tγ，
s.t.Ax+γ≥b，
x∈{0，1}n，
γ∈{Z+∪{0}}m，
wherein q represents a weight vector, x represents an indicator variable, a represents an observable matrix, and γ represents a relaxation variable; b is a preset multi-dimensional vector, each element in b is a non-negative integer, and the dimension of b is equal to the number of all sampling position points; e is a constant scalar quantity, Z+Represents a positive integer; n represents the number of all beacon nodes; m represents the number of all sampled location points.
The beacon node placement method for positioning according to any one of claims 1 to 27, wherein the positioning requirement includes:
enabling at least a first threshold percentage of the sampling location points within the area to be located to receive signals from at least a predetermined number of beacon nodes.
In an aspect 29, according to the beacon node layout method for positioning in aspect 28, a value of the first threshold ranges from 80% to 100%.
Scheme 30. the method for beacon node placement for positioning according to any one of schemes 21 to 29, the predetermined number being 3.
Scheme 31. the beacon node placement method for positioning according to any one of schemes 1 to 30, further comprising:
and when the pre-layout of the current beacon nodes cannot meet the positioning requirements of part of the sampling position points, re-layout is carried out on the beacon nodes, and then the minimum coverage problem of the re-laid beacon nodes is solved based on all the sampling position points until the final layout of the beacon nodes with the minimum quantity and meeting the positioning requirements of all the sampling position points is obtained.
Scheme 32. according to the beacon node placement method for positioning of scheme 31, the step of re-placing the beacon nodes includes:
changing the position of at least part of the current beacon nodes; and/or
Adding one or more beacon nodes; and/or
One or more beacons are removed.
Scheme 33. a positioning method, comprising:
setting beacon nodes in an area to be positioned according to the beacon node layout method for positioning in any one of the schemes 1 to 32 in advance;
and obtaining the positions of at least a predetermined number of beacon nodes according to the signals of the predetermined number of beacon nodes received by the position point to be positioned, and further determining the position of the position point to be positioned.

Claims (25)

1. A method for arranging beacons for positioning, comprising:
pre-laying out beacon nodes in an area to be positioned, and modeling the signal coverage range of the beacon nodes; and
based on all sampling position points in the area to be positioned, an integer linear programming method is adopted to approximately solve the minimum coverage problem of the beacon nodes, and the final layout of the beacon nodes with the minimum quantity and meeting the positioning requirement is obtained, wherein the method comprises the following steps:
representing the beacons with indicator variables, each element in the indicator variables representing the state of the respective beacon;
approximately solving the indicator variable by adopting iterative computation to approximately solve the minimum coverage problem of the beacon node;
setting beacon nodes according to the final layout;
the approximate solving of the minimum coverage problem of the beacon nodes comprises observing signals of the beacon nodes at all sampling positions to form an observable matrix;
elements in the observable matrix represent beacon node signal receiving results obtained by observing all sampling position points;
the method for representing the signal receiving result of the beacon node in the observable matrix comprises the steps of representing that the corresponding beacon node is an unobservable node aiming at the current sampling position point by 0, and representing that the corresponding beacon node is an observable node aiming at the current sampling position point by 1;
the approximate solution of the indicator variable by adopting iterative computation comprises the following steps:
presetting a weight vector corresponding to a beacon node, wherein each element in the weight vector represents the weight of the corresponding beacon node;
the dot product of the weight vector and the indicator variable is made as small as possible by iterative calculation, and the following conditions are made during the iterative calculation: making the number of observable nodes corresponding to each sampling position point greater than or equal to a predetermined number; and making the value of each element in the indicator variable be 0 or 1, wherein the element with the value of 1 represents that the beacon node corresponding to the element is reserved, and the element with the value of 0 represents that the beacon node corresponding to the element is deleted;
based on an observable matrix, converting the pre-layout beacon node optimization problem into an integer linear programming problem:
min qTx，
s.t.Ax≥b，
x∈{0，1}n，
wherein q represents a weight vector, X represents an indicator variable, A represents an observable matrix, b is a preset multi-dimensional vector, each element in b is a non-negative integer, and the dimension of b is equal to the number of all sampling position points; n represents the number of all beacons.
2. A beacon node placement method for positioning according to claim 1, characterized in that: the beacon nodes are pre-arranged based on a map of an area to be positioned.
3. The beacon node placement method for positioning according to claim 2, wherein: the map comprises a two-dimensional map or a three-dimensional map.
4. A beacon node placement method for positioning according to any one of claims 1 to 3, characterized by: the pre-arrangement mode of the beacon nodes comprises manual arrangement according to a preset rule.
5. A beacon node placement method for positioning according to any one of claims 1 to 3, characterized by: the pre-arrangement mode of the beacon nodes comprises the step of randomly arranging by adopting a computer.
6. A beacon node placement method for positioning according to any one of claims 1 to 3, characterized by: the modeling of the signal coverage of the beacon comprises modeling based on signal attenuation characteristics of the beacon.
7. A beacon node placement method for positioning according to claim 3, characterized in that: modeling the signal coverage of the beacon nodes includes establishing a semi-circular signal coverage model for each beacon node with a first predetermined distance as a radius and towards an open area, in the case of a two-dimensional map.
8. A beacon node placement method for positioning according to claim 3, characterized in that: modeling the signal coverage of the beacon nodes includes establishing a hemispherical signal coverage model for each beacon node with a second predetermined distance as a radius and towards the open area, in the case of a three-dimensional map.
9. A beacon node placement method for positioning according to any one of claims 1 to 3, characterized by: the sampling position points are obtained by means of random sampling.
10. The beacon node placement method for positioning according to claim 9, wherein: the random sampling comprises randomly selecting a sampling location point on a map of the area to be located.
11. A beacon node placement method for positioning according to claim 10, characterized in that: the random sampling comprises randomly selecting a sampling location point on a predetermined path or area.
12. A beacon node placement method for positioning according to claim 1, characterized in that: the initial value of all elements in the indicator variable is 1.
13. A beacon node placement method for positioning according to claim 1, characterized in that: the indicating variable is a multi-dimensional vector, and the dimension of the indicating variable is the same as the number of the beacon nodes.
14. A beacon node placement method for positioning according to claim 1, characterized in that: the observable nodes include beacon nodes that place the sampling location points within their signal coverage model.
15. A beacon node placement method for positioning according to claim 1, characterized in that:
and the relaxation variable is used for guiding the increase of the arranged beacon nodes when the pre-arranged beacon nodes cannot meet the positioning requirement of the partial sampling position points.
16. The beacon node placement method for positioning according to claim 15, wherein:
the directing incremental placement of beacons includes directing incremental placement of a number of beacons.
17. The beacon node placement method for positioning according to claim 15, wherein:
the guided incremental placement beacons include guided incremental placement beacon locations.
18. The beacon node placement method for positioning according to claim 15, wherein:
the approximate solution of the indicator variable by adopting iterative computation comprises the following steps:
presetting a weight vector corresponding to the beacon node, wherein each element of the weight vector represents the weight of the corresponding beacon node;
the sum of the dot product of the weight vector and the indication variable and the dot product of the preset constant vector and the relaxation variable is made as small as possible through iterative calculation, and the following conditions are satisfied during the iterative calculation: the sum of the number of observable nodes corresponding to each sampling position point and the corresponding element value in the relaxation variable is larger than or equal to a preset number; making the value of each element in the indicator variable be 0 or 1, wherein the element with the value of 1 represents that the beacon node corresponding to the element is reserved, and the element with the value of 0 represents that the beacon node corresponding to the element is deleted; and making the value of each element in the relaxation variable a non-negative integer;
wherein, the relaxation variable is a multidimensional vector, and the dimension of the relaxation variable is equal to the number of all sampling position points.
19. A beacon node placement method for positioning according to claim 18, characterized in that:
the approximate solution of the indicator variable by adopting iterative computation comprises the following steps:
based on an observable matrix, converting the pre-layout beacon node optimization problem into an integer linear programming problem:
min qTx+∈1Tγ，
s.t.Ax+γ≥b，
x∈{0，1}n
γ∈{Z+∪{0}}m，
wherein q represents a weight vector, X represents an indicator variable, a represents an observable matrix, and γ represents a relaxation variable; b is a preset multi-dimensional vector, each element in b is a non-negative integer, and the dimension of b is equal to the number of all sampling position points; e is a constant scalar quantity, Z+Represents a positive integer; n represents the number of all beacon nodes; m represents the number of all sampled location points.
20. A method as claimed in any one of claims 1 to 3, wherein the location requirements include:
enabling at least a first threshold percentage of the sampling location points within the area to be located to receive signals from at least a predetermined number of beacon nodes.
21. The method of claim 20, wherein the first threshold value ranges from 80% to 100%.
22. A beacon node placement method for positioning according to claim 1, characterized in that said predetermined number is 3.
23. A beacon node placement method for positioning according to any one of claims 1 to 3, further comprising:
and when the pre-layout of the current beacon nodes cannot meet the positioning requirements of part of the sampling position points, re-layout is carried out on the beacon nodes, and then the minimum coverage problem of the re-laid beacon nodes is solved based on all the sampling position points until the final layout of the beacon nodes with the minimum quantity and meeting the positioning requirements of all the sampling position points is obtained.
24. The method of claim 23, wherein the step of replanning beacons comprises:
changing the position of at least part of the current beacon nodes; and/or
Adding one or more beacon nodes; and/or
One or more beacons are removed.
25. A method of positioning, comprising:
the setting of the beacon nodes in the area to be positioned is completed in advance according to the beacon node layout method for positioning in any one of claims 1 to 24;
and obtaining the positions of at least a predetermined number of beacon nodes according to the signals of the predetermined number of beacon nodes received by the position point to be positioned, and further determining the position of the position point to be positioned.
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