Rapid positioning method and device for sensor network, terminal and storage medium

Abstract

The invention discloses a sensor network-oriented rapid positioning method and device, a terminal and a storage medium, which can improve the positioning speed of a linear positioning method. The method comprises the following steps: on a two-dimensional plane, establishing linear constraint equations corresponding to three measurement quantities of distance, azimuth angle and angle; constructing a first linear positioning algorithm corresponding to the linear constraint equation by adopting a least square method; in order to improve the speed of obtaining the real position of a sensor node by a first linear positioning algorithm, a linear constraint condition is set, and when the sensor node meets the linear constraint condition, a decision variable is introduced into a first positioning matrix of a sensor network to generate a second positioning matrix; constructing a positioning speed model by adopting the minimum characteristic value of the second positioning matrix; solving the optimal solution of the positioning speed model by adopting the designed centralized optimization algorithm or distributed optimization algorithm; and obtaining a target position of each free node in the sensor network based on the optimal solution, the first positioning matrix and a first linear positioning algorithm.

Description

Technical Field

[0001] The present invention relates to the technical field of system positioning, and more specifically, to a sensor network-oriented rapid positioning method, device, terminal and storage medium. Background Art

[0002] The sensor network positioning method usually uses a linear positioning method to determine the target position of the free node in the sensor network. This linear positioning method determines the network locatable topological conditions by establishing a linear constraint equation under two-dimensional spatial angle measurement; using the network locatable topological conditions, a sensor network is established, and sensors are configured with triangles as unit nodes, and the inner angle of the triangle is obtained through the Bluetooth direction finding function; based on the linear constraint equation under two-dimensional spatial angle measurement, combined with the inner angle of the triangle, the target position of the free node in the sensor network is obtained. This linear positioning method models the positioning problem as a problem of solving a linear equation. However, this linear positioning method has a major defect, that is, the positioning speed is slow, which makes the sensor network not suitable for application scenarios with high positioning speed requirements, reducing the user experience. Summary of the invention

[0003] The purpose of the embodiments of the present application is to provide a fast positioning method, device, terminal and storage medium for sensor networks, which can improve the positioning speed of the linear positioning method. The embodiments of the present application are mainly implemented by the following technical solutions:

[0004] A first aspect of an embodiment of the present application provides a rapid positioning method for a sensor network, comprising:

[0005] On a two-dimensional plane, establish the distance measurement linear constraint equation, azimuth measurement linear constraint equation and angle measurement linear constraint equation between each sensor node in the sensor network and its neighboring nodes in the corresponding local coordinate system;

[0006] A first linear positioning algorithm corresponding to the distance measurement linear constraint equation, the azimuth measurement linear constraint equation and the angle measurement linear constraint equation is constructed by using the least square method;

[0007] When all sensor nodes in the sensor network satisfy linear constraints, a decision variable is introduced into the first positioning matrix of the sensor network to generate a second positioning matrix;

[0008] Using the minimum eigenvalue of the second positioning matrix to construct a positioning speed model, wherein the minimum eigenvalue is used to optimize the convergence speed of the first linear positioning algorithm;

[0009] Using a centralized optimization algorithm or a distributed optimization algorithm to solve the optimal solution of the positioning speed model;

[0010] Based on the optimal solution, the first positioning matrix and the first linear positioning algorithm, a target position of each free node in the sensor network is obtained.

[0011] According to one embodiment of the present application, the calculation formula of the distance measurement linear constraint equation is:

[0012] I 2 p i -a ij (d)I 2 p j -a ik (d)I 2 p k -a il (d)I 2 p l =0

[0013] Among them, I 2 represents the two-dimensional identity matrix, p i Represents the sensor node i in the global coordinate system ∑ g The coordinates of the ij (d) represents p i Relative to p j The coordinates in the barycentric coordinate system, p j Represents the sensor node j in the global coordinate system ∑ g The coordinates of the ik (d) represents p i Relative to p k The coordinates in the barycentric coordinate system, p k Represents the sensor node k in the global coordinate system ∑ g The coordinates of the il (d) represents p i Relative to p l The coordinates in the barycentric coordinate system, p l Represents the sensor node l in the global coordinate system ∑ g The coordinates below.

[0014] According to one embodiment of the present application, the calculation formula of the azimuth angle measurement linear constraint equation is:

[0015] B ij (p j -p i )+B ik (p k -p i )=0

[0016] Among them, B ij The matrix representation of the azimuth angle between sensor node i and sensor node j, p jRepresents the sensor node j in the global coordinate system ∑ g The coordinates below, p i Represents the sensor node i in the global coordinate system ∑ g The coordinates of B ik The matrix representation of the azimuth angle between sensor node i and sensor node k, p k Represents the sensor node k in the global coordinate system ∑ g The coordinates below represent .

[0017] According to one embodiment of the present application, the calculation formula of the angle measurement linear constraint equation is:

[0018] (sinα jki I 2 -sinα ijk R T (α kij ))p i +(sinα ijk R T (α kij ))p j -sinα jki I 2 p k =0

[0019] Among them, α iki represents the measurement angle formed by sensor node j, sensor node k and sensor node i, I 2 represents the two-dimensional identity matrix, α ijk represents the measurement angle formed by sensor nodes i, j and k, R T (α kij ) represents the transpose of the two-dimensional rotation matrix corresponding to the measurement angle formed by sensor node k, sensor node i and sensor node j, α kij represents the measurement angle formed by sensor node k, sensor node i and sensor node j, p i Represents the sensor node i in the global coordinate system ∑ g The coordinates below, p j Represents the sensor node j in the global coordinate system ∑ g The coordinates below, p k Represents the sensor node k in the global coordinate system ∑ g The coordinates below.

[0020] According to one embodiment of the present application, the calculation formula of the first linear positioning algorithm is:

[0021]

[0022] Among them, L ffis a first positioning matrix of the sensor network, represents the coordinate position of the free node, p f is the real coordinate position of each free node.

[0023] According to one embodiment of the present application, the calculation formula of the positioning speed model is:

[0024]

[0025] Among them, max β Represents the optimal weight in the sensor network, L ff (β) represents the second positioning matrix, λ min (L ff (β)) represents the minimum eigenvalue of the second positioning matrix, β i represents the i-th decision variable, The sum representing all decision variables introduces a normalization constraint.

[0026] According to one embodiment of the present application, the step of using a centralized optimization algorithm to solve the optimal solution of the positioning velocity model includes:

[0027] Converting the positioning velocity model into a first conversion model;

[0028] The first conversion model is solved by using an interior point method to obtain the optimal solution.

[0029] According to one embodiment of the present application, the step of using a distributed optimization algorithm to solve the optimal solution of the positioning velocity model includes:

[0030] converting the positioning velocity model into a second conversion model;

[0031] A preset optimization algorithm is used to solve the second conversion model to obtain the optimal solution.

[0032] According to an embodiment of the present application, the step of obtaining the target position of each free node in the sensor network based on the optimal solution, the first positioning matrix and the first linear positioning algorithm includes:

[0033] modifying the first positioning matrix into a third positioning matrix based on the optimal solution;

[0034] Substitute the third positioning matrix into the first linear positioning algorithm to obtain the target position of each free node.

[0035] A second aspect of the embodiment of the present application provides a rapid positioning device for a sensor network, including:

[0036] A linear constraint equation establishment module is used to establish, on a two-dimensional plane, a distance measurement linear constraint equation, an azimuth measurement linear constraint equation and an angle measurement linear constraint equation between each sensor node in the sensor network and its neighboring nodes in a corresponding local coordinate system;

[0037] A first linear positioning algorithm construction module, used for constructing a first linear positioning algorithm corresponding to the distance measurement linear constraint equation, the azimuth measurement linear constraint equation and the angle measurement linear constraint equation by using a least square method;

[0038] A second positioning matrix generating module is used to introduce decision variables into the first positioning matrix of the sensor network to generate a second positioning matrix when all sensor nodes in the sensor network meet the linear constraint condition;

[0039] A positioning speed model construction module, used to construct a positioning speed model using the minimum eigenvalue of the second positioning matrix, wherein the minimum eigenvalue is used to optimize the convergence speed of the first linear positioning algorithm;

[0040] An optimal solution solving module, used for solving the optimal solution of the positioning speed model by using a centralized optimization algorithm or a distributed optimization algorithm;

[0041] The target position acquisition module is used to obtain the target position of each free node in the sensor network based on the optimal solution, the first positioning matrix and the first linear positioning algorithm.

[0042] In a third aspect of an embodiment of the present application, a terminal device is provided, including: a processor and a memory, the memory being used to store a computer program, the processor being used to call and run the computer program stored in the memory to execute the steps of the rapid positioning method for sensor networks described in the first aspect above.

[0043] According to a fourth aspect of the embodiments of the present application, a computer-readable storage medium is provided, wherein the computer-readable storage medium is used to store a computer program, wherein the computer program enables a computer to execute the steps of the rapid positioning method for a sensor network as described in the first aspect above.

[0044] The beneficial effects of the embodiments of the present application include:

[0045] The embodiment of the present application uses the minimum eigenvalue corresponding to the first positioning matrix of the sensor network as a factor to determine the convergence speed of the first linear positioning algorithm, and uses this factor in combination with decision variables to model the problem of improving the speed of the first linear positioning algorithm as a constrained eigenvalue optimization problem, that is, to construct a positioning speed model, and then use a centralized optimization algorithm or a distributed optimization algorithm to solve the positioning speed model, thereby obtaining the optimal solution of the positioning speed model, and finally, based on the optimal solution, the first positioning matrix and the first linear positioning algorithm, the target position of each free node in the sensor network is obtained. Compared with the prior art, the present application can determine the convergence speed of the linear positioning algorithm, thereby optimizing the convergence speed of the linear positioning algorithm, and combined with the optimal solution solved by the centralized optimization algorithm or the distributed optimization algorithm, together achieve the purpose of improving the positioning speed of the linear positioning algorithm, so that the rapid positioning method for sensor networks can be applied to more application scenarios with higher positioning speed requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the conventional technology, the drawings required for use in the embodiments or the conventional technology descriptions are briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0047] Figure 1 A flowchart of a fast positioning method for a sensor network according to some embodiments of the present invention;

[0048] Figure 2 A structural block diagram of a rapid positioning device for a sensor network according to some embodiments of the present invention;

[0049] Figure 3 It is a principle block diagram of the terminal device of the present invention in some embodiments. DETAILED DESCRIPTION

[0050] In order to make the above-mentioned purposes, features and advantages of the present application more obvious and easy to understand, the specific implementation methods of the present application are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present application. However, the present application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present application, so the present application is not limited by the specific embodiments disclosed below.

[0051] It should be noted that the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include at least one of the features. In the description of this application, the meaning of "plurality" is at least two, such as two, three, etc., unless otherwise clearly and specifically defined.

[0052] The terms "exemplary" or "for example" are used to indicate examples, illustrations or explanations. Any embodiment or design described as "exemplary" or "for example" in the embodiments of the present application should not be interpreted as being more preferred or more advantageous than other embodiments or designs. Specifically, the use of words such as "exemplary" or "for example" is intended to present related concepts in a specific way.

[0053] The terms "comprises," "includes," or any other variations thereof are intended to cover a non-exclusive inclusion, for example, a process, method, system, product, or apparatus that comprises a series of steps or elements is not necessarily limited to those steps or elements explicitly listed but may include other steps or elements not explicitly listed or inherent to such process, method, product, or apparatus.

[0054] Unless otherwise defined, all technical and scientific terms used in the specification of this application have the same meaning as those commonly understood by those skilled in the art to which this application belongs. The terms used in the specification of this application are only for the purpose of describing specific embodiments and are not intended to limit this application. The term "and / or" used in the specification of this application includes any and all combinations of one or more related listed items.

[0055] Early sensor network positioning methods often rely on global positioning systems (such as GPS) or central control nodes, but these methods have limitations, such as high energy consumption, heavy communication burden, and strong dependence on the external environment. With the development of wireless sensor networks, the Internet of Things, and mobile ad hoc networks, distributed strategies have become a more robust and scalable solution. Therefore, distributed positioning of wireless sensor networks has become an important research direction. Traditional distributed positioning methods are mostly nonlinear methods, which means that the relationship from the input to the output of the method is nonlinear. However, this type of nonlinear method has several defects: First, it is difficult to guarantee global convergence. The nonlinear dynamics in nonlinear iterative methods often lead to the existence of multiple equilibrium points (also known as local optimal solutions or saddle points). Therefore, nonlinear solution algorithms often cannot guarantee global convergence; second, when using nonlinear methods to solve positioning problems, as the network scale or the number of free nodes increases, the variables to be solved in the entire network will increase. Due to the nonlinearity of the iterative equations, the number of saddle points obtained by solving these nonlinear algebraic equations will also increase.

[0056] Based on the defects of the aforementioned nonlinear sensor network positioning method, a linear positioning method has gradually developed in recent years. The sensor node positions of this type of method meet linear constraints. Based on this linear constraint, this type of method models the positioning problem as a problem of solving a linear equation. Specifically, the linear positioning method determines the network locatable topological conditions by establishing a linear constraint equation under two-dimensional spatial angle measurement; using the network locatable topological conditions, a sensor network is established, and sensors are configured with triangles as unit nodes, and the inner angle of the triangle is obtained through the Bluetooth direction finding function; based on the linear constraint equation under two-dimensional spatial angle measurement, combined with the inner angle of the triangle, the target position of the free node in the sensor network is obtained. Compared with the nonlinear positioning method, the advantages of this linear positioning method are: first, after the linear equation is established, there is a corresponding linear positioning algorithm, and the linear positioning algorithm has global convergence; second, for the linear iterative method, the system does not have a saddle point. However, the existing linear positioning algorithm still has shortcomings, that is, the positioning speed is slow. Therefore, studying how to improve the positioning speed of the linear positioning method is of great significance to improving the applicability of the linear positioning algorithm in practical application scenarios.

[0057] The specific implementation of the present application is further described below in conjunction with the accompanying drawings.

[0058] <Fast Positioning Method for Sensor Networks>

[0059] like Figure 1 FIG. 1 is a flowchart of a fast positioning method for a sensor network provided in an embodiment of the present application. Figure 1In the method, the rapid positioning method for the sensor network includes:

[0060] S1. On a two-dimensional plane, establish the distance measurement linear constraint equation, azimuth measurement linear constraint equation and angle measurement linear constraint equation between each sensor node in the sensor network and its neighboring nodes in the corresponding local coordinate system.

[0061] Furthermore, the calculation formula of the distance measurement linear constraint equation is:

[0062] I 2 p i -a ij (d)I 2 p j -a ik (d)I 2 p k -a il (d)I 2 p l =0

[0063] Among them, I 2 represents the two-dimensional identity matrix, p i Represents the sensor node i in the global coordinate system ∑ g The coordinates of the ij (d) represents p i Relative to p j The coordinates in the barycentric coordinate system, p j Represents the sensor node j in the global coordinate system ∑ g The coordinates of the ik (d) represents p i Relative to p k The coordinates in the barycentric coordinate system, p k Represents the sensor node k in the global coordinate system ∑ g The coordinates of the il (d) represents p i Relative to p l The coordinates in the barycentric coordinate system, p l Represents the sensor node l in the global coordinate system ∑ g The coordinates below.

[0064] Further, in, Represents the set of real numbers.

[0065] Further, in the embodiment of the present application, the distance measurement between any two sensor nodes is expressed as d. For example, taking sensor node i and sensor node j as an example ( is the set of anchor nodes and free nodes), the distance measurement between sensor node i and sensor node j is expressed as Among them, p i Represents the sensor node i in the global coordinate system ∑ g The coordinates under j Represents the sensor node j in the global coordinate system ∑ g The coordinates under, ||·|| represents the Euclidean norm of the vector, Represents the set of positive real numbers.

[0066] Furthermore, there are two types of direction measurement, one is direction measurement when the local coordinate systems of the sensor nodes are consistent, and the other is direction measurement when the local coordinate systems of the sensor nodes are inconsistent.

[0067] When the local coordinate system of the sensor node is consistent, the basic unit for establishing the azimuth-induced linear equation is (i, j), that is, Among them, p i Represents the sensor node i in the global coordinate system ∑ g The coordinates under j Represents the sensor node j in the global coordinate system ∑ g The coordinates below, I 2 represents the two-dimensional identity matrix, b ij represents the azimuth of sensor node i and sensor node j, Representative b ij The transpose of Represents the set of square matrices of order 2 consisting of all real numbers.

[0068] In the case of inconsistent local coordinate systems of sensor nodes, the basic unit for establishing the azimuth-induced linear equation is a triple (i, j, k), namely b′ ij (p′ j -p′ i )+b′ ik (p′ k -p′ i )=0, where b′ ij represents the azimuth angle between sensor node i and sensor node j, p′ j Represents the sensor node j in the global coordinate system ∑ g The coordinates under, p′ i Represents the sensor node i in the global coordinate system ∑ g The coordinates below, b′ ik represents the azimuth angle between sensor node i and sensor node k, p′ k Represents the sensor node k in the global coordinate system ∑ g The coordinates below. is defined as The complex number representation of , where x is a two-dimensional vector, x 1 is a real number, x 2 is a real number, is a two-dimensional real number set, i is the sensor node i, is a set of complex numbers. In the embodiment of the present application, the basic unit of establishing the linear equation induced by the azimuth angle when the local coordinate system of the sensor node is consistent is used as a special case of the basic unit of establishing the linear equation induced by the azimuth angle when the local coordinate system of the sensor node is inconsistent. The field of matrix addition and matrix multiplication is isomorphic to the field of complex numbers x′, complex addition and complex multiplication. The linear equation induced by the azimuth angle can be reformulated as B ij (P j -P i )+B ik (P k -P i )=0 2×2 ,in, B ij b′ ij The matrix representation of B ik b′ ik The matrix representation of P i is p′ i The matrix representation of P j is p′ j The matrix representation of P k is p′ k The matrix representation of is the set of 2-order square matrices consisting of all real numbers. ij (P j -P i )+B ik (P k -P i )=0 2×2 Multiply both sides of the equation by [1, 0] T , you can get B ij (p j -p i )+B ik (p k -p i )=0 It should be understood that all Ts in this application represent transposition.

[0069] Furthermore, the calculation formula of the azimuth measurement linear constraint equation is:

[0070] B ij (p j -p i )+B ik (p k -p i )=0

[0071] Among them, B ij The matrix representation of the azimuth angle between sensor node i and sensor node j, p j Represents the sensor node j in the global coordinate system ∑ g The coordinates under i Represents the sensor node i in the global coordinate system ∑ g The coordinates of B ik The matrix representation of the azimuth angle between sensor node i and sensor node k, p k Represents the sensor node k in the global coordinate system ∑ g The coordinates below.

[0072] Furthermore, the unit azimuth angle between sensor node i and sensor node j can be expressed as Among them, p j Represents the sensor node j in the global coordinate system ∑ g The coordinates under i Represents the sensor node i in the global coordinate system ∑ g The coordinates under, ||·|| represents the Euclidean norm of the vector, Represents the two-dimensional set of real numbers.

[0073] Furthermore, the calculation formula of the angle measurement linear constraint equation is:

[0074] (sinα jki I 2 -sinα ijk R T (α kij ))p i +(sinα ijk R T (α kij ))p j -sina jki I 2 p k =0

[0075] Among them, α jki represents the measurement angle formed by sensor node j, sensor node k and sensor node i, I 2 represents the two-dimensional identity matrix, α ijk represents the measurement angle formed by sensor nodes i, j and k, R T (αkij ) represents the transpose of the two-dimensional rotation matrix corresponding to the measurement angle formed by sensor node k, sensor node i and sensor node j, α kij represents the measurement angle formed by sensor node k, sensor node i and sensor node j, p i Represents the sensor node i in the global coordinate system ∑ g The coordinates below, p j Represents the sensor node j in the global coordinate system ∑ g The coordinates below, p k Represents the sensor node k in the global coordinate system ∑ g The coefficient matrix is ​​related only to the angle measurement α jki , α kij and α ijk related.

[0076] Furthermore, in the counterclockwise direction, the ray and The interior angle α kij ∈[0, 2π) can be expressed as:

[0077]

[0078] in, represents the transpose of the azimuth angle between sensor node i and sensor node j, and the azimuth angle between sensor node i and sensor node j is in the local coordinate system of sensor node i itself ∑ i Measured below; The azimuth angle between sensor node i and sensor node k is in the local coordinate system of sensor node i itself ∑ i Measured below; represents the transpose of the azimuth angle between sensor node i and sensor node j, and the azimuth angle between sensor node i and sensor node j is in the global coordinate system ∑ g Measured below; R represents the two-dimensional rotation matrix; b ik represents the azimuth angle between sensor node i and sensor node k; otherwise represents Less than 0.

[0079] Furthermore, the present application embodiment adopts a multiple graph To describe the communication topology of the sensor network, represents a basic unit in the network topology, l∈{1,2,…,m} represents the index of the basic unit, represents a set of sensor nodes, represents the index of the node in each basic unit, Represents the set of positive integers.

[0080] Sensor networks based on different measurement types can be described by a unified structure, namely Represents the set of vertices in the topology (i.e., the set of sensor nodes), whose size is is a multigraph of size represents the set of positive integers, is a 2n-dimensional real number set. Based on this definition, for distance measurement, its basic unit is a four-tuple; for azimuth measurement, its basic unit is an edge; for angle measurement, its basic unit is a three-tuple. Each unit A linear equation can be given, so it can be obtained from Construct m independent linear equations from the equation. The compact form of these m linear equations can be expressed as Mp = 0, where is defined as the measurement matrix, is a 2m×2n dimensional real number set, m is the size of the multigraph, n is the size of the sensor node set, is a 2n-dimensional real number set. Its specific structure is:

[0081]

[0082] in, Indicates L ff d ij and b ij The coefficient matrix in the calculation formula is a compact form that is only related to the measurement. More specifically, L ff =E 1 +E 2 +…+E m , where L ff is the first positioning matrix, i∈{1, 2, …, m}, is 2×2n f The set of real numbers of dimension n f is the number of free nodes; d ij and b ij The calculation formula is the same as above and will not be repeated here.

[0083] To make it clearer The communication relationship between the nodes defines an undirected graph To represent this communication relationship, where (i, j)∈ε, if but

[0084] S2. Use the least square method to construct a first linear positioning algorithm corresponding to the distance measurement linear constraint equation, the azimuth measurement linear constraint equation and the angle measurement linear constraint equation.

[0085] In the embodiment of the present application, the positioning problem of the sensor network is modeled as a least squares optimization problem, and its objective function is:

[0086]

[0087] in, represents sensor node i 1 An estimate of the coordinates of ; represents sensor node i 2 The estimated coordinates of represents sensor node i s The estimated coordinates of (p i Represents the sensor node i in the global coordinate system ∑ g coordinates below); ( represents the set of anchor nodes, and Location is known); the matrix They are all coefficient matrices, and their specific forms can refer to the matrices multiplied before p in the distance measurement linear constraint equation, the azimuth measurement linear constraint equation, and the angle measurement linear constraint equation; is the estimation of sensor node coordinates, for The transpose of M is the measurement matrix, M T is the transpose of the matrix M. Set By transforming the matrix M = [M a M f ]Split into anchor node parts and the free node part M T is the transpose of the matrix M, is a set of real numbers of 2n×2n dimensions, 2m×2n a dimensional set of real numbers, 2m×2n f dimensional real number set, m is the size of the multigraph, n is the size of the sensor node set, n a is the number of anchor nodes, n f is the number of free nodes, the matrix L can be expressed as:

[0088]

[0089] in, Among them, M a is the anchor node matrix, M a The transpose of is 2n a ×2n a The set of real numbers of dimension n a is the number of anchor nodes, M f is the free node matrix, is 2n a ×2n f The set of real numbers of dimension n f is the number of free nodes, M f The transpose of is 2n f ×2n a dimensional set of real numbers, is 2n f +2n f dimensional set of real numbers.

[0090] Based on the above formula, the distance measurement linear constraint equation is given with respect to The gradient of , we can get a unified first linear positioning algorithm, where is the estimate of the true coordinate position of each free node, is the sensor node n a +1 Transpose of coordinate estimate, is the transpose of the coordinate estimate of sensor node n.

[0091] Furthermore, the calculation formula of the first linear positioning algorithm is:

[0092]

[0093] Among them, L ff is a first positioning matrix of the sensor network, represents the coordinate position of the free node, p f is the real coordinate position of each free node.

[0094] More specifically, the evolution process of the first linear positioning algorithm formula is:

[0095]

[0096] in, is the estimate of the true coordinate position of each free node, is the objective function, L ff is a first positioning matrix of the sensor network, is the coordinate position of the free node, And na ≥2, is a set of natural numbers, is 2n a dimensional set of real numbers, is the transpose of the free node matrix, M a is the anchor node matrix, is 2n f +2n a The set of real numbers of dimension p f is the real coordinate position of each free node. In the embodiment of the present application, since L ff p f +L fa p a =0, and L ff is non-singular if and only if the sensor network is localizable, so,

[0097] It should be understood that the first linear positioning algorithm is distributed.

[0098] Furthermore, when the measurement noise is taken into account, the noise matrix introduced by the measurement noise is defined as ΔL ff and ΔL fa , and define and Among them, L in these two formulas ff The meaning and L fa The meaning of L mentioned above ff The meaning and L fa Based on this definition, the first linear positioning algorithm is modified into a second linear positioning algorithm, and the calculation formula of the second linear positioning algorithm is: in, represents the coordinate position of the free node, And n a ≥2, is a set of natural numbers, is 2n a dimensional real number set. When it is non-singular, the following algorithm is effective:

[0099]

[0100] S3. When all sensor nodes in the sensor network satisfy linear constraints, a decision variable is introduced into the first positioning matrix of the sensor network to generate a second positioning matrix.

[0101] The linear constraint condition is Mp=0, where M is the measurement matrix and p is the coordinate of the sensor node.

[0102] In the embodiment of the present application, by adjusting the decision variable (β l , l=1, ..., m) to modify the structure of the first positioning matrix.

[0103] When all sensor nodes in the sensor network satisfy the linear constraint conditions, the following formula exists: Among them, β 1 ,···,β m All are decision variables, and each decision variable is greater than or equal to 0; is the Kronecker product; I 2 is a two-dimensional unit matrix (i.e., a 2*2 unit matrix); M is a measurement matrix; and p is the coordinate of the sensor node. The “*” mentioned in this article can be understood as a multiplication symbol in the mathematical field.

[0104] According to the above calculation formula related to the decision variables, the first positioning matrix L ff is modified into a second positioning matrix. The calculation formula of the second positioning matrix is:

[0105]

[0106] Among them, β 1 Represents E 1 The decision variable, β 2 Represents E 2 The decision variables of β m Represents E m The decision variables, (E i Selected from E 1 To E m Any one of ), (e i Selected from e 1 To e m Any one of ), is 2×2n f dimensional set of real numbers, Yes i The transpose of is 2m×2n f dimensional real number set, T in this application means transposition, is the Kronecker product, I 2 is the two-dimensional identity matrix.

[0107] S4. Use the minimum eigenvalue of the second positioning matrix to construct a positioning speed model, wherein the minimum eigenvalue is used to optimize the convergence speed of the first linear positioning algorithm.

[0108] In an embodiment of the present application, the positioning speed of the first linear positioning algorithm is mainly determined by the minimum eigenvalue of the second positioning matrix. Therefore, the present application models the problem of improving the positioning speed as the positioning speed model. The calculation formula of the positioning speed model is:

[0109]

[0110] Among them, max β Represents the optimal weight (max β The α in the equation refers to the sensor network The weight of each unit in ff (β) represents the second positioning matrix, λ min (L ff (β)) represents the minimum eigenvalue of the second positioning matrix, β i represents the i-th decision variable, The sum representing all decision variables introduces a normalization constraint.

[0111] It should be understood that in the embodiment of the present application, the minimum eigenvalue λ min (L ff (β))(or λ min (L ff ))The larger the value, the greater the positioning error. The faster it approaches zero, the smaller the eigenvalue λ min (L ff (β))(or λ min (L ff )) is larger, the more robust the first linear positioning algorithm is to noise.

[0112] In the embodiment of the present application, all the decision variables are normalized and constrained, that is, The feasibility of the solution to the positioning velocity model in the present application (ie, the solution to the eigenvalue optimization problem) in practice can be guaranteed.

[0113] In the positioning velocity model, when β i When the sum is enlarged, β i The optimal value of is enlarged by the same proportion; when β i When the sum of i The optimal value of is scaled down by the same proportion.

[0114] In some embodiments, if the sum of all decision variables (i.e., constraints) is changed to The optimal solution is modified to The eigenvalues ​​of the second positioning matrix become in, is the optimal solution of the positioning velocity model, is the optimized eigenvalue of the positioning velocity model.

[0115] S5. Using a centralized optimization algorithm or a distributed optimization algorithm to find the optimal solution of the positioning speed model.

[0116] Furthermore, the step of using a centralized optimization algorithm to solve the optimal solution of the positioning speed model includes:

[0117] S51, converting the positioning velocity model into a first conversion model.

[0118] The calculation formula of the first conversion model is:

[0119]

[0120] Among them, min λ，β The β in is defined as represents the feasible solution set, λ represents the optimal eigenvalue, I is the unit matrix, β i For E i The decision variable, E i The meaning is the same as that of the second positioning matrix E i The meaning of this article is the same as The symbol is used to compare the size of the matrix and can be understood as the ">=" symbol. This application sets in, represents the normalized constraints for all the decision variables.

[0121] S52: Using an interior point method to solve the first conversion model to obtain the optimal solution.

[0122] Specifically, the interior point method uses logarithmic barrier functions log(·) and logdet(·) to reformulate the first conversion model into a third conversion model. The calculation formula of the third conversion model is as follows:

[0123]

[0124] in, is the set of positive real numbers, Represents a c The transpose of Representative b c Transpose, is a set of m+1 dimensional real numbers, and the β corresponding to x is the same as min λ,β The meaning of β in is the same as that of λ, λ represents the optimal eigenvalue, I is the unit matrix, and E iThe meaning is the same as that of the second positioning matrix E i The domain of φ(x) is defined as like Then x satisfies all the constraints of the first transformation model, The symbol is used to compare the size of matrices and can be understood as the ">=" symbol. c (x) and φ(x) are convex functions, then wf c (x)+φ(x) is also a convex function, which indicates that the third conversion model has a global optimal solution β i . And, because wf c (x) and φ(x) are second-order differentiable, then the objective function of the third conversion model is also second-order differentiable. Therefore, when the value of w is fixed, Newton's method can be used to solve the third conversion model to obtain the optimal solution β i . w represents a weight coefficient, which can be calculated according to the formula w k+1 =μw k Update, where μ>1, μ represents a positive amplification factor, w k represents the weight matrix, and k represents the number of iterations. It should be understood that the selection of the parameter μ involves a trade-off between the number of inner and outer iterations in the interior point method. When the value of μ is between 3 and 100, the total number of iterations of the algorithm (i.e., the product of the number of inner iterations and the number of outer iterations) remains roughly unchanged.

[0125] Furthermore, the step of using a distributed optimization algorithm to solve the optimal solution of the positioning speed model includes:

[0126] S53: Convert the positioning velocity model into a second conversion model.

[0127] In the embodiment of the present application, the positioning velocity model is first converted into a fourth conversion model and a decoupling operation is performed, and the fourth conversion model is the same as the first conversion model. Therefore, the calculation formula of the fourth conversion model is:

[0128]

[0129] Since the calculation formula of the fourth conversion model is the same as the calculation formula of the first conversion model, the meaning of the parameters will not be described in detail here.

[0130] The decoupling operation of the fourth conversion model is as follows: first define the decision variable x of unit i i =[λ i , β i ] T , the feasible solution set of this decision variable is B represents the set of feasible solutions. The objective function is decomposed into m decoupled local objective functions, namely a T is the transpose of a, The meaning of is the same as above and will not be repeated here. i The linear matrix inequality constraint (LMI constraint) in the fourth transformation model is modified as At this point, the fourth conversion model is successfully decoupled. Finally, the equality constraint It can be equivalently expressed as in, The meaning of is the same as above and will not be repeated here; c T is the transpose of c; l i＝1 (i) represents the indicator function. That is, if i = 1, then l i＝1 (i)=1, otherwise l i＝1 (i)=0.

[0131] After the decomposition is completed, the fourth conversion model is converted into the second conversion model.

[0132] The calculation formula of the second conversion model is:

[0133]

[0134] in, is a 2m-dimensional set of real numbers, m is the size of the multigraph, is a 2-dimensional real number set, the ≥ symbol is used to compare the size of the matrix and can be understood as the ">=" symbol. The other parameters in the second transformation model have the same meaning as the parameters in the aforementioned formula and will not be repeated here.

[0135] S54: Using a preset optimization algorithm to solve the second conversion model to obtain the optimal solution.

[0136] The preset optimization algorithm is as follows:

[0137] The equality constraint for any cell i is expressed as The equality constraints for other units are expressed as

[0138] set up The meaning of the parameters is the same as above, so they will not be repeated here; in, It is B i The transpose of is the Kronecker product, is 2n f dimensional identity matrix, n f is the number of free nodes, The meaning of the parameters is the same as above, so they are not repeated here.

[0139] The Lagrangian function L of the second transformation model 1 (x, R, v) is expressed as in, is a 2m-dimensional set of real numbers, m is the size of the multigraph, is 2n f ×2n f The set of symmetric positive semidefinite matrices, n f is the number of free nodes, is the Lagrange multiplier, is a 1-dimensional set of real numbers.

[0140] For the second transformation model with a dual difference of zero, solving its optimal solution is equivalent to finding the Lagrangian function L 1 The saddle point (x) of (x, R, v) * , R * , v * ). The Lagrangian function L 1 The Lagrangian operator R and v of (x, R, v) are global dual variables, which are related to the decision variables of all units. Since there is no global node in the system, each unit in the system cannot directly obtain the value of R and v. In order to solve this problem, the present application converts the Lagrangian function L 1 (x, R, v) is converted into a fifth conversion model, and the fifth conversion model is:

[0141]

[0142] in, is a 2m-dimensional set of real numbers, m is the size of the multigraph, 2mn f ×2n f dimensional real number set, m is the size of the multigraph, n f is the number of free nodes, is an m-dimensional set of real numbers, the dual variable R of unit i i and v i are the estimates of the true R and v by i, and the dual variable R of unit j j and v j are j’s estimates of the true R and v, respectively. is a multigraph. It should be understood that R i and v i The introduction of consistency constraints is to ensure that R i and v i can converge to R and v respectively. Therefore, the optimal solution of the fifth conversion model is equivalent to the Lagrangian function L1 The optimal solution for (x, R, v).

[0143] In some embodiments, the present application solves the fifth conversion model through the following distributed algorithm and optimization algorithm to obtain the optimal solution β i The distributed algorithm is:

[0144]

[0145] in, is a 2m-dimensional set of real numbers, m is the size of the multigraph;

[0146] is the projection operator, 2mn f ×2n f dimensional real number set, m is the size of the multigraph, n f is the number of free nodes, is an m-dimensional set of real numbers, and All are damping terms. This application introduces and To ensure convergence from a control perspective;

[0147] in, is the projection operator, L 2 (x, R, v) has the same meaning as the formula in the fifth conversion model, L stands for The Laplace matrix of , the auxiliary variable U is the integral term of R, Same meaning as above, is 2n f dimensional identity matrix, n f is the number of free nodes, The symbols have the same meanings as above; For maximizing the Lagrangian function;

[0148] is the projection operator, v, L 2 The meanings of (x, R, v) and L are the same as above, and the auxiliary variable η is the integral term of v, has the same meaning as above;

[0149] k 1 belong And k 1 represents a constant gain; k 2 belong And k 2 Represents a constant gain.

[0150] In addition, the optimization algorithm for each sensor node is:

[0151]

[0152] in, is the projection operator, k 1 、x i 、a、 R i 、v i The meanings of and c are the same as those mentioned above and are therefore not repeated here;

[0153] is the projection operator, R i , B i T 、x i , and R j The meaning of is the same as the above, so it will not be repeated. Representation unit U i The set of neighbors of ;

[0154] v i 、c T 、x i , l i＝1 (i) v j and The meaning of is the same as the above, so it is not repeated here. i is the auxiliary variable corresponding to unit i, η j is the auxiliary variable corresponding to unit j. j and η j All selected from η 1 ,···,η m Any one of them.

[0155] S6. Based on the optimal solution, the first positioning matrix and the first linear positioning algorithm, obtain the target position of each free node in the sensor network.

[0156] Furthermore, the step S6 comprises:

[0157] S61. Modify the first positioning matrix into a third positioning matrix based on the optimal solution.

[0158] Based on the optimal solution β i , modify the first positioning matrix into a third positioning matrix. The calculation formula of the third positioning matrix is ​​L ff (β) = β 1 E1 +β 2 E 2 +…β m E m It should be noted that at this time, L ff (β) represents the third positioning matrix, β 1 is the optimal solution when i is 1, β 2 is the optimal solution when i is 2, ···, β m is the optimal solution for i to be m, E 1 、E 2 、···、E m With the second positioning matrix E 1 、E 2 、···、E m have the same meaning.

[0159] S62: Substitute the third positioning matrix into the first linear positioning algorithm to obtain the target position of each free node.

[0160] The embodiment of the present application uses the minimum eigenvalue corresponding to the first positioning matrix of the sensor network as a factor to determine the convergence speed of the first linear positioning algorithm, and uses this factor in combination with decision variables to model the problem of improving the speed of the first linear positioning algorithm as a constrained eigenvalue optimization problem, that is, to construct a positioning speed model, and then use a centralized optimization algorithm or a distributed optimization algorithm to solve the positioning speed model, thereby obtaining the optimal solution of the positioning speed model, and finally, based on the optimal solution, the first positioning matrix and the first linear positioning algorithm, the target position of each free node in the sensor network is obtained. Compared with the prior art, the present application can determine the convergence speed of the linear positioning algorithm, thereby optimizing the convergence speed of the linear positioning algorithm, and combined with the optimal solution solved by the centralized optimization algorithm or the distributed optimization algorithm, together achieve the purpose of improving the positioning speed of the linear positioning algorithm, so that the rapid positioning method for sensor networks can be applied to more application scenarios with higher positioning speed requirements.

[0161] In addition, it should be noted that this application also makes the following definition: The inner product of a matrix is ​​defined as Where tr(·) represents the trace of the matrix. ||·|| F is the Frobenius norm of the matrix. Set for A stacked column matrix. is the set of free nodes, The number of Location It is certain. n is the n×n identity matrix. n is an n×1 column vector whose elements are all ones.max is the maximum eigenvalue of the matrix. min is the minimum eigenvalue of the matrix. Define R(θ) as a two-dimensional rotation matrix with a rotation angle of θ. is a set of n×n symmetric matrices. is a set of n×n symmetric positive semidefinite matrices.

[0162] <Rapid positioning device for sensor networks>

[0163] like Figure 2 As shown, a fast positioning device for a sensor network is provided in the second aspect of the embodiment of the present application. Figure 2 In the embodiment, the sensor network-oriented rapid positioning device 700 comprises:

[0164] The linear constraint equation establishment module 701 is used to establish, on a two-dimensional plane, a distance measurement linear constraint equation, an azimuth measurement linear constraint equation and an angle measurement linear constraint equation between each sensor node in the sensor network and its neighboring nodes in a corresponding local coordinate system;

[0165] A first linear positioning algorithm construction module 702 is used to construct a first linear positioning algorithm corresponding to the distance measurement linear constraint equation, the azimuth measurement linear constraint equation and the angle measurement linear constraint equation by using the least square method;

[0166] A second positioning matrix generating module 703 is used to introduce decision variables into the first positioning matrix of the sensor network to generate a second positioning matrix when all sensor nodes in the sensor network meet the linear constraint condition;

[0167] A positioning speed model construction module 704 is used to construct a positioning speed model using the minimum eigenvalue of the second positioning matrix, wherein the minimum eigenvalue is used to optimize the convergence speed of the first linear positioning algorithm;

[0168] The optimal solution solving module 705 is used to solve the optimal solution of the positioning speed model by using a centralized optimization algorithm or a distributed optimization algorithm;

[0169] The target position obtaining module 706 is used to obtain the target position of each free node in the sensor network based on the optimal solution, the first positioning matrix and the first linear positioning algorithm.

[0170] <Terminal Equipment>

[0171] The embodiment of the present application also provides a terminal device. The principle block diagram of the terminal device can be as follows: Figure 3As shown. The terminal device includes a processor, a memory, a network interface, a display screen and a temperature sensor connected via a system bus. The processor is used to provide computing and control capabilities. The memory includes a non-volatile storage medium and an internal memory. The non-volatile storage medium stores an operating system and a computer program. The internal memory provides an environment for the operation of the operating system and the computer program in the non-volatile storage medium. The network interface of the terminal device is used to communicate with an external terminal via a network connection. When the computer program is executed by the processor, a rapid positioning method for a sensor network is implemented. The display screen can be a liquid crystal display screen or a terminal ink display screen, and the temperature sensor is pre-set inside the terminal device to detect the operating temperature of the internal device.

[0172] Those skilled in the art will understand that Figure 3 The principle block diagram shown in the figure is only a block diagram of a partial structure related to the scheme of the present invention, and does not constitute a limitation on the terminal device to which the scheme of the present invention is applied. The specific terminal device may include more or fewer components than those shown in the figure, or combine certain components, or have a different arrangement of components.

[0173] In some embodiments, an embodiment of the present application provides a terminal device, which includes a processor and a memory, the memory is used to store a computer program, and the processor is used to call and run the computer program stored in the memory to execute the steps of the rapid positioning method for sensor networks provided in the first aspect of the embodiment of the present application.

[0174] <Computer Readable Storage Medium>

[0175] According to a fourth aspect of the embodiments of the present application, a computer-readable storage medium is provided, wherein the computer-readable storage medium is used to store a computer program, wherein the computer program is used to implement the steps of the rapid positioning method for a sensor network provided in the first aspect of the embodiments of the present application.

[0176] Those skilled in the art can understand that all or part of the processes in the above-mentioned embodiment methods can be completed by instructing the relevant hardware through a computer program, and the computer program can be stored in a non-volatile computer-readable storage medium. When the computer program is executed, it can include the processes of the embodiments of the above-mentioned methods. Among them, any reference to memory, storage, database or other media used in the embodiments provided by the present invention can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM) or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. As an illustration and not limitation, RAM is available in many forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link (Synchlink) DRAM (SLDRAM), memory bus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).

[0177] The technical features of the above embodiments can be combined without changing the basic principles of the present invention. To make the description concise, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0178] The above embodiments only express several implementation methods of the present application, and the descriptions thereof are relatively specific and detailed, but they cannot be understood as limiting the scope of the patent application. It should be pointed out that, for a person of ordinary skill in the art, several variations and improvements can be made without departing from the concept of the present application, and these all belong to the protection scope of the present application. Therefore, the scope of patent protection of the present application shall be subject to the attached claims.

Claims

1. A rapid positioning method for sensor networks, characterized in that: include: On a two-dimensional plane, establish the distance measurement linear constraint equation, azimuth measurement linear constraint equation and angle measurement linear constraint equation between each sensor node in the sensor network and its neighboring nodes in the corresponding local coordinate system; A first linear positioning algorithm corresponding to the distance measurement linear constraint equation, the azimuth measurement linear constraint equation and the angle measurement linear constraint equation is constructed by using the least square method; When all sensor nodes in the sensor network satisfy linear constraints, a decision variable is introduced into the first positioning matrix of the sensor network to generate a second positioning matrix; Using the minimum eigenvalue of the second positioning matrix to construct a positioning speed model, wherein the minimum eigenvalue is used to optimize the convergence speed of the first linear positioning algorithm; Using a centralized optimization algorithm or a distributed optimization algorithm to solve the optimal solution of the positioning speed model; Based on the optimal solution, the first positioning matrix and the first linear positioning algorithm, a target position of each free node in the sensor network is obtained.

2. The rapid positioning method for sensor networks according to claim 1, characterized in that: The calculation formula of the distance measurement linear constraint equation is: I2pi-a i j (d)I2p j -a ik (d)I2p k -a il (d)I2p l =0 Among them, I2 represents the two-dimensional identity matrix, p i Represents the sensor node i in the global coordinate system Σ g The coordinates of the ij (d) represents p i Relative to p j The coordinates in the barycentric coordinate system, p j Represents the sensor node j in the global coordinate system ∑ g The coordinates of the ik (d) represents p i Relative to p k The coordinates in the barycentric coordinate system, p k Represents the sensor node k in the global coordinate system ∑ g The coordinates of the il (d) represents p i Relative to p l The coordinates in the barycentric coordinate system, p l Represents the sensor node l in the global coordinate system ∑ g The coordinates below; The calculation formula of the azimuth measurement linear constraint equation is: B ij (p j -p i )+B ik (p k -p i )=0;=0 Among them, B ij The matrix representation of the azimuth angle between sensor node i and sensor node j, p j Represents the sensor node j in the global coordinate system ∑ g The coordinates below, p i Represents the sensor node i in the global coordinate system ∑ g The coordinates of B ik The matrix representation of the azimuth angle between sensor node i and sensor node k, p k Represents the sensor node k in the global coordinate system Σ g The coordinates below represent; The calculation formula of the angle measurement linear constraint equation is: (sina) jki I2-sina ijk R T (a kij ))p i +(sina ijk R T (a kij ))p j -sina jki I2P k =0 Among them, α jki represents the measurement angle formed by sensor node j, sensor node k and sensor node i, I2 represents the two-dimensional unit matrix, α ijk represents the measurement angle formed by sensor nodes i, j and k, R T (α kij ) represents the transpose of the two-dimensional rotation matrix corresponding to the measurement angle formed by sensor node k, sensor node i and sensor node j, α kij represents the measurement angle formed by sensor node k, sensor node i and sensor node j, p i Represents the sensor node i in the global coordinate system ∑ g The coordinates below, p j Represents the sensor node j in the global coordinate system ∑ g The coordinates below, p k Represents the sensor node k in the global coordinate system ∑ g The coordinates below.

3. The rapid positioning method for sensor networks according to claim 1, characterized in that: The calculation formula of the first linear positioning algorithm is: Among them, L ff is a first positioning matrix of the sensor network, represents the coordinate position of the free node, p f is the real coordinate position of each free node.

4. The rapid positioning method for sensor networks according to claim 1, characterized in that: The calculation formula of the positioning speed model is: max β l min (L ff (b)) Among them, max β Represents the optimal weight in the sensor network, L ff (β) represents the second positioning matrix, λ min (L ff (β)) represents the minimum eigenvalue of the second positioning matrix, β i represents the i-th decision variable, The sum representing all decision variables introduces a normalization constraint.

5. The rapid positioning method for sensor networks according to claim 1, characterized in that: The step of using a centralized optimization algorithm to solve the optimal solution of the positioning speed model includes: Converting the positioning velocity model into a first conversion model; The first conversion model is solved by using an interior point method to obtain the optimal solution.

6. The rapid positioning method for sensor networks according to claim 1, characterized in that: The step of using a distributed optimization algorithm to solve the optimal solution of the positioning speed model includes: Converting the positioning velocity model into a second conversion model; A preset optimization algorithm is used to solve the second conversion model to obtain the optimal solution.

7. The rapid positioning method for sensor networks according to claim 1, characterized in that: The step of obtaining the target position of each free node in the sensor network based on the optimal solution, the first positioning matrix and the first linear positioning algorithm comprises: modifying the first positioning matrix into a third positioning matrix based on the optimal solution; Substitute the third positioning matrix into the first linear positioning algorithm to obtain the target position of each free node.

8. A rapid positioning device for a sensor network, characterized in that: include: A linear constraint equation establishment module is used to establish, on a two-dimensional plane, a distance measurement linear constraint equation, an azimuth measurement linear constraint equation and an angle measurement linear constraint equation between each sensor node in the sensor network and its neighboring nodes in a corresponding local coordinate system; A first linear positioning algorithm construction module, used for constructing a first linear positioning algorithm corresponding to the distance measurement linear constraint equation, the azimuth measurement linear constraint equation and the angle measurement linear constraint equation by using a least square method; A second positioning matrix generating module, used for introducing decision variables into the first positioning matrix of the sensor network to generate a second positioning matrix when all sensor nodes in the sensor network satisfy linear constraints; A positioning speed model construction module, used to construct a positioning speed model using the minimum eigenvalue of the second positioning matrix, wherein the minimum eigenvalue is used to optimize the convergence speed of the first linear positioning algorithm; An optimal solution solving module, used for solving the optimal solution of the positioning speed model by using a centralized optimization algorithm or a distributed optimization algorithm; The target position acquisition module is used to obtain the target position of each free node in the sensor network based on the optimal solution, the first positioning matrix and the first linear positioning algorithm.

9. A terminal device, characterized in that: include: A processor and a memory, the memory being used to store a computer program, the processor being used to call and run the computer program stored in the memory to execute the steps of the rapid positioning method for sensor networks as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that Used to store a computer program, wherein the computer program enables a computer to execute the steps of the rapid positioning method for sensor networks as described in any one of claims 1 to 7.

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