Sensor network-oriented fast positioning method and device, terminal and storage medium

Abstract

The application discloses a kind of fast positioning method, device, terminal and storage medium for sensor network, which can improve the positioning speed of linear positioning method.The method includes establishing linear constraint equations corresponding to three kinds of measurement quantities of distance, azimuth and angle on two-dimensional plane;Using least square method to construct the first linear positioning algorithm corresponding to linear constraint equation;To improve the speed of obtaining the real position of sensor node by the first linear positioning algorithm, linear constraint condition is set, when sensor node meets linear constraint condition, decision variable is introduced in the first positioning matrix of sensor network, to generate the second positioning matrix;Using the minimum eigenvalue of second positioning matrix to construct positioning speed model;Using the optimal solution of the designed centralized optimization algorithm or distributed optimization algorithm to solve positioning speed model;Based on optimal solution, first positioning matrix and first linear positioning algorithm, the target position of each free node in sensor network is obtained.

Description

Technical Field

[0001] This invention relates to the field of system positioning technology. More specifically, this invention relates to a rapid positioning method, apparatus, terminal, and storage medium for sensor networks. Background Technology

[0002] Sensor network localization methods typically employ linear localization to determine the target location of free nodes within the sensor network. This method establishes linear constraint equations based on two-dimensional spatial angle measurements to define the network's localizable topology. Using this topology, a sensor network is built, with sensors configured as unit nodes in triangles. Bluetooth direction finding is used to obtain the interior angles of these triangles. Based on the linear constraint equations and the triangle's interior angles, the target location of the free nodes in the sensor network is obtained. This linear localization method models the localization problem as a problem of solving a linear equation. However, this method has a significant drawback: slow localization speed. This makes sensor networks unsuitable for applications requiring high localization speeds, thus reducing the user experience. Summary of the Invention

[0003] The purpose of this application is to provide a fast positioning method, apparatus, terminal, and storage medium for sensor networks, which can improve the positioning speed of linear positioning methods. This application is mainly achieved through the following technical solutions:

[0004] A first aspect of this application provides a fast localization method for sensor networks, comprising:

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

[0006] A first linear positioning algorithm is constructed using the least squares method, corresponding to the linear constraint equations for distance measurement, azimuth measurement, and angle measurement.

[0007] When all sensor nodes in the sensor network satisfy the linear constraint condition, a decision variable is introduced into the first localization matrix of the sensor network to generate a second localization matrix.

[0008] A positioning speed model is constructed 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;

[0009] The optimal solution of the positioning speed model is obtained by using a centralized optimization algorithm or a distributed optimization algorithm.

[0010] 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.

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

[0012] I2p i -a ij (d)I2p j -a ik (d)I2p k -a il (d)I2p l =0

[0013] Where I2 represents the two-dimensional identity matrix, p i Represents sensor node i in the global coordinate system ∑ g The coordinates below, a ij (d) represents p i Relative to p j The coordinates of p in the barycentric coordinate system j Represents sensor node j in the global coordinate system ∑ g The coordinates below, a ik (d) represents p i Relative to p k The coordinates of p in the barycentric coordinate system k Represents sensor node k in the global coordinate system ∑ g The coordinates below, a il (d) represents p i Relative to p l The coordinates of p in the barycentric coordinate system l Represents sensor node l in the global coordinate system ∑ g The coordinates below.

[0014] According to one embodiment of this application, the calculation formula for the linear constraint equation for azimuth measurement is as follows:

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

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

[0018] (sinα jki I2-sinα ijk R T (α kij ))p i +(sinα ijk R T (α kij ))p j -sinα jki I2p k =0

[0019] Where, α iki I2 represents the measurement angle formed by sensor nodes j, k, and i, and I2 represents the two-dimensional identity matrix. ijk R represents the measurement angle formed by sensor nodes i, j, and k. T (α kij α represents the transpose of the two-dimensional rotation matrix corresponding to the measurement angle formed by sensor nodes k, i, and j. kij p represents the measurement angle formed by sensor nodes k, i, and j. i Represents sensor node i in the global coordinate system ∑ g The coordinates below, p j Represents sensor node j in the global coordinate system ∑ g The coordinates below, p k Represents sensor node k in the global coordinate system ∑ g The coordinates below.

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

[0021]

[0022] Among them, L ff This is the first localization matrix of the sensor network. p represents the coordinate position of a free node. f The actual coordinates of each free node.

[0023] According to one embodiment of this application, the calculation formula for the positioning speed model is as follows:

[0024]

[0025] Where, max β L represents the optimal weight in the sensor network. 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. A normalization constraint is introduced to represent the sum of all decision variables.

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

[0027] Convert the positioning speed model into a first conversion model;

[0028] The optimal solution is obtained by solving the first transformation model using the interior point method.

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

[0030] The positioning speed model is converted into a second conversion model;

[0031] The second transformation model is solved using a preset optimization algorithm to obtain the optimal solution.

[0032] According to one embodiment of this 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] Based on the optimal solution, the first positioning matrix is ​​modified into the third positioning matrix;

[0034] Substituting the third positioning matrix into the first linear positioning algorithm, the target position of each free node is obtained.

[0035] A second aspect of this application provides a rapid positioning device for sensor networks, comprising:

[0036] The linear constraint equation establishment module is used to establish linear constraint equations for distance measurement, azimuth measurement, and angle measurement for each sensor node in the sensor network in the corresponding local coordinate system on a two-dimensional plane.

[0037] The first linear positioning algorithm construction module 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 using the least squares method.

[0038] The second positioning matrix generation 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 satisfy the linear constraint conditions.

[0039] A positioning speed model construction module 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;

[0040] The optimal solution solving module is used to solve the optimal solution of the positioning speed model using a centralized optimization algorithm or a distributed optimization algorithm;

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

[0042] A third aspect of this application provides a terminal device, including a processor and a memory, the memory for storing a computer program, and the processor for calling and running the computer program stored in the memory to perform the steps of the rapid localization method for sensor networks described in the first aspect.

[0043] A fourth aspect of this application provides a computer-readable storage medium for storing a computer program that causes a computer to perform the steps of the rapid localization method for sensor networks described in the first aspect.

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

[0045] This application embodiment uses the minimum eigenvalue corresponding to the first localization matrix of the sensor network as a factor determining the convergence speed of the first linear localization algorithm. By combining this factor with decision variables, the problem of improving the speed of the first linear localization algorithm is modeled as a constrained eigenvalue optimization problem, i.e., a localization speed model is constructed. Then, a centralized optimization algorithm or a distributed optimization algorithm is used to solve the localization speed model, thereby obtaining the optimal solution. Finally, based on the optimal solution, the first localization matrix, and the first linear localization algorithm, the target position of each free node in the sensor network is obtained. Compared with the prior art, this application can determine the convergence speed of the linear localization algorithm, thereby optimizing the convergence speed of the linear localization algorithm. Combined with the optimal solution obtained by the centralized or distributed optimization algorithm, the goal of improving the localization speed of the linear localization algorithm is achieved, thus making the fast localization method for sensor networks applicable to more application scenarios with high localization speed requirements. Attached Figure Description

[0046] To more clearly illustrate the technical solutions in the embodiments of this application or the conventional technology, the drawings used in the description of the embodiments or the conventional technology will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0047] Figure 1 The flowcharts for some embodiments of the fast localization method for sensor networks of the present invention are shown below;

[0048] Figure 2 The diagram shows a structural block diagram of the rapid positioning device for sensor networks according to some embodiments of the present invention.

[0049] Figure 3 This is a schematic diagram of the terminal device of the present invention in some embodiments. Detailed Implementation

[0050] To make the above-mentioned objectives, features, and advantages of this application more apparent and understandable, the specific embodiments of this application are described in detail below with reference to the accompanying drawings. Many specific details are set forth in the following description to provide a thorough understanding of this application. However, this application can be implemented in many other ways different from those described herein, and those skilled in the art can make similar modifications without departing from the spirit of this application. Therefore, this application is not limited to 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 construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. Therefore, a feature defined as "first" or "second" may explicitly or implicitly include at least one of that feature. In the description of this application, "multiple" means at least two, such as two, three, etc., unless otherwise explicitly specified.

[0052] The terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or illustration. Any embodiment or design described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or designs. Specifically, the use of terms such as "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0053] The terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, system, product, or apparatus that includes a series of steps or units is not necessarily limited to those steps or units that are expressly listed, but may include other steps or units that are not expressly listed or that are inherent to such process, method, product, or apparatus.

[0054] Unless otherwise defined, all technical and scientific terms used in this application have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in this application is for the purpose of describing particular embodiments only and is not intended to be limiting of the application. The term "and / or" as used in this application includes any and all combinations of one or more of the associated listed items.

[0055] Early sensor network localization methods often relied on global positioning systems (such as GPS) or central control nodes. However, 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 (IoT), and mobile ad hoc networks, distributed strategies have become a more robust and scalable solution. Therefore, distributed localization in wireless sensor networks has become an important research direction. Traditional distributed localization methods are mostly nonlinear, meaning the relationship between the method's input and output is nonlinear. However, these nonlinear methods have several drawbacks: 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 optima or saddle points). Therefore, nonlinear solution algorithms often cannot guarantee global convergence. Second, when using nonlinear methods to solve localization problems, as the network size or the number of free nodes increases, the number of variables to be solved in the entire network increases. Due to the nonlinearity of the iterative equations, the number of saddle points obtained by solving these nonlinear algebraic equations also increases.

[0056] Based on the shortcomings of the aforementioned nonlinear sensor network localization methods, a linear localization method has gradually developed in recent years. This type of method ensures that the sensor node positions satisfy linear constraints. Based on these constraints, the localization problem is modeled as a problem of solving a linear equation. Specifically, the linear localization method establishes linear constraint equations under two-dimensional spatial angle measurements to determine the network's localizable topology; using these topology conditions, a sensor network is established, and sensors are configured with triangles as unit nodes. The interior angles of the triangles are obtained through Bluetooth direction finding; based on the linear constraint equations under two-dimensional spatial angle measurements, combined with the interior angles of the triangles, the target positions of free nodes in the sensor network are obtained. Compared to nonlinear localization methods, this linear localization method has the following advantages: first, after the linear equations are established, a corresponding linear localization algorithm exists, and this algorithm has global convergence; second, for linear iterative methods, the system does not have saddle points. However, existing linear localization algorithms still have shortcomings, namely, slow localization speed. Therefore, researching how to improve the localization speed of linear localization methods is of great significance for improving the applicability of linear localization algorithms in practical application scenarios.

[0057] The specific embodiments of this application will be further described below with reference to the accompanying drawings.

[0058] <Fast Localization Methods for Sensor Networks>

[0059] like Figure 1 The diagram shown is a flowchart of a fast localization method for sensor networks provided in an embodiment of this application. Figure 1The fast localization method for sensor networks includes:

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

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

[0062] I2p i -a ij (d)I2p j -a ik (d)I2p k -a il (d)I2p l =0

[0063] Where I2 represents the two-dimensional identity matrix, p i Represents sensor node i in the global coordinate system ∑ g The coordinates below, a ij (d) represents p i Relative to p j The coordinates of p in the barycentric coordinate system j Represents sensor node j in the global coordinate system ∑ g The coordinates below, a ik (d) represents p i Relative to p k The coordinates of p in the barycentric coordinate system k Represents sensor node k in the global coordinate system ∑ g The coordinates below, a il (d) represents p i Relative to p l The coordinates of p in the barycentric coordinate system l Represents sensor node l in the global coordinate system ∑ g The coordinates below.

[0064] Furthermore, in, It represents the set of real numbers.

[0065] Furthermore, in the embodiments of this application, the distance measurement between any two sensor nodes is expressed as d. For example, consider sensor node i and sensor node j (…). (Given a set of anchor nodes and free nodes), the distance measurement between sensor node i and sensor node j is expressed as: Where, p i Represents sensor node i in the global coordinate system ∑ gThe coordinates below, p j Represents sensor node j in the global coordinate system ∑ g The coordinates below, ||·|| denote the Euclidean norm of the vector. It represents the set of positive real numbers.

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

[0067] When the local coordinate systems of the sensor nodes are consistent, the basic unit for establishing the linear equation induced by the azimuth angle is (i, j), that is... Where, p i Represents sensor node i in the global coordinate system ∑ g The coordinates below, p j Represents sensor node j in the global coordinate system ∑ g The coordinates below, I2 represents a two-dimensional identity matrix, b ij Represents the azimuth angles of sensor node i and sensor node j. Representative b ij transpose, It represents the set of all real numbers in a 2x2 square matrix.

[0068] When the local coordinate systems of the sensor nodes are inconsistent, the basic unit for establishing the azimuth-induced linear equation is a triple (i, j, k), i.e., b′ ij (p′ j -p′ i )+b′ ik (p′ k -p′ i ) = 0, where b′ ij p′ represents the azimuth angle between sensor node i and sensor node j. j Represents sensor node j in the global coordinate system ∑ g The coordinates below, p′ i Represents sensor node i in the global coordinate system ∑ g The coordinates below, b′ ik p′ represents the azimuth angle between sensor node i and sensor node k. k Represents sensor node k in the global coordinate system ∑ g The coordinates below. Defined as The complex representation of , where x is a two-dimensional vector, x1 is a real number, x2 is a real number, It is a two-dimensional set of real numbers, where i is the sensor node i. It is a set of complex numbers. In the embodiments of this application, the basic unit for establishing the azimuth-induced linear equation when the local coordinate systems of the sensor nodes are consistent is used as a special case of establishing the basic unit for establishing the azimuth-induced linear equation when the local coordinate systems of the sensor nodes are inconsistent. Based on the following form The set of matrices, the field formed by matrix addition and matrix multiplication, is isomorphic to the field formed by 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 For b′ ij The matrix representation, B ik For b′ ik The matrix representation, P i p′ i The matrix representation, P j p′ j The matrix representation, P k p′ k The matrix representation, Let B be the set of all real numbers in a 2x2 square matrix. ij (P j -P i )+B ik (P k -P i ) = 0 2×2 Multiply both sides of the equation by [1, 0] on the right. T You can get B. ij (p j -p i )+B ik (p k -p i When we understand that ) = 0, all T in this application means transpose.

[0069] Furthermore, the calculation formula for the linear constraint equation for azimuth measurement is as follows:

[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 sensor node j in the global coordinate system ∑ g The coordinates below, p i Represents sensor node i in the global coordinate system ∑ g The coordinates below, B ik The matrix representation of the azimuth angle between sensor node i and sensor node k, p k Represents 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: Where, p j Represents sensor node j in the global coordinate system ∑ g The coordinates below, p i Represents sensor node i in the global coordinate system ∑ g The coordinates below, ||·|| denote the Euclidean norm of the vector. Represents the set of real numbers in two dimensions.

[0073] Furthermore, the calculation formula for the linear constraint equation for angle measurement is as follows:

[0074] (sinα jki I2-sinα ijk R T (α kij ))p i +(sinα ijk R T (α kij ))p j -sina jki I2p k =0

[0075] Where, α jki I2 represents the measurement angle formed by sensor nodes j, k, and i, and I2 represents the two-dimensional identity matrix. ijk R represents the measurement angle formed by sensor nodes i, j, and k. T (α kij α represents the transpose of the two-dimensional rotation matrix corresponding to the measurement angle formed by sensor nodes k, i, and j. kij p represents the measurement angle formed by sensor nodes k, i, and j. i Represents sensor node i in the global coordinate system ∑ gThe coordinates below, p j Represents sensor node j in the global coordinate system ∑ g The coordinates below, p k Represents sensor node k in the global coordinate system ∑ g The coordinates below. The coefficient matrix is ​​only related to the angle measurement value α. jki α kij and α ijk related.

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

[0077]

[0078] in, Let represent the transpose of the azimuth angle between sensor node i and sensor node j, and let ∑ represent the azimuth angle between sensor node i and sensor node j in the local coordinate system of sensor node i itself. i The measurement was taken below; The azimuth angle between sensor node i and sensor node k is represented in the local coordinate system of sensor node i itself. i The measurement was taken below; The transpose of the azimuth angle between sensor node i and sensor node j is given by the global coordinate system ∑. g The measurement is below; R represents a 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, embodiments of this application employ a multi-graph To describe the communication topology of the sensor network, where, Let l represent a basic unit in the network topology, where l∈{1,2,…,m} represents the index of the basic unit. Represents a set of sensor nodes. This represents the index of the node in each basic unit. It represents the set of positive integers.

[0080] Sensor networks based on different measurement types can be described by a unified structure, namely The representative is the set of vertices in the topology (i.e., the set of sensor nodes), whose size is... It is a multigraph with a size of Represents the set of positive integers. Let be a 2n-dimensional set of real numbers. Based on this definition, for distance measurements, the basic unit is a quad; for azimuth measurements, the basic unit is an edge; and for angle measurements, the basic unit is a triple. Since Each unit A linear equation can be given, therefore it can be derived from... We construct m independent linear equations. These m linear equations can be expressed in compact form as Mp = 0, where... Defined as a measurement matrix, Let m be a 2m×2n dimensional set of real numbers, where m is the size of the multigraph and n is the size of the sensor node set. It is a set of real numbers with 2n dimensions. Its specific structure is as follows:

[0081]

[0082] in, L represents ff d ij and b ij The compact form of the coefficient matrix in the calculation formula is only related to measurement. More specifically, L ff =E1+E2+…+E m , where L ff This is the first positioning matrix. i∈{1,2,…,m}, For 2×2n f The set of real numbers of dimension n f d represents the number of free nodes. ij and b ij The calculation formula is the same as described above, and will not be repeated here.

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

[0084] S2. 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 using the least squares method.

[0085] In this embodiment of the application, the localization problem of the sensor network is modeled as a least-squares optimization problem, with the objective function being:

[0086]

[0087] in, This represents an estimate of the coordinates of sensor node i1; This represents an estimate of the coordinates of sensor node i2. Indicates sensor node i s The estimation of the coordinates, (p i Represents sensor node i in the global coordinate system ∑ g (Coordinates below); ( Represents the set of anchor nodes, and Location (It is known); matrix All of these are coefficient matrices, the specific forms of which can be found in the matrix multiplied before p in the linear constraint equations for distance measurement, azimuth measurement, and angle measurement. For the estimation of sensor node coordinates, for The transpose of M, where M is the measurement matrix. T This is the transpose of matrix M. (Settings...) By using matrix M = [M a M f Divided into anchor node parts and free node part M T Let M be the transpose of matrix M. Let be the set of real numbers of 2n×2n dimensions. For 2m×2n a The set of real numbers of dimension 1 For 2m×2n f A set of real numbers of dimension m, where m is the size of the multigraph and n is the size of the sensor node set. a n is the number of anchor nodes. f Given the number of free nodes, matrix L can be represented as:

[0088]

[0089] in, Among them, M a For the anchor node matrix, For M a transpose, For 2n a ×2n a The set of real numbers of dimension n a M represents the number of anchor nodes. f For a free node matrix, For 2n a ×2n f The set of real numbers of dimension n fThe number of free nodes, For M f transpose, For 2n f ×2n a The set of real numbers of dimension 1 For 2n f +2n f The set of real numbers of dimension .

[0090] Based on the above formula, the linear constraint equation for distance measurement is given relative to... The gradient can be used to obtain the unified first linear localization algorithm, where, Estimate the true coordinates of each free node. For sensor node n a +1 coordinate estimation transpose This is the transpose of the coordinate estimation for sensor node n.

[0091] Furthermore, the calculation formula for the first linear positioning algorithm is as follows:

[0092]

[0093] Among them, L ff This is the first localization matrix of the sensor network. p represents the coordinate position of a free node. f The actual coordinates of each free node.

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

[0095]

[0096] in, Estimate the true coordinates of each free node. Let L be the objective function. ff This is the first localization matrix of the sensor network. Let be the coordinates of the free node. And n a ≥2, The set of natural numbers, For 2n a The set of real numbers of dimension 1 M is the transpose of the free node matrix. a For the anchor node matrix, For 2n f +2n a The set of real numbers of dimension p f This refers to the actual coordinates of each free node. In this embodiment, since L... ff pf +L fa p a =0, and L ff It is non-singular if and only if the sensor network is localizable, therefore,

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

[0098] Furthermore, when taking into account the presence of measurement noise, the noise matrix introduced by the measurement noise is defined as ΔL. ff and ΔL fa and define and In these two formulas, L ff The meaning of L fa The meaning of is the same as the L mentioned above. ff The meaning of L fa The meaning is the same, therefore, it will not be repeated here. 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, Indicates the coordinate position of the free node. And n a ≥2, The set of natural numbers, For 2n a A set of real numbers of dimension . When When the expression is non-singular, the following algorithm is valid:

[0099]

[0100] S3. When all sensor nodes in the sensor network satisfy the linear constraint condition, 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] This application embodiment adjusts the decision variable (β) l The values ​​of l = 1, ..., m are used to modify the structure of the first positioning matrix.

[0103] When all sensor nodes in the sensor network satisfy the linear constraint condition, the following formula holds: Among them, β1, ..., β m All are decision variables, and each decision variable is greater than or equal to 0; I² is the Kronecker product; M is the measurement matrix; and p is the coordinates of the sensor node. The asterisk (*) mentioned in this article can be understood as the multiplication symbol in mathematics.

[0104] Based on the calculation formulas related to the decision variables mentioned above, the first positioning matrix L ff It was modified to a second positioning matrix. The formula for calculating the second positioning matrix is:

[0105]

[0106] Where β1 represents the decision variable of E1, β2 represents the decision variable of E2, and so on, β m E m Decision variables, (E i Selected from E1 to E m (any one of them), (e i Selected from e1 to e m (any one of them) It is 2×2n f The set of real numbers of dimension 1 It is e i transpose, It is 2m×2n f The set of real numbers of dimension T. In this application, T represents transpose. I is the Kronecker product, and I2 is the two-dimensional identity matrix.

[0107] S4. 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.

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

[0109]

[0110] Where, max β The optimal weight (max) in the sensor network β In this context, α refers to the sensor network. The weight of each unit in 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. A normalization constraint is introduced to represent the sum of all decision variables.

[0111] It should be understood that, in the embodiments of this 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 The larger the value of ), the better the robustness of the first linear positioning algorithm to noise.

[0112] In the embodiments of this application, all decision variables are subject to normalization constraints, that is... This ensures the feasibility of the solution to the positioning velocity model in this application (i.e., the solution to the eigenvalue optimization problem) in practice.

[0113] In the positioning velocity model, when β i When amplified, β i The optimal value is scaled up proportionally; when β i When the sum and shrink, β i The optimal value is reduced by the same proportion.

[0114] In some implementations, if the sum of all decision variables (i.e., the constraints) is changed... The optimal solution is then modified to The eigenvalues ​​of the second positioning matrix become in, This is the optimal solution for the positioning velocity model. These are the optimized feature values ​​of the positioning speed model.

[0115] S5. Use a centralized optimization algorithm or a distributed optimization algorithm to solve for the optimal solution of the positioning speed model.

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

[0117] S51. Convert the positioning speed model into the first conversion model.

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

[0119]

[0120] Where, min λ，β β is defined as Let λ represent the feasible solution set, λ represent the optimal eigenvalue, I be the identity matrix, and β be the eigenvalue. i For E i The decision variable, E i The meaning of E in the second positioning matrix i The meaning is the same as that recorded in this article. The symbol, used for comparing the size of matrices, can be understood as the ">=" symbol. This application sets... in, Normalization constraints are applied to all the aforementioned decision variables.

[0121] S52. Solve the first transformation model using the interior point method to obtain the optimal solution.

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

[0123]

[0124] in, Let be the set of positive real numbers. Represents a c transpose, Representative b c Transpose Given a set of real numbers of dimension m+1, the β corresponding to x and the min λ,β The meaning of β in this context is the same as that in E, where λ represents the optimal eigenvalue, I is the identity matrix, and E is the eigenvalue. i The meaning of E in the second positioning matrix i The meanings are the same. The domain of φ(x) is defined as follows: 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. Because wf c If φ(x) and φ(x) are convex functions, then wf c (x)+φ(x) is also a convex function, which indicates that the third transformation model has a global optimal solution β. i Furthermore, due to WF cSince φ(x) and φ(x) are twice differentiable, the objective function of the third transformation model is also twice differentiable. Therefore, when the value of w is fixed, Newton's method can be used to solve the third transformation model to obtain the optimal solution β. i w represents a weighting coefficient, which can be calculated using the formula w k+1 =μw k Update, where μ > 1, μ represents a positive amplification factor, w k Let μ represent the weight matrix, and k represent the number of iterations. It should be understood that the choice of parameter μ involves a trade-off between the number of inner and outer iterations in the interior-point method. When μ takes a value between 3 and 100, the total number of iterations (i.e., the product of the number of inner and outer iterations) remains approximately constant.

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

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

[0127] In this embodiment, the positioning velocity model is first converted into a fourth conversion model and then decoupled. The fourth conversion model is the same as the first conversion model. Therefore, the calculation formula for the fourth conversion model is:

[0128]

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

[0130] The decoupling operation for the fourth transformation model is as follows: first define the decision variable x of unit i. i =[λ i ,β i ] T The feasible solution set for this decision variable is B represents the set of feasible solutions. The objective function is decomposed into m decoupled local objective functions, i.e. a T For the transpose of a, The meaning is the same as described above, and will not be repeated here. Based on x i With the introduction of [the relevant factor], the linear matrix inequality constraint (LMI constraint) in the fourth transformation model is modified to [the relevant factor]. At this point, the fourth transformation model has been successfully decoupled. Finally, equality constraints... It can be equivalently represented as in, The meaning of is the same as described above, and will not be repeated here; c T For 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 transformation model is converted into the second transformation model.

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

[0133]

[0134] in, Let m be the set of real numbers in 2m dimensions, where m is the size of the multigraph. The set of real numbers is 2-dimensional. The ≥ symbol is used to compare the size of matrices 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. Solve the second transformation model using a preset optimization algorithm to obtain the optimal solution.

[0136] The preset optimization algorithm is as follows:

[0137] The equality constraint of any element i is expressed as: The equality constraints of other units are expressed as follows:

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

[0139] The Lagrangian function L1(x, R, v) of the second transformation model is expressed as: in, Let m be the set of real numbers in 2m dimensions, where m is the size of the multigraph. For 2n f ×2n f The set of symmetric positive semidefinite matrices, n f The number of free nodes, For Lagrange multipliers, It is a 1-dimensional set of real numbers.

[0140] For the second transformation model with a dual difference of zero, solving for its optimal solution is equivalent to finding the saddle point (x, R, v) of the Lagrangian function L1(x, R, v). * R * v * The Lagrange operators R and v of the Lagrange function L1(x, R, v) are used as global dual variables, which are related to the decision variables of all units. Since there are no global nodes in the system, each unit in the system cannot directly obtain the values ​​of R and v. To solve this problem, this application transforms the Lagrange function L1(x, R, v) into a fifth transformation model, which is as follows:

[0141]

[0142] in, Let m be the set of real numbers in 2m dimensions, where m is the size of the multigraph. 2mn f ×2n f A set of real numbers of dimension m, where m is the size of the multigraph, and n f The number of free nodes, Let R be the dual variable of element i, which is an m-dimensional set of real numbers. i and v i These are the estimates of the true R and v for i, respectively, and the dual variable R for unit j. j and v j These are j's estimates of the true R and v, respectively. It 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 It can converge to R and v respectively. Therefore, the optimal solution of the fifth transformation model is equivalent to the optimal solution of the Lagrangian function L1(x, R, v).

[0143] In some implementations, this application solves the fifth transformation model using the following distributed algorithm and optimization algorithm to obtain the optimal solution β. i The distributed algorithm is as follows:

[0144]

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

[0146] For projection operators, 2mnf ×2n f A set of real numbers of dimension m, where m is the size of the multigraph, and n f The number of free nodes, Let m be the set of real numbers. and All are damping terms, which are introduced in this application. and This is used to ensure convergence from a control perspective;

[0147] in, For projection operators, L2(x, R, v) has the same meaning as the formula in the fifth transformation model. L indicates The Laplace matrix, where the auxiliary variable U is the integral term of R. Same as the meaning mentioned above, For 2n f n-dimensional identity matrix f The number of free nodes, The symbols have the same meaning as described above; Used to maximize the Lagrange function;

[0148] For the projection operator, v, L2(x, R, v), and L have the same meanings as described above, and the auxiliary variable η is the integral term of v. The meaning is the same as described above;

[0149] k1 belongs to And k1 represents constant gain; k2 belongs to And k2 represents constant gain.

[0150] Furthermore, the optimization algorithm for each sensor node is as follows:

[0151]

[0152] in, Let k1 and x be projection operators. i a, R i v i The meanings of 'c' and 'c' are the same as those mentioned above, so they will not be repeated here.

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

[0154] v i c T x i l i＝1 (i), v j and The meaning of η is the same as that mentioned above, so it will not be repeated here. i η is the auxiliary variable corresponding to unit i. j η is the auxiliary variable corresponding to unit j. j and η j All are selected from η1, ..., η m Any one of them.

[0155] S6. 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.

[0156] Further, step S6 includes:

[0157] S61. Based on the optimal solution, modify the first positioning matrix into a third positioning matrix.

[0158] Based on the optimal solution β i The first positioning matrix is ​​modified into a third positioning matrix. The formula for calculating the third positioning matrix is ​​L. ff (β)=β1E1+β2E2+…β m E m It should be noted that L at this time ff (β) represents the third positioning matrix, where β1 is the optimal solution for i=1, β2 is the optimal solution for i=2, ..., β m The optimal solutions for i = m are E1, E2, ..., E m With E1, E2, ..., E in the second positioning matrix m The meanings are the same.

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

[0160] This application embodiment uses the minimum eigenvalue corresponding to the first localization matrix of the sensor network as a factor determining the convergence speed of the first linear localization algorithm. By combining this factor with decision variables, the problem of improving the speed of the first linear localization algorithm is modeled as a constrained eigenvalue optimization problem, i.e., a localization speed model is constructed. Then, a centralized optimization algorithm or a distributed optimization algorithm is used to solve the localization speed model, thereby obtaining the optimal solution. Finally, based on the optimal solution, the first localization matrix, and the first linear localization algorithm, the target position of each free node in the sensor network is obtained. Compared with the prior art, this application can determine the convergence speed of the linear localization algorithm, thereby optimizing the convergence speed of the linear localization algorithm. Combined with the optimal solution obtained by the centralized or distributed optimization algorithm, the goal of improving the localization speed of the linear localization algorithm is achieved, thus making the fast localization method for sensor networks applicable to more application scenarios with high localization speed requirements.

[0161] Additionally, it should be noted that this application also defines the inner product of matrices as follows: Where tr(·) represents the trace of the matrix. F Let be the Frobenius norm of the matrix. for A stacked column matrix. For the set of free nodes, The quantity is Location It is certain. n It is an n×n identity matrix. n λ is an n×1 column vector with all elements equal to one. max λ is the largest eigenvalue of the matrix. min Let θ be the smallest eigenvalue of the matrix. Define R(θ) as a two-dimensional rotation matrix with a rotation angle of θ. Let be a set of n×n symmetric matrices. Let be the set of n×n symmetric positive semidefinite matrices.

[0162] Rapid localization device for sensor networks

[0163] like Figure 2 As shown, this is a rapid positioning device for sensor networks provided as a second aspect of an embodiment of this application. Figure 2 The rapid positioning device 700 for sensor networks includes:

[0164] The linear constraint equation establishment module 701 is used to establish linear constraint equations for distance measurement, azimuth measurement, and angle measurement of each sensor node in the sensor network in the corresponding local coordinate system on a two-dimensional plane.

[0165] The 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 using the least squares method.

[0166] The second positioning matrix generation 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 satisfy the linear constraint conditions.

[0167] The 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 using a centralized optimization algorithm or a distributed optimization algorithm;

[0169] The target location acquisition module 706 is used to obtain the target location 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] This application also provides a terminal device, the schematic diagram of which can be as follows: Figure 3 As shown. The terminal device includes a processor, memory, network interface, display screen, and temperature sensor connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs in the non-volatile storage media. The network interface of the terminal device is used for communication with external terminals via a network connection. When the computer program is executed by the processor, it implements a rapid positioning method for sensor networks. The display screen can be an LCD screen or a terminal e-ink display screen, and the temperature sensor is pre-installed inside the terminal device to detect the operating temperature of internal components.

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

[0173] In some embodiments, this application provides a terminal device, which includes a processor and a memory. The memory stores a computer program, and the processor calls and runs the computer program stored in the memory to execute the steps of the fast localization method for sensor networks provided in the first aspect of this application.

[0174] Computer-readable storage media

[0175] A fourth aspect of this application provides a computer-readable storage medium for storing a computer program that implements the steps of the rapid localization method for sensor networks provided in the first aspect of this application.

[0176] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided by this 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. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), RAMbus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and RAMbus dynamic RAM (RDRAM), etc.

[0177] The technical features of the above embodiments can be combined without changing the basic principle of the present invention. For the sake of brevity, 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 merely illustrate several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the patent protection scope of this application should be determined by the appended claims.

Claims

1. A fast localization method for sensor networks, characterized in that, include: On a two-dimensional plane, establish linear constraint equations for distance measurement, azimuth measurement, and angle measurement for each sensor node in the sensor network in its corresponding local coordinate system with its neighboring nodes. A first linear positioning algorithm is constructed using the least squares method, corresponding to the linear constraint equations for distance measurement, azimuth measurement, and angle measurement. When all sensor nodes in the sensor network satisfy the linear constraint condition, a decision variable is introduced into the first localization matrix of the sensor network to generate a second localization matrix. A positioning speed model is constructed 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; The optimal solution of the positioning speed model is obtained by using a centralized optimization algorithm or a distributed optimization algorithm. 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.

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

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

4. The rapid localization method for sensor networks according to claim 1, characterized in that, The calculation formula for the positioning speed model is as follows: max β l min (L ff (b)) Where, max β L represents the optimal weight in the sensor network. 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. A normalization constraint is introduced to represent the sum of all decision variables.

5. The rapid localization method for sensor networks according to claim 1, characterized in that, The steps for solving the optimal solution of the positioning velocity model using a centralized optimization algorithm include: Convert the positioning speed model into a first conversion model; The optimal solution is obtained by solving the first transformation model using the interior point method.

6. The rapid localization method for sensor networks according to claim 1, characterized in that, The steps of using a distributed optimization algorithm to solve for the optimal solution of the positioning velocity model include: The positioning speed model is converted into a second conversion model; The second transformation model is solved using a preset optimization algorithm to obtain the optimal solution.

7. The rapid localization 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 includes: Based on the optimal solution, the first positioning matrix is ​​modified into the third positioning matrix; Substituting the third positioning matrix into the first linear positioning algorithm, the target position of each free node is obtained.

8. A rapid positioning device for sensor networks, characterized in that, include: The linear constraint equation establishment module is used to establish linear constraint equations for distance measurement, azimuth measurement, and angle measurement for each sensor node in the sensor network in the corresponding local coordinate system on a two-dimensional plane. The first linear positioning algorithm construction module 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 using the least squares method. The second positioning matrix generation 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 satisfy the linear constraint conditions. A positioning speed model construction module 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; The optimal solution solving module is used to solve the optimal solution of the positioning speed model using a centralized optimization algorithm or a distributed optimization algorithm; The target location acquisition module is used to obtain the target location 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 for storing a computer program, the processor for calling and running the computer program stored in the memory to perform the steps of the rapid localization 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 that causes a computer to perform the steps of the rapid localization method for sensor networks as described in any one of claims 1 to 7.

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