An optimal anchor point deployment optimization strategy method based on an improved grey wolf optimization algorithm

Abstract

An optimal anchor point deployment optimization strategy method based on an improved gray wolf optimization algorithm is disclosed. The method divides the optimal anchor point optimization process into a first stage and a second stage according to the order of model establishment; in the first stage, a precision factor function and a fitness optimization function are established according to the deployment range of the anchor point and the target point. In the second stage, the gray wolf individual is substituted into the first stage for iterative search and calculation until the optimal anchor point deployment plan is obtained. The system includes a TDoA positioning modeling module, a precision factor construction module, and an iterative optimization search module. The present invention shows that the improved gray wolf optimization algorithm is based on its own adaptive convergence factor and information feedback mechanism, making it more outstanding in terms of convergence speed and solution accuracy. Experiments show that the indoor anchor point optimization scheme based on the improved gray wolf optimization algorithm (MGWO) achieves a smaller DoP value and the anchor point deployment scheme obtained after optimization can achieve high-precision positioning, which can play a greater role in indoor positioning.

Description

Technical Field

[0001] The present invention relates to the technical field of algorithm optimization, and in particular to an optimal anchor point deployment optimization strategy method of an improved grey wolf optimization algorithm. Background Art

[0002] In recent years, indoor positioning has received continuous attention. Common indoor positioning algorithms include methods based on time of arrival (TOA), time difference of arrival (TDOA), angle of arrival (AOA), and frequency difference of arrival (FDOA). Among them, the positioning algorithm based on time difference of arrival has been widely studied in indoor positioning. At the same time, many achievements have been made in the research on the algorithm principle and settlement extension of this algorithm. At the algorithm level, the above research has provided continuous help for achieving high-precision indoor positioning. However, a correct and reasonable anchor point deployment structure can greatly improve the accuracy of the entire positioning system. The positioning deployment of anchor points also plays a vital role in indoor positioning. The key goal of indoor positioning is to determine the position of the positioning point based on several landmark nodes. Based on this, the anchor point deployment positioning problem is formulated as an optimization problem, and a meta-heuristic algorithm is used to deal with the problem of multi-variable dimensional space. A meta-heuristic algorithm is proposed to solve this challenge.

[0003] However, despite these efforts to obtain an optimal deployment structure, the limitations of various optimization algorithms often lead to disadvantages such as local optimality, slow convergence, and difficulty in implementation during the anchor deployment process. Therefore, based on the improved Grey Wolf Optimization Algorithm (MGWO), this paper optimizes the anchor deployment process through its unique adaptive convergence factor and feedback mechanism, making it more outstanding in terms of convergence speed and solution accuracy. Summary of the invention

[0004] In view of the defects of the prior art, the present invention proposes an optimal anchor point deployment strategy method for an improved grey wolf optimization algorithm, which optimizes the local and global search capabilities of the traditional swarm intelligence algorithm in the search phase, improves the convergence speed of subsequent calculations, and ensures the efficiency and solution accuracy of the calculation process.

[0005] In order to solve the above problems, the present invention provides the following technical solutions:

[0006] On the one hand, the present invention provides an optimal anchor point deployment optimization strategy of an improved gray wolf optimization algorithm, the method comprising:

[0007] Step 1. Divide the optimal anchor point optimization process into the first stage and the second stage according to the order of model establishment;

[0008] Step 2. In the first stage, the precision factor function and the fitness optimization function are established according to the deployment range of the anchor points and the target points to obtain the first stage results;

[0009] Step 3. In the second stage, the gray wolf individuals are substituted into the first stage for iterative search calculation until the optimal anchor point deployment plan under the improved gray wolf optimization algorithm is obtained.

[0010] Furthermore, the step 2 comprises:

[0011] Step 2-1. In the first stage, the constraint range of the four anchor points and the positioning points of the TDoA positioning system is determined according to the experimental environment;

[0012] Step 2-2. Under the above constraints, calculate the coordinate information, distance information and information matrix J between each anchor point and the experimental positioning point;

[0013] Step 2-3. Perform singular value decomposition on the multidimensional information matrix J to construct the precision factor matrix DoP and fitness optimization function Fitness.

[0014] Furthermore, the step 2-1 includes:

[0015] Step 2-1a. In the first stage, according to the intended deployment area of ​​the four anchor points, the model constraint range is formulated. Assuming that the position of the anchor point is s and the deployment area of ​​the TDoA positioning system is R1, the constraint condition is s∈R1;

[0016] Step 2-1b. Specify the constraint position according to the intended deployment position of the experimental positioning point. Assuming that the radiation source of the experimental point is c and the target deployment area is R2, the constraint condition is c∈R2.

[0017] Further, the step 2-2 includes:

[0018] Step 2-2a. In the first stage, under the constraints of step 2-1, the coordinate information, distance information and information matrix J between each anchor point and the experimental positioning point are calculated. After removing the redundant information, the dimension of the information matrix is

[0019] Further, the steps 2-3 include:

[0020] Step 2-3a. In the first stage, the information matrix J is subjected to singular value decomposition, and the decomposed singular values ​​are summed and squared.

[0021] Step 2-3b. Construct the precision factor matrix DoP and fitness optimization function Fitness:

[0022]

[0023] Where M is the number of target positioning points, m = 1, 2, 3, ...M.

[0024] Furthermore, the step 3 comprises:

[0025] Step 3-1. In the second stage, generate initialization parameter conditions: the number of wolves, the maximum number of iterations, the variable dimension, and the fitness value and position initialization of the gray wolf.

[0026] Step 3-2. Based on the previous step, the wolf pack is divided into groups in order, and the fitness value of the current round and C are iteratively calculated for each group. α , C β , C δ . Update the nonlinear attenuation parameters and the barrier coefficient a α 、a β 、a δ , A, C.

[0027] Step 3-3. Update the positions of the three gray wolves α, β, δ and the prey (optimal anchor point deployment coordinates); and determine whether the iteration meets the threshold condition. If the answer is yes, output the optimal anchor point deployment coordinates; otherwise, return to step 3-1 to continue the iteration.

[0028] Furthermore, the step 3-1 includes:

[0029] Step 3-1a. In the second stage, generate initialization parameters: the number of wolves, the number of iterations T, the variable dimension dim, and the growth factors k1 and k2 of the α and β wolves;

[0030] Step 3-1b. Under the above parameters, initialize the fitness value and position of each gray wolf.

[0031] Further, the step 3-2 includes:

[0032] Step 3-2a. Group the above initialized wolf pack by level.

[0033] Calculate the fitness value and parameter C of the current iteration round α , C β , C δ .

[0034] Update the nonlinear attenuation parameter a α 、a β 、a δ And search barrier coefficients A and C.

[0035]

[0036]

[0037]

[0038] Among them, a max 、a min are the maximum and minimum values ​​of the linear attenuation factor a, which are initialized to 2 and 0.01 respectively. k1 and k2 are attenuation factors, which are 2 and 4 respectively.

[0039] A α =2a α (t)·r1-a α (t)

[0040] A β =2a β (t)·r1-a β (t)

[0041] A δ =2a δ (t)·r1-a δ (t)

[0042] Among them, r1 and r2 are random vectors in the interval [0,1];

[0043] Further, the step 3-3 includes:

[0044] Step 3-3a. Perform iterative calculations under the above conditions to update the positions of the three gray wolves α, β, δ and the prey (optimal anchor point deployment coordinates);

[0045] c1=c α (t)-(2a α (t)·r1-a α (t))·D α

[0046] c2=c β (t)-(2a β (t)·r1-a β (t))·D β

[0047] c3=c δ (t)-(2a δ (t)·r1-a δ (t))·D δ

[0048]

[0049] Step 3-3b. Under the above conditions, determine whether the iteration meets the threshold T=100.

[0050] If the answer is affirmative, the optimal anchor point deployment coordinates S1, S2, S3, and S4 are output;

[0051] Otherwise, return to step 3-1 to continue the iteration until the optimal anchor point deployment task is completed.

[0052] It can be known from the above technical scheme that the optimal anchor point deployment strategy method of the improved gray wolf optimization algorithm described in the present invention attempts to find a balance between global search and local search. Linear representation method of convergence factor a in traditional algorithms: As the number of iterations increases, the convergence factor decreases from 2 to 0. However, this method cannot fully guarantee the global and local search processes. Therefore, we try to convert the linear decrease of the convergence factor into an exponential decay form in the alpha, beta, and delta wolf search processes. This method can balance global search and local search. The remaining position update steps are consistent with the gray wolf optimization algorithm. Therefore, based on the improved gray wolf optimization algorithm, this paper optimizes the anchor point deployment process through its unique adaptive convergence factor and feedback mechanism, making it more outstanding in terms of convergence speed and solution accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solutions of the implementation of the present invention or the existing algorithms, the following briefly introduces the drawings required for the technical description of the implementation or the existing algorithms. Obviously, the drawings described below are some implementation examples of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any effort.

[0054] Figure 1 It is a flow chart of the optimal anchor point deployment strategy method based on the improved grey wolf optimization algorithm in the present invention;

[0055] Figure 2 It is the constraint condition of each anchor point in the experimental environment of the present invention, that is, the distribution range schematic diagram of each anchor point;

[0056] Figure 3 It is an optimization curve diagram of the fitness function in the application example, including the genetic algorithm, the gray wolf optimization algorithm and the improved gray wolf optimization algorithm in the present invention;

[0057] Figure 4 It is the DoP three-dimensional surface and optimal anchor point deployment diagram in the application example using the genetic algorithm;

[0058] Figure 5 It is the DoP three-dimensional surface and optimal anchor point deployment diagram in the application example using the Grey Wolf optimization algorithm;

[0059] Figure 6It is a DoP three-dimensional surface and an optimal anchor point deployment diagram in an application example using the improved grey wolf optimization algorithm proposed in the present invention. DETAILED DESCRIPTION

[0060] In order to make the purpose, algorithm scheme and advantages of the embodiment of the present invention clearer, the technical scheme in the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all the embodiments. Based on the embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0061] Embodiment 1 of the present invention provides a specific implementation of an optimal anchor point deployment strategy method based on an improved gray wolf optimization algorithm. Figure 1 , the optimization method specifically includes the following contents:

[0062] Step 100: Divide the optimal anchor point optimization process into the first stage and the second stage according to the order of model establishment. Figure 1 .

[0063] In step 100, in the first stage, a precision factor function and a fitness optimization function are established according to the deployment range of the anchor points and the target points to obtain the first stage result; in the second stage, the gray wolf individuals are substituted into the first stage for iterative search calculation until the optimal anchor point deployment plan under the improved gray wolf optimization algorithm is obtained. Figure 1 .

[0064] Step 200: In the first stage, the four anchor points and the constraint range of the positioning point of the TDoA positioning system are determined according to the experimental environment. Figure 2 .

[0065] In step 200, under the condition of the above-mentioned constraint range, the coordinate information, distance information and information matrix J between each anchor point and the experimental positioning point are calculated; the multi-dimensional information matrix J is subjected to singular value decomposition to construct the precision factor matrix DoP and the fitness optimization function Fitness.

[0066] Step 300: In the second stage, the gray wolf individuals are substituted into the first stage for iterative search calculation until the optimal anchor point deployment scheme under the improved gray wolf optimization algorithm is obtained.

[0067] In step 300, in the second stage, the initialization parameter conditions are generated: the number of wolves, the maximum number of iterations, the variable dimension, and the fitness value and position initialization of the gray wolf. Based on the previous step, the wolves are grouped in order, and the fitness value of the current round and C are iteratively calculated for each group.α , C β , C δ . Update the nonlinear attenuation parameters and the barrier coefficient a α 、a β 、a δ , A, C. Update the positions of the three gray wolves α, β, δ and the prey (optimal anchor point deployment coordinates); and determine whether the iteration meets the threshold condition. If the answer is affirmative, output the optimal anchor point deployment coordinates; otherwise, return to continue the iteration.

[0068] In order to further illustrate the algorithm flow of this solution, the present invention provides an application example of an optimal anchor point deployment solution based on an improved grey wolf optimization algorithm. The optimization method specifically includes the following contents:

[0069] The key goal of indoor positioning is to determine the location of the positioning point based on several landmark nodes. Among them, anchor point deployment also plays a vital role in indoor positioning. Based on this, we formulate the anchor point deployment problem as an optimization problem and use a meta-heuristic algorithm to deal with the problem in multi-variable dimensional space.

[0070] We define the estimated value and true value of the distance difference between each anchor point and the positioning point as a mean square error optimization model as follows:

[0071]

[0072] In the above formula, the absolute value internal terms are represented as the true distance and the estimated distance, respectively. Indicates the optimized positioning point coordinates.

[0073] We express the residual term as and its matrix form So rewrite the above formula as:

[0074]

[0075] Pick Because the first-order partial derivative is continuous, the first-order condition is satisfied The above problem can be solved by Newton's method. Therefore, given the initial iteration point c0, the following iteration equation can be obtained:

[0076]

[0077] In the above formula, let Assuming that the residual term is approximately 0 at the optimal solution, we can obtain the Gauss-Newton iteration relationship:

[0078] c τ+1 =c τ +[J T J]-1 J T r(c τ ). Since the dimension of J is R n×n×3 , which is difficult to deal with using a flat mathematical model, so we give the two-dimensional form of J * Considering the symmetric information and redundant information of the two anchor points, we can get J after removing the above elements. ** .

[0079] Then construct the precision factor matrix DoP and fitness optimization function Fitness:

[0080]

[0081] Where M is the number of target positioning points, m = 1, 2, 3, ... M

[0082] The GWO algorithm is inspired by the social behavior of gray wolves, which follow a strict hierarchy. In order to mathematically model the social management of gray wolves, we named the three wolves closest to the prey as α, β, and δ, corresponding to the best solution determined by the fitness function with the lowest fitness value. β wolf and δ wolf are considered the second and third best solutions, respectively. The remaining wolves are uniformly named w wolves, corresponding to other candidate solutions. The hunting work is guided by α, β, and δ wolves, while w wolf follows the above groups to find the global best wolf position.

[0083] The traditional grey wolf optimization algorithm attempts to find a balance between global search and local search, and linearizes the convergence factor a. As the number of iterations increases, the convergence factor decreases from 2 to 0. However, this method cannot fully guarantee the global and local search process. Therefore, we try to convert the linear decrease of the convergence factor into an exponential decay in the α, β, and δ wolf search process. This method can balance the global search and local search. The remaining position update steps are consistent with the GWO algorithm.

[0084] During the entire iterative search process, α, β, and δ wolves are used, and w wolves follow the above groups to find the global best wolf position. The wolf groups update their positions according to the following formula:

[0085]

[0086]

[0087] In the above formula, t is the iteration round, Represents the Euclidean distance between the gray wolf and the prey (optimal deployment coordinates). represents the coefficient vector, Represents the location coordinates of the prey and the gray wolf. can be expressed as:

[0088]

[0089]

[0090] Among them, we try to increase the convergence factor in the gray wolf search process The linear descent method is converted into an exponential decay descent, which can balance the global search and local search.

[0091] So the nonlinear attenuation parameter a α 、a β 、a δ And the search barrier coefficients A and C are expressed as:

[0092]

[0093]

[0094]

[0095] Among them, a max 、a min are the maximum and minimum values ​​of the linear attenuation factor a, which are initialized to 2 and 0.01 respectively. k1 and k2 are attenuation factors, which are 2 and 4 respectively.

[0096] The search barrier coefficient can be expressed as:

[0097] A α =2a α (t)·r1-a α (t)

[0098] A β =2a β (t)·r1-a β (t)

[0099] A δ =2a δ (t)·r1-a δ (t)

[0100] Among them, r1 and r2 are random vectors in the interval [0,1].

[0101] Then, the Euclidean distance between α, β, δ wolves and their prey can be rewritten as:

[0102]

[0103]

[0104]

[0105] are random vectors in the interval [0,1].

[0106] Further, the step 3-3 includes:

[0107] Under the above conditions, iterative calculations are performed to update the positions of the three gray wolves α, β, and δ as well as the prey (optimal anchor point deployment coordinates);

[0108] c1=c α (t)-(2a α (t)·r1-a α (t))·D α

[0109] c2=c β (t)-(2a β (t)·r1-a β (t))·D β

[0110] c3=c δ (t)-(2a δ (t)·r1-a δ (t))·D δ

[0111]

[0112] Algorithm example: Parameter settings: The population size is set to 30 and 50 respectively; the number of iterations T = 100; k1 and k2 are set to 2 and 4 respectively. max 、a min are the maximum and minimum values ​​of the linear attenuation factor a, which are initialized to 2 and 0.01 respectively.

[0113] Anchor deployment range, anchor model constraints such as Figure 2 As shown in Figure 2, the number of optimization parameters is 12, which are the coordinates of each anchor point.

[0114] Comparison algorithm: GA-30:Fitness=3.2369; GA-50:Fitness=3.17616; GWO-30:Fitness=3.166; GWO-50:Fitness=3.166;

[0115] The algorithm in this paper has the following results: MGWO-30: Fitness = 3.153; MGWO-50: Fitness = 3.146. Figure 3 shown.

[0116] Furthermore, the heat map of the optimal deployment precision factor of anchor points under the above comparison algorithm conditions is as follows: Figure 4 , Figure 5 shown.

[0117] The heat map of the precision factor of the optimal deployment of anchor points under the algorithm proposed in this paper is as follows Figure 6 shown.

[0118] Therefore, based on the improved Grey Wolf Optimization Algorithm, this paper optimizes the anchor point deployment process through its unique adaptive convergence factor and feedback mechanism, making it more outstanding in terms of convergence speed and solution accuracy.

[0119] The above implementation is only used to illustrate the technical solution of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, it should be understood by those skilled in the art that the technical solutions described in the aforementioned embodiments may still be modified, or some of the technical features thereof may be replaced by equivalents. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An anchor point deployment optimization strategy method based on an improved grey wolf optimization algorithm, characterized by: Step 1. Divide the optimal anchor point optimization process into the first stage and the second stage according to the order of model establishment; Step 2. In the first stage, the precision factor function and the fitness optimization function are established according to the deployment range of the anchor points and the target points to obtain the first stage results; Step 3. In the second stage, the gray wolf individuals are substituted into the first stage for iterative search calculation until the optimal anchor point deployment scheme under the improved gray wolf optimization algorithm is obtained; Wherein, the step 2 comprises: Step 2-1. In the first stage, the constraint range of the four anchor points and the positioning points of the TDoA positioning system is determined according to the experimental environment; Step 2-2. Under the above constraints, calculate the coordinate information, distance information and information matrix J between each anchor point and the experimental positioning point; Step 2-3. Perform singular value decomposition on the multidimensional information matrix J to construct the precision factor matrix DoP and fitness optimization function Fitness.

2. The anchor point deployment optimization strategy method based on the improved gray wolf optimization algorithm according to claim 1 is characterized in that: The step 2-1 comprises: Step 2-1a. In the first stage, according to the intended deployment area of ​​the four anchor points, the model constraint range is formulated. Assuming that the position of the anchor point is s and the deployment area of ​​the TDoA positioning system is R1, the constraint condition is s∈R1; Step 2-1b. Specify the constraint position according to the intended deployment position of the experimental positioning point. Assuming that the radiation source of the experimental point is c and the target deployment area is R2, the constraint condition is c∈R2.

3. The anchor point deployment optimization strategy method based on the improved gray wolf optimization algorithm according to claim 2 is characterized in that: The step 2-2 comprises: Step 2-2a. In the first stage, under the constraints of step 2-1, the coordinate information, distance information and information matrix J between each anchor point and the experimental positioning point are calculated. After removing the redundant information, the dimension of the information matrix is 4. The anchor point deployment optimization strategy method based on the improved gray wolf optimization algorithm according to claim 3 is characterized in that: The steps 2-3 include: Step 2-3a. In the first stage, the information matrix J is subjected to singular value decomposition, and the decomposed singular values ​​are summed and the square root is taken; Step 2-3b. Construct the precision factor matrix DoP and fitness optimization function Fitness: Where M is the number of target positioning points, m = 1, 2, 3, ...M.

5. The anchor point deployment optimization strategy method based on the improved gray wolf optimization algorithm according to claim 4 is characterized in that: The step 3 comprises: Step 3-1. In the second stage, generate initialization parameter conditions: the number of wolves, the maximum number of iterations, the variable dimension, and the fitness value and position initialization of the gray wolf; Step 3-2. Based on the previous step, the wolf pack is divided into groups in order, and the fitness value of the current round and C are iteratively calculated for each group. α , C β , C δ ; Update the nonlinear attenuation parameters and the barrier coefficient a α 、a β 、a δ , A, C; Step 3-3. Update the optimal anchor point deployment coordinate positions of the three gray wolves α, β, δ and the prey; and determine whether the iteration meets the threshold condition; if the answer is affirmative, output the optimal anchor point deployment coordinates; otherwise, return to step 3-1 to continue to complete the iteration.

6. The anchor point deployment optimization strategy method based on the improved gray wolf optimization algorithm according to claim 5 is characterized in that: The step 3-1 comprises: Step 3-1a. In the second stage, generate initialization parameters: the number of wolves, the number of iterations T, the variable dimension dim, and the growth factors k1 and k2 of the α and β wolves; Step 3-1b. Under the above parameters, initialize the fitness value and position of each gray wolf.

7. The anchor point deployment optimization strategy method based on the improved gray wolf optimization algorithm according to claim 5 is characterized in that: The step 3-2 comprises: Step 3-2a. Group the initialized wolf packs by level and calculate the fitness value and parameter C of the current iteration round. α , C β , C δ ; Update the nonlinear attenuation parameter a α 、a β 、a δ And search barrier coefficients A and C.

8. The anchor point deployment optimization strategy method based on the improved gray wolf optimization algorithm according to claim 5 is characterized in that: The step 3-3 comprises: Step 3-3a. Perform iterative calculations under the above conditions to update the optimal anchor point deployment coordinates of the three gray wolves α, β, δ and prey: Step 3-3b. Under the above conditions, determine whether the iteration meets the threshold condition; if the answer is affirmative, output the optimal anchor point deployment coordinates; otherwise, return to step 3-1 to continue to complete the iteration until the optimal anchor point deployment task is completed.

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