CN116684960A - Anchor node optimization method based on improved gray wolf optimization algorithm - Google Patents
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Abstract
An anchor node optimization method based on an improved gray wolf optimization algorithm relates to an anchor node optimization method. The invention aims to solve the problem that a positioning scene with TDOA measurement errors and anchor node position errors exist simultaneously and an anchor node optimal solution which can be used for reference is lacking. The invention adopts the cosine annealing convergence factor, so that the convergence factor has higher value at the early stage of iteration and slower attenuation speed, and has smaller value and faster attenuation speed at the later stage of iteration, thereby being beneficial to enhancing the global exploration capacity at the early stage of iteration and the local accurate solving capacity at the later stage of iteration. The invention belongs to the technical field of communication radiation source positioning.
Description
Technical Field
The invention relates to an anchor node optimization method, and belongs to the technical field of communication radiation source positioning.
Background
With the development of electronic technology in recent years, various warship-based, vehicle-mounted, airborne and other military radio equipment plays an increasingly important role in battlefield, and war forms gradually evolve to informatization. The electromagnetic spectrum is used as the only medium for battlefield information transmission, and the priority competing for the electromagnetic rights gradually plays a decisive role in battlefield situation in modern informatization electronic battlefield, and has important significance for military reconnaissance and communication countermeasure. The communication radiation source is used as an important carrier of electromagnetic spectrum space, and can depict battlefield target portraits in the dimensions of electromagnetic spectrum, motion state, geographic position, appearance characteristics and the like, so that various fields are enthusiastic for researching how to mine the characteristics of the communication radiation source to obtain more information. The communication radiation source positioning technology for estimating the space position of the communication target radiation source by means of information fusion, processing and the like according to the parameters of the intercepted communication target radiation source also becomes an important research direction.
With the development of electronic reconnaissance technology, the active positioning easily exposes the position of the self equipment, and has relatively poor performance in aspects of concealment, reconnaissance resistance, interference resistance and the like. Compared with the passive positioning technology, the passive positioning technology utilizes the signals sent by the target or scattered passively to determine the position, the motion state and other information of the target, and has the advantages of good concealment and anti-interference. The passive positioning based on TDOA measurement parameters is also called time difference positioning, compared with TOA positioning technology, TDOA positioning does not need to know signal transmitting/receiving time of a target radiation source, positioning accuracy is better than that of RSS, AOA and the like, and therefore students tend to study TDOA positioning algorithms at home and abroad.
The factors influencing the TDOA positioning accuracy are not only TDOA measurement deviation, but also the positioning error of the target radiation source is too high due to the position deviation introduced by the self-positioning of the anchor nodes in a scene of real-time change of the positions of certain anchor nodes. When the number of the anchor nodes is fixed, the positioning accuracy of different station arrangement modes to the same monitoring area is different. Therefore, a considerable part of scholars research the anchor node selection algorithm, thereby achieving the purposes of improving the positioning precision of the passive positioning system on the target radiation source and improving the system performance
In 2015, LIU S et al study a sparse promotion node selection algorithm based on covariance matrix structure sparsity, under the condition of power consumption and information constraint, cooperative positioning is realized by sharing measured values between anchor nodes and adjacent nodes, and then a cooperative positioning result is transmitted to a processing center for fusion positioning. YANG X in 2018 et al artificially solves the problem of adaptive sensor selection for nonlinear tracking, performs sparse selection vector design on the problem, selects the cardinality of a sparse vector as a sparsity penalty term of a cost function, and updates the weight value of the sparse selection vector by using a gradient descent method and an ADMM iteration method so as to minimize the L1 norm, thereby realizing optimization of anchor nodes. 2019 Hao Benjian et al then investigated selecting the optimal anchor node with trace minimization of the localization error covariance of the WLS estimation algorithm when TDOA measurement errors are present, and solving the SDP problem using the CVX toolkit. DAI Z et al in 2020 built a sensor selection problem with a trace that minimizes the CRLB matrix, and relaxed the problem to an SDP problem, and preferentially select a sensor with a large weight as the optimal sensor, when the number of fixed sensors is selected. In 2020, xia Wei et al research the optimal station arrangement algorithm when the number of observation stations is fixed, derive an optimal station arrangement model, and respectively design a scheme for solving the optimal station arrangement problem based on a PSO algorithm and a GA algorithm, so as to realize automatic station arrangement in the observation area. Wu at university of electronics and technology 2021 proposes to use the minimum non-zero eigenvalue maximization of the weighted positioning error matrix as a criterion for screening the anchor nodes and to solve the final result using an iterative method. The heuristic algorithm is a trial-and-error algorithm based on experience and heuristic knowledge, and is used for iteratively searching candidate optimal solutions in a solution space, and then evaluating and updating the current solutions according to heuristic information.
The main flow idea at present is to solve the anchor node optimization problem by using a heuristic algorithm, most of research focuses on mathematical modeling of the anchor node optimization problem under the condition of single errors such as TDOA measurement errors or anchor node position errors, and design an efficient heuristic algorithm to solve the problem, but for a positioning scene where the TDOA measurement errors and the anchor node position errors exist at the same time, an anchor node optimization solution which can be used for reference is lacking. Aiming at the problems, the invention comprehensively considers the anchor node position error and the TDOA measurement error, deduces a positioning observation model under the double-error condition, analyzes a CTLS closed solution and a positioning error covariance matrix based on the model, then uses the trace of the positioning error covariance matrix as an anchor node optimization criterion to construct a mathematical model of the anchor node optimization problem, and provides an anchor node optimization method based on an improved gray wolf optimization algorithm.
Disclosure of Invention
The invention aims to solve the problem that a positioning scene with TDOA measurement errors and anchor node position errors exist simultaneously and lacks an anchor node optimization solution for reference, and further provides an anchor node optimization method based on an improved gray wolf optimization algorithm.
The technical scheme adopted by the invention for solving the problems is as follows: the method comprises the following specific steps:
step one, coding all N anchor nodes participating in selection, wherein the reference anchor node is number 1, and the other nodes are coded according to numbers 2 to N;
step two, setting wolf parameters including wolfnum number wolfnum and total iteration times t max And a wolf individual solution parameter dimension dim;
step three, calculating the fitness value of the wolf group individuals through an Ackley function;
step four, searching three wolves according to the fitness value, wherein the grades are alpha, beta and delta from high to low, t=0, t is the iteration number, and iteration is started;
step five, carrying out position update on all the wolves with the grades of omega, and calculating the current position fitness value;
step six, according to the calculated fitness value, selecting three gray wolves with the maximum fitness value and with the omega grades, and comparing the gray wolves with the alpha, beta and delta grades, and if the gray wolves meet the requirements, replacing the first wolves;
step seven, carrying out Laiweiling flight or random swimming on the head wolves, if the adaptability value of the head wolves is reduced, allowing updating, otherwise, keeping the original position;
step eight, judging whether the head wolves with the grades of beta and delta need to follow the action, if so, updating the positions of the head wolves with the grades of beta and delta, otherwise, keeping the original positions;
step nine, let t=t+1, judge whether to meet the condition that the iteration terminates, if meet, output the first wolf position of the grade alpha, otherwise, jump to step three, continue the iteration.
Further, in the first step, all N anchor nodes participating in selection are encoded, the reference anchor node is number 1, and the other nodes are encoded according to numbers 2 to N; a vector B of N boolean variables is introduced, which can be expressed as:
B＝[B 1 B 2 ... B N ] T ,B i ∈{0,1} (1)，
in the formula (1), B i =0 indicates that the ith anchor node is not selected, whereas a value equal to 1 indicates that it is selected; suppose that the operating state of the reference anchor node is defined by B 1 Indicating that the value is often 1.
Further, in the third step, an Ackley function in the benchmark function is selected as an fitness function to evaluate the fitness value of each individual. The formula is as follows:
in the formula (2), n represents the dimension of the wolf group individual; e represents a natural constant; x is x i Representing the position solution vector of the ith gray wolf only.
Further, in the fourth step, the grade of each gray wolf in the group is determined according to the fitness function value, the first three grades are alpha, beta and delta, and the lowest grade is omega, wherein the higher the fitness is, the higher the grade is.
Furthermore, in the fifth step, the position of each common wolf is updated by utilizing a position updating formula of an algorithm according to the position of the optimal wolf, and the hunting process of the wolf population mainly comprises three stages of searching, following and trapping;
in the searching stage, when the hunting object moves, the individual wolves search the hunting object from four sides in the direction far away from three head wolves in a random walk mode, each wolf searches three middle position solutions according to the independent command of the three head wolves, and in the following stage of the next step, the middle solutions are fused to obtain the final position;
in the following stage, the wolf group updates the final position according to the result of the searching stage, and recalculates the fitness value of each individual to update the position of each individual in the group, and reelects the wolves with the grades of alpha, beta and delta in the group, namely three wolves closest to the prey, and the wolves with other grades of omega move towards the positions of the three wolves, so that the wolves with the high grade are led by the individual group to approach towards the global optimal solution;
in the trapping stage, three wolves in the wolf group are locked in the scope of the prey, so that the wolves with the grade omega do not need to search the prey everywhere, the wolves with the grade omega give a trapping command, the wolves with the grade omega move towards the direction close to the wolves and gather, when the prey is in a rest state, the wolves can attack the prey, and the position of the wolves with the grade alpha is the optimal solution of the optimized objective function;
the formula for updating the position of the gray wolf with the grade omega by random walk is as follows:
in formula (3), i=1, 2,..l represents the i-th wolf, L represents the total number of wolves rated ω; j=α, β, δ represents three top wolves; k=1, 2..m represents the kth dimension (each wolf has its own direction vector, here representing the direction vector of the kth wolf), the maximum dimension of the solution space is M, equal to the number of best anchor nodes that need to be selected;representing the position of the selected head wolf j in the kth dimension after the t-th iteration; />Representing the ith grade omega of the wolf in the kth dimension after completing the move behavior of the following head wolf in the t-th iterationA location; />Representing the position of the ith gray wolf with omega after randomly walking towards the first wolf j in the kth dimension space when the (t+1) th iteration is carried out;
is the radius of the enclosure, representing the distance of the ith class omega of wolves from the first wolf j in the kth dimension, when in the hunting phase, the first wolf is located very close to the prey, when>Also understood as the distance between the wolf of class ω and the prey; />Representing the weight of the first wolf j on the ith gray wolf of class omega at the kth dimension position,/>Weight representing the radius enclosed by the first wolf j on the ith grade omega by the gray wolf at the kth dimension position, +.>And->Belonging to the group of adjustable parameters, their expressions are as follows:
in the formula (4), r 1 And r 2 Is subject to uniform distribution and is in the range of [0,1 ]]Random numbers of (a); a represents a convergence factor, and the cosine annealing convergence factor is adopted and expressed as follows:
in the formula (5), lambda is an adjusting factor, and the specific gravity relation of global and local search in complete iteration is controlled;
the gray wolf algorithm relies on step weightsAnd head wolf weight->The global searching capability and the local searching capability are considered, and the excellent performance of the method in global optimization and solving precision is ensured; finally, the formula of the step strategy of the i-th gray wolf with omega following the updated position of the head wolf is as follows:
in the formula (6), a represents a convergence factor obtained according to the formula (5); w (W) α ,W β ,W δ The step-up update weights for the top wolves of class α, β, δ, respectively, are calculated as follows:
W i ＝exp(-F i )/(exp(-F α )+exp(-F β )+exp(-F δ ))i＝α,β,δ (7)，
in the formula (7), F α ,F β ,F δ The adaptability function values of the first wolves with the grades of alpha, beta and delta are respectively; the individual position of the wolf at this time is updated and a fitness value is calculated.
Further, in step seven, the head wolves are subjected to Levy Flight or random swimming. The Levy Flight and random swimming strategy are introduced to endow the wolf hunting capability, and the wolf position updating method based on the Levyflight is as follows:
in the formula (8), the expression "a",the position of the head wolf with the grade of j updated after Levy Flight is carried out in the kth dimension is represented, and the value of j is alpha, beta and delta; />The position of the top wolf with the grade of j in the kth dimension is represented, and the value of j is alpha, beta and delta; l represents the lewy step weight, let l=0.01 in general; epsilon represents the step size obeying the Lewy distribution, and is generally generated by using the Mantegna method:
formula (9), v obeysNormal distribution of (a), general sigma υ The value is 1; mu compliance->The standard deviation of the normal distribution of (2) is:
in formula (10), Γ (·) represents a gamma function; gamma-U (0, 2) represents random variables subject to uniform distribution within the range of [0,2 ];
the random walk strategy adopts random numbers obeying uniform distribution to update the positions of the head wolves, and the head wolves position updating method based on random walk is mainly used for improving the local refined searching capability of the head wolves and comprises the following steps of:
in the formula (11), ρ represents a random variable subject to uniform distribution of ρ to U (0, 1);representing the current location;representing the updated location;
when the convergence factor a is greater than or equal to 1, updating the head wolf position by adopting Levy Flight; otherwise, updating the position using a random walk strategy:
further, in step eight, it is determined whether the first wolf of class β, δ needs to follow the action by introducing a complianceDistributed decision parameters->Comparing it with a decision threshold to determine whether the top wolf of class β and δ is following, the decision threshold is calculated as follows:
in the formula (13), N represents the number of the total grades of the wolf group, and N represents the grade of the wolf group.
The beneficial effects of the invention are as follows: 1. the cosine annealing convergence factor is adopted, so that the convergence factor has higher value at the early stage of iteration and slower attenuation speed, and has smaller value and faster attenuation speed at the later stage of iteration, thereby being beneficial to enhancing the global exploration capacity at the early stage of iteration and the local accurate solving capacity at the later stage of iteration; 2. the hunting capability of the head wolves is increased, the following capability of beta and delta of the head wolves is enhanced, so that the problem of waste of wolf cluster resources is reduced, and the optimizing efficiency of an algorithm is improved; 3. the self-adaptive weighting stepping strategy is adopted to give the three wolves different weights, so that the global and local searching capability of the algorithm is balanced
Drawings
FIG. 1 is a flow chart of the gray wolf optimization algorithm in the present invention;
FIG. 2 is a three-dimensional schematic diagram of a benchmark test function;
FIG. 3 is a diagram of a gray wolf scale pyramid;
FIG. 4 is a schematic diagram of a Hunting process for a Hunting wolf population;
FIG. 5 is a diagram of wolf pack search and hunting behavior;
FIG. 6 is a comparison of the convergence factor before and after improvement;
FIG. 7 is a graph of comparison before and after step weight improvement;
FIG. 8 is a two-dimensional trajectory of the Lewy fly and random walk;
FIG. 9 is a graph of performance comparisons between the improved gray wolf optimization algorithm;
FIG. 10 is a graph comparing the change of the optimizing time with the total number of anchor nodes;
FIG. 11 is a graph showing the comparison of the adaptation value of different algorithms with the number of iterations;
FIG. 12 is a graph showing the comparison of the fitness value of an optimization algorithm with the standard deviation of the position measurement error;
FIG. 13 is a graph showing the adaptation value of an optimization algorithm versus the standard deviation of TDOA measurement errors;
FIG. 14 is a two-dimensional distribution of anchor node combinations sought by various optimization algorithms.
Detailed Description
The first embodiment is as follows: describing the present embodiment with reference to fig. 1 to 14, a preferred method for anchor node based on the improved gray wolf optimization algorithm according to the present embodiment is implemented by the following steps:
step one, coding all N anchor nodes participating in selection, wherein the reference anchor node is number 1, and the other nodes are coded according to numbers 2 to N;
step two, setting wolf parameters including wolfnum number wolfnum and total iteration times t max And a wolf individual solution parameter dimension dim;
step three, calculating the fitness value of the wolf group individuals through an Ackley function;
step four, searching three wolves according to the fitness value, wherein the grades are alpha, beta and delta from high to low, t=0, t is the iteration number, and iteration is started;
step five, carrying out position update on all the wolves with the grades of omega, and calculating the current position fitness value;
step six, according to the calculated fitness value, selecting three gray wolves with the maximum fitness value and with the omega grades, and comparing the gray wolves with the alpha, beta and delta grades, and if the gray wolves meet the requirements, replacing the first wolves;
step seven, carrying out Laiweiling flight or random swimming on the head wolves, if the adaptability value of the head wolves is reduced, allowing updating, otherwise, keeping the original position;
step eight, judging whether the head wolves with the grades of beta and delta need to follow the action, if so, updating the positions of the head wolves with the grades of beta and delta, otherwise, keeping the original positions;
step nine, let t=t+1, judge whether to meet the condition that the iteration terminates, if meet, output the first wolf position of the grade alpha, otherwise, jump to step three, continue the iteration.
The second embodiment is as follows: referring to fig. 1 to 14, the present embodiment is described, in which all N anchor nodes participating in selection are encoded in the first step of an anchor node optimization method based on an improved gray wolf optimization algorithm, the reference anchor node is number 1, and the remaining nodes are encoded according to numbers 2 to N; a vector B of N boolean variables is introduced, which can be expressed as:
B＝[B 1 B 2 ... B N ] T ,B i ∈{0,1} (1)，
in the formula (1), B i =0 indicates that the ith anchor node is not selected, whereas a value equal to 1 indicates that it is selected; suppose that the operating state of the reference anchor node is defined by B 1 Indicating that the value is often 1.
And a third specific embodiment: referring to fig. 1 to 14, a description is given of the present embodiment, in which an Ackley function in a benchmark test function is selected as an fitness function in step three of an anchor node optimization method based on an improved gray wolf optimization algorithm to evaluate fitness values of each individual. The formula is as follows:
in the formula (2), n represents the dimension of the wolf group individual; e represents a natural constant; x is x i Representing the position solution vector of the ith gray wolf only.
The specific embodiment IV is as follows: in the fourth step of the anchor node optimization method based on the improved wolf optimization algorithm according to the present embodiment, the grade of each wolf in the population is determined according to the fitness function value, the first three grades are alpha, beta, delta, and the lowest grade is omega, wherein the higher the fitness is, the higher the grade is.
Fifth embodiment: referring to fig. 1 to 14, in the fifth step of the anchor node optimization method based on the improved wolf optimization algorithm according to the present embodiment, the position of each common wolf is updated by using the position update formula of the algorithm, and the hunting process of the wolf population mainly includes three stages of searching, following and capturing;
in the searching stage, when the hunting object moves, the individual wolves search the hunting object from four sides in the direction far away from three head wolves in a random walk mode, each wolf searches three middle position solutions according to the independent command of the three head wolves, and in the following stage of the next step, the middle solutions are fused to obtain the final position;
in the following stage, the wolf group updates the final position according to the result of the searching stage, and recalculates the fitness value of each individual to update the position of each individual in the group, and reelects the wolves with the grades of alpha, beta and delta in the group, namely three wolves closest to the prey, and the wolves with other grades of omega move towards the positions of the three wolves, so that the wolves with the high grade are led by the individual group to approach towards the global optimal solution;
in the trapping stage, three wolves in the wolf group are locked in the scope of the prey, so that the wolves with the grade omega do not need to search the prey everywhere, the wolves with the grade omega give a trapping command, the wolves with the grade omega move towards the direction close to the wolves and gather, when the prey is in a rest state, the wolves can attack the prey, and the position of the wolves with the grade alpha is the optimal solution of the optimized objective function;
the formula for updating the position of the gray wolf with the grade omega by random walk is as follows:
in formula (3), i=1, 2,..l represents the i-th wolf, L represents the total number of wolves rated ω; j=α, β, δ represents three top wolves; k=1, 2..m represents the kth dimension (each wolf has its own direction vector, here representing the direction vector of the kth wolf), the maximum dimension of the solution space is M, equal to the number of best anchor nodes that need to be selected;representing the position of the selected head wolf j in the kth dimension after the t-th iteration; />Representing the position of the ith grade omega of the wolf in the kth dimension after completing the movement behavior of the following head wolf in the t-th iteration; />Representing the position of the ith gray wolf with omega after randomly walking towards the first wolf j in the kth dimension space when the (t+1) th iteration is carried out;
is the radius of the enclosure, representing the distance of the ith class omega of wolves from the first wolf j in the kth dimension, when in the hunting phase, the first wolf is located very close to the prey, when>Also understood as the distance between the wolf of class ω and the prey; />Representing the weight of the first wolf j on the ith gray wolf of class omega at the kth dimension position,/>Weight representing the radius enclosed by the first wolf j on the ith grade omega by the gray wolf at the kth dimension position, +.>And->Belonging to the group of adjustable parameters, their expressions are as follows:
in the formula (4), r 1 And r 2 Is subject to uniform distribution and is in the range of [0,1 ]]Random numbers of (a); a represents a convergence factor, and the cosine annealing convergence factor is adopted and expressed as follows:
in the formula (5), lambda is an adjusting factor, and the specific gravity relation of global and local search in complete iteration is controlled;
the gray wolf algorithm relies on step weightsAnd head wolf weight->To give consideration to global and local searching capability, ensure global optimization and solving precisionExcellent performance; finally, the formula of the step strategy of the i-th gray wolf with omega following the updated position of the head wolf is as follows:
in the formula (6), a represents a convergence factor obtained according to the formula (5); w (W) α ,W β ,W δ The step-up update weights for the top wolves of class α, β, δ, respectively, are calculated as follows:
W i ＝exp(-F i )/(exp(-F α )+exp(-F β )+exp(-F δ ))i＝α,β,δ (7)，
in the formula (7), F α ,F β ,F δ The adaptability function values of the first wolves with the grades of alpha, beta and delta are respectively; the individual position of the wolf at this time is updated and a fitness value is calculated.
Specific embodiment six: referring to fig. 1 to 14, in the step seven of the anchor node optimization method based on the improved gray wolf optimization algorithm according to the present embodiment, the first wolf is subjected to Levy Flight or random swimming. The Levy Flight and random swimming strategy are introduced to endow the wolf hunting capability, and the wolf position updating method based on the Levy Flight is as follows:
in the formula (8), the expression "a",the position of the head wolf with the grade of j updated after Levy Flight is carried out in the kth dimension is represented, and the value of j is alpha, beta and delta; />The position of the top wolf with the grade of j in the kth dimension is represented, and the value of j is alpha, beta and delta; l represents the lewy step weight, let l=0.01 in general; epsilon represents the step size obeying the Lewy distribution, typically using the Mantegna squareGenerating a step length epsilon by a method:
formula (9), v obeysNormal distribution of (a), general sigma υ The value is 1; mu compliance->The standard deviation of the normal distribution of (2) is:
in formula (10), Γ (·) represents a gamma function; gamma-U (0, 2) represents random variables subject to uniform distribution within the range of [0,2 ];
the random walk strategy adopts random numbers obeying uniform distribution to update the positions of the head wolves, and the head wolves position updating method based on random walk is mainly used for improving the local refined searching capability of the head wolves and comprises the following steps of:
in the formula (11), ρ represents a random variable subject to uniform distribution of ρ to U (0, 1);representing the current location;representing the updated location;
when the convergence factor a is greater than or equal to 1, updating the head wolf position by adopting Levy Flight; otherwise, updating the position using a random walk strategy:
seventh embodiment: referring to fig. 1 to 14, a description is given of the present embodiment, in which it is determined whether or not the first wolf with the grade of β, δ needs to follow the action in the step eight of the anchor node optimization method based on the improved wolf optimization algorithm, by introducing a complianceDistributed decision parameters->Comparing it with a decision threshold to determine whether the top wolf of class β and δ is following, the decision threshold is calculated as follows:
in the formula (13), N represents the number of the total grades of the wolf group, and N represents the grade of the wolf group.
Performance evaluation was performed on the anchor node optimization method based on the modified wolf optimization algorithm. Performing performance comparison on the improved gray wolf optimization algorithm by taking F (x) as a target optimization function (fitness function), wherein simulation experiment parameter setting comprises the following steps: the total number of wolves is 30, the iteration number is set to 300, the adaptation degree average of each iteration is calculated by using 200 Monte Carlo experiments, and the logarithmic values of the adaptation degree of an original wolf optimization algorithm (GWO curve), an improved wolf optimization algorithm based on a nonlinear convergence factor (IGWO-1 curve), an improved wolf optimization algorithm based on the hunting and follow-up capability of increasing head wolves (IGWO-2 curve), an improved wolf optimization algorithm based on an adaptive weighted walking strategy (IGWO-3 curve) and an improved wolf optimization algorithm (IGWO-4 curve) combined with three improvement points are respectively drawn, and the change curve of the logarithmic values of the adaptation degree with the iteration number is shown in fig. 9. It can be concluded that under the same iteration times, the optimizing speed and optimizing precision of the gray wolf optimizing algorithm can be improved by all three improving points, and the optimizing performance of the IGWO algorithm is better than that of the original GWO algorithm; descent downThe fastest is the IGWO-4 curve combined with three improvement points, which shows that the global searching capacity is strongest; the convergence accuracy of the IGWO-4 algorithm combined with three improvement points is highest and reaches 10 -10 On the order of magnitude of (2).
By changing the total number of anchor nodes, setting optimizing termination conditions, and when the number of anchor nodes is increased, drawing an IGWO algorithm, a global traversal algorithm, a GA algorithm, a PSO algorithm and a GWO algorithm optimizing average time length change histogram and a graph, which are shown in figure 10. From the above, it can be concluded that, from the whole, the time for searching the optimal anchor node combination by using the global traversal algorithm is longer, and the optimizing time of the global traversal algorithm increases exponentially with the increase of the number of anchor nodes; the IGWO algorithm performs best overall.
Comparing the optimizing precision and optimizing capability of each optimizing algorithm from the iteration number dimension, and comparing the performance of the IGWO algorithm with that of the GA algorithm, the PSO algorithm and the GWO algorithm by drawing a curve of the fitness value changing along with the iteration number, as shown in figure 11. The parameters are shown in table 1.
Table 1 iterative optimization versus simulation experiment parameter settings for different optimization algorithms
From the results, from the early iteration stage, the descending speeds of the IGWO algorithm and the GWO algorithm are equivalent, and secondly, the PSO algorithm is the slowest in the early iteration stage, which means that the global searching performance of the GA algorithm is poorer, and the optimization capacity of the GA algorithm is poorer than that of other algorithms; from the later iteration stage, the GA algorithm has the worst iteration precision, the IGWO algorithm is the best, and the fine solving capability of the IGWO algorithm is higher in the aspect of local exploration, and the optimizing precision is higher under the same iteration times.
The performance influence of the anchor node position measurement error on the optimization algorithm is explored, and the standard deviation sigma of the anchor node position measurement error is changed m And (3) drawing a change curve of the fitness value of each algorithm, as shown in fig. 12. Wherein the anchor node specific location information is shown in table 2.
Table 2 anchor node location
It can be derived therefrom that with sigma m The relative fitness value of various optimization algorithms is also increased, the oscillation rising trend is shown, and the estimation performance of the optimization algorithm is influenced by the position measurement error. The relative fitness value of the GA algorithm rises most obviously, and the rising trend of the IGWO algorithm is slowest, so that the IGWO algorithm has the strongest resistance to position measurement errors and the GA algorithm has the weakest resistance to position measurement errors.
The influence of TDOA distance measurement errors on the performance of an optimization algorithm is explored, and the TDOA distance measurement error standard deviation sigma is changed t And (3) drawing a fitness value change curve of each algorithm, as shown in fig. 13. Wherein the anchor node specific location information is shown in table 3.
TABLE 3 Anchor node position
From the condition of the change of the relative fitness value, when the standard deviation of the TDOA measurement error is smaller than 7m, the algorithm has good fitting effect on the optimal fitness curve, the maximum difference value is not more than 2, but the fitting difficulty is increased along with the increase of the error; second, with TDOA ranging error standard deviation sigma t The relative fitness value of each optimization algorithm is also increased in oscillation, which shows that TDOA measurement errors can affect the optimization performance of the optimization algorithm, and the difference between the curves of each algorithm is also increased, thus proving that the effect of the IGWO algorithm for inhibiting the TDOA measurement errors is the best.
The anchor node combination two-dimensional distribution diagram of the final iterative optimizing result of the last Monte Carlo experiment of each algorithm is shown in fig. 14.
Table 4 shows the standard deviation sigma of the TDOA range error t When=15m, each algorithm is at the last timeAnd (3) final iterative optimization results of the Monte Carlo experiments, wherein the anchor node numbers marked red represent different anchor nodes in the optimal anchor node combination obtained by the global traversal algorithm.
TABLE 4 iterative optimization results of optimization algorithms (TDOA Range error standard deviation sigma) t ＝15m)
In combination with the optimizing results of each algorithm in table 4 and fig. 14, it is found that, although the PSO algorithm has 4 anchor nodes and the best combination result of the global traversal method is different, the anchor node combination selected by the GA algorithm is different from the best combination by only 2 anchor nodes, but the fitness value of the PSO algorithm is smaller than that of the GA algorithm; secondly, the optimizing results of the GWO algorithm and the IGWO algorithm are different from the optimal combination of 3 anchor nodes, the fitness value is the same, the difference between the optimizing results and the fitness value of the optimal combination is the least, and the optimizing results are better than those of the PSO algorithm and the GA algorithm.
The test result shows that although the global traversal algorithm can obtain the optimal anchor node combination, the time consumption of the algorithm is greatly increased along with the increase of the number of the anchor nodes, but the optimization algorithm is not affected by the time consumption, and the method is more suitable for solving the node selection problem and the station arrangement problem of the large-scale sensor network. Meanwhile, the IGWO algorithm is compared with the GA algorithm, the PSO algorithm and the GWO algorithm in many aspects, so that the influence of the anchor node position measurement error and the TDOA ranging error on the positioning accuracy can be well restrained by the IGWO algorithm due to good global searching and local refinement capability.
The present invention is not limited to the preferred embodiments, but is capable of modification and variation in detail, and other embodiments, such as those described above, of making various modifications and equivalents will fall within the spirit and scope of the present invention.
Claims (7)
1. An anchor node optimization method based on an improved gray wolf optimization algorithm is characterized by comprising the following steps of: the anchor node optimization method based on the improved gray wolf optimization algorithm is realized by the following steps:
step one, coding all N anchor nodes participating in selection, wherein the reference anchor node is number 1, and the other nodes are coded according to numbers 2 to N;
step two, setting wolf parameters including wolfnum number wolfnum and total iteration times t max And a wolf individual solution parameter dimension dim;
step three, calculating the fitness value of the wolf group individuals through an Ackley function;
step four, searching three wolves according to the fitness value, wherein the grades are alpha, beta and delta from high to low, t=0, t is the iteration number, and iteration is started;
step five, carrying out position update on all the wolves with the grades of omega, and calculating the current position fitness value;
step six, according to the calculated fitness value, selecting three gray wolves with the maximum fitness value and with the omega grades, and comparing the gray wolves with the alpha, beta and delta grades, and if the gray wolves meet the requirements, replacing the first wolves;
step seven, carrying out Laiweiling flight or random swimming on the head wolves, if the adaptability value of the head wolves is reduced, allowing updating, otherwise, keeping the original position;
step eight, judging whether the head wolves with the grades of beta and delta need to follow the action, if so, updating the positions of the head wolves with the grades of beta and delta, otherwise, keeping the original positions;
step nine, let t=t+1, judge whether to meet the condition that the iteration terminates, if meet, output the first wolf position of the grade alpha, otherwise, jump to step three, continue the iteration.
2. An anchor node optimization method based on an improved gray wolf optimization algorithm as claimed in claim 1, wherein: coding all N anchor nodes participating in selection, wherein the reference anchor node is number 1, and the other nodes are coded according to numbers 2 to N; a vector B of N boolean variables is introduced, which can be expressed as:
B＝[B 1 B 2 ... B N ] T ,B i ∈{0,1} (1)，
in the formula (1), B i =0 indicates that the ith anchor node is not selected, whereas a value equal to 1 indicates that it is selected; suppose that the operating state of the reference anchor node is defined by B 1 Indicating that the value is often 1.
3. An anchor node optimization method based on an improved gray wolf optimization algorithm as claimed in claim 1, wherein: and thirdly, selecting an Ackley function in the benchmark test function as an fitness function to evaluate the fitness value of each individual. The formula is as follows:
in the formula (2), n represents the dimension of the wolf group individual; e represents a natural constant; x is x i Representing the position solution vector of the ith gray wolf only.
4. An anchor node optimization method based on an improved gray wolf optimization algorithm as claimed in claim 1, wherein: and step four, determining the grade of each wolf in the group according to the fitness function value, wherein the first three grades are alpha, beta and delta, and the lowest grade is omega, and the higher the fitness is, the higher the grade is.
5. An anchor node optimization method based on an improved gray wolf optimization algorithm as claimed in claim 1, wherein: in the fifth step, the position of each common wolf is updated by utilizing a position updating formula of an algorithm according to the position of the optimal wolf, and the hunting process of the wolf population mainly comprises three stages of searching, following and capturing;
in the searching stage, when the hunting object moves, the individual wolves search the hunting object from four sides in the direction far away from three head wolves in a random walk mode, each wolf searches three middle position solutions according to the independent command of the three head wolves, and in the following stage of the next step, the middle solutions are fused to obtain the final position;
in the following stage, the wolf group updates the final position according to the result of the searching stage, and recalculates the fitness value of each individual to update the position of each individual in the group, and reelects the wolves with the grades of alpha, beta and delta in the group, namely three wolves closest to the prey, and the wolves with other grades of omega move towards the positions of the three wolves, so that the wolves with the high grade are led by the individual group to approach towards the global optimal solution;
in the trapping stage, three wolves in the wolf group are locked in the scope of the prey, so that the wolves with the grade omega do not need to search the prey everywhere, the wolves with the grade omega give a trapping command, the wolves with the grade omega move towards the direction close to the wolves and gather, when the prey is in a rest state, the wolves can attack the prey, and the position of the wolves with the grade alpha is the optimal solution of the optimized objective function;
the formula for updating the position of the gray wolf with the grade omega by random walk is as follows:
in formula (3), i=1, 2,..l represents the i-th wolf, L represents the total number of wolves rated ω; j=α, β, δ represents three top wolves; k=1, 2..m represents the kth dimension (each wolf has its own direction vector, here representing the direction vector of the kth wolf), the maximum dimension of the solution space is M, equal to the number of best anchor nodes that need to be selected;indicating that the selected first wolf j after the t-th iteration is at the t-thThe position of the k dimension; />Representing the position of the ith grade omega of the wolf in the kth dimension after completing the movement behavior of the following head wolf in the t-th iteration; />Representing the position of the ith gray wolf with omega after randomly walking towards the first wolf j in the kth dimension space when the (t+1) th iteration is carried out;
is the radius of the enclosure, representing the distance of the ith class omega of wolves from the first wolf j in the kth dimension, when in the hunting phase, the first wolf is located very close to the prey, when>Also understood as the distance between the wolf of class ω and the prey; />Representing the weight of the first wolf j on the ith gray wolf of class omega at the kth dimension position,/>Weight representing the radius enclosed by the first wolf j on the ith grade omega by the gray wolf at the kth dimension position, +.>And->Belonging to the group of adjustable parameters, their expressions are as follows:
in the formula (4), r 1 And r 2 Is subject to uniform distribution and is in the range of [0,1 ]]Random numbers of (a); a represents a convergence factor, and the cosine annealing convergence factor is adopted and expressed as follows:
in the formula (5), lambda is an adjusting factor, and the specific gravity relation of global and local search in complete iteration is controlled;
the gray wolf algorithm relies on step weightsAnd head wolf weight->The global searching capability and the local searching capability are considered, and the excellent performance of the method in global optimization and solving precision is ensured; finally, the formula of the step strategy of the i-th gray wolf with omega following the updated position of the head wolf is as follows:
in the formula (6), a represents a convergence factor obtained according to the formula (5); w (W) α ,W β ,W δ The step-up update weights for the top wolves of class α, β, δ, respectively, are calculated as follows:
W i ＝exp(-F i )/(exp(-F α )+exp(-F β )+exp(-F δ ))i＝α,β,δ (7)，
in the formula (7), F α ,F β ,F δ The adaptability function values of the first wolves with the grades of alpha, beta and delta are respectively; the individual position of the wolf at this time is updated and a fitness value is calculated.
6. An anchor node optimization method based on an improved gray wolf optimization algorithm as claimed in claim 1, wherein: in step seven, the first wolf is subjected to Levy Flight or random swimming. The Levy Flight and random swimming strategy are introduced to endow the wolf hunting capability, and the wolf position updating method based on the Levy Flight is as follows:
in the formula (8), the expression "a",the position of the head wolf with the grade of j updated after Levy Flight is carried out in the kth dimension is represented, and the value of j is alpha, beta and delta; />The position of the top wolf with the grade of j in the kth dimension is represented, and the value of j is alpha, beta and delta; l represents the lewy step weight, let l=0.01 in general; epsilon represents the step size obeying the Lewy distribution, and is generally generated by using the Mantegna method:
formula (9), v obeysNormal distribution of (a), general sigma υ The value is 1; mu compliance->The standard deviation of the normal distribution of (2) is:
in formula (10), Γ (·) represents a gamma function; gamma-U (0, 2) represents random variables subject to uniform distribution within the range of [0,2 ];
the random walk strategy adopts random numbers obeying uniform distribution to update the positions of the head wolves, and the head wolves position updating method based on random walk is mainly used for improving the local refined searching capability of the head wolves and comprises the following steps of:
in the formula (11), ρ represents a random variable subject to uniform distribution of ρ to U (0, 1);representing the current location; />Representing the updated location;
when the convergence factor a is greater than or equal to 1, updating the head wolf position by adopting Levy Flight; otherwise, updating the position using a random walk strategy:
7. an anchor node optimization method based on an improved gray wolf optimization algorithm as claimed in claim 1, wherein: step eight, judging whether the wolf with the grade of beta, delta needs to follow the action or not by introducing a complianceDistributed decision parameters->Comparing it with decision threshold to determine whether the first wolf of class beta and delta is proceedingFollowing the action, the decision threshold is calculated as follows:
in the formula (13), N represents the number of the total grades of the wolf group, and N represents the grade of the wolf group.
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