LU500797A1 - Ranging positioning method suitable for sparse anchor node wsn - Google Patents
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W12/00—Security arrangements; Authentication; Protecting privacy or anonymity
- H04W12/009—Security arrangements; Authentication; Protecting privacy or anonymity specially adapted for networks, e.g. wireless sensor networks, ad-hoc networks, RFID networks or cloud networks
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/0278—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves involving statistical or probabilistic considerations
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- H04W—WIRELESS COMMUNICATION NETWORKS
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- H04W12/60—Context-dependent security
- H04W12/63—Location-dependent; Proximity-dependent
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- H04W—WIRELESS COMMUNICATION NETWORKS
- H04W4/00—Services specially adapted for wireless communication networks; Facilities therefor
- H04W4/02—Services making use of location information
- H04W4/023—Services making use of location information using mutual or relative location information between multiple location based services [LBS] targets or of distance thresholds
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- H04W4/38—Services specially adapted for particular environments, situations or purposes for collecting sensor information
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- H04W64/00—Locating users or terminals or network equipment for network management purposes, e.g. mobility management
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- G—PHYSICS
- G01—MEASURING; TESTING
- G01S—RADIO DIRECTION-FINDING; RADIO NAVIGATION; DETERMINING DISTANCE OR VELOCITY BY USE OF RADIO WAVES; LOCATING OR PRESENCE-DETECTING BY USE OF THE REFLECTION OR RERADIATION OF RADIO WAVES; ANALOGOUS ARRANGEMENTS USING OTHER WAVES
- G01S5/00—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations
- G01S5/02—Position-fixing by co-ordinating two or more direction or position line determinations; Position-fixing by co-ordinating two or more distance determinations using radio waves
- G01S5/14—Determining absolute distances from a plurality of spaced points of known location
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Abstract
A ranging positioning method suitable for a sparse anchor node WSN, comprising: obtaining coordinate parameters of anchor nodes in a network and ranging information of all sensor nodes by a positioning center, constructing a positioning model, and generating a blind node positioning matrix; generating a fitness function according to the positioning model, and constructing an adaptive operator; and running an adaptive firework algorithm to carry out iterative optimization, outputting an optimal elite individual to be parsed as coordinates of all blind nodes. The positioning model of the present disclosure utilizes the ranging information of all sensor nodes, especially the ranging information among the blind nodes, remarkably improves the positioning precision of the sensor nodes, reduces the dependence on the density of the anchor nodes, and support two-dimensional plane and three-dimensional space positioning at the same time, so the positioning method is suitable for the WSN of sparse anchor nodes.
Description
DESCRIPTION 500797
[01] This patent application claims the benefit and priority of Chinese Patent Application No. 202010240155.8 filed on March 31, 2020, with a title of "Ranging Positioning Method Suitable for Sparse Anchor Node WSN" with the China Intellectual Property Administration, the disclosure of which is incorporated by reference herein in its entirety as part of the present application.
[02] The present disclosure belongs to the WSN positioning technical field, and more particularly, relates to a ranging positioning method suitable for a sparse anchor node WSN.
[03] As the key supporting technology of the perception layer in the Internet of Things, WSN has been widely used. Since sensor nodes have relatively low cost, and usually are not equipped with positioning modules such as GPS, there is a high demand for coordinated and precise positioning among the sensor nodes. Generally, WSN positioning methods can be divided into ranging positioning methods and non-ranging positioning methods. The accuracy of non-ranging positioning methods is usually low, and sometimes it is difficult to meet practical application requirements.
[04] The general process of the WSN coordinated positioning method is as follows: an anchor node with a known location broadcasts its own location information in the network; then a blind node to be located with an unknown location acquires distance characteristic information of the distance to the anchor node, such as received information strength instruction, a number of propagation hops, etc., to obtain anchor node location information synchronously; finally, after the information of the multiple anchor nodes is acquired, the positioning is finished by converting the distance 500797 characterization information into ranging information.
[05] However, since the communication radius of the sensor nodes is short, there may not necessarily be three (two-dimensional plane positioning) or four (three-dimensional space positioning) or more anchor nodes within the communication range of each blind node. That is, WSN often faces a sparse anchor node environment during practical application. Generally, non-ranging positioning methods are the first choice for positioning in a sparse anchor node environment, such as positioning algorithms of DV-Hop and APIT. However, due to the poor error of the distance characterization information in the non-ranging positioning method, this type of positioning method has the defect of low positioning accuracy. In view of this, ranging positioning methods suitable for a sparse anchor node environment has gradually become the focus of scholars’ research.
[06] Therefore, some scholars have proposed upgrading the blind nodes that have completed positioning to anchor nodes, so as to deal with sparseness of anchor nodes and participate in the positioning of subsequent blind nodes. However, this method has a problem of error accumulation, that is, the positioning error of the blind nodes will be further transmitted to the subsequent blind nodes after the blind nodes are upgraded to anchor nodes, and thus the positioning error increases gradually. Some scholars have also proposed to adjust the transmission power of anchor nodes to cover more blind nodes, to ensure that the blind nodes receive the position information of three anchor nodes at the same time as much as possible. However, this kind of wireless communication module with adjustable transmission power will significantly increase the cost of the anchor nodes, and restrict the adaptability of the solution.
[07] To sum up, for the WSN positioning requirements of sparse anchor nodes, the existing non-ranging positioning technology has the problem of low positioning accuracy, while the existing ranging positioning technology has the defects of accumulating positioning error and over-high node cost.
[08] For the problems in the prior arts, the present disclosure provides a ranging 500797 positioning method suitable for a sparse anchor node WSN.
[09] The ideas to solve the above technical problems are as follows:
[10] The present disclosure solves the positioning problem of the sparse anchor node WSN from the perspective of utilizing the ranging information among all sensor nodes as much as possible. Through in-depth analysis of the source of positioning errors, it is found that ignoring the ranging information among blind nodes and other blind nodes (hereinafter referred to as the ranging information among blind nodes) is the root cause of the high positioning error. Therefore, by incorporating the ranging information among blind nodes and constructing a positioning model, we can improve the positioning accuracy effectively. Meanwhile, by representing coordinates of all the blind nodes to be sought as a blind node positioning matrix, converting multi-node positioning into a single-objective optimization problem, and performing positioning synchronously, it can avoid the problem of error accumulation while only requiring a small number of anchor nodes.
[11] The significance of solving the above technical problem:
[12] As the key supporting technology of the Internet of Everything, WSN has a wide range of application prospects in smart cities, smart homes, smart military camps, smart agriculture, smart logistics and other fields. Moreover, sensor node positioning is the foundation to implement intelligence and smart applications, and sensor information of missing locations is even worthless in some scenarios. Solving the WSN positioning problem suitable for sparse anchor node environments will effectively expand the application scenarios of WSN.
[13] In order to achieve the above objective, the technical solution of the present disclosure is: a ranging positioning method suitable for a sparse anchor node WSN, and the ranging positioning method suitable for a sparse anchor node WSN comprises:
[14] a first step: obtaining coordinate parameters of anchor nodes in a network and ranging information of all sensor nodes by a positioning center, constructing a positioning model, and generating a blind node positioning matrix;
[15] a second step: generating a fitness function according to the positioning model,
and constructing an adaptive operator; 500797
[16] a third step: running an adaptive firework algorithm to carry out iterative optimization, outputting an optimal elite individual to be parsed as coordinates of all blind nodes.
[17] Preferably, the positioning model of the ranging positioning method suitable for a sparse anchor node WSN includes ranging information among the blind nodes, and adjusts weights of different types of ranging information by designing a positioning optimization factor /, to be suitable for different WSN environments.
[18] Preferably, a blind node positioning matrix representation method of the ranging positioning method suitable for a sparse anchor node WSN converts a multi-objective optimization problem of multi-node synchronous positioning into a single-objective optimization problem, and finally is reversely parsed as all blind node coordinates.
[19] Another objective of the present disclosure is to provide a WSN ranging positioning simulation platform applying the ranging positioning method suitable for a sparse anchor node WSN.
[20] The ranging positioning method suitable for a sparse anchor node WSN proposed by the present disclosure has the following advantageous effects: the positioning method proposed by the solution can obviously increase the positioning accuracy of the sparse anchor node WSN without increasing network cost, and meanwhile support the two-dimensional plane and three-dimensional space positioning scenarios, and has good applicability, compared with the non-ranging positioning method in the current sparse anchor node environment, the present disclosure makes use of the ranging information among the sensor nodes, and has higher positioning accuracy; compared with the ranging positioning method in the current sparse anchor node environment, the positioning model of the present disclosure incorporates the ranging information among blind nodes, and meanwhile converts the multi-node positioning problem into a single-objective optimization problem by using the blind nodes positioning matrix representation method to realize synchronous positioning, so as to effectively avoid the problem of error accumulation.
BRIEFT DESCRIPTION OF THE DRAWINGS 500797
[21] The following will further describe the present disclosure by referring to the accompanying drawings.
[22] FIG. 1 is a flow chart of the ranging positioning method suitable for a sparse anchor node WSN according to the present disclosure;
[23] Fig. 2 is a composition diagram of the WSN ranging positioning simulation platform according to the present disclosure.
[24] The following will describe the technical solutions in the embodiments of the present disclosure clearly and completely by combining with the accompanying drawings of the embodiments of the present disclosure. Obviously, the embodiments described are merely part of the embodiments, rather than all of the embodiments, of the present disclosure.
[25] Refer to Fig. 1: a ranging positioning method suitable for a sparse anchor node WSN, and the ranging positioning method suitable for a sparse anchor node WSN comprises:
[26] a first step: obtaining coordinate parameters of anchor nodes in a network and ranging information among all sensor nodes by a positioning center, constructing a positioning model, and generating a blind node positioning matrix.
[27] The positioning center is responsible for gathering sensor node parameters in the network and running positioning algorithms. After obtaining the anchor node coordinate parameters in the network and the ranging information among all the sensor nodes, it ~~ pre-processes the sensor node position coordinates. C= {€ | k= 1,2,---,m,} is denoted as a set of sensor nodes, wherein C, = {aici . ©} is the Æ sensor node, Mis a number of sensor nodes, VE {2,3} is a node coordinate dimension (v=2 represents two-dimension plane positioning, while v=3 represents three-dimensional positioning). Similarly, in the set of anchor
_ _ 1 2 LU500797 nodes À = {a, |i=12-—,m,}, the i” anchor node is à, = fa! a „4, a7} , and m, is a number of anchor nodes; and in the set of blind nodes B = {b, | j= 12, My}, the j blind node is b, = {61,0707}, and m, is a number of blind nodes. The positioning region is denoted as D.
[28] A difference between a given neighboring node ranging distance d, and the geographic distance d . 18 called a positioning error d°
[29] d(5,,6,)=4,(5,.6)-4.(5,,6)
[30] By making full use of the ranging information among the blind nodes, the positioning model is established with the goal of minimizing the positioning error: my Me _ min f (B)= >> axd(b,.E) j=1 k=1 d(b,ë,)<R
[31] _ 1-6 ceA s.t.4a-— _ B Cc. eB pe [0.1)
[32] The model objective function is designed to minimize the sum of the positioning errors of all nodes. Among the restrictions, R is a communication radius of the node, and thus d, (5,.) < R defines that node b, and node C, are a pair of neighboring nodes; ß is a positioning optimization factor, representing the sensitivity of the model positioning error to the ranging information among the nodes, and its value has a greater impact on the positioning accuracy. Usually, the bigger the value of ß is, the bigger the contribution of the ranging information among the blind nodes to the model positioning is; and on the contrary, the function of the ranging information among the blind nodes and the anchor nodes is more obvious. Specifically, f=0 denotes ignoring the ranging information among the blind nodes. Meanwhile, since considering that anchor nodes must participate in the positioning process, that is, the weight of the ranging information among the anchor nodes and the blind nodes must be greater than 1,
fP<1, it can enhance the adaptability of the mode for different networks by reasonably 500797 adjusting the value of ß. For example, when the anchor nodes have better signal transmission power as compared with that of the blind nodes, the weight of the ranging information among the anchor nodes and the blind nodes is increased by properly lowering the value of ß.
[33] According to the positioning mathematical model, multi-blind nodes positioning belongs to a multi-objective optimization problem. Therefore, the multi-objective optimization problem is converted into a single-objective optimization problem by integrating all the position coordinates to be solved of all blind nodes into a blind node positioning matrix, and synchronous positioning is realized to avoid error accumulation.
[34] Given fireworks, explosion sparks and mutation sparks are collectively referred to as evolutionary individuals, denoted as E, and a blind node positioning matrix _- — representation is used, ie, LK = (56,6) = (5 ), , and Æ1, 2, ..., v. Obviously, an evolutionary individual Æ is a positioning matrix of row m and column y, and the row vector is the blind nodes (mms), while the element is a dimension of the corresponding node coordinate (dimension v).
[35] a second step: generating a fitness function according to the positioning model, and constructing an adaptive operator: my, (m LL m, _ min f (E)= 33s xd(b, Bb, ) + (1- B)x (5,4) EE i=l
[36] bb eEEeD s.t.{d, (5,6, ) = O;d. (5,4) AO Be [0,1)
[37] Wherein, positioning errors are d(5,,5,)=14.(5,6,)-4.(5,.5,,)d(b, à )=14,(5, à )-d,(5,ä) ; in the restriction, d, (bb, ) O;d,(b,à,)# (J denotes that blind node b, and
= +000 LU500797 anchor node d, are both neighboring node of b, , and b,,b, € F,F € D denotes that b, and b, need to be located within the positioning region D.
[38] The firework algorithm is used to solve the above-mentioned single-objective optimization problem and improve its adaptability. The given adaptive firework algorithm operators include adaptive explosion operator, adaptive mutation operator and selection strategy, which together affect the adaptive search performance of the algorithm.
[39] The operation of fireworks adaptively generating explosion sparks is called adaptive explosion operator, denoted as D: EF > F + 14,0 . Adaptive explosion operator is implemented in a polar coordinate system, wherein AA, are 0 a polar diameter matrix and a polar angle matrix respectively. The polar coordinate system can make the explosion sparks better distributed in the circular area randomly. In the polar > ,- = — \T angle matrix O0= (4.6.6, , the j/ polar angle vector is 1 1 ci Al 2 in Ola 92 3 ein Al... cin gr v 6, = {cos0} sin 6) cos: sin 6, sing; cosO; ,-,sin 0; sin 0; cos 0, } ; wherein 0, = rand(0,2m). In the polar diameter matrix, a random matrix is A=(4) ; A=rand(0,1); 4, is an explosion radius, and is calculated by a VX, fitness function: R E)- futé op 4 = By LED fu, a , DE) Faim) + € r=1
[41] Wherein fain= min /(Z)) ‚E= {E" |r= 1,2,+,n} and is fireworks population, n is a size of the fireworks population; € is a machine minimum amount, to avoid the possible operation of division by zero; @ is an adaptive search factor designed to improve algorithm search performance: a — a, y+e
[43] Wherein, / denotes an adaptive firework algorithm evolution efficiency,
andy >1; and o,, and © pin are the maximum value and the minimum value of @ respectively, and obviously there is @ € [0 ins max |» @ oC y. Therefore, when the algorithm evolves quickly, @ can effectively accelerate the global search ability; when the algorithm evolves slowly, it usually means that the algorithm has entered a fine optimization stage, so the value of @ becomes larger, making the explosion radius 4, smaller, thereby further enhancing local search performance.
[44] According to the adaptive explosion operator, the firework can produce explosion sparks within the explosion radius, and the 7” firework E” produces a number S = of explosion sparks: -f(E") +e
[45] Ser EC Fam = FEN) +e r=l
[46] Wherein, f, = max f (E )) Consider that a number of the fireworks should be an integer, and meanwhile in order to prevent fireworks with a too large fitness value from generating too few sparks or fireworks with a too small fitness value from generating too many sparks, the number S Of the explosion sparks is corrected as S os that is, a number of the explosion sparks should be an integer and a lower threshold is set: un 3 otto ya <hxoxm,
ET round(S,, ), S, zhxoxm,0<h<1
[48] Wherein h is a correction parameter, and ceil(*) and round (*) are rounding up and rounding function respectively.
[49] The operation of adaptively generating mutation sparks by a given firework is called an adaptive mutation operator, denoted as l': EF — E+ A,€ . The adaptive mutation operator uses a rectangular coordinate system for displacement, and performs random mutation based on Gaussian distribution. Wherein, the Gaussian mutation
_ ,Ç LU500797 matrix isë = (e x round(rand(0,1))) , e-N(L1), and Aisa mutation radius, mp Xv and is calculated according to the fitness function: -f(E") +e
[50] A ,=Rx Jun SE JTE D (Fax > FEN +e r=l
[51] According to the adaptive mutation factor, the fireworks can produce mutation sparks within the range of the mutation radius, and the 7” fireworks E” produces a number Sh of the mutation sparks: — f(L)+E
[52] St. =5x0xm, x mx SEITE Los, D fa = FE) +e r=l
[53] Wherein, 6 € [0.1] is a coefficient of the mutation sparks, and it optimizes the number of the mutation sparks together with the adaptive search factor @. In addition, in order to further prevent the algorithm from falling into local optima when optimizing the search performance, @ only acts on the number of explosion sparks and does not affect the radius of the explosion sparks. Similar to the explosion sparks, the number of mutation sparks is modified as S!, = ceil(ss”, ) .
[54] It should be noted that the evolutionary individuals generated by the adaptive explosion operator and the adaptive mutation operator may exceed the feasible range D and violate the model restrictions. Therefore, when a certain coordinate dimension b, of an evolutionary individual is out of bounds, the out-of-bounds coordinate is remapped to D through the following coordinate mapping rule:
[55] b) > By + BD % (Dias — Bi)
[56] Wherein, bl and bl are the maximum value and the minimum value of D respectively in this dimension, and "%" is a modulo operator.
[57] a third step: running an adaptive firework algorithm to carry out iterative optimization, outputting an optimal elite individual to be parsed as coordinates of all blind nodes.
[58] After the fireworks produce explosive sparks and mutation sparks, it is 7500797 necessary to select excellent evolutionary individuals from them to pass them to the next generation, so as to continuously search for the best. First, elements corresponding to fa are selected from the set of evolutionary individuals K according to the elite retention strategy, and they become the next generation of fireworks. Then, a roulette strategy is used to select n-/ elements from the remaining elements of K, which form the next generation of fireworks population E together with the elite evolutionary individuals.
[59] In order to enhance the evolution effect, the probability of the roulette strategy is determined by the crowding degree of the elements, that is, the denser the elements, the lower the probability of being selected. The degree of congestion is derived from the location of the element, and it gives the probability p(E” ) that the evolutionary individual E”is selected : Yd, (h..h,) r b,eK [so] p(E SSA Sa (7.7) b eK hek
[61] In consideration of the energy efficiency and positioning timeliness, the termination condition of the adaptive firework algorithm is set as that the algorithm iteration reaches the specified number or the fitness value of the elite evolution individual meets the same for g consecutive times.
[62] When the positioning result is output, the elite evolution individual positioning matrix output by the firework algorithm is parsed by row into the position coordinates of each blind node, i.e., the finished positioning result is optimized.
[63] Embodiment
[64] Another objective of the present disclosure is to provide a WSN ranging positioning simulation platform applying the ranging positioning method suitable for a sparse anchor node WSN.
[65] As illustrated in Fig. 2, the implementing processes of the WSN ranging positioning simulation platform in the sparse anchor node environment provided by the 500797 embodiment of the present disclosure are:
[66] S1: a data import module is responsible for importing the collected WSN positioning data from the external, and supports the import of RSSI and TOA ranging data. The import of distance data is optional and is only used to evaluate the data positioning error.
[67] S2: in the parameter configuration module, the data parameter configuration is used to configure the attributes of the imported positioning data, such as ranging information type, anchor node information, node position coordinate dimension, etc.; the model parameter configuration is responsible for setting the parameters of the positioning model, such as positioning optimization factor, communication radius of the node, etc., the algorithm parameter configuration is responsible for setting the parameters of the firework algorithm operation process, e.g., the initial firework population, the maximum number of iterations, the coefficient of mutation sparks, boundary values of the adaptive search factor, etc.; the result parameter configuration mainly configures the output information of the positioning result, including positioning time, a number of iterations, and positioning accuracy, etc.
[68] S3: the algorithm operation module is responsible for controlling the operation of the algorithm. The initial control of the population is mainly responsible for completing initialization of the population; the operation control of the operator is responsible for generating explosive sparks and mutation sparks, and processing the sparks that are out of bounds; the population evolution control is responsible for controlling the iterative optimization of fireworks, and terminals the algorithm to output the optimal elite individuals when conditions are met.
[69] S4: in the result output module, the positioning coordinate analysis is responsible for parsing by row the positioning matrix of the optimal elite individual into the position coordinates of the respective blind node; the positioning result evaluates a number of iteration of the algorithms, algorithm running time, and calculates the positioning error based on the imported distance data; the positioning error output outputs positioning result by way of an average positioning error curve and a node positioning error graph, etc.. 7500797
[70] To sum up, the positioning method proposed by the present disclosure can significantly improve the positioning accuracy of the sparse anchor node WSN without increasing the network cost, and supports two-dimensional plane and three-dimensional spatial positioning at the same time, and has good applicability; compared with the existing non-ranging positioning method in the sparse anchor node environment, the present disclosure utilizes the ranging information among the sensor nodes and has higher positioning accuracy; compared with the existing ranging positioning method in the sparse anchor node environment, the positioning model of the present disclosure incorporates the ranging information among the blind nodes, and meanwhile coverts the multi-node positioning problem into a single-objective optimization problem by using a blind node positioning matrix representation method, realizes synchronous positioning and effectively avoids the problem of error accumulation.
[71] The above embodiments are provided only for the purpose of describing the present disclosure, rather than restricting the scope of the present disclosure. The scope of the present disclosure is defined by the appended claims. Various equivalent replacements and modifications made without departing from the spirit and principle of the present disclosure should all fall in the scope of the present disclosure.
Claims (4)
1. A ranging positioning method suitable for a sparse anchor node WSN, wherein the ranging positioning method suitable for a sparse anchor node WSN comprises: a first step: obtaining coordinate parameters of anchor nodes in a network and ranging information among all sensor nodes by a positioning center, constructing a positioning model, and generating a blind node positioning matrix; a second step: generating a fitness function according to the positioning model, and constructing an adaptive operator; a third step: running an adaptive firework algorithm to carry out iterative optimization, outputting an optimal elite individual to be parsed as coordinates of all blind nodes.
2. The ranging positioning method suitable for a sparse anchor node WSN according to claim 1, wherein the positioning model of the ranging positioning method suitable for a sparse anchor node WSN includes ranging information among the blind nodes, and adjusts weights of different types of ranging information by designing a positioning optimization factor /, to be suitable for different WSN environments.
3. The ranging positioning method suitable for a sparse anchor node WSN according to claim 1, wherein a blind node positioning matrix representation method of the ranging positioning method suitable for a sparse anchor node WSN converts a multi-objective optimization problem of multi-node synchronous positioning into a single-objective optimization problem, and finally is reversely parsed as all blind node coordinates.
4. A WSN ranging positioning simulation platform applying the ranging positioning method suitable for a sparse anchor node WSN according to any one of claims 1~3.
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| CN111432368B (en) * | 2020-03-31 | 2022-10-21 | 中国人民解放军国防科技大学 | Ranging and positioning method suitable for sparse anchor node WSN |
| CN113038475B (en) * | 2021-03-15 | 2023-01-20 | 中山大学 | Malicious anchor node detection and target node positioning method based on sparse item recovery |
| CN113923590B (en) * | 2021-09-24 | 2023-07-21 | 西北工业大学 | TOA positioning method under condition of uncertainty of anchor node position |
| CN113959448B (en) * | 2021-10-26 | 2023-08-29 | 江苏海洋大学 | Underwater topography auxiliary navigation method based on improved goblet sea squirt swarm algorithm |
| CN114173281B (en) * | 2021-12-24 | 2023-10-27 | 长安大学 | TOA-based positioning system beacon node optimization layout method in indoor NLOS environment |
| CN114554569A (en) * | 2022-01-25 | 2022-05-27 | 河南大学 | Distributed iterative convex optimization node positioning method based on multi-hop strategy |
| CN115766779B (en) * | 2022-11-03 | 2023-07-07 | 北京邮电大学 | High-precision positioning method, system, equipment and medium for target node in Internet of things |
| CN116930864B (en) * | 2023-06-27 | 2024-02-23 | 中铁第四勘察设计院集团有限公司 | Indoor and outdoor seamless unified reference construction method and device |
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| WO2021196656A1 (en) | 2021-10-07 |
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