CN115665659A - Tensor-based mobile internet of things coverage reliability assessment method - Google Patents
Tensor-based mobile internet of things coverage reliability assessment method Download PDFInfo
- Publication number
- CN115665659A CN115665659A CN202211243473.5A CN202211243473A CN115665659A CN 115665659 A CN115665659 A CN 115665659A CN 202211243473 A CN202211243473 A CN 202211243473A CN 115665659 A CN115665659 A CN 115665659A
- Authority
- CN
- China
- Prior art keywords
- coverage
- tensor
- sensor
- network
- reliability
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Images
Classifications
-
- Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
- Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
- Y02D—CLIMATE CHANGE MITIGATION TECHNOLOGIES IN INFORMATION AND COMMUNICATION TECHNOLOGIES [ICT], I.E. INFORMATION AND COMMUNICATION TECHNOLOGIES AIMING AT THE REDUCTION OF THEIR OWN ENERGY USE
- Y02D30/00—Reducing energy consumption in communication networks
- Y02D30/70—Reducing energy consumption in communication networks in wireless communication networks
Landscapes
- Mobile Radio Communication Systems (AREA)
Abstract
The invention discloses a tensor-based mobile internet of things coverage reliability assessment method, which comprises the following steps: establishing a network model according to a monitoring scene; considering node state, energy, communication robustness, coverage rate and link reliability, and defining credible information coverage reliability; constructing a state and energy tensor, and predicting the node state by adopting a multi-mode Markov state probability prediction model; constructing a coverage tensor to calculate a coverage rate; enumerating communication links and calculating the communication robustness; adopting Monte Carlo simulation to evaluate the coverage reliability of the credible information of the designated network until the simulation times reach the upper limit; the method comprehensively considers the node state, energy, communication robustness, coverage rate and link reliability to accurately measure the coverage reliability, dynamically predicts the node state by adopting a multi-mode Markov state probability prediction model, and performs high-dimensional unified representation on network heterogeneous factors by utilizing tensor to realize high-efficiency calculation of the coverage reliability of the mobile Internet of things.
Description
Technical Field
The invention belongs to the technical field of Internet of things, and particularly relates to a mobile Internet of things coverage reliability assessment method based on tensor.
Background
Reliability characterizes and measures the ability of a mobile internet of things to perform desired functions and services within specified conditions and time. Due to the characteristics of the mobile internet of things and the particularity of a network application environment and a scene, the mobile internet of things can be influenced by the number of nodes, node faults, node polymorphism, connection interruption, coverage holes, passive eavesdropping, active malicious attack and other factors in the operation process, so that the network coverage can not meet the requirements, even can not normally operate, and the service interruption is caused. In order to avoid the consequences of the adverse consequences of this and to maintain long-term network functionality, network reliability is one of the important factors that must be considered.
The coverage reflects and describes the sensing state of the monitoring target area of the Internet of things, and reliable coverage can ensure network data perception and transmission, thereby improving the quality of service (QoS). Therefore, the coverage reliability is one of the core factors influencing the network reliability and is also an important support for ensuring the normal operation of the network.
The difficulty of mobile internet of things coverage reliability assessment is mainly reflected in five aspects. Firstly, the influence of node multi-state, communication robustness, coverage area, energy efficiency and link reliability on the coverage reliability is not comprehensively considered, and the definition of accurately measuring the coverage reliability is lacked; secondly, reliable coverage of the target area not only depends on the deployment position, the coverage area, the sensing capability and the coverage rate of the network of the node, but also is closely related to the capability of the node for transmitting data to a processing center, network connectivity and the like, and a reasonable coverage reliability model is constructed according to the characteristics of the Internet of things, the network coverage and the reliability requirements thereof so as to ensure the availability of network coverage reliability evaluation; thirdly, the network coverage model defines the coverage capability of the sensor, and the selection of the coverage model directly influences the accuracy and the applicability of the reliability evaluation method for the network coverage area measurement of different scenes; fourthly, when network connectivity, which is one of the reliability reference indexes, is measured, a reasonable connectivity definition needs to be designed, so that incomplete reliability evaluation is avoided, and the effectiveness of the reliability evaluation method is improved. Fifthly, the state of the sensor is influenced by various factors, and a model for dynamically and accurately predicting the state of the sensor needs to be designed along with the dynamic change of time and environment.
Disclosure of Invention
Aiming at the defects or improvement requirements of the prior art, the invention provides a tensor-based coverage reliability assessment method for a mobile internet of things, aiming at comprehensively and effectively assessing the coverage reliability of the mobile internet of things and assisting in deploying a sensor network. The reliability assessment method defines the sensor coverage range from the perspective of prediction and information reconstruction by adopting a credible information coverage model, fully utilizes the spatial correlation of monitored physical parameters and the cooperation between adjacent nodes, introduces communication robustness to measure the network fault-tolerant capability, comprehensively considers the factors influencing the network reliability, calculates the network reliability by a Monte Carlo simulation method, improves the assessment efficiency and the application range, solves the problem of reliability assessment of the Internet of things, and has better guidance reference value.
To achieve the above object, according to an aspect of the present invention, there is provided a tensor-based mobile internet of things coverage reliability evaluation method, including the steps of:
(1) Monitoring a coverage scene according to a target area, and establishing a network model;
(1.1) dividing the target region into a plurality of reconstruction regions according to the relevant radius CR, wherein the center of each reconstruction region is a reconstruction point;
(1.2) determining the sensing radius and the communication radius of the sensor node, wherein the sensor operates according to a random duty ratio and has the following states in the operation process: ACTIVE, RELAY, SLEEP, SLEEPR, FAIL;
(1.3) directed arrows between Sensors represent the communication Link CM i,j Link as link working reliability r ；
(1.4) recording the number kappa of the mobile sink node and the number N of the sensor nodes, and recording the number i and the position (x) of the sensor nodes according to the distribution of the sensor nodes i ,y i )；
(1.5) modeling of Mobile Internet of things (MIoT) as graph G = { { s { (S) } sink }∪S∪CM i,j }；
(2) Comprehensively considering node multi-state, communication robustness, coverage area, energy efficiency and link reliability, and defining credible information coverage reliability;
(3) Constructing a node state tensor and an energy tensor, and predicting a sensor state by adopting a multi-mode Markov sensor state probability prediction model;
(4) Constructing a network coverage tensor, and calculating the network coverage rate based on the coverage tensor and the credible information coverage model;
(5) Enumerating a network node connection matrix and calculating network connection robustness;
(6) And evaluating the reliability of the coverage of the trusted information of the specified network by adopting a Monte Carlo simulation method until the simulation times reach a set upper limit.
In an embodiment of the present invention, the step (2) specifically includes the following sub-steps:
(2.1) define trusted information coverage reliability (CICR) to refer to the probability that an MIoT will be able to successfully transmit at least the required CIC-oriented data to a mobile aggregation point in the event of failure of any k-1 sensors;
(2.2) according to the step (2.1), the network with reliable coverage by the obtained trusted information needs to meet three conditions:
condition 1: residual energy E of the sensor res Can support it for data perception E S Data reception R E And data transmission E T ；
Condition 2: coverage meets network coverage requirements, C r ≥C req ；
Condition 3: the connectivity robustness meets the network connectivity robustness requirement, K r ≥k。
In one embodiment of the present invention, data reception E in condition 1 of the step (2.2) R And data transmission E T The calculation formula of (a) is as follows:
E R (l)＝lE elec
wherein l is the size of the transmission data, d is the transmission distance, E elec Is the energy consumed by the transceiver circuit to process each bit of data, ε fs And epsilon mp Common parameters associated with a free space channel model and a multipath fading model, respectively
Is a distance threshold that determines the channel model;
the ACTIVE state sensor has sensing and communication capabilities, and the RELAY state sensor has communication capabilities; for the ACTIVE sensor, condition 1 translates to: e res ≥E T +E R +E R (ii) a For the RELAY sensor, condition 1 is: e res ≥E T +E R 。
In one embodiment of the present invention, the coverage rate C in condition 2 of the step (2.2) r The calculation formula of (a) is as follows:
wherein, W L And W B The length and the width of the monitoring area are respectively; c (X) is the network coverage area, which is the sum of its areas covered by the reconstruction points:
wherein x is i For a reconstruction point, X is the reconstruction point X i Is the number of reconstruction points, | X |;
for each reconstruction point x i ACTIVE sensor pass-cooperation pair x in reconstruction region satisfying condition 1 i The information is reconstructed, if the root mean square error RMSE is smaller than the threshold value, the information is covered by the credible information, and the coverage area C (x) of the information is covered i )：
In one embodiment of the present invention, the condition 3 of the step (2.2) is connected with robustness K r Is calculated as follows:
the communication link describes the network connectivity situation and is the basis of connectivity robustness; for sensors at ACTIVE or RELAY i If it can transmit data to a sensor s located within the communication radius Rc j Then S is i And s j With a communication link CM between i,j Link reliability is link r Generating a random number following a uniform distribution to determine the link CM i,j Available, 1 is available, 0 is not available:
network connectivity robustness K r Conversion to graph G = { { s { { S { (S) } sink }∪S∪CM i,j K (G) of a graph equal to the largest internally disjoint path λ (s 'of each pair of vertices in the graph' i ,s' j )。
In an embodiment of the present invention, the step (3) specifically includes the following sub-steps:
(3.1) construction of three-dimensional node State tensorSAnd an energy tensorEElements thereofS itq AndE itq are respectively shown inThe state and the residual energy of a node i at the t time point in the q simulation;
(3.2) constructing a multi-mode Markov sensor state probability prediction model;
(3.3) adjusting the Joint State probability distribution tensor by an iterative approachMUp toMStabilizing to obtain steady state joint state probability distribution tensorMThe adjustment formula is as follows:
where β (0 < β < 1) is the regularization parameter and G is the regularization joint probability distribution tensor;
(3.4) according to tensorS、EAnd actual situation, obtaining the state value of the previous m-1 time, and starting from the steady state based on the state valueMExtracting h-order tensorB；
(3.5) extracting Multistate fiber L from tensor B, wherein the state corresponding to the highest element value in L is sensor s i Status.
In an embodiment of the present invention, the step (3.2) specifically includes the following sub-steps:
(3.2.1) constructing an h-ary m-order Markov modelPTo be the state transition probability tensor,Mfor the joint state probability distribution tensor:
∑M＝1.
(3.2.2) Using the State transition principles of the m-order Markov modelMThe state conversion of the sensor is realized through tensor unity multiplication;
wherein D is t Indicating the state of the sensor at t,
the expression tensor unity multiplication operation.
In an embodiment of the present invention, the step (4) specifically includes the following sub-steps:
(4.1) calculating the reconstruction point x i Coverage area C (x) i )；
(4.2) construction of three-dimensional coverage tensorAElements thereofS itq Representing the coverage area of the point i reconstructed at the t-th time point in the q-th simulation, and updating the tensor by using the value obtained in the step (4.1)A；
(4.3) extraction of Sensor fiberA(t, q), the sum of the elements of the simulation model represents the coverage area of the network at the time t of the q simulation; the network coverage is calculated as follows:
in an embodiment of the present invention, the step (4.1) specifically includes the following sub-steps:
(4.1.1) tensor-basedS、EFinding x i ACTIVE sensor satisfying condition 1 in the reconstruction region;
(4.1.2) in the trusted information overlay model, for a reconstruction point x i By using ordinary kriging interpolation functionsCalculating a reconstruction point x i Estimation of the environment variable, i.e. using the reconstructed neighborhood Z (x) i ) Calculating an environment variable estimate by a weighted average of the measurements of the sensors screened in step (4.1.1); interpolation weight coefficient omega of sensor node in neighborhood i Satisfy the requirement of
|Z(x i ) I is the reconstructed neighborhood Z (x) i ) Inner sensor node s i The number of (2);
(4.1.3) calculating the root mean square error phi (x) of the reconstruction point x by combining the common kriging interpolation function, wherein the calculation expression is as follows:
wherein
And δ (x) is solved by steps (4.1.3.1) and (4.1.3.2);
(4.1.4) according to the definition of the credible information coverage model, if phi (x) > mu, namely the time average root mean square error is larger than a set coverage threshold, covering the sub-grid, otherwise, not covering the sub-grid; the reconstruction point coverage area is calculated according to the formula in claim 4.
In an embodiment of the present invention, the step (4.1.3) specifically includes the following sub-steps:
(4.1.3.1) interpolation weight coefficient ω i Obtaining a group of optimal solutions through the minimum kriging variance; introducing a Lagrange multiplier delta (x) to generate a linear Krigin system consisting of n +1 equation sets with n +1 unknowns, and solving to obtain an interpolation weight coefficient omega i ；
Wherein, gamma(s) i ,s j ) And gamma(s) i X) is calculated by a variation function;
(4.1.3.2) calculating γ(s) in step (3.3.2) i ,s j ) And gamma(s) i ,x i ) (ii) a Selecting a Gaussian variation function as a variation function of the environment variable for describing the sensor node s i Collecting spatial correlation between data; the gaussian variation function is formulated as:
wherein d is sx As sensor node s i And a reconstruction point x i The Euclidean distance of (a) is,
as sensor node s i And s j Euclidean distance of H 0 And H 1 Are all constants.
In an embodiment of the present invention, the step (5) specifically includes the following sub-steps:
(5.1) determining sensors capable of forming a communication link using the fibers S (: t, q) and E (: t-1,q) according to the conditions described in claim 5;
(5.2) for each communication link CM i,j Link with link reliability r Adopting a Monte Carlo method to confirm the availability of the link;
(5.3) calculating the network connection robustness;
in an embodiment of the present invention, the step (5.3) specifically includes the following sub-steps:
(5.3.1) map conversion; conversion chart G = { { s { [ S ] sink }∪S∪X∪CM i,j Where θ = { ξ ≡ β }, specifically, a point s in G is to be mentioned i Conversion to two points xi in theta i And xi i+n And xi is i And xi i+n Arc capacity of 1; the edge CM in G i,j ＝(s i ,s j ) Conversion of =1 into two edges β in θ i+n,j ＝(ξ i+n ,ξ j ) And beta i,j+n ＝(ξ i ,ξ j+n ) The arc capacity is infinite;
(5.3.2) calculating; calculating the point connectivity of graph G, i.e. all the point pairs ([ xi ]) in graph theta i+n ,ξ j ) The minimum value of the maximum flow in between; the point connectivity of the graph G is the connectivity robust value of the network.
In an embodiment of the present invention, the step (6) specifically includes the following sub-steps:
(6.1) calculating the coverage reliability of the network trusted information by adopting a Monte Carlo simulation method, wherein the calculation formula is as follows:
wherein Q represents Monte Carlo simulation times, T represents cycle times, namely the time of the moving convergent point moving at the edge of the monitored area;
and (6.2) updating the energy of each sensor node after the simulation is finished every time, and repeating the steps (3), (4) and (5) until the simulation times reach the set upper limit.
In general, compared with the prior art, the technical scheme conceived by the invention has the following beneficial effects:
(1) The method has high coverage reliability, comprehensively excavates the spatial correlation of the monitoring reconstruction point of the coverage target area from the angle of information cooperation, estimates the coverage error by utilizing the root mean square error, completes the coverage prediction, improves the coverage rate and further improves the coverage reliability;
(2) The evaluation speed is high, the Monte Carlo simulation method used in the invention takes the simulation result of a certain simulation times as the network coverage reliability value, thereby avoiding the problem of complex calculation caused by network node full-state enumeration and saving the evaluation time;
(3) The evaluation indexes are comprehensive, and the influence of factors such as multi-state nodes, node energy consumption, link reliability, network coverage area, network communication robustness and the like on the network coverage reliability is comprehensively considered. The tensor is adopted to carry out high-dimensional unified representation on the internet of things coverage multi-source heterogeneous association factors, all the factors are fused into a frame, and the state of the sensor is dynamically predicted by using a tensor Markov state probability prediction model, so that the network coverage reliability can be comprehensively reflected;
(4) The method has strong universality, adopts Monte Carlo simulation to evaluate the network coverage reliability, and is suitable for high-density large-range networks. In addition, the Internet of things related to the invention is a universal network and is suitable for various application scenes. The credible information coverage model adopted in the invention can be used for covering different terrains, regions and different data monitoring targets.
Drawings
FIG. 1 is a flowchart of a method for evaluating coverage reliability of a mobile Internet of things based on tensor according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of a mobile Internet of things network model according to an embodiment of the invention;
fig. 3 is a schematic diagram of the coverage reliability affected by the duty cycle in the embodiments of the present invention and the prior art (MCMc, ACR), wherein: fig. 3 (a) is a schematic diagram of the number of nodes N = 30; fig. 3 (b) is a schematic diagram of the number of nodes N = 40; fig. 3 (c) is a diagram illustrating the number of nodes N = 50; fig. 3 (d) is a diagram of the number of nodes N = 60; fig. 3 (e) is a diagram illustrating the number of nodes N = 70;
fig. 4 is a schematic diagram of coverage reliability affected by coverage rate in the embodiments of the present invention and the prior inventions (MCMc, ACR), wherein: fig. 4 (a) is a schematic diagram of the number of nodes N = 30; fig. 4 (b) is a diagram illustrating the number of nodes N = 40; fig. 4 (c) is a diagram illustrating the number of nodes N = 50; fig. 4 (d) is a diagram of the number of nodes N = 60; fig. 4 (e) is a diagram illustrating the number of nodes N = 70;
FIG. 5 shows the coverage reliability perceived radius R in the embodiments of the present invention and the prior inventions (MCMc, ACR) S Schematic representation of the effects, wherein: fig. 5 (a) is a schematic diagram of the number of nodes N = 30; fig. 5 (b) is a diagram illustrating the number of nodes N = 40; fig. 5 (c) is a diagram illustrating the number of nodes N = 50; fig. 5 (d) is a schematic diagram of node number N = 60; fig. 5 (e) is a diagram illustrating the number of nodes N = 70;
FIG. 6 is a diagram illustrating the influence of the RMS error threshold μ on the coverage reliability in an embodiment of the invention;
FIG. 7 is a diagram illustrating coverage reliability linked list in an embodiment of the present inventionDependent link r An influence schematic diagram;
FIG. 8 is a diagram illustrating that coverage reliability is affected by a connected robustness threshold k in an embodiment of the present invention;
the same reference numbers will be used throughout the drawings to refer to the same or like elements or structures, wherein: the hexagram represents a grid reconstruction point, the pentagram represents a movable aggregation node, the dots represent sensor nodes, the directed connecting lines represent communication links, CR represents a variable range, and N represents the number of the sensor nodes in the current state network.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The technical terms of the present invention are explained and explained first:
variation Range (CR): a distance threshold characterizing the spatial correlation of the environmental variable. For a particular environment variable and spatial point, only the values of other spatial points within the range of the variable are relevant to the current spatial point.
Root Mean Square Error (RMSE): the reconstruction and estimation quality, i.e. the measure of the error between the estimated values and the reference point values, is measured and evaluated without taking the values of the spatial environment variables.
Trusted information overlay (configntinformationcoverage): in the target monitoring area, if the root mean square error of the reconstructed information on a space point in the area is less than or equal to a threshold value mu set forth by the practical application requirement, the space point is covered by the credible information.
Euclidean distance: the absolute distance between two points or vectors in a multidimensional space, i.e. the square root of the difference between the vectors, is measured. Point A (x) i ,y i ) To point B (x) j ,y j ) Has an Euclidean distance of
Kriging interpolation: the kriging method is essentially a moving weighted average method and has the characteristics of being optimal, linear, unbiased and the like. Kriging (Kriging) is a regression algorithm that spatially models and predicts (interpolates) random processes or random fields according to a covariance function. The kriging method can give an optimal linear unbiased estimate in a specific stochastic process, such as an inherently stationary process, and is therefore also referred to as a spatially optimal unbiased estimator in geostatistical.
And (4) adjacent nodes: and a sensor node s i In its communication range R c Other sensor nodes in s i Of the neighboring node.
Monte Carlo simulation method: when the problem to be solved is the probability of occurrence of a certain event or the expected value of a certain random variable, the problem can be simulated by a mathematical method by grasping the geometric quantity and the geometric characteristics of the movement of the object, and the frequency of occurrence of the event or the average value of the random variable can be obtained and used as the approximate solution of the problem.
Tensor: is a multiple linear mapping defined on the cartesian product of some vector spaces and some dual spaces, is a generalization of the concept of vectors, which are first order tensors, multi-linear functions that can be used to represent linear relationships between some vectors, scalars, and other tensors.
The solution to the difficulties existing in the prior art is as follows:
aiming at the difficulty I, the coverage reliability is defined by the existing research work of the coverage reliability of the Internet of things without comprehensively considering factors influencing the coverage reliability. Credible information coverage reliability is defined by comprehensively considering node multi-state, communication robustness, coverage area, energy efficiency and link reliability so as to accurately measure the coverage reliability; for the second difficulty, the existing research work of the coverage reliability of the internet of things does not consider the spatial correlation and the node cooperative sensing capability of the monitored variables, does not consider the influence of factors such as network connectivity, multi-state nodes and malicious node interference on the network coverage reliability, and fails to uniformly represent and model a plurality of factors influencing the coverage reliability. Factors influencing network coverage reliability are comprehensively considered, and a tensor is utilized to construct an Internet of things coverage reliability evaluation model. The reliability model based on the tensor can carry out high-dimensional unified representation on the heterogeneous correlation factors of the multi-source coverage of the Internet of things, and maintain the correlation among all dimensions. Aiming at the third difficulty, the existing Internet of things coverage research work mostly selects an oversimplified and ideal disc coverage model to depict the node coverage capability, and does not accord with practical scenes. And the sensor coverage range can be defined from the perspective of prediction and information reconstruction by adopting a credible information coverage model. The credible information coverage model makes full use of the spatial correlation of the monitored physical parameters and the cooperative cooperation of adjacent nodes, and can be well applied to practice. Aiming at the fourth difficulty, most of the existing methods measure the network connectivity from the perspective of whether an effective path from a sensor to a sink node exists or not, and the measured network connectivity is used as one of the reliability evaluation standards. But these methods do not take into account the important impact of critical node failures in the communication path on network reliability. The communication robustness is adopted as one of coverage reliability standards, the network connectivity is evaluated, meanwhile, the fault tolerance capability of the network is also measured, and the network coverage reliability is better described. Aiming at the difficulty of five, the existing method mostly models the state of the sensor into two modes, and ignores the influence of multiple factors on the multiple states of the sensor. The state of the sensor is dynamically predicted by adopting a tensor Markov state probability-based prediction model, dynamic factors influencing the change of the node state can be highly fused, and the time sequence change of the node state in a certain time range and the communication relation of a network are effectively represented.
As shown in fig. 1, the tensor-based internet of things coverage reliability evaluation method of the present invention includes the following steps:
(1) Monitoring a coverage scene according to a target area, and establishing a network model;
and (1.1) dividing the target region into a plurality of reconstruction regions according to the relevant radius CR, wherein the center of each reconstruction region is a reconstruction point.
(1.2) determining the sensing radius and the communication radius of the sensor node, wherein the sensor operates according to a random duty ratio and has the following states in the operation process: ACTIVE, RELAY, SLEEP, SLEEPR, FAIL.
(1.3) directed arrows between Sensors represent the communication Link CM i,j Link as link working reliability r 。
(1.4) recording the number kappa of the mobile sink node and the number N of the sensor nodes, and recording the number i and the position (x) of the sensor nodes according to the distribution of the sensor nodes i ,y i )。
(1.5) Mobile Internet of things (MIoT) modeling as graph G = { { s { (S) sink }∪S∪CM i,j }
(2) Comprehensively considering node multi-state, communication robustness, coverage area, energy efficiency and link reliability, and defining credible information coverage reliability;
(2.1) define trusted information coverage reliability (CICR) to refer to the probability that an MIoT will be able to successfully transmit at least the required CIC-oriented data to a mobile aggregation point in the event of failure of any k-1 sensors.
(2.2) according to the step (2.1), the network with reliable coverage by the obtained trusted information needs to meet three conditions:
condition 1: residual energy E of sensor res Can support it for data perception E S Data reception E R And data transmission E T ；
Data reception E R And data transmission E T The calculation formula of (c) is as follows:
E R (l)＝lE elec
wherein l is the size of the transmission data, d is the transmission distance, E elec Is the energy consumed by the transceiver circuit to process each bit of data, ε fs And ε mp Common parameters associated with a free space channel model and a multipath fading model, respectively
Is to determine the distance threshold of the channel model。
The ACTIVE state sensor has sensing and communication capabilities, and the relax state sensor has communication capabilities. For the ACTIVE sensor, condition 1 translates to: e res ≥E T +E R +E S (ii) a For the RELAY sensor, condition 1 is: e res ≥E T +E R 。
Condition 2: coverage meets network coverage requirements, C r ≥C req ；
Coverage rate C r The calculation formula of (a) is as follows:
wherein, W L And W B Respectively the length and width of the monitored area. C (X) is the network coverage area, which is the sum of its areas covered by the reconstruction points:
wherein x is i For a reconstruction point, X is the reconstruction point X i Is the number of reconstruction points, | X |.
For each reconstruction point x i ACTIVE sensor pass-pair x in reconstruction region satisfying condition 1 i The information is reconstructed, if the root mean square error RMSE is smaller than the threshold value, the information is covered by the credible information, and the coverage area C (x) of the information is covered i )：
Condition 3: the connectivity robustness meets the network connectivity robustness requirement, K r ≥k。
Connectivity robustness K r Is calculated as follows:
the communication link describes the network connectivity situation and is the basis for connectivity robustness. For sensors at ACTIVE or RELAY i Such asIf it can transmit data to sensors s located within the communication radius Rc j Then s i And s j Having a communication link CM between them i,j Link reliability is link r . Generating a random number following a uniform distribution to determine the link CM i,j Available, 1 is available, 0 is not available:
network connectivity robustness K r Conversion to graph G = { { s { { S { (S) } sink }∪S∪CM i,j K (G) of a graph equal to the largest internally disjoint path λ (s 'of each pair of vertices in the graph' i ,s' j )。
(3) Constructing a node state tensor and an energy tensor, and predicting a sensor state by adopting a multi-mode Markov sensor state probability prediction model;
(3.1) construction of three-dimensional node State tensorSAnd energy tensorEElements thereofS itq AndE itq respectively representing the state and the residual energy of the node i at the t-th time point in the q-th simulation;
and (3.2) constructing a multi-mode Markov sensor state probability prediction model.
(3.2.1) constructing h-gram m-order Markov modelPTo be the state transition probability tensor,Mfor the joint state probability distribution tensor:
∑M＝1.
(3.2.2) utilizing the State transition principle of the mth order Markov modelMAnd the state conversion of the sensor is realized by tensor unity multiplication.
Wherein D is t Indicating the state of the sensor at t,
the expression tensor unity multiplication operation.
(3.3) adjusting the Joint State probability distribution tensor by an iterative approachMUp toMStabilizing to obtain steady state joint state probability distribution tensorMThe adjustment formula is as follows:
where β (0 < β < 1) is the adjustment parameter and G is the adjustment joint probability distribution tensor.
(3.4) according to tensorS、EAnd actual situation, obtaining the state value of the previous m-1 time, and starting from the steady state based on the state valueMExtracting h-order tensorB；
(3.5) extracting Multistate fiber L from tensor B, wherein the state corresponding to the highest element value in L is sensor s i Status.
(4) Constructing a network coverage tensor, and calculating the network coverage rate based on the coverage tensor and the credible information coverage model;
(4.1) calculating the reconstruction point x i Coverage area C (x) i )；
(4.1.1) tensor-basedS、EFinding x i ACTIVE sensor satisfying condition 1 in the reconstruction region;
(4.1.2) in the trusted information overlay model, for a reconstruction point x i Calculating the reconstruction point x by using a common kriging interpolation function i Estimation of the environment variable, i.e. using the reconstructed neighborhood Z (x) i ) Calculating an environment variable estimate by a weighted average of the measurements of the sensors screened in step (4.1.1); interpolation weight coefficient omega of sensor node in neighborhood i Satisfy the requirements of
|Z(x i ) I is the reconstructed neighborhood Z (x) i ) Sensor node s in i The number of (2);
(4.1.3) calculating the root mean square error phi (x) of the reconstruction point x by combining the common kriging interpolation function, wherein the calculation expression is as follows:
wherein
And δ (x) is solved by steps (4.1.3.1) and (4.1.3.2);
(4.1.4) according to the definition of the credible information coverage model, if phi (x) > mu, namely the time average root mean square error is larger than a set coverage threshold, covering the sub-grid, otherwise, not covering the sub-grid; the reconstruction point coverage area is calculated according to the formula in claim 4.
(4.1.3.1) interpolation weight coefficient ω i Obtaining a group of optimal solutions through the minimum kriging variance; introducing a Lagrange multiplier delta (x) to generate a linear Krigin system consisting of n +1 equation sets with n +1 unknowns, and solving to obtain an interpolation weight coefficient omega i ；
Wherein, gamma(s) i ,s j ) And gamma(s) i X) is calculated by a variation function;
(4.1.3.2) calculating γ(s) in step (3.3.2) i ,s j ) And gamma(s) i ,x i ) (ii) a Selecting a Gaussian variation function as a variation function of the environment variable for describing the sensor node s i Collecting spatial correlation between data; the gaussian variation function is formulated as:
wherein d is sx As sensor node s i And a reconstruction point x i The Euclidean distance of (a) is,
as sensor node s i And s j Euclidean distance of, H 0 And H 1 Are all constants.
(4.2) construction of three-dimensional coverage tensorAElements thereofS itq Representing the coverage area of the point i reconstructed at the t-th time point in the q-th simulation, and updating the tensor by using the value obtained in the step (4.1)A；
(4.3) extraction of Sensor fiberAAnd the sum of elements of the simulation model represents the coverage area of the network at the time t of the q simulation. The network coverage is calculated as follows:
(5) Enumerating a network node connectivity matrix and calculating network connectivity robustness;
(5.1) determining sensors capable of forming a communication link using the fibers S (: t, q) and E (: t-1,q) according to the conditions described in the claim 5;
(5.2) CM for each communication link i,j Link with link reliability r Adopting a Monte Carlo method to confirm the availability of the link;
(5.3) calculating the network connection robustness;
(5.3.1) map conversion; conversion chart G = { { s { [ S ] sink }∪S∪X∪CM i,j Where θ = { ξ ≡ β }, specifically, a point s in G is to be mentioned i Conversion to two points xi in theta i And xi i+n And xi is i And xi i+n The arc capacity between is 1; the edge CM in G i,j ＝(s i ,s j ) Conversion of =1 into two edges β in θ i+n,j ＝(ξ i+n ,ξ j ) And beta i,j+n ＝(ξ i ,ξ j+n ) The arc capacity is infinite.
(5.3.2) calculating; calculating the point connectivity of graph G, i.e. all the point pairs ([ xi ]) in graph theta i+n ,ξ j ) The minimum value of the maximum flow in between; the point connectivity of the graph G is the connectivity robust value of the network.
(6) Evaluating the reliability of the credible information coverage of the specified network by adopting a Monte Carlo simulation method until the simulation times reach a set upper limit;
(6.1) calculating the coverage reliability of the network trusted information by adopting a Monte Carlo simulation method, wherein the calculation formula is as follows:
wherein Q represents the number of monte carlo simulations and T represents the number of cycles, i.e. the time for the moving convergent point to move at the edge of the monitored area.
And (6.2) updating the energy of each sensor node after the simulation is finished every time, and repeating the steps (3), (4) and (5) until the simulation times reach the set upper limit.
Fig. 3 is a schematic diagram illustrating that the coverage reliability is affected by duty cycle in the embodiments of the present invention (T-CICR) and the prior inventions (MCMc, ACR), wherein: fig. 3 (a) is a schematic diagram of the number of nodes N = 30; fig. 3 (b) is a schematic diagram of the number of nodes N = 40; fig. 3 (c) is a diagram illustrating the number of nodes N = 50; fig. 3 (d) is a diagram of the number of nodes N = 60; fig. 3 (e) is a diagram illustrating the number of nodes N = 70;
fig. 4 is a schematic diagram illustrating coverage reliability affected by coverage rate in embodiments of the present invention (T-CICR) and the prior inventions (MCMc, ACR), wherein: fig. 4 (a) is a schematic diagram of the number of nodes N = 30; fig. 4 (b) is a schematic diagram of the node number N = 40; fig. 4 (c) is a diagram illustrating the number of nodes N = 50; fig. 4 (d) is a diagram of the number of nodes N = 60; fig. 4 (e) is a diagram illustrating the number of nodes N = 70;
fig. 5 is a schematic diagram showing the coverage reliability affected by the sensing radius Rs in the embodiments of the present invention (T-CICR) and the prior inventions (MCMc, ACR), wherein: fig. 5 (a) is a schematic diagram of the number of nodes N = 30; fig. 5 (b) is a diagram illustrating the number of nodes N = 40; fig. 5 (c) is a schematic diagram of the node number N = 50; fig. 5 (d) is a diagram of the number of nodes N = 60; fig. 5 (e) is a diagram illustrating the number of nodes N = 70;
FIG. 6 is a schematic diagram illustrating the coverage reliability affected by the RMS error threshold μ according to an embodiment of the invention; FIG. 7 is a link with coverage reliability subject to link reliability in an embodiment of the present invention r An influence schematic; FIG. 8 is a schematic diagram illustrating that coverage reliability is affected by a connectivity robustness threshold k in the embodiment of the present invention; fig. 3-8 demonstrate the versatility of the method, allowing network designers to achieve a better understanding of the impact of random duty cycle, coverage, node communication radius, link reliability, root mean square error threshold, and connectivity robustness threshold on reliability. It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (10)
1. A tensor-based mobile Internet of things coverage reliability assessment method is characterized by comprising the following steps:
(1) Monitoring a coverage scene according to a target area, and establishing a network model;
(1.1) dividing the target region into a plurality of reconstruction regions according to the relevant radius CR, wherein the center of each reconstruction region is a reconstruction point;
(1.2) determining the sensing radius and the communication radius of the sensor node, wherein the sensor operates according to a random duty ratio and has the following states in the operation process: ACTIVE, RELAY, SLEEP, SLEEPR, FAIL;
(1.3) directed arrows between Sensors represent the communication Link CM i,j Link as link working reliability r ；
(1.4) recording the serial number kappa of the mobile sink node and the number N of the sensor nodes, and recording the serial number i and the position (x) of the sensor nodes according to the distribution of the sensor nodes i ,y i )；
(1.5) mobile Internet of things MIoT modeling as graph G = { { s) sink }∪S∪CM i,j }；
(2) Comprehensively considering node multi-state, communication robustness, coverage area, energy efficiency and link reliability, and defining credible information coverage reliability;
(3) Constructing a node state tensor and an energy tensor, and predicting a sensor state by adopting a multi-mode Markov sensor state probability prediction model;
(4) Constructing a network coverage tensor, and calculating the network coverage rate based on the coverage tensor and the credible information coverage model;
(5) Enumerating a network node connection matrix and calculating network connection robustness;
(6) And evaluating the reliability of the coverage of the trusted information of the specified network by adopting a Monte Carlo simulation method until the simulation times reach a set upper limit.
2. The tensor-based mobile internet of things coverage reliability assessment method as recited in claim 1, wherein the step (2) specifically comprises the following sub-steps:
(2.1) defining credible information coverage reliability, CICR, refers to the probability that in the event of failure of any k-1 sensors, MIoT can successfully transmit at least the required CIC-oriented data to the mobile aggregation point;
(2.2) according to the step (2.1), obtaining a reliable network covered by the credible information, wherein the reliable network needs to meet three conditions:
condition 1: of sensorsResidual energy E res Can support it for data perception E S Data reception E R And data transmission E T ；
Condition 2: coverage meets network coverage requirements, C r ≥C req ；
Condition 3: the connectivity robustness meets the network connectivity robustness requirement, K r ≥k。
3. The tensor-based mobile internet of things coverage reliability assessment method as set forth in claim 2, wherein the data reception E in condition 1 of the step (2.2) R And data transmission E T The calculation formula of (c) is as follows:
E R (l)＝lE elec
wherein l is the size of the transmission data, d is the transmission distance, E elec Is the energy consumed by the transceiver circuit to process each bit of data, ε fs And ε mp Common parameters associated with a free space channel model and a multipath fading model, respectively
Is a distance threshold that determines the channel model;
ACTIVE status sensor possesses sensing and communication capabilities, while relax status sensor possesses communication capabilities, for ACTIVE sensor, condition 1 translates to: e res ≥E T +E R +E S (ii) a For the RELAY sensor, condition 1 is: e res ≥E T +E R 。
4. The tensor-based mobile internet of things coverage reliability assessment method as set forth in claim 2, wherein the coverage rate C in condition 2 of the step (2.2) r The calculation formula of (a) is as follows:
wherein, W L And W B The length and the width of the monitoring area are respectively; c (X) is the network coverage area, which is the sum of its areas covered by the reconstruction points:
wherein x is i For a reconstruction point, X is the reconstruction point X i Is the number of reconstruction points, | X |;
for each reconstruction point x i ACTIVE sensor pass-cooperation pair x in reconstruction region satisfying condition 1 i The information is reconstructed, if the root mean square error RMSE is smaller than the threshold value, the information is covered by the credible information, and the coverage area C (x) of the information is covered i )：
5. The tensor-based mobile internet of things coverage reliability assessment method as claimed in claim 2, wherein the condition 3 of the step (2.2) is that the robustness K of connectivity is in a condition 3 r Is calculated as follows:
the communication link describes the network connectivity situation and is the basis of connectivity robustness; for sensors at ACTIVE or RELAY i If it can transmit data to a sensor s located within the communication radius Rc j Then s is i And s j With a communication link CM between i,j Link reliability is link r Generating a random number following a uniform distribution to determine the link CM i,j Available, 1 is available, 0 is not available:
network connectivity robustness K r Conversion to graph G = { { s { { S { (S) } sink }∪S∪CM i,j A degree of point connectivity K (G) of graph equal to the largest internally disjoint path λ (s ') of each pair of vertices in the graph' i ,s' j )。
6. The tensor-based mobile internet of things coverage reliability assessment method as recited in claim 1, wherein the step (3) specifically comprises the following sub-steps:
(3.1) construction of three-dimensional node State tensorSAnd energy tensorEElements thereofS itq AndE itq respectively representing the state and the residual energy of the node i at the t-th time point in the q-th simulation;
(3.2) constructing a multi-mode Markov sensor state probability prediction model;
(3.3) adjusting the Joint State probability distribution tensor by an iterative approachMUp toMStabilizing to obtain steady state joint state probability distribution tensorMThe adjustment formula is as follows:
where β (0 < β < 1) is the tuning parameter and G is the tuning joint probability distribution tensor;
(3.4) according to tensorS、EAnd actual situation, obtaining the state value of the previous m-1 time, and starting from the steady state based on the state valueMExtracting h-order tensorB；
(3.5) extracting Multistate fiber L from tensor B, wherein the state corresponding to the highest element value in L is sensor s i Status.
7. The tensor-based mobile internet of things coverage reliability assessment method according to claim 6, wherein the step (3.2) comprises the sub-steps of:
(3.2.1) constructing an h-ary m-order Markov modelPTo change over to stateThe rate tensor is such that,Mfor the joint state probability distribution tensor:
ΣM＝1.
(3.2.2) Using the State transition principles of the m-order Markov modelMThe state conversion of the sensor is realized through tensor unity multiplication;
wherein D is t Indicating the state of the sensor at t,
the tensor unity multiplication operation is represented.
8. The tensor-based mobile internet of things coverage reliability assessment method according to claim 1, wherein the step (4) comprises the substeps of:
(4.1) calculating the weightBuilding point x i Coverage area C (x) i )；
(4.2) construction of three-dimensional coverage tensorAElements thereofS itq Representing the coverage area of the point i reconstructed at the t-th time point in the q-th simulation, and updating the tensor by using the value obtained in the step (4.1)A；
(4.3) extraction of Sensor fiberA(t, q), the sum of the elements of the simulation model represents the coverage area of the network at the time t of the q simulation; the network coverage is calculated as follows:
9. the tensor-based mobile internet of things coverage reliability assessment method according to claim 8, wherein the step (4.1) comprises the sub-steps of:
(4.1.1) tensor-basedS、EFinding x i ACTIVE sensor satisfying condition 1 in the reconstruction region;
(4.1.2) in the trusted information overlay model, for a reconstruction point x i Calculating a reconstruction point x by using a common kriging interpolation function i Estimation of the environment variable, i.e. using the reconstructed neighborhood Z (x) i ) Calculating an environment variable estimate by a weighted average of the measurements of the sensors screened in step (4.1.1); interpolation weight coefficient omega of sensor node in neighborhood i Satisfy the requirement of
|Z(x i ) I is the reconstructed neighborhood Z (x) i ) Sensor node s in i The number of (2);
(4.1.3) calculating the root mean square error phi (x) of the reconstruction point x by combining the common kriging interpolation function, wherein the calculation expression is as follows:
wherein
And δ (x) is solved by the following formula;
(4.1.3.1) interpolation weight coefficient ω i Obtaining a group of optimal solutions through the minimum kriging variance; introducing a Lagrange multiplier delta (x) to generate a linear Krigin system consisting of n +1 equation sets with n +1 unknowns, and solving to obtain an interpolation weight coefficient omega i ；
Wherein, gamma(s) i ,s j ) And gamma(s) i X) is calculated by a variation function;
(4.1.3.2) calculating γ(s) in step (3.3.2) i ,s j ) And gamma(s) i ,x i ) (ii) a Selecting a Gaussian variation function as a variation function of the environment variable for describing the sensor node s i Collecting spatial correlation between data; the gaussian variation function is formulated as:
wherein d is sx As sensor node s i And a reconstruction point x i The Euclidean distance of (a) is,
as sensor node s i And s j Euclidean distance of H 0 And H 1 Are all constants;
(4.1.4) according to the definition of the credible information coverage model, if phi (x) > mu, namely the time average root mean square error is larger than a set coverage threshold, covering the sub-grid, otherwise, not covering the sub-grid; the reconstruction point coverage area is calculated according to the formula in claim 4.
10. The tensor-based mobile internet of things coverage reliability assessment method as recited in claim 1, wherein the step (5) specifically comprises the following sub-steps:
(5.1) determining sensors capable of forming a communication link using the fibers S (: t, q) and E (: t-1,q) according to the conditions described in the claim 5;
(5.2) CM for each communication link i,j Link with link reliability r Adopting a Monte Carlo method to confirm the availability of the link;
(5.3) computing network connectivity robustness, comprising:
(5.3.1) map conversion; conversion graph G = { { s { } sink }∪S∪X∪CM i,j Where θ = { ξ ≡ β }, specifically, a point s in G is to be mentioned i Conversion to two points xi in theta i And xi i+n And xi is i And xi i+n Arc capacity of 1; the edge CM in G i,j ＝(s i ,s j ) Conversion of =1 into two edges β in θ i+n,j ＝(ξ i+n ,ξ j ) And beta i,j+n ＝(ξ i ,ξ j+n ) The arc capacity is infinite;
(5.3.2) calculating; calculating the point connectivity of graph G, i.e. all the point pairs ([ xi ]) in graph theta i+n ,ξ j ) The minimum value of the maximum flow in between; the point connectivity of the graph G is the connectivity robust value of the network.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211243473.5A CN115665659A (en) | 2022-10-12 | 2022-10-12 | Tensor-based mobile internet of things coverage reliability assessment method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN202211243473.5A CN115665659A (en) | 2022-10-12 | 2022-10-12 | Tensor-based mobile internet of things coverage reliability assessment method |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN115665659A true CN115665659A (en) | 2023-01-31 |
Family
ID=84987359
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN202211243473.5A Pending CN115665659A (en) | 2022-10-12 | 2022-10-12 | Tensor-based mobile internet of things coverage reliability assessment method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN115665659A (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116456356A (en) * | 2023-03-13 | 2023-07-18 | 华中科技大学 | Reliability evaluation method for large-scale wireless sensor network based on reliable information coverage |
| CN118338334A (en) * | 2024-06-13 | 2024-07-12 | 华中科技大学 | Internet of things reliability multidimensional assessment method and system based on Monte Carlo |
| CN118691184A (en) * | 2024-08-23 | 2024-09-24 | 广州纳诺科技股份有限公司 | Goods dynamic traceability management method and system based on industrial Internet of things |
-
2022
- 2022-10-12 CN CN202211243473.5A patent/CN115665659A/en active Pending
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116456356A (en) * | 2023-03-13 | 2023-07-18 | 华中科技大学 | Reliability evaluation method for large-scale wireless sensor network based on reliable information coverage |
| CN116456356B (en) * | 2023-03-13 | 2024-02-02 | 华中科技大学 | Reliability evaluation method for large-scale wireless sensor network based on reliable information coverage |
| CN118338334A (en) * | 2024-06-13 | 2024-07-12 | 华中科技大学 | Internet of things reliability multidimensional assessment method and system based on Monte Carlo |
| CN118338334B (en) * | 2024-06-13 | 2024-09-27 | 华中科技大学 | Internet of things reliability multidimensional assessment method and system based on Monte Carlo |
| CN118691184A (en) * | 2024-08-23 | 2024-09-24 | 广州纳诺科技股份有限公司 | Goods dynamic traceability management method and system based on industrial Internet of things |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN115665659A (en) | Tensor-based mobile internet of things coverage reliability assessment method | |
| Giridhar et al. | Distributed clock synchronization over wireless networks: Algorithms and analysis | |
| CN103648108B (en) | Sensor network distributed consistency object state estimation method | |
| CN110278571B (en) | Distributed signal tracking method based on simple prediction-correction link | |
| CN116186643B (en) | Multi-sensor collaborative target tracking method, system, equipment and medium | |
| CN114168971B (en) | Internet of things coverage vulnerability repairing method based on reinforcement learning | |
| CN104539266B (en) | Kalman's uniformity wave filter based on the adaptation rate factor | |
| Fang et al. | Noise-aware localization algorithms for wireless sensor networks based on multidimensional scaling and adaptive Kalman filtering | |
| CN103313386B (en) | Based on the radio sensing network method for tracking target of consistency on messaging right-value optimization | |
| CN115426661A (en) | Credible coverage reliability assessment method for Internet of things based on trust management | |
| CN104331630B (en) | A kind of multi tate observes the state estimation and data fusion method of data | |
| Saha et al. | An evolved algorithm for underwater acoustic sensor node localization enhancement using reference node | |
| CN103313384B (en) | A kind of radio sensing network method for tracking target based on consistency on messaging | |
| CN116390112A (en) | Wireless sensor network coverage reliability assessment method based on trusted information coverage | |
| CN109188424B (en) | Distributed multi-sensor multi-target tracking method based on measurement consistency | |
| Xiaofeng et al. | Improvement of the local prediction of chaotic time series | |
| Chowdappa et al. | Distributed clustering algorithm for spatial field reconstruction in wireless sensor networks | |
| Van Herbruggen et al. | Multihop Self-Calibration Algorithm for Ultra-Wideband (UWB) Anchor Node Positioning | |
| Champ et al. | Adnl-angle: accurate distributed node localization for wireless sensor networks with angle of arrival information | |
| CN111683377B (en) | Real-time reliable relay deployment method for power distribution network | |
| CN112333236B (en) | Fault-tolerant cooperative positioning method based on two-layer filtering in three-dimensional dynamic cluster network | |
| Siddavaatam et al. | intel-LEACH: An optimal framework for node selection using dynamic clustering for wireless sensor networks | |
| Banihashemian et al. | A new range‐free PCA‐based localization algorithm in wireless sensor networks | |
| CN116456356B (en) | Reliability evaluation method for large-scale wireless sensor network based on reliable information coverage | |
| CN103517411B (en) | Wireless sensor network node localization method and device |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination |