Data collection and offloading method for distributed nodes in uav-assisted internet of things

Abstract

The application provides a method for data collection and unloading of distributed nodes in an unmanned aerial vehicle (UAV) assisted Internet of Things (IoT), and belongs to the technical field of UAV assisted mobile communication networks.The method is used for solving the joint data collection and computing unloading task of large-scale IoT nodes and realizing energy efficiency maximization in an UAV assisted mobile edge computing (MEC) system.The application is attributed to a nested mixed integer optimization problem, wherein an external problem is to select a specific number of key INs from potential INs for data transmission, and an internal problem is to maximize the energy efficiency of the UAV by optimizing the scheduling, three-dimensional flight trajectory and computing resource allocation of the UAV so as to perform data collection and computing unloading from the selected INs.The external problem is solved by using a method based on Gale circle alignment to convert the selection of INs into a matrix eigenvalue optimization problem, the external problem is divided into three sub-problems, and the model is convexized by using equivalent transformation, convex difference and continuous convex approximation to solve the problem.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of unmanned aerial vehicle assisted mobile communication network, and particularly relates to a data collection and unloading method for distributed nodes in an unmanned aerial vehicle assisted Internet of Things. BACKGROUND

[0002] With the development of Internet of Things technology, Internet of Things terminals represented by wireless sensors are widely used in intelligent transportation, forest monitoring, traffic safety and other scenarios. These sensing terminals do not need wired power connection and can be deployed more flexibly, thereby reducing installation and maintenance costs. In actual operation, these Internet of Things nodes (Ins) will generate a large amount of various data, which needs to be further transmitted to the central or distributed base station (BS) for further processing or analysis. However, in most cases, wireless connection will limit the energy of IN. The wide distribution of IN and the limited transmission power make long-distance data communication unreliable.

[0003] At the same time, the sensor nodes in the Internet of Things usually have limited computing power and are difficult to independently handle complex computing-intensive tasks. When handling delay-sensitive tasks, transmitting data to centralized or distributed BS for further processing or analysis can cause high network delay, especially in the case of long data transmission path or network congestion. In order to meet the demand for high-performance computing, which far exceeds the inherent ability of IN, mobile edge computing (MEC) technology has been widely used in Internet of Things applications. MEC allows IN to offload computing tasks to nearby edge servers (such as BS, access point) to achieve fast and energy-efficient task processing. However, in most cases, it is difficult and expensive to establish ground MEC infrastructure to provide services for a large number of INs distributed in a large geographical area.

[0004] The next generation mobile network such as the fifth generation (5G), beyond 5G (B5G) and even the sixth generation (6G) has attracted more and more research power in recent years. Among them, unmanned aerial vehicle (UAV) assisted mobile communication network has recently attracted much attention. The high mobility, low cost, easy deployment and line of sight link (LoS) of unmanned aerial vehicles make them applicable to different scenarios, thereby improving the performance of wireless networks. In addition, unmanned aerial vehicles not only can collect data, but also can act as edge computing nodes. During flight, data can be pre-processed or compressed on the unmanned aerial vehicle, thereby reducing the computing burden of Internet of Things sensor nodes and cloud computing. The present application comprehensively considers the energy efficiency, communication throughput and data offloading demand of unmanned aerial vehicles, and proposes a three-dimensional trajectory and resource allocation strategy based on Gershgorin disc alignment and multivariate alternating iteration optimization to realize the overall energy efficiency maximization of unmanned aerial vehicle assisted Internet of Things system. SUMMARY

[0005] Therefore, the present application aims to provide a method for data collection and offloading of distributed nodes in a UAV-assisted IoT, which establishes a system model for scenarios involving a single UAV and multiple IoT nodes, optimizes energy efficiency, and maximizes the overall performance of the UAV-assisted IoT system.

[0006] To achieve the above-mentioned purpose, the present application provides the following technical solutions:

[0007] A method for data collection and offloading of distributed nodes in a UAV-assisted IoT, comprising the following steps:

[0008] Step 1: Design a UAV-assisted mobile edge computing system, in which the UAV needs to select appropriate ground IoT nodes from a large number of distributed wireless ground IoT nodes to complete data collection and computing offloading tasks under the requirement of ensuring data integrity; the system includes a UAV 3D trajectory model, a node signal model, a fusion center signal reconstruction model, a probabilistic line-of-sight channel model, and a UAV energy consumption and computing model;

[0009] Step 2: Propose a nested optimization problem; the inner problem selects a certain number of IoT nodes from a set of potential IoT nodes to enable the data transmitted by the IoT nodes to reconstruct the global data with a certain accuracy, and the outer problem optimizes the UAV's scheduling, three-dimensional flight trajectory, and computing resource allocation to maximize the energy efficiency of the UAV by performing data collection and computing offloading from the selected IoT nodes;

[0010] Step 3: To solve the nested optimization problem P1, a two-stage algorithm is used to solve the problem.

[0011] The UAV-assisted mobile edge computing system in step 1 is composed of one UAV and N IoT nodes, each of which can observe an unknown parameter x and send its observation results to the fusion center, which estimates the parameter x based on the received information; the UAV acts as an aerial collector and mobile edge computing terminal, collecting data from ground IoT nodes and bringing the data back to the fusion center;

[0012] The cooperation relationship between the IoT nodes is represented by a connected undirected graph ; the undirected graph is represented by a triple , where represents the set of N IoT nodes in the undirected graph , s1, s2,..., s N represent the nodes in the undirected graph , and ε represents the undirected graph A set of middle E edges, A is edge weight A ij ; wherein weight A ij reflects the correlation or similarity between two connected nodes s i and s j ; an undirected graph The coordinates of a certain node Internet of Things node s n in the undirected graph are represented by w n = (x n , y n , H s ), wherein the height H s of the Internet of Things node in the coordinates is negligible and is approximately zero.

[0013] The 3D trajectory model of the unmanned aerial vehicle is as follows:

[0014] It is assumed that the starting point and the ending point of the unmanned aerial vehicle are predetermined, and the coordinates are represented by s and s , respectively.

[0015] The flight time T of the unmanned aerial vehicle is divided into M equal time slots δ t , and is represented by T = Mδ t ; each time slot δ t is short enough to assume that the unmanned aerial vehicle is approximately stationary within the time slot δ t ; therefore, the trajectory q(t) of the unmanned aerial vehicle is approximately a sequence of discrete points Due to limited energy, the flight time and the maximum speed of the unmanned aerial vehicle are T and V max , respectively; the maximum and minimum flight heights are H max and H max ,

[0016] Due to the maximum speed limit of the unmanned aerial vehicle, the positions between two time slots need to satisfy the following constraint condition:

[0017] H min ≤ q z [m] ≤ H max (1)

[0018] In equation (1), q z [m] is the trajectory of the unmanned aerial vehicle in the vertical ground direction within the mth time slot;

[0019]

[0020] In equation (2), D represents the displacement of the unmanned aerial vehicle, and has:

[0021]

[0022] In formula (3), v[m] is the speed of the UAV in the mth time slot, a[m] is the acceleration of the UAV in the mth time slot, and there are:

[0023] v[0]=v s , v[M]=v F (4)

[0024] v s and v F are the initial speed and final speed of the UAV, respectively;

[0025]

[0026]

[0027] The acceleration of the UAV is limited to not more than a max ;

[0028]

[0029] The speed of the UAV is limited to be greater than V min to maintain flight;

[0030] q[0]=q ori ; q[M]=q des (8)

[0031] Since the rotor UAV needs to maintain balance during flight, the limit of the pitch angle of the UAV is given by the following formula:

[0032]

[0033] where v z [m] is the speed of the UAV in the vertical ground direction in the mth time slot, and ε is a constant;

[0034] Considering the UAV using time division multiple access in the present application, a Boolean variable t is defined to describe the scheduling of all Internet of Things nodes, where t n [m]=1 indicates that the nth Internet of Things node can transmit data to the UAV in the mth time slot with a transmission power P k and a transmission rate R n [m], and t n [m]=0 indicates that the nth Internet of Things node remains in a sleep state in the mth time slot;

[0035] The scheduling variable t n [m] is described as:

[0036] and

[0037] The node signal model is as follows:

[0038] Undirected graph The IoT node s n The graph domain signal value at s n is x N , so the complete graph domain signal is represented in the form of a vector, that is, x = (x1, x2,..., xN) ∈ RN N ; each IoT node s n observes x with noise observation, so the real value observation value y n of the IoT node s n is represented as

[0039] y n = x n + n n ;

[0040] where n n represents the noise in the real value observation of the IoT node s n .

[0041] If the signal of an IoT node is completely collected by the UAV, we call the signal of the IoT node an effective observation signal, and the fusion center can reconstruct the complete signal by using the signal of the effective observation IoT node. Then, all the observation signals that can be collected by the UAV in one flight can be represented as

[0042]

[0043] where n represents an additive noise vector, Ω represents the effective node data selectively collected by the UAV in one flight; Ω ∈ {0, 1} K×N is a K × N matrix, each row of Ω represents a sampling vector with a modulus of 1, and each column corresponds to an IoT node, when a column is set to 1, the UAV will completely collect the data of the IoT node corresponding to the column, K is the number of nodes planned to be collected; Ω[m] represents the set of nodes whose data has been completely collected at time slot m;

[0044] It is assumed that the time series data collected by the IoT nodes are respectively stored in their storage areas; in one flight of the UAV, the IoT node s n needs to transmit a data amount of S n .

[0045] For a given undirected graph G related to the IoT nodes , the corresponding graph Laplacian matrix L can be represented as

[0046]

[0047] where D = diag(A1) is a diagonal matrix, 1 is a vector of all ones, and diag(-) denotes a diagonal matrix with the elements of the input vector on the main diagonal;

[0048] Signal vector x ∈ R N Smoothness of signal x smooth The smoothness of signal is quantified by constructing the following smoothness quantification model on a given undirected weighted graph:

[0049]

[0050] The smaller the smoothness of signal is, the smoother the signal is;

[0051] The fusion center signal reconstruction model is as follows:

[0052] Given a noisy graph signal y on a graph, the goal of the fusion center is to recover the smooth graph signal; assuming the fusion center employs a biased graph signal reconstruction scheme based on graph Laplacian regularization, the biased signal reconstruction is achieved by unconstrained l2 norm minimization. Specifically, the graph Laplacian regularization can be expressed as an optimization over the target signal, whose formula is as follows:

[0053]

[0054] Where μ is a trade-off parameter balancing the graph Laplacian regularization and the l2 normal data fidelity term; the optimal solution x of the quadratic objective function can be obtained by solving the following linear equation:

[0055]

[0056] For the L constructed on the graph Ω T Ω+μL is positive definite, therefore, the above linear equation has a unique solution:

[0057] (Ω T Ω+μL) -1 Ω T y;

[0058] The minimum mean square error between the original signal x and the reconstructed signal x is equivalent to

[0059]

[0060] Let B = Ω T Ω+μL, and B is a symmetric positive definite matrix, therefore, given μ, L and x, minimizing ||B -1 ||2 can minimize the mean square error;

[0061] The probabilistic line-of-sight channel model is as follows:

[0062] The quasi-static block fading channel model is used for the IoT node-UAV link, where there are Z fading blocks in each time slot, and the channel within each fading block remains constant and can change with the block. The UAV and IoT node s n The downlink channel power gain of the wireless communication link between the UAV and IoT node s is denoted as

[0063]

[0064] where, denotes the large-scale attenuation coefficient, denotes the small-scale Rician attenuation coefficient, denotes the mean value; and The calculation formula of

[0065]

[0066]

[0067] where w n is the coordinate of the IoT node s n , a is the path loss factor, the value of a is 2, β0represents the power gain when the reference distance is 1m, K1represents the small-scale Rician attenuation coefficient, denotes the LoS channel part, denotes the random scattering part,

[0068] The uplink transmission power of the IoT node s n to the UAV in time slot m is P k Therefore, the calculation formula of the achievable transmission rate of the zth fading block in time slot m is

[0069]

[0070] where ξ is the signal-to-noise ratio difference between the actual modulation scheme and the theoretical Gaussian signal, B is the channel bandwidth, σ 2 represents the additive white Gaussian noise at the receiving end. The outage probability between the IoT node s n and the UAV in time slot m is given by

[0071]

[0072] where, denotes the probability density function, F n，m is the cumulative distribution function of in time slot m, relative to Rn [m] is a non-decreasing function; when the maximum allowed interruption probability is ∈, R n [m] satisfies the following formula

[0073]

[0074] wherein is the inverse function of F n，m .

[0075] Therefore, the total transmission data D total of the distributed sensor in the entire duration T can be defined as

[0076]

[0077] The energy consumption and calculation model of the UAV are as follows:

[0078] The energy consumption of the unmanned aerial vehicle is generally composed of three main parts: communication-related energy consumption, propulsion energy consumption, and calculation energy consumption; wherein the communication-related energy consumption is much smaller than the propulsion energy consumption, and therefore the communication-related energy consumption can be ignored;

[0079] For a rotor UAV, the propulsion energy consumption of 3D flight can be expressed as

[0080]

[0081] wherein c1 and c2 are two constants related to the UAV wing span efficiency, wing surface area, and mass; g = 9.7 m / s is the gravitational acceleration, a z is the acceleration in the vertical ground direction, v x is the speed in the x-axis direction of the Cartesian coordinate system, and v y is the speed in the y-axis direction of the Cartesian coordinate system;

[0082] The calculation energy of the UAV in each time slot is as follows:

[0083]

[0084] wherein r is a constant representing the effective switching capacitor, f n [m] represents the calculation resource allocated by the UAV to the Internet of Things node s n in the time slot m;

[0085] In summary, the total energy consumption of the UAV can be obtained, as shown in the following formula:

[0086]

[0087] When the initial position and final position and speed of the unmanned aerial vehicle are determined, the third and fourth terms in the above formula are constants, and therefore the optimization process can not need to be considered;

[0088] In addition, considering the limited computing resources of the UAV, each time slot limits the maximum allocatable computing resources of the UAV:

[0089]

[0090] All the processing of the collected data should be completed within one flight cycle, which results in the following limitations:

[0091]

[0092] where s k represents the number of CPU cycles required to compute each data bit, and this constraint ensures that the data collected by the UAV in the mth time slot and thereafter can be completely offloaded after the mth time slot;

[0093] The nested optimization problem proposed in step two is as follows:

[0094] By optimizing the trajectory the scheduling vector the computing resource allocation vector and the set of Internet of Things nodes collecting data The energy efficiency maximization optimization problem P1 can be expressed as

[0095]

[0096] The optimization problem P1 is nested by an outer problem and an inner problem; in the outer problem, the goal is to find a set of optimal access Internet of Things nodes so that the reconstruction error Δ satisfies a certain accuracy; at the same time, the goal of the inner problem is to determine the scheduling vector t of the nodes, the optimal trajectory q, and the computing resource allocation f of the given optimal access Internet of Things node set.

[0097] In step three, a two-stage algorithm is used to solve the nested optimization problem P1; the specific method is as follows:

[0098] In the first stage, a method based on Gale circle alignment is used to transform the selection of Internet of Things nodes into a matrix eigenvalue optimization problem to solve the inner problem in the optimization problem P1; the specific method is as follows:

[0099] The problem to be solved in the first stage is shown in problem P1.1:

[0100]

[0101] Since B is a symmetric positive definite matrix, it satisfies Therefore, the maximum λ min(B) can minimize the upper bound of mean square error; therefore, problem P1.1 can be converted into the form of problem P1.1a of maximizing the minimum eigenvalue of matrix B:

[0102]

[0103] The present application solves problem P1.1a using the method based on the alignment of Gerschgorin circles by converting the above-mentioned matrix eigenvalue optimization problem into the scaling and translation operation of Gerschgorin circles, and the steps are as follows:

[0104] 1) Input the undirected graph of Internet of Things nodes Reconstruction error Δ and IN number budget K;

[0105] 2) Initialize the set of Internet of Things nodes N is the number of Internet of Things nodes in the set;

[0106] 3) From node n = 1 to node n = N, estimate the covering subset of each Gerschgorin circle by using the method based on Gerschgorin circle theorem And the obtained subset Merging, get the set

[0107] 4) At the same time, if n ≤ K, select the subset With the largest intersection set Subsets And the set of Internet of Things nodes Take the intersection, then take the complement of the set and the set of Internet of Things nodes Reassign the node set Then integrate the current node n into the selected set of Internet of Things nodes Return to step 3) to take the next value of n;

[0108] 5) If n > K, output the current selected set of Internet of Things nodes End of solution;

[0109] Iterative solution is performed for different reconstruction errors Δ ∈ (0, 1), and the set of Internet of Things nodes That is, the set of Internet of Things nodes Θ;

[0110] In the second stage, the external problem is divided into three sub-problems, and the model is convexized by using equivalent transformation, convex difference and continuous convex approximation; the specific method is as follows:

[0111] In the second stage of the problem, the collection and unloading of data sent by the selected Internet of Things nodes of the external problem are completed by reasonably planning the flight path of the unmanned aerial vehicle and allocating computing resources, and the problem to be solved in the second stage is shown in problem P1.2:

[0112]

[0113] Problem P1.2 is divided into three sub-problems as follows:

[0114] a. IN node access sub-problem

[0115] Given the UAV flight trajectory q and the computation resource allocation f, the denominator of problem P1.2 is determined, and the sub-problem becomes the design of the UAV data collection node access time slots, with the goal of maximizing the total data collection amount.

[0116] To solve this integer programming problem, the binary constraint condition is relaxed to

[0117] The UAV data collection node access time slot problem is designed as:

[0118]

[0119]

[0120]

[0121]

[0122]

[0123]

[0124] b. UAV three-dimensional trajectory optimization sub-problem

[0125] According to the given set of nodes to be accessed Θ, the scheduling vector t and the resource allocation vector f, the UAV trajectory q and the related speed v and acceleration a are optimized, and the optimization problem P1.2 can be re-expressed as:

[0126]

[0127] where and R n [m] in the numerator of the objective function are non-convex with respect to q;

[0128] The denominator of the objective function is also non-convex with respect to v and a, and the denominator of the objective function is non-convex with respect to v and a.

[0129] |v z [m]| 2 ≤ε 2 ||v[m]|| 2 is also non-convex; therefore, it needs to be transformed into a mathematically solvable problem;

[0130] (b1) Convexity of the objective function numerator with respect to a

[0131] Because of a z [m] may be non-negative, therefore a slack variable α[m] is introduced. 2 Thus obtain

[0132]

[0133]

[0134]

[0135] so, It will be converted to

[0136]

[0137] (b2) Convexity of the objective function numerator with respect to v

[0138] In It is a non-convex function. We use a first-order Taylor expansion to transform it into a convex function and apply the continuous convex approximation.

[0139]

[0140] Introducing auxiliary variables and This is to handle v[m] in the non-convex denominator. Thus, the above equation becomes...

[0141]

[0142] κ 2 [m]≤||v[m]|| 2 and ρ[m]≤||v[m]|| 3 The terms to the right are non-concave terms, and their lower bound is obtained through the local point v. (r) [m] is obtained by performing a first-order Taylor expansion on the right side:

[0143]

[0144]

[0145] Through the above transformation, the formula The terms in the equation can be transformed into a standard form consistent with convex optimization:

[0146]

[0147] (b3)|v z [m]| 2 ≤ε2 ||v[m]|| 2 convexification of

[0148] |v z [m]| 2 ≤ε 2 ||v[m]|| 2 The right-hand side Taylor expansion gives also

[0149] and convexification of the objective function’s numerator

[0150] Let denote the given trajectory in the rthiteration; by applying a first-order Taylor expansion, R n [m] can be lower bounded by

[0151] where

[0152]

[0153]

[0154] J n，r [m] = ||q (r) [m] - w n || 2 .

[0155] By the above operation, the numerator of the objective function becomes the following concave form

[0156]

[0157] Again, replace with

[0158]

[0159] (b4) convexification of

[0160] At the local point q (r) [m], ||q[m] - w n || 2 with respect to q[m], we have

[0161] ||q[m] - w n || 2 ≥ A 3，n，r [m] + 2(A 4，n，r [m]) T q[m];

[0162] where A 4，n，r [m] = q (r)[m] - w n and A 3，n，r [m] = ||q (r) [m] - w n || 2 -2(A 4，n，r [m]) T q (r) [m];

[0163]

[0164] Substituting we get

[0165]

[0166] By the above transformation, the optimization problem P1.2.2 related to the UAV trajectory can be transformed into the following form:

[0167]

[0168] c. Computing resource allocation optimization subproblem

[0169] The computing resource offloading problem is formulated as a maximization problem of the lower bound of the offloaded data volume, i.e., problem P1.2.3:

[0170]

[0171] d. A multivariate fixed-alternating iteration method is employed to optimize the second-stage problem, which has the following steps:

[0172] d1) Initialize the iteration number i, the initial trajectory q (0) , the initial resource allocation f (0) , the initial velocity v (0) , the initial acceleration a (0) , the intermediate variables a (0) and u (0) ;

[0173] d2) Solve problem (P1.2.1) with given q (i) and f (i) to obtain the optimal solution t (i+1) of the scheduling vector;

[0174] d3) Solve problem P1.2.2a with given q (i) , v (i) , a (i) , f (i) , t (i+1) , a (i) and u (i) to obtain the optimal trajectory q (i+1) , velocity v​(i+1) , acceleration a (i+1) , auxiliary variable p (i+1) and k (i+1) , intermediate variable a (i+1) and v (i+1) ;

[0175] d4) solving problem P1.2.3 based on the optimal trajectory q (i+1) and the scheduling vector t (i+1) obtained in step d2), obtaining the optimal resource allocation f (i+1) ;

[0176] d5) if the multivariate fixed-alternating iterative algorithm converges, exit the iteration; otherwise, update the iteration number i = i + 1, and bring the trajectory q (i+1) , the resource allocation f (i+1) , the speed v (i+1) , the acceleration a (i+1) , the intermediate variable a (i+1) and v (i+1) into step d1) for the next iteration.

[0177] The beneficial effects of the present application are:

[0178] The present application designs a 3D trajectory optimization and resource allocation strategy based on unmanned aerial vehicle assistance, and constructs an unmanned aerial vehicle assisted Internet of Things (IoT) data collection and computing offloading model. The Gershgorin disc alignment algorithm is used to select key nodes, reduce redundant data transmission, and reduce the total energy consumption of the system. The unmanned aerial vehicle flies under the optimized 3D trajectory, and collects and processes the data of the key nodes according to the allocated computing resources. After the task is completed, the unmanned aerial vehicle will return to the ground base station or fusion center (FC). The present application aims to maximize the system energy efficiency, and proposes a joint algorithm for node selection and three-dimensional trajectory optimization, and improves the communication throughput and computing offloading performance of the unmanned aerial vehicle through a multivariate alternating iterative optimization method. The simulation results show that compared with other benchmark schemes, the algorithm based on joint 3D trajectory optimization and resource allocation proposed by us significantly improves the performance of data collection and computing offloading, and verifies the effectiveness of the optimization of unmanned aerial vehicles and selective key node data collection in the Internet of Things network. This shows that by optimizing the flight trajectory of the unmanned aerial vehicle and the computing resource allocation strategy, the data transmission efficiency and energy utilization rate of the unmanned aerial vehicle assisted Internet of Things system can be greatly improved, further proving the necessity and importance of the method in complex Internet of Things environments.

[0179] Additional advantages, objects, and features of the application will be apparent from the following specification, taken in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF DRAWINGS

[0180] Figure 1 System scenario; Computational Offloading-Computational Offloading, 3D Trajectory-3D Trajectory, Data Collection-Data Collection, Correlation between INs- Correlation between INs, The selected IN-The selected IN;

[0181] Figure 2 Random IN graph and graph signal on IN; (a) Distribution of 50 random Ins, (b) Selected Ins;

[0182] Figure 3 The impact of different flight durations T on the trajectory of the unmanned aerial vehicle;

[0183] Figure 4 The impact of different flight times T on the flight height of the unmanned aerial vehicle;

[0184] Figure 5 The impact of different flight times T on the speed of the unmanned aerial vehicle;

[0185] Figure 6 Node access time slot allocation under different data collection lower limits (a) T = 100 s, S k = 9 Mbit, (b) T = 100 s, S k = 14 Mbit.

[0186] Figure 7 Unmanned aerial vehicle assisted system under different flight durations T Computational resource offloading allocation results (a) T = 105 s, (b) T = 115 s, (c) T = 120 s;

[0187] Figure 8 Under different data collection lower limits S kThe EE of the proposed method is compared with three benchmarks of the UAV under different conditions. In the figure: Energy Efficiency for the proposed scheme - Energy Efficiency for the proposed scheme, Energy Efficiency for 2D scheme - Energy Efficiency for 2D scheme, Equal computational resource allocation - Equal computational resource allocation, Fixed trajectory method - Fixed trajectory method.

[0188] Figure 9 For different data collection lower limit S k Comparison of the flight height of the UAV at different times.

[0189] Figure 10 For the comparison of the proposed method of the UAV with three benchmarks EE under different flight duration T conditions. In the figure, the figure legend is the same as Figure 8 .

[0190] Figure 11 For the comparison of the EE of the proposed method with three benchmarks of the UAV under different maximum computational resource limits . In the figure, the figure legend is the same as Figure 8 . DETAILED DESCRIPTION

[0191] The technical solutions in the embodiments of the present application will be described in detail below with reference to the drawings in the embodiments of the present application. The described embodiments are only a part of the embodiments of the present application.

[0192] The data collection and unloading method of a UAV-assisted distributed node in an Internet of Things in the present embodiment includes the following steps:

[0193] Step one: design a UAV-assisted MEC system, in which the UAV needs to select a suitable ground IN from a large number of distributed wireless ground INs to complete the data collection and computing unloading tasks, including a UAV 3D trajectory model, a node signal model, a fusion center (FC) signal reconstruction model, a probabilistic line-of-sight channel model, a UAV energy consumption and computing model;

[0194] The UAV-assisted MEC system is composed of one UAV and N INs, each IN can observe an unknown parameter x and send its observation result to the fusion center (FC), the FC estimates the parameter x according to the received information, the UAV acts as an air collector and a mobile edge computing terminal, collects data from the ground IN, and takes the data back to the FC, as shown in Figure 1 .

[0195] There is a cooperative relationship between INs, which is represented by a connected undirected graph The graph is defined by a triple , where represents the set of N INs in the undirected graph , s1, s2,..., s N represent a node in the undirected graph , respectively, ε represents the set of E edges in the graph, and A is the set of edge weights A ij ; wherein the weight A ij reflects the correlation or similarity between two connected nodes s i and s j . The coordinates of a node IN s n in the graph are represented by w n = (x n , y n , H s ). The height H s of the IN can be ignored compared with the height of the UAV, and will not affect the conclusion of the application.

[0196] 1. UAV 3D trajectory model

[0197] Assuming that the starting and ending positions of the UAV are predetermined, the coordinates are represented as The real-time three-dimensional trajectory of the UAV is represented by q(t).

[0198] wherein, due to limited energy, the flight time and maximum speed of the UAV are T and V max respectively. The maximum and minimum flight heights are H max and H max , respectively, satisfying H min ≤ q z [m] ≤ H max (1),

[0199] This is for safety considerations (such as avoiding buildings).

[0200] In the case of continuous time, the position variable of the UAV is infinite and difficult to obtain. For ease of illustration, we divide T into M equal time slots, denoted as T = Mδ t , where δ t is the time slot length. Each time slot is short enough to assume that the UAV is approximately stationary within the time slot. In view of this, the UAV trajectory q(t) can be approximated as a sequence of discrete points Due to the maximum speed limit of the UAV, the positions between two time slots need to satisfy the following constraint condition:

[0201] ​

[0202] in

[0203] v[0]=v s v[M]=v F (4)

[0204] v s and v F These are the initial and final velocities of the drone, respectively.

[0205]

[0206] The acceleration of unmanned aerial vehicles must not exceed a max ;

[0207] The speed of the unmanned aerial vehicle needs to be greater than V. min Only then can it maintain flight;

[0208] q[0]=q ori ; q[M]=q des (8)

[0209] Since rotary-wing drones need to maintain balance during flight, the pitch angle limit for the drone is given by the following formula:

[0210] Where ε is a constant;

[0211] Consider using a drone with Time Division Multiple Access (TDMA) and define a Boolean variable. Describe the scheduling of all IN operations, where t n [m]=1 indicates that the nth IN can achieve the required transmission power P in the mth time slot to meet the interruption probability. k and transmission rate R n [m] transmits data to the drone, t n [m] = 0 indicates that the nth IN operation remains in a sleep state during the mth time slot. Scheduling variable t n [m] can be described as

[0212] and

[0213] 2. Node signal model

[0214] This invention uses x n Representation diagram Chinese INs n The graph domain signal value at point X. The complete graph domain signal can be written in vector form, i.e.: x = (x1, x2, ..., xn). N )∈RN Each IN n will make a noisy observation of a deterministic parameter x (e.g. temperature). INs n make real-valued observations y n which can be modeled as

[0215] y n = x n + n n ;

[0216] where n n represents the noise in the real-valued observations of INs n .

[0217] If the signal of an IN is fully collected by the UAV, we call the signal of the IN an effective observation signal, FC can reconstruct the complete signal using the signal of the effective observation IN. Then, all the observation signals that the UAV can collect in one flight can be represented as

[0218]

[0219] where Ω ∈ {0, 1} K×N is a K x N matrix, n represents the additive noise vector, represents the effective node data that the UAV selectively collects in one flight. Each row of Ω represents a sampling vector with modulus 1, and each column corresponds to an IN. When a column is set to 1, the UAV will fully collect the data of the IN corresponding to the column. K is the number of nodes planned to be collected. We use Ω[m] to represent the set of nodes whose data has been fully collected at time slot m.

[0220] Suppose the time series data collected by INs are stored in their storage areas respectively. In one flight of the UAV, INs n need to transmit S n amount of data.

[0221] For a given graph G associated with INs its corresponding graph Laplacian matrix L can be represented as

[0222]

[0223] where D = diag(A1) is a diagonal matrix. 1 is a vector of all 1s, and diag(·) represents a diagonal matrix whose input vector elements lie on the main diagonal. The signal vector x ∈ R N The smoothness of the signal can be quantified by constructing the following smoothness quantification model on a given unweighted graph:

[0224] The smaller the smoothness of the signal, the smoother the signal.

[0225] 3. FC signal reconstruction model

[0226] Given a noisy graph signal y on a graph, the goal of FC is to recover a smooth graph signal.

[0227] Assume that FC employs a biased graph signal reconstruction scheme based on graph Laplacian regularization (GLR) to achieve biased signal reconstruction via unconstrained l2 norm minimization. Specifically, GLR can be expressed as an optimization over the target signal x, which is formulated as follows:

[0228]

[0229] where μ is a trade-off parameter that balances GLR and the l2 normal data fidelity term. The optimal solution x of the quadratic objective function can be obtained by solving the following linear equation:

[0230]

[0231] For L constructed on a connected graph Ω T Ω+μL. Therefore, the above equation has a unique solution:

[0232] (Ω T Ω+μL) -1 Ω T y;

[0233] MSE minimization between the original signal x and the reconstructed signal x is equivalent to

[0234]

[0235] Let B = Ω T Ω+μL, and B is a symmetric positive definite matrix. Therefore, given μ, L and x, minimizing ||B -1 ||2 can minimize the MSE.

[0236] 4. Probabilistic line-of-sight channel model

[0237] A quasi-static block fading channel model is used for the IN-UAV link, with Z fading blocks in each time slot, where the channel within each fading block remains constant and can change from block to block. The downlink channel power gain of the wireless communication link between the UAV and the INs n in time slot m is denoted as and expressed as

[0238]

[0239] where, denotes the large-scale attenuation coefficient, denotes the small-scale Rician attenuation coefficient, and The calculation formula is

[0240]

[0241]

[0242] Wherein, α≥2 is the path loss factor, β0represents the power gain when the reference distance is 1m. The small-scale Rician attenuation coefficient is K1. In the present application, the value of α is 2. denotes the LoS channel part denotes the random scattering part (zero-mean unit-variance circularly symmetric complex Gaussian random variable connected with the NloS channel part). Therefore, we get

[0243] IN s n The uplink transmission power of the data transmitted to the unmanned aerial vehicle at time slot m is P k . Therefore, the calculation formula of the achievable transmission rate of the zth attenuation block at time slot m is

[0244]

[0245] Wherein, ξ is the signal-to-noise ratio difference between the actual modulation scheme and the theoretical Gaussian signal, B is the channel bandwidth, σ 2 represents the additive white Gaussian noise at the receiving end. At time slot m, the wake-up IN s n The outage probability between the unmanned aerial vehicle and the IN s is given by

[0246]

[0247] Wherein, F n，n is the cumulative distribution function (CDF) of at time slot m, and R n [m] is a non-decreasing function. When the maximum allowed outage probability is ∈, R n [m] satisfies the following formula

[0248]

[0249] Wherein is the inverse function of F n，m .

[0250] Therefore, the total transmission data D total of the distributed sensor within the entire duration T can be defined as

[0251]

[0252] 5. Energy consumption and computation model of UAV

[0253] The energy consumption of a UAV is generally composed of three main parts: communication-related energy consumption, propulsion energy consumption, and computation energy consumption. For a rotor UAV, the propulsion energy consumption of 3D flight can be expressed as

[0254]

[0255] where c1 and c2 are two constants related to the UAV wing span efficiency, wing surface area, and mass; g = 9.7 m / s is the gravity acceleration.

[0256] The computation energy of the UAV in each time slot is as follows:

[0257]

[0258] where r is a constant representing the effective switched capacitance, f n [m] represents the computation resource allocated to INs n by the UAV in time slot m.

[0259] The IN is limited to the maximum energy E max , which can be determined according to the actual IN type. Considering that the communication-related energy consumption is generally within a few joules, which is much smaller than the propulsion energy consumption, the present application ignores it, which does not affect the subsequent conclusion. According to the above description, we can obtain the total energy consumption of the UAV, as shown in the following formula.

[0260]

[0261] When the initial position and final position and velocity of the UAV are determined, the third and fourth terms in the above formula are constants, which can be ignored in the optimization process. Considering that the computation resource of the UAV is limited, the maximum allocatable computation resource of the UAV in each time slot is limited:

[0262]

[0263] All the processing of collected data should be completed within one flight cycle. This results in the following limitation:

[0264]

[0265] where s k represents the number of CPU cycles required to compute each data bit. This constraint ensures that the data collected by the UAV in the mth time slot and thereafter can be completely offloaded after the mth time slot.

[0266] Step two: propose a nested optimization problem; where the inner problem selects a certain number of INs from a set of potential INs, such that the data transmitted by the INs can reconstruct the global data with a certain accuracy, and the outer problem optimizes the scheduling of the UAVs, the 3D flight trajectories, and the computation resource allocation, to maximize the energy efficiency of the UAVs by performing data collection and computation offloading from the selected Ins;

[0267] The proposed optimization problem is as follows:

[0268] By optimizing the trajectory The scheduling vector The computation resource allocation vector And the set of INs that collect data The energy efficiency (EE) maximization optimization problem can be formulated as

[0269]

[0270] Problem (P1) is a nested optimization problem, consisting of an outer problem and an inner problem. In the outer problem, the goal is to find a set of optimal visiting INs, such that the reconstruction error Δ satisfies a certain accuracy. Meanwhile, the goal of the inner problem is to determine the scheduling vector t of the nodes, the optimal trajectory q, and the computation resource allocation f given the optimal set of visiting INs.

[0271] This nested structure makes (P1) a non-convex mixed combinatorial optimization problem, with highly coupled optimization variables, which poses great challenges for finding a solution.

[0272] Step three: to solve this non-convex problem, a two-stage algorithm is proposed to solve the above nested optimization problem;

[0273] The first stage, using the method of Gerschgorin disc alignment (GDA), transforms the selection of Ins into a matrix eigenvalue optimization problem to solve the inner problem; the specific method is as follows:

[0274] The first stage mainly solves the outer combinatorial optimization problem, i.e., the node selection sub-problem, which aims to select a certain number of ground node set from the IN set for transmitting data to the UAV, so that the reconstruction error of the FC when reconstructing the global data from these data meets the requirements. The problem of the first stage is shown as problem (P1.1).

[0275]

[0276] Since B is a symmetric positive definite matrix, it satisfies Therefore, maximizing λ min (B) can minimize the upper bound of MSE. Therefore, problem (P1.1) can be transformed into the form of maximizing the minimum eigenvalue of matrix B as problem (P1.1a).

[0277]

[0278] The present application solves the problem (P1.1a) by converting the above matrix eigenvalue optimization problem into scaling and translation operations of Gershgorin disks, using a GDA-based method, and the algorithm 1 steps are as follows:

[0279] 1) Input IN undirected graph Error bound Δ and IN number budget K;

[0280] 2) Initialize IN set N is the number of set IN;

[0281] 3) From node n=1 to node n=N, use the method based on Gershgorin disk theorem to estimate the covering subset of each Gershgorin disk And the resulting subset Merge to get set

[0282] 4) At the same time, if n≤K, select the subset The intersection of the set Subsets Take the intersection of the IN set Take the complement of the set and the IN set After taking the intersection, reassign the node set Then the current node n is merged into the selected IN set Return to step 3) to take the next value of n;

[0283] 5) If n>K, output the current selected IN set End of solution.

[0284] Algorithm 1 is iteratively solved for different Δ∈(0,1), and a binary search is used to obtain the optimal boundary. Iterative solution can obtain the set of IN And the corresponding Θ.

[0285] The second stage, the external problem is divided into three sub-problems, and the model is convexified by using equivalent transformation, convex difference and continuous convex approximation (SCA); the specific method is as follows:

[0286] In the second stage of the problem, the unmanned aerial vehicle aims to solve the internal problem. By reasonably planning the flight path of the unmanned aerial vehicle and allocating computing resources, the collection and unloading of data sent by the selected IN of the external problem are completed. The problem of the second stage is shown as problem (P1.2).

[0287]

[0288] The second stage of problem (P1.2) is still a mixed integer non-convex problem, which is generally difficult to obtain the optimal solution. Therefore, the goal of solving is to obtain an effective suboptimal solution of (P1.2).

[0289] Problem (P1.2) is divided into three sub-problems as follows:

[0290] a. IN node access sub-problem

[0291] Given the UAV flight trajectory q and the computation resource allocation f, the denominator of problem (P1.2) is determined, and the sub-problem becomes the design of the UAV data collection node access time slot, with the goal of maximizing the total amount of data collection.

[0292] To solve this integer programming problem, we need to relax the binary constraint condition to

[0293] The UAV data collection node access time slot problem is designed as:

[0294]

[0295]

[0296]

[0297]

[0298]

[0299]

[0300] This problem is a standard linear programming (LP) problem, which is easy to solve.

[0301] b. UAV three-dimensional trajectory optimization

[0302] We optimize the UAV trajectory q and the related speed v and acceleration a according to the given set of nodes to be accessed Θ, the scheduling vector t and the resource allocation vector f. The optimization problem can be re-expressed as

[0303]

[0304] where and R n [m] in the numerator of the objective function are non-convex with respect to q.

[0305] The denominator of the objective function is also non-convex with respect to v and a, and the numerator of the objective function is non-convex with respect to q.

[0306] |v z [m]| 2 ≤ε 2 ||v[m]|| 2 They are also non-convex. Therefore, we need to transform them into mathematically solvable problems.

[0307] (b1) Convexity of the objective function numerator with respect to a

[0308] Because of a z [m] may be non-negative, therefore a slack variable α[m] is introduced. 2 Thus obtain

[0309]

[0310]

[0311]

[0312] so, It can be converted

[0313]

[0314] (b2) Convexity of the objective function numerator with respect to v

[0315] In It is a non-convex function. We transform it into a convex function using a first-order Taylor expansion and then apply the SCA.

[0316]

[0317] Introducing auxiliary variables and This is to handle v[m] in the non-convex denominator. Thus, the above equation becomes...

[0318]

[0319] κ 2 [m]≤||v[m]|| 2 and ρ[m]≤||v[m]|| 3 The terms to the right are non-concave terms, and their lower bound is obtained through the local point v. (r) [m] is obtained by performing a first-order Taylor expansion on the right side:

[0320]

[0321]

[0322] Through the above transformation, the formula The terms in the middle can be converted to a standard form consistent with convex optimization:

[0323]

[0324] (b3) |v z [m] 2 ≤ ε 2 ||v[m]||2 2 convexification of the numerator of the objective function

[0325] |v z [m] 2 ≤ ε 2 ||v[m]||2 2 The Taylor expansion on the right also gives

[0326] and convexification of the numerator of the objective function

[0327] Let denote the given trajectory in the rthiteration. By applying a first order Taylor expansion, R n [m] can be lower bounded by

[0328] where

[0329]

[0330]

[0331] J n，r [m] = ||q (r) [m] - w n ||2 2 .

[0332] By the above operation, the numerator of the objective function

[0333]

[0334] Similarly, we can replace with

[0335]

[0336] (b4) convexification of the numerator of the objective function

[0337] At the local point q (r) [m], we have n ||q[m] - w 2 ||2

[0338] ||q[m] - w n|| 2 ≥A 3，n，r [m]+2(A 4，n，r [m]) T q[m];

[0339] where A 4，n，r [m]=q (r) [m]-w n and A 3，n，r [m]=||q (r) [m]-w n || 2 -2(A 4，n，r [m]) T q (r) [m]。

[0340]

[0341] Substituting we get

[0342]

[0343] By the above transformation, the optimization of the problem related to the UAV trajectory (P1.2.2) can be transformed into the following problem

[0344]

[0345] c. Optimization of computing resource allocation

[0346] Through the above analysis and optimization, we can get q, V, a and the scheduling vector t related to the UAV trajectory. The total data collected and the propulsion energy consumption during the flight of the UAV can be determined. The computing energy consumption is much smaller than the propulsion energy consumption and the amount of data collected, and has little effect on energy efficiency, so we ignore the computing energy consumption. In the computing resource allocation task, the computing resource offloading capability of the UAV is released to the maximum extent so that the UAV can collect more data, thereby improving EE.

[0347] The computing resource offloading problem is formulated as a form of maximizing the lower bound of the offloaded data volume, i.e., problem (P1.23).

[0348]

[0349] The first two constraints in the problem seek to maximize the lower bound of the offloaded data, and the remaining constraints ensure that the computing resources allocated for each IN will offload the data collected. This problem is a convex optimization problem, which can be solved using standard convex optimization techniques.

[0350] Based on the above analysis and derivation, we propose a multivariate fixed alternating iteration method to optimize the second stage problem.

[0351] d. Algorithm 2 is used to solve (P1.2). The optimal trajectory q, velocity v, acceleration a, scheduling vector t and computational resource allocation f can be obtained by iteratively solving (P1.2.1), (P1.2.2a) and (P1.2.3) as follows:

[0352] d1) Initialize iteration number i, initial trajectory q (0) , initial resource allocation f (0) , initial velocity v (0) , initial acceleration a (0) , intermediate variables a (0) and υ (0) ;

[0353] d2) Solve problem (P1.2.1) with given q (i) and f (i) to obtain the optimal solution of scheduling vector t (i+1) ;

[0354] d3) Solve problem (P1.2.2a) with given q (i) , v (i) , a (i) , f (i) , t (i+1) , a (i) and υ (i) to obtain the optimal trajectory q (i+1) , velocity v (i+1) , acceleration a (i+1) , auxiliary variables p (i+1) and K (i+1) , intermediate variables a (i+1) and υ (i+1) ;

[0355] d4) Solve problem (P1.2.3) based on the optimal trajectory q (i+1) obtained in step d3) and the scheduling vector t (i+1) obtained in step 2) to obtain the optimal resource allocation f (i+1) ;

[0356] d5) If the multivariate fixed-alternating iterative algorithm converges, exit the iteration; otherwise, update the iteration number i = i + 1, and bring the trajectory q (i+1) , resource allocation f (i+1) , velocity v (i+1) , acceleration a (i+1) , intermediate variables a (i+1) and υ (i+1) into step d1) for the next iteration.

[0357] The total computational complexity of Algorithm 2 is

[0358] Numerical simulation results

[0359] Next we simulate and verify the performance of the designed three-dimensional trajectory optimization and resource allocation joint algorithm for distributed data collection and offloading in UAV-aided wireless networks. We generate a random sensor graph with IN number 50 according to "gsp_sensors" in GSPBOX. Thus, INs are randomly distributed in the geographical area of [0-2000m]x[0-2000m], whose distribution is shown in Figure 2 (a). Assume that the signal at IN is an artificial graph signal with bandwidth K=5, which satisfies the smoothness assumption. In graph signal theory, the necessary condition for a graph signal with bandwidth K to be perfectly recovered from its noiseless samples is that the number of selected sensors is greater than or equal to the signal bandwidth K. Specifically, if rank(ΩV K )=K and V K is the eigenvector of the Laplacian matrix L corresponding to K nodes, then the minimum mean square error solution can provide perfect reconstruction from the sampled graph signal. In the first stage, the positions of INs for transmitting data to the UAV obtained by solving problem (P1.1) are shown in Figure 2 (b).

[0360] The start and end positions of the UAV are set to q ori =[0, 0, 500] T and q des =[0, 2000, 500] T (unit: meters), respectively. The selection of other simulation parameters is shown in Table 1.

[0361] Table 1

[0362]

[0363] We evaluate the performance of the proposed algorithm by the following three benchmarks:

[0364] Two-dimensional trajectory planning scheme: make the UAV plan the trajectory at a fixed height, replace (P1.2.2) with 2D trajectory planning, and use the method proposed in the application for the node access subproblem and the calculation resource allocation subproblem.

[0365] Fixed trajectory method: that is, fix the trajectory of the UAV as a parabola when solving the UAV trajectory optimization problem, and alternately optimize (P1.2.1) and (P1.2.3) to obtain the optimal solution of this example.

[0366] Equivalent calculation resource allocation: specifically, when solving the optimization problem, the calculation resources of all INs are the same, and (P1.2.1) and (P1.2.2a) are alternately optimized to obtain the optimal solution.

[0367] Figure 3 The influence of different flight durations T on the flight trajectory of the UAV is shown. It can be found that when the flight duration T increases, the UAV covers a wider range during the entire flight process. The UAV always tries to fly close to the IN, because flying close to the IN can improve the data transmission rate and communication quality, thereby ensuring the completion of the lower bound data collection task of each node. In addition, more time periods can allow the UAV to unload more data computation tasks, thereby flying closer to the IN and collecting more data.

[0368] Figure 4 The trend of the flight height of the UAV under different flight durations T is shown. When the flight time is 105s, the flight height of the UAV is relatively low. As the flight duration increases, the average flight height of the UAV also increases. This has two reasons. On the one hand, the UAV has more time to collect data, so the UAV can be relatively less close to the IN. On the other hand, the computing power of the UAV is limited, and the flight height needs to be increased to reduce the amount of data collection so that the collected data can meet the computing offloading capability. Figure 5 The trend of the speed of the UAV under different flight durations T at different time periods is given. From the figure, it can be seen that the speed of the UAV is fluctuating. When the UAV approaches the IN that is collecting data, its speed will decrease in order to collect more data. When the UAV is in the process of going to the next node, the UAV will increase the speed to approach the next node in order to arrive at the destination faster. In addition, as the flight time T continues to increase, the UAV has more time to collect data from the IN, thereby reducing the speed to obtain more EE.

[0369] Figure 6 (a) and Figure 6 (b) shows the data collection time slot allocation of the UAV under different data collection lower bounds when the flight duration T = 100s. From the figure, it can be seen that the UAV visits IN 3, IN 4, IN 5, IN 2 and IN 1 along the flight trajectory in turn. Compared with the data collection lower bound of 14Mbit, when the data collection lower bound is 9Mbit, the UAV reserves less time for IN 5 and IN 2. This is because the UAV chooses to collect more data near IN 4 to obtain higher EE, and the lower data collection lower bound allows the UAV to meet the data transmission needs of IN 5 and IN 2 in a short time.

[0370] Figure 7 The calculation resource allocation result of the UAV-assisted system computation offloading is shown. Combined with Figure 3The trajectory shown illustrates that during each IN (Input / Output) data acquisition process, the drone tends to allocate more computing resources to the current IN to process its data. Furthermore, we can observe that the color of the allocated computing resource heatmap lightens as the drone's flight time increases. The increased flight time allows the drone more time to offload computations from the collected data, thus allocating more computation time to each node and reducing the size of the allocated computing resources.

[0371] Figure 8 Comparison of lower limits S for different IN data collection k Under the given conditions, the proposed 3D-EE scheme and the EE of the three benchmarks are compared. It is easy to see from the figure that the proposed strategy has the highest EE compared to the three benchmarks. Specifically, compared with the 2D trajectory planning scheme, the equal allocation of computational resources method, and the fixed trajectory method, the average performance improvement is 34.76%, 60.65%, and 71.65%, respectively, which fully demonstrates the effectiveness of the proposed strategy. Furthermore, the EE of the proposed scheme increases with S... k It increases with the increase of. For example, Figure 9 As shown, this is because, under higher data acquisition threshold requirements, the proposed solution can appropriately adjust the drone's flight altitude. When the data acquisition threshold increases, the drone's flight altitude decreases, thereby increasing EE.

[0372] Figure 10 The impact of the proposed method on the EE of unmanned aerial vehicles under different flight durations T is shown. Figure 10 The proposed scheme was compared with three benchmarks. The minimum data acquisition amount S for all four schemes was... k All values ​​were set to 7 Mbit. The results show that the proposed solution achieves better EE performance regardless of the flight duration T. Furthermore, as the flight duration T increases, the proposed solution exhibits a peak in EE, located around T = 105-110 s in the figure. The peak value of the baseline for equal computational resource allocation is located around T = 120 s. This is because the introduction of 3D UAV trajectory planning and UAV attitude changes affects data acquisition. The UAV can flexibly adjust its flight position to reach the EE peak within an appropriate flight time.

[0373] Figure 11 Given different maximum computing resource limits Below, the proposed method is compared with the EE of three benchmarks. It can be seen that, with the limitation of maximum computational resources... With the increase of [value], the recommended solution's EE significantly increases, exhibiting the best EE. Meanwhile, at higher [values]... In the following, the EE of the proposed scheme still increases rapidly, which indicates that the increase of the computational energy consumption in the proposed scheme does not significantly affect the change of EE, which further confirms the rationality of ignoring the computational energy consumption in the optimization of the third sub-problem in the second phase of the algorithm. The computational energy consumption of the equal computational resource allocation method also shows an upward trend with the increase of the maximum computational resource limit , while the computational energy consumption of the fixed flight trajectory method and the two-dimensional scheme strategy shows a downward trend with the increase of the maximum computational resource limit . This is because although the efficiency values of the three are close, the fixed flight trajectory method and the two-dimensional scheme strategy are both two-dimensional flight strategies, and the amount of data collected is significantly less than that of the three-dimensional flight strategy, so The change will have a certain impact on EE.

[0374] In summary, the present application proposes an optimization strategy for the MEC system assisted by unmanned aerial vehicles, which is used to maximize the energy efficiency when solving the joint data collection and computation offloading task of large-scale Internet of Things nodes. We propose a nested mixed integer optimization problem, where the external problem is to select a certain number of key INs from the potential INs for data transmission. The internal problem optimizes the scheduling of unmanned aerial vehicles, three-dimensional flight trajectories and computation resource allocation to maximize the energy efficiency of unmanned aerial vehicles in order to perform data collection and computation offloading from the selected INs. First, the eigenvalue optimization technique based on Gerschgorin disc alignment is used to solve the external IN selection problem. Second, a multivariate fixed-alternating iteration algorithm is proposed to optimize the scheduling of unmanned aerial vehicles and energy efficiency by decomposing the external problem and combining convex difference technology and continuous convex approximation method. Simulation results show that the optimization strategy proposed in the present application performs well in improving the energy efficiency of unmanned aerial vehicles, and can significantly improve the energy efficiency of unmanned aerial vehicles and system performance compared with the two-dimensional trajectory optimization and equal computational resource allocation algorithm. Future research can further explore optimization problems in more complex environments, such as multiple unmanned aerial vehicles working together or optimization problems under dynamic environmental changes. In addition, considering the continuous expansion of future wireless networks, how to improve the real-time performance and scalability of the algorithm will also be an important research direction.

Claims

1. A method for data collection and offloading of distributed nodes in UAV-assisted IoT, characterized in that, The method comprises the following steps: Step one: design a UAV-assisted mobile edge computing system, wherein the UAV needs to select appropriate ground IoT nodes from a plurality of distributed wireless ground IoT nodes to complete data collection and computing offloading tasks under the requirement of ensuring data integrity; Step two: propose a nested optimization problem; wherein the internal problem selects a certain number of IoT nodes from a set of potential IoT nodes to enable the data transmitted by the IoT nodes to reconstruct the global data with a certain accuracy, and the external problem optimizes the scheduling, three-dimensional flight trajectory and computing resource allocation of the UAV to maximize the energy efficiency of the UAV by performing data collection and computing offloading from the selected IoT nodes; Step three: to solve the nested optimization problem, a two-stage algorithm is used to solve the problem; the specific method is as follows: 1) In the first stage, the selection of IoT nodes is converted into a matrix eigenvalue optimization problem by using a method based on Gale circle alignment to solve the internal problem in the optimization problem; By converting the above matrix eigenvalue optimization problem into scaling and translation operations of Gale circles, the steps of using the Gale circle alignment method are as follows: 1.1) Input an undirected graph of IoT nodes , reconstruction error and the number of nodes K planned to be acquired; 1.2) initialize the set of IoT nodes N is the number of IoT nodes in the set; 1.3) Estimate the covering subset of each Gershgorin disc from node n = 1 to node n = N in turn using the method based on Gershgorin's theorem , and merge the resulting subsets to obtain the set ; 1.4) At the same time, if n≤K, choose the set. The largest subset of intersection subset With IoT node set Find the intersection of the two sets and then calculate the intersection of that set with the set of IoT nodes. The complement of the set of nodes Reassign the value; then merge the current node n into the selected IoT node set. Return to step 1.3) and get the next value of n; 1.5) If n > K, output the current selected set of IoT nodes End of solution; 2) In the second stage, the external problem is divided into three sub-problems, and the model is convexized by using equivalent transformation, convex difference and continuous convex approximation to solve; the three sub-problems are as follows: a, IoT node access sub-problem; b, UAV three-dimensional trajectory optimization sub-problem; c, computing resource allocation optimization sub-problem.

2. The method for data collection and offloading of distributed nodes in UAV assisted IoT network according to claim 1, wherein, The UAV-assisted mobile edge computing system in step one comprises a UAV 3D trajectory model, a node signal model, a fusion center signal reconstruction model, a probabilistic line-of-sight channel model, and a UAV energy consumption and computing model; The unmanned aerial vehicle assisted mobile edge computing system is composed of an unmanned aerial vehicle and an Internet of Things node, each Internet of Things node can observe unknown parameters and send the observation results to the fusion center, and the fusion center estimates the parameters according to the received information The unmanned aerial vehicle acts as an aerial collector and a mobile edge computing terminal, collects data from the ground Internet of Things nodes, and takes the data back to the fusion center; The collaborative relationships between the IoT nodes are mediated by a connected undirected graph. To represent; the undirected graph By triplet It means that, among them Represents an undirected graph In A collection of IoT nodes They represent undirected graphs respectively. The nodes in Represents an undirected graph middle The set of edges, edge weight A set; where weights Reflects two connected nodes and Correlation or similarity between them; undirected graph IoT nodes coordinates This indicates the height of the IoT node in the coordinate system. Negligible, approximately zero. 3.The method of claim 2, wherein, The UAV 3D trajectory model is as follows: Assuming that the start and end positions of the UAV are predetermined, the coordinates are denoted as The real-time three-dimensional trajectory of the UAV is denoted as ​ Flight time of the UAV is divided into equal time slots , denoted as ; each time slot is chosen to be short enough so that the UAV is assumed to be approximately stationary within the time slot ; accordingly, the UAV trajectory is approximately a sequence of discrete points ; due to energy limitation, the flight time of the UAV and the maximum speed are and respectively; the maximum and minimum flight heights are and , Due to the maximum speed limit of the UAV, the positions between two time slots need to satisfy the following constraint condition: （1） In formula (1) is the trajectory of the UAV in the vertical ground direction in the mth time slot; （2） In formula (2), D represents the displacement of the UAV, and has: （3） In formula (3), is the speed of the UAV in the mth time slot, is the acceleration of the UAV in the mth time slot, and has: （4） and Vi and Vf are the initial and final velocities of the drone, respectively; （5） （6） limiting the acceleration of the unmanned aerial vehicle to not exceed ; （7） Limiting the speed of the unmanned aerial vehicle requires greater to maintain flight; （8） Since the rotor UAV needs to maintain balance during flight, the limit of the pitch angle of the UAV is given by the following formula: （9） wherein, is the vertical ground direction speed of the drone in the mth time slot, is a constant; Considering the drone using time division multiple access in the present application, define Boolean variable Describe the scheduling of all Internet of Things nodes, wherein, The transmission power of the th Internet of Things node in the th time slot to meet the interruption probability requirement and transmission rate Transmit data to the drone, The th Internet of Things node keeps sleep state in the th time slot; Scheduling variable Described as: and .

4. The method for data collection and offloading of distributed nodes in UAV assisted IoT network according to claim 3, wherein, The node signal model is as follows: undirected graph intermediate iot node the graph domain signal value at The complete graph domain signal is thus represented in vector form, i.e. each iot node observations Noise observations are made at each iot node The real-valued observation value is represented as ； wherein represents a noise in the real-valued observation of the internet of things node ; If the signal of an IoT node is completely collected by the UAV, we call the signal of the IoT node an effective observation signal, and the fusion center can reconstruct the complete signal by using the signal of the effective observation IoT node; then, all the observation signals that can be collected by the UAV in one flight can be represented as ； wherein represents an additive noise vector, represents the effective node data selectively collected by the UAV in one flight; is a KxN matrix, each row of the matrix represents a sampling vector with modulo 1, and each column corresponds to an IoT node, when a column is set to 1, the UAV will fully collect the data of the IoT node corresponding to the column, and K is the number of nodes planned to be collected; represents the set of nodes whose data has been fully collected in the time slot . It is assumed that the time series data collected by the Internet of Things nodes are stored in their storage areas respectively; in one flight of the unmanned aerial vehicle, the Internet of Things nodes The amount of data to be transmitted is ; For a given undirected graph related to the Internet of Things nodes Its corresponding graph Laplacian matrix L can be expressed as ； wherein is a diagonal matrix, is a vector of all 1s, denotes a diagonal matrix with the input vector elements on the main diagonal; signal vector smoothness by constructing a smoothing quantification model of the following formula on a given undirected weighted graph: ， The smaller the smoothness of the signal, the smoother the signal. 5.The method of claim 4, wherein, The fusion center signal reconstruction model is as follows: Noisy graph signals on a given graph The goal of the fusion center is to recover the smooth graph signal; assuming the fusion center employs a biased graph signal reconstruction scheme based on graph Laplacian regularization, the biased signal reconstruction is achieved by unconstrained norm minimization; specifically, the graph Laplacian regularization can be expressed as an optimization over the target signal, which is formulated as follows: ； where is a trade-off parameter between the fidelity term and the regularization term; the optimal solution of the quadratic objective function can be obtained by solving the following linear equations: ； For L constructed on an undirected graph has a positive definite Thus, the linear equation above has a unique solution: ； original signal between the reconstructed signal minimizing the mean square error between the original signal ； Let , and is a symmetric positive definite matrix, so that, given , and , minimizing minimizes the mean squared error.

6. The method for data collection and offloading of distributed nodes in UAV-assisted IoT according to claim 5, wherein, The probabilistic line-of-sight channel model is as follows: For IoT node-drone links, a quasi-static block fading channel model is used, with each time slot having A series of fading blocks, where the channel within each block remains constant but may change as the block changes; connecting drones with IoT nodes. Wireless communication links between time slots The downlink channel power gain in the middle is denoted as , and represent as ； wherein, represents large-scale attenuation loss, represents small-scale Rician attenuation loss, , represents a mean function; and the calculation formula is ； ； wherein is a coordinate of the Internet of Things node , is a path loss factor, has a value of 2, denotes a power gain for a reference distance of 1 m, denotes a small-scale Rician attenuation coefficient, denotes a small-scale Rician attenuation loss LoS channel portion, , denotes a small-scale Rician attenuation loss random scattering portion, ; Internet of things node In time slots The uplink transmission power for transmitting data to the UAV is Therefore, the achievable transmission rate of the first attenuation block of the time slot is calculated as ； wherein, is the signal-to-noise ratio difference between the actual modulation scheme and the theoretical Gaussian signal, is the channel bandwidth, represents the additive white Gaussian noise at the reception; at time slot wakes up the IoT node The probability of interruption between the drone and the IoT node is given by: ； wherein denotes a probability density function, is a time slot time cumulative distribution function, with respect to is a non-decreasing function; when the maximum allowed outage probability is then, satisfies the following equation ； wherein is the inverse function of Thus, the total transmission data of the distributed sensors over the entire duration may be defined as 。 7. The method of claim 6, wherein, The UAV energy consumption and computing model is as follows: The energy consumption of the UAV generally consists of three main parts: communication-related energy consumption, propulsion energy consumption and computing energy consumption; wherein the communication-related energy consumption is much smaller than the propulsion energy consumption, and therefore the communication-related energy consumption can be ignored; For a rotor UAV, the propulsion energy consumption of 3D flight can be represented as ； wherein, and are two constants related to the wing span efficiency of the unmanned aerial vehicle, the wing surface area and the mass; is the acceleration of gravity, is the acceleration in the vertical ground direction, is the velocity in the x-axis direction of the Cartesian coordinate system, is the velocity in the y-axis direction of the Cartesian coordinate system; The computing energy of the UAV in each time slot is as follows: ； wherein, is a constant representing the effective switched capacitance, represents the computing resources allocated to the IoT node by the UAV in the time slot ; Based on the above, the total energy consumption of the UAV can be obtained, as shown in the following formula: ； When the initial position and final position and speed of the UAV are determined, the third and fourth terms in the above formula are constants, so the optimization process does not need to be considered; Moreover, considering the limited computing resources of UAV, each time slot limits the maximum allocatable computing resources of UAV: ； All the processing of collected data should be completed within one flight cycle, which results in the following constraints: ； wherein, represents the number of CPU cycles required to compute each data bit, this constraint ensures that the unmanned aerial vehicle is able to completely offload data collected in the time slot and after in the time slot.

8. The method for data collection and offloading of distributed nodes in UAV-assisted IoT according to claim 7, wherein, The proposed nested optimization problem is as follows: By optimizing trajectories , scheduling vectors , computing resource allocation vectors , and a set of IoT nodes collecting data , the energy efficiency maximization optimization problem P1 can be formulated as ； The optimization problem P1 is nested by an outer problem and an inner problem; in the outer problem, the goal is to find a set of optimal access IoT nodes so that the reconstruction error Δ satisfies a certain accuracy; meanwhile, the goal of the inner problem is to determine the scheduling vector of the nodes , the optimal trajectory , and the computation resource allocation given the optimal set of access IoT nodes . 9.The method of claim 8, wherein, Step 3: To solve the nested optimization problem P1, a two-stage algorithm is used to solve the problem; the specific method is as follows: 1) The first stage uses the method based on Gerschgorin disc alignment to transform the selection of Internet of Things nodes into a matrix eigenvalue optimization problem to solve the internal problem in optimization problem P1; the specific method is as follows: The problem to be solved in the first stage is shown as problem P1.1: Since is a symmetric positive definite matrix satisfying ; therefore, maximizing can minimize the upper bound of the mean square error; Thus, problem P1.1 can be transformed into the form of problem P1.1a of maximizing the smallest eigenvalue of the matrix ​ By transforming the above matrix eigenvalue optimization problem into scaling and translation operations of Gerschgorin discs, the method based on Gerschgorin disc alignment is used to solve problem P1.1a; for different reconstruction errors iteratively to obtain a set of internet of things nodes that is, the set of internet of things nodes . 10.The method of claim 9, wherein, In step 2) of step 3, in the second stage, the external problem is divided into three sub-problems, and the model is convexized by using equivalent transformation, convex difference and continuous convex approximation to solve; the specific method is as follows: In the second stage of the problem, the collection and unloading of data sent by selected Internet of Things nodes are completed by reasonably planning the flight path and allocating computing resources of the UAV, and the problem to be solved in the second stage is shown as problem P1.2: Problem P1.2 is divided into three sub-problems as follows: a. Internet of Things node access sub-problem In the case of a given drone flight trajectory and computation resource allocation the denominator of problem P1.2 is determined and the subproblem becomes the design of the drone data collection node access slots with the goal of maximizing the total amount of data collected; To solve this integer programming problem, the binary constraint condition is relaxed to ; The UAV data collection node access time slot problem is designed as: ； b. UAV three-dimensional trajectory optimization sub-problem According to the given set of nodes to visit , a scheduling vector and a resource allocation vector Optimizing the drone trajectory as well as the related speed and acceleration The optimization problem P1.2 can be reformulated as: wherein and the target function molecule is non-concave with respect to are non-concave; with respect to is also non-convex, the denominator of the objective function with respect to and is non-convex; are also non-convex; thus, they need to be transformed into mathematically solvable problems; (1) convexity of the objective function numerator with respect to the denominator Due to may be non-negative, so a slack variable is introduced , so that ； ； ； Thus, to convert ； (2) convexity of the objective function numerator with respect to the convexity of the objective function numerator in is a non-convex function, it is transformed into a convex function using a first order Taylor expansion and applying a continuous convex approximation; ； Introducing auxiliary variables and to deal with non-convex denominators ; so the above becomes and The right side of the inequality is non-concave, whose lower bound is obtained by first-order Taylor expansion of the right side at the local point x = 0: ； ； By the above transformation, the term in the formula can be transformed into the standard form consistent with convex optimization: ； (3) convexing The Taylor expansion on the right side also gives ; and convexification of objective function molecules Let denotes the given trajectory in the rth iteration; by applying a first order Taylor expansion, the lower bound of wherein ； ； ； Through the above operation, the numerator of the objective function becomes the following concave form ； Likewise, replace is ; (4) convexing At the local point , With respect to the first order Taylor expansion of , there is ； wherein and ; ； By substituting one obtains ； Through the above transformation, the optimization of problem P1.2.2 related to the UAV trajectory can be transformed into the following form: c. Computing resource allocation optimization sub-problem The computing resource unloading problem is expressed in the form of maximizing the lower limit of the amount of computing unloading data, i.e. problem P1.2.3: d) A multivariate fixed alternating iteration method is used to optimize the second stage problem, and the specific steps are as follows: d1) initializing the iteration number i, an initial trajectory , an initial resource allocation , an initial velocity , an initial acceleration , an intermediate variable and ; d2) using the given and solving problem P1.2.1 to obtain the optimal solution of the scheduling vector ; d3) solving problem P1.2.2a with given , , , , , and yields the optimal trajectory , the velocity , the acceleration , the auxiliary variables and , the intermediate variables and ; d4) based on the optimal trajectory obtained in step d3) and the scheduling vector obtained in step d2) solving problem PI.2.3, obtaining the optimal resource allocation ; d5) If the multivariate fixed-alternating iteration algorithm converges, exit the iteration; otherwise, update the iteration number i = i + 1 and proceed with the next iteration with the trajectory , resource allocation , velocity , acceleration , intermediate variable and into step d2).

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