An unmanned aerial vehicle spectrum sensing algorithm based on bayesian matrix completion

Abstract

The application provides a kind of unmanned aerial vehicle spectrum sensing algorithm based on bayesian matrix completion, belongs to unmanned aerial vehicle spectrum sensing algorithm field, comprising the following steps: step one, considering the size of spectrum sensing area and the number of unmanned aerial vehicles, the spectrum sensing area is divided into several single unmanned aerial vehicle sensing cell blocks, and each unmanned aerial vehicle is responsible for one cell block;Step two, use Kuhn-Munkres algorithm to calculate the shortest path of unmanned aerial vehicle from the initial position to the responsible block;Step three, for each cell block, use genetic algorithm to solve the shortest path of all sampling points;Step four, using bayesian matrix completion algorithm to estimate the spectrum of the whole block area for the obtained sampling point data;The application solves the problem of large number of sampling points, large scale of path planning and long calculation time in order to obtain the spectrum of the whole area in the prior art.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of unmanned aerial vehicle spectrum sensing algorithm, and relates to an unmanned aerial vehicle spectrum sensing algorithm based on Bayesian matrix completion. BACKGROUND

[0002] When the spectrum in a certain space region needs to be known, a traditional method traverses the entire space region using an unmanned aerial vehicle carrying a sensor to obtain the real value of the spectrum at all position points in the space. The traversal method can obtain the accurate value of the space spectrum, but the traversal method needs a great cost in time and distance, and the traversal involves a large-scale path planning problem, which is often difficult to solve in practice. The matrix completion algorithm makes it no longer necessary to traverse all position points to obtain the real value of the spectrum, but the entire matrix can be completed with high precision through sampling data far lower than the number required by the Nyquist sampling theorem. Compared with traversing the entire region, only a certain number of sampling points need to be traversed to restore the spectrum of the entire region through the matrix completion algorithm. However, even if the number of required sampling points is reduced, solving the path planning is still a difficult problem, and the scale of the path planning problem needs to be further reduced so that the solution of the problem can be calculated within an acceptable time. SUMMARY

[0003] The purpose of the application is to provide an unmanned aerial vehicle spectrum sensing algorithm based on Bayesian matrix completion, which solves the problems of too many sampling points, large-scale path planning and long calculation time in the prior art to obtain the spectrum in a certain space region.

[0004] Technical content: An unmanned aerial vehicle spectrum sensing algorithm based on Bayesian matrix completion, comprising the following steps:

[0005] Step one, comprehensively consider the size of the spectrum sensing region and the number of unmanned aerial vehicles, divide the spectrum sensing region into several small blocks sensed by a single unmanned aerial vehicle, and let each unmanned aerial vehicle be responsible for a small block;

[0006] Step two, use the Kuhn-Munkres algorithm to calculate the shortest path of the unmanned aerial vehicle from the initial position to the block responsible for each unmanned aerial vehicle;

[0007] Step three, for each small block, use a genetic algorithm to solve the shortest path of traversing all sampling points;

[0008] Step four, use the Bayesian matrix completion algorithm to estimate the spectrum of the entire block region for the obtained sampling point data.

[0009] Further, the specific operation method of step one is as follows:

[0010] (1) The spectrum sensing in three-dimensional space is considered as the superposition of spectrum sensing in two-dimensional space, so only two-dimensional region is considered;

[0011] (2) Assuming that the region which needs to be sensed is a region of 100x100 unit length, the number of UAVs is 100, and the sampling rate is 0.3:

[0012] (3) According to the size of the spectrum sensing region and the number of UAVs, the spectrum sensing region is divided into 100 small blocks of 10x10, and 100 UAVs are responsible for one block respectively;

[0013] The specific algorithm is represented as:

[0014] X represents the unknown spectrum matrix in the spectrum sensing region; Ω represents the sampling matrix, Ω ij =1 indicates that the {i,j} position element of X is sampled; Y=Ω*X represents the sampled data matrix;

[0015] According to the assumption, X, Ω, Y ∈ R M×N , M, N=100, R M×N represents the set of MxN real matrices; X, Ω, Y are uniformly divided into 100 10x10 matrices, and X ij ∈ R m×n , i ∈ [1, M], j ∈ [1, N], m, n=10, R m×n represents the set of m*n real matrices; similarly, Ω, Y, so Y ij =Ω ij *X ij .

[0016] Further, the specific operation method of step two is as follows:

[0017] (1) The subscript of the spectrum matrix of the spectrum sensing region represents the position coordinates of the point;

[0018] (2) Assuming that the initial formation of the UAV cluster is A, and the target formation is B; the initial position of the i-th initial position in the initial formation is ai, and the target position of the j-th target position in the target formation is bj j , a i , b j ∈ R 1×2 is the position coordinates in the formation; K=100 is the number of UAVs;

[0019] (3) The initial formation A is the initial position state of the UAV cluster, and the initial position of the UAV cluster is assumed to be a rectangular formation position at the center of the spectrum sensing region, i.e. a i =[a i1 , ai2 ],a i1 ,a i2 ∈[41,50];

[0020] (4) For the target formation B, first calculate the position center of the initial formation A as the coordinates [45.5, 45.5] at point p0; for each small block, its sampling matrix is Ω ij , record the coordinates of all 1 elements in Ω ij corresponding to the sampling points of the block, and record the positions of all 1 elements as On average, there are 30 sampling points in each small block; calculate the position point closest to p0 in P, that is For each small block, add the selected position point to the target formation B;

[0021] (5) For the initial formation A and the target formation B, use the Kuhn-Munkres algorithm to solve the moving route of each unmanned aerial vehicle.

[0022] Further, the specific operation method of step three is as follows:

[0023] (1) First, obtain all the sampling point coordinates in the small block, that is, Ω ij All 1 elements or all sampling points in the block correspond to the coordinates in Ω, denoted as Suppose that the block is divided into q sampling points, then

[0024] (2) Traverse all the sampling points as a traveling salesman problem, and use a genetic algorithm to solve it;

[0025] In the genetic algorithm solving step, the unmanned aerial vehicle responsible for the block has moved to the sampling point p i closest to the initial formation center p0 in the block, so the first coordinate sequence number in the coordinate sequence of all individual genes is the sequence number of p i , and the first visited coordinate sequence number is not changed in the subsequent selection, crossover and mutation, so that the TSP problem always starts from p i and does not return to the initial position.

[0026] Further, the specific operation method of step four is as follows:

[0027] After steps one to three, for Y = Ω * X, Ω is known, and Y is obtained by sampling, and the Bayesian matrix completion algorithm is used to estimate X, and in the process of using the Bayesian matrix completion algorithm to estimate X, the GAMP algorithm is used for acceleration.

[0028] Beneficial effects:

[0029] The present application reduces the number of required sampling points, reduces the scale of the path planning problem, and makes the solution of the problem be calculated within an acceptable time when obtaining the spectrum in a certain space region compared with the prior art. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 is a genetic algorithm flow chart;

[0031] Figure 2 is a prior art process of using all drones to traverse the entire region to obtain all the spectrum in the region;

[0032] Figure 3 is a drone spectrum sensing sampling process of the present application;

[0033] Figure 4A is a schematic diagram of moving all drones from the initial position in the center of the region to the respective responsible small blocks using the Kuhn-Munkres algorithm in the present application;

[0034] Figure 4B is a schematic diagram of solving the traveling salesman problem using a genetic algorithm in the present application, so that a single drone traverses the sampling points in the responsible small region;

[0035] Figure 4C is a schematic diagram of the effect of drone spectrum sensing;

[0036] Figure 5 is the relationship between the distance cost, time cost, recovery error and sampling rate of the drone sensing of the present application. DETAILED DESCRIPTION

[0037] The technical solutions of the present application will be described in detail below in combination with the drawings and specific implementation cases.

[0038] Consider using drones to sense the uniformly distributed spectrum in a certain space, assume that there is a 100x100 unit length region, the spectrum in the region is low rank, and use 100 drones to sense the spectrum in the region. The most common method is to use all drones to traverse the entire region, as shown in Figure 2 , in the ideal case, let 100 drones be equidistantly distributed on one side of the region, and scan the entire region from left to right in turn, so that the complete true value of the spectrum in the region can be obtained, and the required time is only 100 unit time, but considering that the initial position of the drone cannot always be in an ideal state, maybe the drones are located in a corner of the entire region in the initial state, maybe the drones are located in the center of the region, and more likely the drones are randomly scattered in the region, which makes it a very tricky path planning problem to completely traverse the entire region.

[0039] The method of the application uses the matrix completion method to perform spectrum sensing, so the UAV does not need to traverse the entire area. In general, for a low-rank matrix, at most 30% of the sampling point information can be obtained to effectively restore the entire matrix. Therefore, the task becomes accessing 30% of the location points in a region using a UAV, and then restoring the spectrum of the entire region using this small amount of information. Traversing a part of the location points in a region using a UAV can be regarded as a TSP problem, and the time complexity of the genetic algorithm is not more than O(N 2 ), that is, the worst-case solution time of the genetic algorithm increases quadratically as the number of points involved in the TSP problem increases. However, in the process of selecting sampling points, because the region is assumed to be a two-dimensional plane, the number of sampling points increases quadratically, and the worst-case time complexity of the entire algorithm is O(N 4 ), that is, the worst-case solution time of the entire algorithm increases quadratically as the length of the region increases. However, solving large-scale TSP problems is not acceptable in terms of time.

[0040] Considering that there are multiple UAVs, a large-scale TSP problem can be divided into multiple small-scale TSP problems and assigned to individual UAVs. Therefore, 100 UAVs can each carry a TSP problem in a 10x10 small region, and a TSP problem of about 3000 points can be divided into 100 TSP problems of an average of 30 points.

[0041] Each UAV is responsible for an average of 30 points in a 10x10 small region. First, each UAV needs to move to the designated area it is responsible for. However, before dispatching the UAV, the initial position of each UAV is uncertain, so a solution is needed to move all UAVs to the designated position standby, and the movement cost is expected to be minimized. This can be regarded as a formation transformation problem, and the Kuhn-Munkres algorithm is used to solve it. The UAV spectrum sensing sampling process is as shown in Figure 3 ;

[0042] Through the above steps, the UAV cluster traverses all the sampling points decided in advance, so the data of these sampling points can be used to estimate the spectrum in the entire region using the Bayesian matrix completion algorithm.

[0043] Specifically, the UAV spectrum sensing algorithm based on Bayesian matrix completion provided by the application comprises the following steps:

[0044] Step 1: Considering the size of the spectrum sensing area and the number of UAVs, divide the spectrum sensing area into small blocks that can be sensed by a single UAV, and let each UAV be responsible for one block.

[0045] The specific operation steps are as follows:

[0046] (1) First, the spectrum sensing in three-dimensional space can be regarded as the superposition of spectrum sensing in two-dimensional space, so the following content only considers two-dimensional region;

[0047] (2) For the convenience of description, it is assumed that the region which needs to be sensed is a region of 100*100 unit length, the number of unmanned aerial vehicles is 100, and the sampling rate is 0.3;

[0048] (3) According to the size of the spectrum sensing region and the number of unmanned aerial vehicles, the spectrum sensing region can be divided into 100 small blocks of 10*10, and 100 unmanned aerial vehicles are responsible for one block respectively;

[0049] X represents the unknown spectrum matrix in the spectrum sensing region; Ω represents the sampling matrix, Ω ij =1 indicates that the {i,j} position element of X is sampled; Y=Ω*X represents the sampled data matrix;

[0050] According to the assumption, X, Ω, Y ∈ R M×N , M, N=100, R M×N represents the set of M*N-dimensional real matrices; X, Ω, Y are all divided into 100 matrices of 10*10, and there are X ij ∈ R m×n , i ∈ [1, M], j ∈ [1, N], m, n=10, R m×n represents the set of m*n-dimensional real matrices; similarly, Ω, Y are derived, so Y ij =Ω ij *X ij .

[0051] Step two, using Kuhn-Munkres algorithm to calculate the shortest path of unmanned aerial vehicles from the initial position to the respective responsible block;

[0052] The specific operation steps are as follows:

[0053] (1) For the convenience of description, only the subscript of the spectrum matrix of the spectrum sensing region is used to represent the position coordinates of the point;

[0054] (2) It is assumed that the initial formation of the unmanned aerial vehicle cluster is A, and the target formation is B; the i-th initial position in the initial formation is a i , the j-th target position in the target formation is b j , a i , b j ∈ R 1×2 is the position coordinates in the formation; K=100 is the number of unmanned aerial vehicles;

[0055] (3) The initial formation A is the initial position state of the UAV swarm. For illustration, it is assumed that the initial position of the UAV swarm is a rectangular formation located at the center of the spectrum sensing area, i.e., a i =[a i1 a i2 ], a i1 a i2 ∈[41, 50];

[0056] (4) For target formation B, first calculate the position center of the initial formation A as coordinates [45.5, 45.5], denoted as point p0; for each small block, its sampling matrix is ​​Ω ij Record Ω ij All 1 elements represent the coordinates of the sampling points of that block within Ω. Let the positions of all 1 elements be denoted as Ω. On average, each cell has approximately 30 sampling points. Calculate the point in cell P that is closest to p0, i.e. For each small block, the selected location point is added to the target group B;

[0057] (5) For the initial formation A and the target formation B, the Kuhn-Munkres algorithm is used to solve the movement path of each UAV;

[0058] The main process of using the Kuhn-Munkres algorithm is as follows:

[0059]

[0060]

[0061] Step 3: For each small block, use a genetic algorithm to find the shortest path to traverse all sampling points. The specific steps are as follows:

[0062] (1) First, obtain the coordinates of all sampling points within the small block, i.e., Ω ij The coordinates of all 1 elements, or rather, all sampling points in this block, corresponding to Ω, are denoted as follows: Assuming the block is divided into q sampling points, then

[0063] (2) Treating the traversal of all sampling points as a traveling salesman problem, a genetic algorithm can be used to solve it. The genetic algorithm process is as follows: Figure 1 As shown:

[0064] Wherein, the gene of each individual in the population is a coordinate sequence, indicating the order of traversing the sampling points; the fitness of the individual is the path length; in the selection operation, a probabilistic-based method is used to select the individual to be operated; in the crossover operation, two individuals are randomly selected, and a gene segment of the same length is randomly selected to exchange, at this time, if a conflict occurs, i.e. a coordinate is accessed twice, the exchanged gene segment is kept unchanged, the position of the conflict gene in the individual within the exchanged segment is recorded, the conflict gene outside the exchanged segment is replaced with the gene at the position of the other individual, and the operation is performed multiple times until there is no conflict; in the mutation operation, for the selected single individual, a pair of coordinates is randomly exchanged to generate a new access path.

[0065] Specifically, in the genetic algorithm solving step, the unmanned aerial vehicle responsible for the block has moved to the sampling point p i closest to the initial formation center p i 0 in the block, therefore some adjustments are made to the above genetic algorithm, the first coordinate sequence number in the coordinate sequence of the gene of all individuals is fixed as the number of p i , and the first accessed coordinate sequence number is not changed in the subsequent selection, crossover and mutation, so that the TSP problem always starts from p x and does not return to the initial position.

[0066] The main process of using the genetic algorithm to solve the traveling salesman problem is as follows:

[0067]

[0068] Step four, using the Bayesian matrix completion algorithm to estimate the spectrum of the entire block area for the obtained sampling point data, the specific operation steps are as follows:

[0069] After steps one to three, for Y = Ω * X, Ω is known, and Y is obtained by sampling, the Bayesian matrix completion algorithm is used to estimate X:

[0070] (1) The main process of the Bayesian matrix completion algorithm is as follows:

[0071]

[0072] Wherein:

[0073] q x (X)、q ∑ (∑)、q γ (γ) represent the probability density functions of X, ∑, and γ;

[0074] represents the expectation with respect to the probability distribution ;

[0075] x n represents the nth column of X, yn Represents the nth column of Y;

[0076] Assume x n It has a Gaussian prior distribution, and ∑ is its precision matrix, which can be initialized as follows.

[0077] Assume that ∑ has Wishart's hyperprior, and that W and v are its hyperparameters. Some possible values ​​for W are: W = ε -1 I, W = F T F v can take a small positive value, such as 10. -10 ;

[0078] γ -1 To observe the variance of the noise, we assume there is no noise, but still initialize it to <γ> = 1;

[0079] Assume that γ has a Gamma prior, and c and d are hyperparameters of γ, which can take a very small value, such as 10. -10 ;

[0080] O n =diag(o n ), o n Represents the nth column of Ω;

[0081] x mn and y mn Let X and Y represent the (m, n)th elements, respectively.

[0082] It is a catalog that indicates which positions of elements in the matrix were observed;

[0083] Ω mn Let represent the (m, n)th element of Ω;

[0084] This represents the number of elements in set S.

[0085] (2) For solving q x (x n When using GAMP, speed it up.

[0086] Consider b = U T x+e, where b∈R M ;x∈R M ;U∈R M×M From singular value decomposition, <∑>=USU T From this, we obtain: e represents additive Gaussian noise with zero mean and covariance matrix S;

[0087] It can be derived that p(x|b) follows a normal distribution with mean and covariance matrix

[0088]

[0089] Let b = 0, κ = y n , ∏ = O n , ξ = <γ>, where there is O n = diag(o n ), ∏ = diag(π), then p(x|b) is the posterior distribution q x (x n ) that we want to get. Its approximate solution can be quickly solved using the GAMP algorithm;

[0090] The main process of the GAMP algorithm is as follows:

[0091]

[0092]

[0093] Wherein:

[0094] is the quantity updated with the algorithm iteration;

[0095]

[0096] obeys a Gaussian distribution, and are its mean and variance:

[0097] are initialized to zero, is initialized to the mean of the preset prior distribution, is initialized to a small positive value, for example, 10;

[0098] denotes the i-th row of U T , u i，m denotes the (i, m)-th element of U T ;

[0099] Define g in (·) and g out (·): Thus, we have

[0100] From the assumption of s , it obeys a Gaussian distribution, and its mean and variance are: Wherein, s iThe i-th diagonal element of S.

[0101] Using the algorithm of the present application, considering single spectrum sensing by simulation, in the spectrum sensing sample: the to-be-sampled matrix is a randomly generated low-rank matrix, both the length and the width are 100, and the rank is 5; the number of UAVs is 100; the sampling rate is 0.3. The distance cost of the formation transformation using the Kuhn-Munkres algorithm is 2969.1763, and the time cost is 58.6941; the cost of one UAV when traversing the sampling points in a small area is 52.3422; the distance cost of the whole sampling process is 8281.0420, and the time cost is 133.5412; the recovery error of the Bayesian matrix completion algorithm this time is The UAV spectrum sensing process (the sampling rate is 0.3) is shown in Figures 4A-4C Figure 4A is a schematic diagram of using the Kuhn-Munkres algorithm to move all UAVs from the initial position at the center of the area to the small blocks responsible by each UAV; Figure 4B is a schematic diagram of using the genetic algorithm to solve the traveling salesman problem to make a single UAV traverse the sampling points in the small area responsible by the UAV; Figure 4C is a UAV spectrum sensing effect schematic diagram, X is the true value of the spectrum to be sensed, Y = Ω * X is the observation matrix obtained by sampling, is the estimated value recovered from the observation matrix Y, as can be seen from the figure, X is very close, and the spectrum sensing algorithm has good sensing effect.

[0102] Similarly, let the to-be-sampled matrix be a randomly generated low-rank matrix, both the length and the width are 100, and the rank is 5; the number of UAVs is 100. Considering the relationship between the distance cost, the time cost, the recovery error and the sampling rate, the results are shown in Figure 5 , wherein, Figure 5 (a) the relationship between the distance cost of the UAV spectrum sensing and the sampling rate; (b) the relationship between the time cost of the UAV spectrum sensing and the sampling rate; (c) the relationship between the recovery accuracy of the UAV spectrum sensing and the sampling rate. As can be seen from Figure 5 , using the UAV for spectrum sensing, the distance cost and the time cost and the sampling rate are roughly linearly related, and increase with the increase of the sampling rate. At a sampling rate of 0.3, the distance cost is 8279.8353, and the average time cost is 136.0501; at the same time, at a sampling rate of 0.3, the recovery error can be reduced to an average of 0.0030. It can be considered that, compared with the traversal method, the present application can basically completely recover the to-be-sensed spectrum matrix using less distance cost and time cost.​

Claims

1. A method for unmanned aerial vehicle spectrum sensing based on Bayesian matrix completion, characterized in that, Comprising the following steps: Step one, considering the size of the spectrum sensing area and the number of unmanned aerial vehicles, the spectrum sensing area is divided into several single unmanned aerial vehicle sensing blocks, and each unmanned aerial vehicle is responsible for one block; Step two, using Kuhn-Munkres algorithm to calculate the shortest path of unmanned aerial vehicles from the initial position to the block they are responsible for; Step three, for each block, use genetic algorithm to solve the shortest path of all sampling points; Step four, using the obtained sampling point data, use the Bayesian matrix completion algorithm to estimate the spectrum of the whole block area; The specific operation method of step one is as follows: (1) The spectrum sensing of three-dimensional space is regarded as the superposition of two-dimensional space spectrum sensing, so only two-dimensional area is considered; (2) assuming that the region that needs to be perceived is a piece of unit length, the number of unmanned aerial vehicles is , and the sampling rate is ; (3) According to the size of the spectrum sensing area and the number of unmanned aerial vehicles, the spectrum sensing area is divided into a plurality of cell blocks, and each unmanned aerial vehicle is responsible for one block. The specific algorithm is represented as: with denotes the unknown spectrum matrix within the spectrum sensing region; denotes the sampling matrix, denotes the position elements are sampled; denotes the sampled data matrix; Let us assume that , , Let us denote a set of real matrices of dimension ; we divide uniformly into matrices of dimension, where , , , , , Let us denote a set of real matrices of dimension ; by analogy , we have . 2.The method of claim 1, wherein, The specific operation method of step two is as follows: (1) The subscript of the spectrum sensing area spectrum matrix represents the position coordinates of the point; (2) assuming that the initial formation of the UAV cluster is , the target formation is ; the initial position of the th in the initial formation is , the target position of the th in the target formation is , is the position coordinate in the formation; , , is the number of UAVs; (3) Initial formation is the initial position state of the UAV cluster, assuming that the initial position of the UAV cluster is a rectangular formation position at the center of the spectrum sensing area, that is , ; (4) For the target formation , first calculate the position center of the initial formation at coordinates , denoted as point ; For each block, the sampling matrix is , record all elements, that is, the sampling points of the block, correspond to the coordinates in , record the positions of all elements as , and there are sampling points in each block on average; calculations mid-range the most recent location point, i.e. ; For each cell block, the selected position points are added to the target formation in the middle; (5) For the initial formation and the target formation , the Kuhn-Munkres algorithm is used to solve the moving route of each UAV.

3. The method of claim 2, wherein, The specific operation method of step three is as follows: (1) First, all the coordinates of the sampling points in the small block are obtained, that is All elements or all the sampling points in the block correspond to the coordinates in , denoted as , assuming that the block is divided into sampling points, then ; (2) Treating the traversal of all sampling points as a traveling salesman problem, a genetic algorithm is used to solve it; In the step of solving by genetic algorithm, the unmanned aerial vehicle responsible for the block has moved to the block center away from the initial formation center The latest sampling point Therefore, the first coordinate sequence number of the coordinate sequence of the fixed individual gene is The first accessed coordinate sequence number is not changed in the subsequent selection, crossover and mutation, so that the TSP problem always starts from And returns to the initial position.

4. The method of claim 3, wherein, The specific operation method of step four is as follows: After steps one to three, for , it is known , and by sampling , it is estimated , using a Bayesian matrix completion algorithm. In the process of estimating , using a Bayesian matrix completion algorithm, the GAMP algorithm is used for acceleration.

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