CN115099385A - Spectrum map construction method based on sensor layout optimization and adaptive Kriging model - Google Patents
Spectrum map construction method based on sensor layout optimization and adaptive Kriging model Download PDFInfo
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Abstract
The invention discloses a frequency spectrum map construction method based on sensor layout optimization and a self-adaptive Kriging model, and belongs to the technical field of communication. The method comprises the steps of carrying out optimization selection on sensor layout by utilizing an improved artificial bee colony algorithm; finding a set of sensor estimates from the preferred sensors; calculating a half variation function value and fitting the half variation function; and constructing a self-adaptive Kriging model, and constructing a frequency spectrum map according to the self-adaptive Kriging model. The method for constructing the frequency spectrum map has higher precision.
Description
Technical Field
The invention belongs to the technical field of communication, and particularly relates to a frequency spectrum map construction method based on sensor layout optimization and a self-adaptive Kriging model.
Background
In order to meet the rapidly growing frequency demand and the increasingly severe "spectrum deficit", cognitive radio technology is proposed and rapidly developed, and the core idea is to adaptively adjust the operating parameters (such as frequency, power, modulation and coding mode and the like) of a radio system to adapt to the external wireless environment by sensing and understanding the electromagnetic environment. The electromagnetic spectrum map visually presents the regional electromagnetic environment condition by converging the use condition of the electromagnetic spectrum in a certain region, including frequency spectrum data such as frequency, intensity, position and historical change rule of each signal, and can provide support for a cognitive radio system to master the occupation condition of the surrounding electromagnetic spectrum, scientifically select available frequency, avoid potential frequency conflict and the like.
The spectrum data required by the electromagnetic spectrum map usually comes from a spectrum sensing network composed of sensors with radio signal monitoring and receiving processing capabilities, such as a cognitive communication network composed of cognitive radio nodes, a spectrum monitoring network composed of networking cooperative spectrum monitoring nodes, and the like. Studies have shown that the placement of nodes in these networks has a large impact on the performance of generating electromagnetic spectrum maps. In recent years, electromagnetic spectrum mapping has been challenged in two major ways. First, the relationship between spectral map generation accuracy and sensor layout is not sufficiently clear. Most of the work today is to randomly sample the sensor locations to return sample data for building a spectrum map. For the traditional random sampling layout, increasing the number of sensors is the most effective scheme facing complex and antagonistic application environments, and meanwhile, the problems of increased data return and calculation overhead, unreliable links and the like are brought. Therefore, if the intrinsic characteristics of the spatial spectrum situation can be fully utilized, it is possible to generate a spectrum map with less data requirements. Second, the influence on the signal propagation model during the spectrum map construction process is considered less. Due to the challenges, the existing method is difficult to construct a spectrum map with high precision.
Disclosure of Invention
The technical problem is as follows: the invention provides a frequency spectrum map construction method based on sensor layout optimization and a self-adaptive Kriging model, which can improve construction accuracy.
The technical scheme is as follows: the invention provides a frequency spectrum map construction method based on sensor layout optimization and a self-adaptive Kriging model, which comprises the following steps:
optimized selection is carried out on the sensor layout by utilizing an improved artificial bee colony algorithm;
finding a set of sensor estimates from the preferred sensors;
calculating a half variation function value and fitting the half variation function;
and constructing a self-adaptive Kriging model, and constructing a frequency spectrum map according to the self-adaptive Kriging model.
Further, the improved artificial bee colony algorithm comprises the improvement on a disturbance mechanism and a fitness function, and the improvement on the artificial bee colony.
Further, the improvement on the perturbation mechanism is as follows: the next state is explored by interchanging selected sensors, representing sensors for interpolation, with unselected sensors representing sensors to be interpolated.
Further, the perturbation mechanism and the fitness function are used for generating a new solution, and the new solution comprises the following steps:
when a sensor to be replaced is selected, the sensor with the smallest influence on the current sensor layout interpolation precision is replaced;
determining a sensor with the smallest influence on interpolation precision in the current layout through m times of interpolation error calculation, wherein the point can be preferentially discarded by a scout bee when the sensor serving as an exploration upper limit is in the next state transition;
when selecting the sensors to be inserted, the respective weights η are taken into account according to the RMSE of each sensor i 。
Further, the fitness function is shown in equation (5):
in the formula (I), the compound is shown in the specification,
is an estimate of the non-selected sensor,
is the true data, m * Is the number of sensors.
Further, the improving the artificial bee colony comprises the following steps:
the hiring bee searches for a new sensor according to a formula (6), namely, a new sensor layout is generated, sensor layout information is shared with the observation bee, the sensor layout with the minimum fitness function value f is selected according to a greedy strategy, and an optimal solution is maintained:
v ij ＝η kj ×x kj (6)
wherein k is 1,2, the.. ang.np j is 1,2, the.. ang.d. and k is not equal to i, η kj Is a weight matrix; v. of ij Representing new solutions that the hiring bee finds.
The observation bees calculate the selection probability of each sensor according to the formula (7), and preferentially select the sensors with higher weights according to the formula on the information shared by the employment bees, so that the convergence speed is improved:
the scout bees discard the sensors reaching the upper exploration limit and having lower weight to find a new valuable sensor according to the formula (8), so that the capability of getting rid of local optimization is enhanced:
in the formula, r ij Is [0,1 ]]A random number in between; x is the number of ij Representing a new solution found by the scout bees;
and
representing the upper and lower bounds of the jth dimension of the problem.
Further, the optimized selection of the sensor layout by using the improved artificial bee colony algorithm comprises the following steps:
initializing a sensor position;
employing bees to generate new solutions according to an improved perturbation mechanism;
observing bees from p according to probability i Generating a new solution;
the scout bee decides the solution to abandon;
and outputting the optimal sensor position through multiple iterations.
Further, the method for searching the sensor estimation group from the preferred sensors comprises the following steps: according to the decorrelation distance d cor Establishing an unknown point s 0 Sensor of (2) estimate group omega 0 The unknown points define the decorrelation distance by the morlan index.
Further, the semi-variance value is calculated using the following formula:
in the formula, s i Is a point (x) i ,y i )，d ij Is a point (x) i ,y i ) And point (x) j ,y j ) Distance of (d), N (d) ij ) The distance between two points is the number of h;
the fitting of the semi-variogram takes an exponential model and is fitted by least squares.
Further, the method for constructing the adaptive Kriging model comprises the following steps: obtaining the weight coefficient omega by solving a set of linear equations called Kriging model through a Lagrange multiplier method i The linear system is given by equation (12):
in the formula, gamma ij Is a point (x) i ,y i ) And point (x) j ,y j ) The half function value of variation between phi is Lagrange multiplier and the weight coefficient omega i Is able to satisfy the point (x) 0 ,y 0 ) Estimate of (c)
With true value P 0 Is the set of optimal coefficients with the smallest difference, i.e.
Simultaneously satisfies the condition of unbiased estimation
γ io Expressed as a half-value of the variation function between position i and the evaluation point.
Calculating an estimated point value according to equation (13)
In the formula (I), the compound is shown in the specification,
is a point (x) 0 ,y 0 ) An estimate of a property of, P i Are sample values.
Compared with the prior art, the optimal sensor layout is generated by utilizing the improved artificial bee colony algorithm, the recovery performance of the frequency spectrum map is greatly improved compared with the random layout, and on the basis, the self-adaptive Kriging model based on shadow fading autocorrelation is provided for constructing the frequency spectrum map. In consideration of the obvious autocorrelation among sensor attributes caused by shadow fading with exponential attenuation of signal propagation, a spatial autocorrelation theory is introduced to establish a sensor estimation group, and an estimation result is obtained through a Kriging model. The simulation result shows that compared with other methods, the method provided by the invention has huge performance advantages, can improve the construction precision of the frequency spectrum map, and simultaneously greatly reduces the expenditure of sensor resources.
Drawings
FIG. 1 is a flow chart of a spectrum map construction method based on sensor layout optimization and an adaptive Kriging model in an embodiment of the present invention;
FIG. 2 is a flow chart of a spectral mapping process in an embodiment of the present invention;
FIG. 3 is a schematic diagram of a set of sensor estimates for establishing points based on decorrelated distances in an embodiment of the present invention;
FIG. 4 is a graph showing performance comparison of a frequency spectrum map constructed in a simulation experiment when the shadow fading standard deviation is 1 dB;
FIG. 5 is a graph showing performance comparison of a frequency spectrum map constructed in a simulation experiment when the shadow fading standard deviation is 3 dB;
FIG. 6 is a graph showing performance comparison of a frequency spectrum map constructed in a simulation experiment when the shadow fading standard deviation is 6 dB;
FIG. 7 is a graph showing comparison of performance of a spectrum map constructed by 4 methods;
FIG. 8(a) is a schematic diagram of a simulation of an original spectrum map;
FIG. 8(b) is a schematic diagram of a spectrum map simulation constructed using ABC-SA;
FIG. 8(c) is a schematic diagram of a spectrum map simulation constructed using Random-IDW;
FIG. 8(d) is a schematic diagram showing a spectrum map simulation constructed using Random-Splines;
FIG. 8(e) is a schematic diagram of a spectral map simulation constructed using Random-NN;
FIG. 9 is a graph of RMSE performance based on actual measured data.
Detailed Description
The invention is further described below with reference to the following examples and the drawings. First, the network architecture of the present application is as follows:
a plurality of radiation sources and a set of sensors are arranged within a target area, wherein the position and emission power of the radiation sources are unknown. P (m) for measuring Received Signal Strength (RSS) by sensor i ) Is represented by the formula (I) in which m i Is the sensor location. Sensor m i The received signal power of (a) can be modeled as:
P(m i )＝K+10εlog 10 (||m p -m i ||)+W p(m) (1)
where K is the free space path loss factor, ε is the path loss exponent, and point m p Representing the position of a certain radiation source, | | · | represents the euclidean distance between two vectors,
is a point m i Subject to a lognormal distribution satisfying the standard deviation sigma 17]Is lost. Thus, point m i Shadow fading
And point m j Shadow fading
The correlation coefficient between is
In the formula d cor To satisfy rho i,j 1/e. In this case, the shading correlation coefficient ρ i,j As the distance between the receivers increases, it decreases exponentially.
The process of modeling the spectrum map building problem is divided into three operations: collecting the measurement results of the sensors, selecting the sensors and evaluating the field strength or power value of any position.
Assuming that the set of the given area grids is N and the set of all the sensors is M, a subset is selected from the N and M
The spectrum map is constructed by using the sensor. The aim of the invention is to determine M and the position of each sensor in the area, and to determine the number M of usable sensors * ＝|M * I, selecting the optimal set m * And the error RMSE between the field intensity estimated value and the actual value of the constructed frequency spectrum map is minimized.
In the formula (I), the compound is shown in the specification,
representing an estimate of all points in the grid,
representing the true value, N is the total number of meshes.
The problem modeling is as follows:
problem (3) is a combinatorial optimization problem, and it is difficult to obtain a globally optimal solution in linear time.
Based on this, fig. 1 shows a flowchart of a spectrum mapping method based on sensor layout optimization and adaptive Kriging model in the present application. As shown in fig. 1, the method of the present application includes the following steps:
step S100: and optimally selecting the sensor layout by using an improved artificial bee colony algorithm. In the application, the improved artificial bee colony algorithm mainly improves the disturbance mechanism and the fitness function of the artificial bee colony algorithm, and improves the artificial bee colony. The process of optimizing and selecting the sensor layout by using the improved artificial bee colony algorithm is described below, and as shown in fig. 2, each improved point is described in detail in the description process.
First, an initial solution x is randomly generated in the search space i (i ═ 1, 2.. NP), NP denotes the number of employed bees, each solution x i Is a vector of dimensions D, which is the dimension of the problem.
Second, a new perturbation mechanism and fitness function are proposed. The next state is explored by interchanging selected sensors with unselected sensors. The selected sensors represent sensors used for interpolation, unselectedThe sensor in (1) represents the sensor to be interpolated. When selecting the sensor to be replaced, the sensor with the least influence on the interpolation precision of the current sensor layout is replaced. The number of sensors in the current state is M * And they are numbered as
Then, here by M * And (4) performing secondary interpolation error calculation to determine the sensor with the smallest influence on interpolation precision in the current layout, wherein the point can be preferentially discarded by the scout bees when the sensor serving as the exploration upper limit is in the next state transition. Meanwhile, when selecting the sensors to be inserted, the respective weight eta is considered according to the RMSE of each sensor i The probability that the sensor with the higher weight (i.e., the larger RMSE) is selected is greater, speeding up the sensor layout optimization selection. Assuming that the number of sensors of the target is m, randomly selecting m * The sensors are used as initial states. Through this m * A sensor for estimating other m-m * And (4) comparing the attribute values of the sensors with known values, and calculating a Root Mean Square Error (RMSE) for artificial bee colony decision. The formula is as follows:
in the formula (I), the compound is shown in the specification,
is an estimate of the non-selected sensor,
is the real data.
Thirdly, improving artificial bee colony. And (3) searching for a new sensor by the hiring bee according to the formula (6), namely generating a new sensor layout, sharing sensor layout information with the observing bee, and selecting the sensor layout with the minimum fitness function value f according to a greedy strategy to maintain an optimal solution.
v ij ＝η kj ×x kj (6)
Where k is 1, 2., NP j is 1, 2., D and k ≠ i, η kj Is a weight matrix; v. of ij Representing new solutions that the hiring bee finds.
The observation bees calculate the selection probability of each sensor according to the formula (7), preferentially select the sensor with higher weight according to the formula (6) according to the information shared by the employment bees, and improve the convergence speed.
Where f is the fitness of each solution.
The scout bees discard the sensors reaching the upper exploration limit and with lower weight, and find a new valuable sensor according to the formula (8), so that the ability of getting rid of local optimization is enhanced.
In the formula, r ij Is [0,1 ]]A random number in between, and a random number,
and
representing the upper and lower bounds of the jth dimension of the problem.
Step S200: a set of sensor estimates is sought from the preferred sensors.
The signal under the propagation model of equation (1) generally exists in the form of clusters, and the hole region is much larger than the spectrum occupation region, so the spatial autocorrelation of the spectrum map is significant in theory. The most common statistic is Global Moran' I (Global Moran index), which is mainly used to describe the average degree of correlation of all spatial units with the surrounding regions over the entire area. The calculation formula is as follows:
wherein I is Moran' I, the value range is generally-1, when I is>0 indicates that the attribute value in the target region has positive correlation in space, 0-I indicates that the attribute value in the target region has random distribution and no spatial correlation, and when I is equal to 0, the spatial correlation is not generated<0 indicates that the attribute values within the target region have a negative correlation in space;
n is the total number of space units; z is a radical of i And z j Attribute values respectively representing the ith spatial unit and the jth spatial unit;
obtaining a mean value for all spatial unit attributes; w is a ij Are spatial weight values. Unknown point s 0 The decorrelation distance, d, is defined by the Moire index cor . As shown in fig. 3, according to the decorrelation distance d cor Set-up point s 0 Set of sensor estimates of (2), omega 0 。
Step S300: and calculating a half variation function value and fitting the half variation function.
The half-variogram is a core part of the Kriging model, quantitatively describes the variable characteristics of the entire region, and is calculated according to equation (10).
In the formula, s i Is a point (x) i ,y i )，d ij Is a point (x) i ,y i ) And point (x) j ,y j ) Distance of (d), N (d) ij ) The distance between two points is the number of h; . And selecting a proper theoretical model to fit an optimal theoretical semi-variation function curve so as to more accurately reflect the variation rule of the variable. Half function of variation gamma ij The method conforms to the first law of geography, has similar spatial attributes, and the theoretical models comprise a pure gold blocking effect model, a spherical model, an exponential model and a Gaussian modelAnd the like. It has been demonstrated by equation (2) that the spatial shadow fading coefficients follow exponential decay, so the fitting of the half-variance function takes an exponential model and fits by least squares:
in the formula, h is the distance between any two points; c 0 Is the gold lump constant; c 0 + C is the base station value; a is the step length corresponding to the intersection of the tangent of the model at the origin and the base station value.
Step S400: and constructing a self-adaptive Kriging model, and constructing a frequency spectrum map according to the self-adaptive Kriging model. Specifically, according to steps S200 and S300, a point (x) is selected and estimated in the sensor sample 0 ,y 0 ) The distance being less than the decorrelation distance d cor The sensors of (2) establish a sensor estimation group, and record omega 0 . Calculating the semi-variation function value gamma between the sensors in the estimation group according to the formula (10) ij And a half value of the variation function between each sensor and the evaluation point. Then, a linear equation set called Kriging model is solved by a Lagrange multiplier method to obtain a weight coefficient omega i The linear system is given by:
in the formula, gamma ij Is a point (x) i ,y i ) And point (x) j ,y j ) The half function value of variation between phi is Lagrange multiplier and the weight coefficient omega i Is able to satisfy the point (x) 0 ,y 0 ) Estimate of (c)
With true value P 0 A set of optimal coefficients with the smallest difference, i.e.
Simultaneously satisfies the condition of unbiased estimation
γ io Expressed as a half-value of the variation function between position i and the evaluation point.
Finally, the estimated point value is calculated according to equation (11)
In the formula (I), the compound is shown in the specification,
is a point (x) 0 ，y 0 ) An estimate of a property of, P i Are sample values.
In the above formula, i, j, k denote only serial numbers.
Compared with the existing method, the method has higher precision in the process of constructing the spectrum map. In this embodiment, the performance of the proposed spectrum map construction scheme is evaluated through simulation data evaluation and real data evaluation. Experiments 1000 sensors were randomly selected from the total number of sensors as known sensors. And analyzing and comparing the frequency spectrum map construction performance of different algorithms under the condition of different shadow fading standard deviations. The parameter settings of the simulation data are shown in table 1.
TABLE 1 simulation parameters Table
| Parameter(s) | Value of |
| Dimension of |
100×100m 2 |
| Power of signal transmission | 30dBm，50dBm，60dBm |
| Cartesian coordinates for signal transmission | (20，80)，(80，80)，(80，20) |
| Frequency of signal | 5000MHz |
| Standard deviation of shadow fading | 1dB，3dB，6dB |
Real data experiments employed the data set disclosed on IEEE Dataport. This data is real spectrum data at 811MHz and 2630MHz using Rohde & Schwarz (R & S) TSMW measurements, including signal power, signal-to-noise ratio, signal received strength, etc., each measurement synchronized with GPS positioning. The experiment is measured in the school district of the university of Denmark technology, and the mobile spectrum observation device runs for about 14km, and about 60000 data points are generated. All the results of the random experiments in the simulation experiment and the real data are the average of 500 random experiments. Accuracy is an important criterion for algorithm performance, so the mean square error (RMSE) is used to analyze the accuracy of RMSE construction, which can be expressed as:
where l and w are the length and width of the target region, respectively,
is an estimate of interpolation, P ij Is the real data.
As shown in FIG. 4, FIG. 5 and FIG. 6, four different algorithms including Random-OK, Random-AK, ABC-OK and ABC-AK spectrum map building performances are analyzed based on different shadow fading standard deviation comparison of simulation data. As can be seen, the RMSE of the four algorithms is increased along with the increase of the shadow fading standard deviation, and the performance of the ABC-AK is better than that of the other three algorithms, which shows that the ABC-AK has stronger robustness. When the number of the sensors is less than 300, the optimal selection of the sensors is better than the randomly selected spectrum construction performance under the same construction method. In the same sensor selection mode, the frequency spectrum construction performance of the self-adaptive Kriging is better than that of the common Kriging.
As shown in FIG. 7, four different algorithms were analyzed for RMSE construction of spectral maps based on measured data comparison, including Random-OK, Random-AK, ABC-OK, and ABC-AK. It can be seen that: (1) the RMSE of all algorithms decreases with increasing number of sensors and ABC-SLO-SA-AK performs best in spectral construction maps. With the sensor optimization, the average reduction of ABC-AK compared with the RMSE of ABC-OK is 0.30 dBm. Under sensor Random selection, the RMSE of the Random-AK algorithm was 0.38dBm lower than that of the Random-OK algorithm. (2) Under the common Kriging construction, the RMSE of the ABC-OK algorithm is 0.71dBm lower than that of Random-OK on average. Under the adaptive Kriging construction, the RMSE of the ABC-AK algorithm is 0.63dBm lower than that of Random-AK on average. In the experiment, the AK algorithm has better performance under the ABC-SLO algorithm, because the AK algorithm adopts a self-adaptive estimation group, the influence of a low-correlation sensor on interpolation errors is reduced, and the generation of an optimized layout is facilitated.
As shown in fig. 8, the position of the original map, the signal source intensity and the spectrum map construction condition are compared between the results of different spectrum map construction methods under the conditions that the standard deviation of shadow fading is 3dB and the number of sensors is 100. It can be seen that the ABC-SA algorithm performs well in terms of signal source localization and source signal strength recovery.
To further demonstrate the broad effectiveness of this algorithm, as shown in FIG. 9, the present document compared different spectrum mapping algorithms based on measured data, including ABC-SA, IDW [24], NN [25], Splines. It can be seen that the RMSE of each algorithm decreases with increasing number of sensors, indicating that increasing the sample sampling rate is an important factor in improving the accuracy of the spectral map. Among the four algorithms, the RMSE of the ABC-AK algorithm is always smaller than that of the other three algorithms and is 1.80dBm, 1.53dBm and 0.97dBm lower than that of the Random-NN, Random-Splines and Random-IDW algorithms on average respectively. The ABC-SLO-SA-AK algorithm proves to have better spectrum mapping performance compared with other algorithms in practice.
The invention provides a spectrum map construction method based on sensor layout optimization selection and a self-adaptive Kriging model in a sensor network, and high-precision spectrum map construction is realized. A large number of simulation results show that the spectrum map construction performance of the proposed method is respectively improved by 37.56%, 25.32% and 12.89% compared with the random-OK performance under the conditions that the shadow fading standard deviation is 1dB,3dB and 6 dB.
The above examples are only preferred embodiments of the present invention, it should be noted that: it will be apparent to those skilled in the art that various modifications and equivalents can be made without departing from the spirit of the invention, and it is intended that all such modifications and equivalents included within the scope of the claims be interpreted as included within the scope of the invention.
Claims (10)
1. A frequency spectrum map construction method based on sensor layout optimization and a self-adaptive Kriging model is characterized by comprising the following steps:
optimized selection is carried out on the sensor layout by utilizing an improved artificial bee colony algorithm;
finding a set of sensor estimates from the preferred sensors;
calculating a half variation function value and fitting the half variation function;
and constructing a self-adaptive Kriging model, and constructing a frequency spectrum map according to the self-adaptive Kriging model.
2. The method according to claim 1, wherein the improved artificial bee colony algorithm comprises improvements to perturbation mechanisms and fitness functions, and to artificial bee colony improvements.
3. The method of claim 2, wherein the improvement to the perturbation mechanism is: the next state is explored by interchanging selected sensors, representing sensors for interpolation, with unselected sensors representing sensors to be interpolated.
4. The method of claim 3, wherein the perturbation mechanism and the fitness function are used to generate a new solution, comprising:
when a sensor to be replaced is selected, the sensor with the smallest influence on the current sensor layout interpolation precision is replaced;
determining a sensor with the smallest influence on interpolation precision in the current layout through m times of interpolation error calculation, wherein the point can be preferentially discarded by a scout bee when the sensor serving as an exploration upper limit is in the next state transition;
when selecting the sensors to be inserted, the respective weights η are taken into account according to the RMSE of each sensor i 。
5. The method of claim 4, wherein the fitness function is as shown in equation (5):
in the formula (I), the compound is shown in the specification,
is an estimate of the non-selected sensor,
is the true data, m * Is the number of sensors.
6. The method of claim 5, wherein the improving the artificial bee colony comprises:
the hiring bee searches for a new sensor according to a formula (6), namely, a new sensor layout is generated, sensor layout information is shared with the observation bee, the sensor layout with the minimum fitness function value f is selected according to a greedy strategy, and an optimal solution is maintained:
v ij ＝η kj ×x kj (6)
where k is 1, 2., NP j is 1, 2., D and k ≠ i, η kj Is a weight matrix; x is the number of ij Representing a new solution found by the scout bees; v. of ij Representing new solutions found by the hiring bees;
the observation bee calculates the selection probability p of each sensor according to formula (7) i And preferentially selecting the sensors with higher weights according to the formula on the information shared by the hiring bees, so that the convergence speed is improved:
the scout bees discard the sensors reaching the upper exploration limit and having lower weight, and a new valuable sensor is searched according to a formula (8), so that the ability of getting rid of local optimization is enhanced:
in the formula, r ij Is [0,1 ]]A random number in between;
and
representing the upper and lower bounds of the jth dimension of the problem.
7. The method of claim 6, wherein the optimized selection of sensor layouts using the improved artificial bee colony algorithm comprises:
initializing a sensor position;
hiring bees to generate new solutions according to an improved perturbation mechanism;
observation bee according to probability p i Generating a new solution from the sensor position;
the scout bee decides the solution to abandon;
and outputting the optimal sensor position through multiple iterations.
8. The method according to any one of claims 1 to 7, wherein the method of finding the set of sensor estimates from the preferred sensors is: according to the decorrelation distance d cor Establishing an unknown point s 0 Sensor of (2) estimate group omega 0 The unknown points define the decorrelation distance by the morlan index.
9. The method of claim 8, wherein the semi-variance value is calculated using the formula:
in the formula s i Is a point (x) i ,y i )，d ij Is a point (x) i ,y i ) And point (x) j ,y j ) Distance of (d), N (d) ij ) The distance between two points is the number of h;
the fitting of the semi-variogram takes an exponential model and is fitted by least squares.
10. The method of claim 9, wherein the method of constructing the adaptive Kriging model is: obtaining the weight coefficient omega by solving a set of linear equations called Kriging model through a Lagrange multiplier method i The linear system is given by equation (12):
in the formula, gamma ij Is a point (x) i ,y i ) And point (x) j ,y j ) The half function value of variation between phi and omega is Lagrange multiplier i Is able to satisfy the point (x) 0 ,y 0 ) Estimate of (c)
With true value P 0 A set of optimal coefficients with the smallest difference, i.e.
Simultaneously satisfies the condition of unbiased estimation
γ io Expressed as a half function of the value of the variation function between position i and the evaluation point;
calculating an estimated point value according to equation (13)
In the formula (I), the compound is shown in the specification,
is a point (x) 0 ,y 0 ) An estimate of a property of, P i Are sample values.
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