A method and device for modeling omnidirectional non-uniform evaporation waveguide profile based on two-dimensional Markov chain

Abstract

The present invention discloses a method for modeling a omnidirectional non-uniform evaporation waveguide profile based on a two-dimensional Markov chain, comprising the following steps: step 1, dividing the area of ​​non-uniform evaporation waveguide height into a plurality of element units of equal size; step 2, dividing the area of ​​change of the two-dimensional non-uniform evaporation waveguide height into two directions, horizontal and vertical; step 3, performing an oblique simulation on the blocks in the waveguide area; step 4, calculating three horizontal, vertical and oblique transfer probability matrices; step 5, estimating the horizontal and vertical extension lengths of different evaporation waveguide heights. The method and device disclosed by the present invention couple one-dimensional Markov chains in multiple directions in order to better describe the spatial distribution of the evaporation waveguide profile, and propose a coupled Markov chain model suitable for multi-dimensional evaporation waveguide profile simulation.

Description

Technical Field

[0001] The invention belongs to the field of ocean atmosphere remote sensing, and particularly relates to a method and a device for modeling an omnidirectional non-uniform evaporation waveguide profile based on a two-dimensional Markov chain in the field. Background Art

[0002] Since the atmospheric environment in different ocean regions is non-uniform, this non-uniform characteristic will have an important impact on radar detection systems and mobile communication systems. In general, the refractive index profile formed by evaporation ducts is a nonlinear function of atmospheric temperature, humidity and air pressure. Since the meteorological conditions over different sea areas are usually different, evaporation ducts are usually spatially and non-uniform when they occur over the sea surface. The traditional atmospheric duct modeling method is based on the inversion of evaporation duct profile parameters in a horizontally uniform atmospheric environment. The results show that in the actual ocean environment, the horizontal non-uniform assumption of the atmospheric refractive index profile will cause large inversion errors.

[0003] Scholars at home and abroad have proposed using one-dimensional Markov chain-Monte Carlo sampling technology to perform spatial sampling of atmospheric refractive index profile parameters to achieve profile inversion of tropospheric ducts. However, traditional methods are all used to invert non-uniform evaporation duct profiles on a single path, and are not suitable for the inversion of regional duct profiles in actual marine environments. In order to achieve the inversion of non-uniform atmospheric ducts on full-space azimuth paths, a large amount of measured data is required for verification. The actual non-uniform evaporation duct data within the low-altitude area of ​​the sea is often very limited, and it is difficult for traditional Markov processes to achieve accurate modeling of non-uniform atmospheric ducts in the entire space. Summary of the invention

[0004] The technical problem to be solved by the present invention is that it is difficult for the traditional one-dimensional Markov chain model to simulate the multi-dimensional evaporation duct profile, and the discrete distribution of the evaporation duct profile at different distances is difficult to obtain. A method and device for modeling an all-round non-uniform evaporation duct profile based on a two-dimensional Markov chain are proposed. The interface modeling of the evaporation duct profile parameters in different inclined directions is realized by using a coupled two-dimensional Markov chain model, thereby achieving effective modeling of regional non-uniform atmospheric ducts and supporting the research on the inversion of regional non-uniform atmospheric ducts based on radar sea clutter data.

[0005] The present invention adopts the following technical solution:

[0006] A method for modeling a omnidirectional non-uniform evaporation waveguide profile based on a two-dimensional Markov chain, the improvement of which is that it comprises the following steps:

[0007] Step 1, dividing the region with non-uniform evaporation waveguide height into a number of element units of equal size, wherein the evaporation waveguide height in each divided element unit remains unchanged;

[0008] Step 2, divide the variation area of ​​the two-dimensional non-uniform evaporation duct height into two directions, horizontally and vertically. The horizontal direction is the expansion of the 100-kilometer data detected by the radar, and the vertical direction has two columns of initial values. There is only one simulation starting point on each unit in the same column or row, that is, the simulated evaporation duct height can only select the Markov chain in one direction from left to right h and from right to left h′ and the Markov chain in the vertical downward v direction for coupling simulation;

[0009] The Markov chain coupling is performed on the evaporation waveguide height in the vertical downward direction v and from left to right direction h. If the evaporation waveguide height of unit (i-1, j) is Z p , the evaporation waveguide height of unit (i,j-1) is Z q , the evaporation waveguide height of unit (i, j) is Z W , Z W The conditional probability is:

[0010]

[0011] If the end point of the h direction (N x ,j) the evaporation waveguide height Z u As a constraint, the evaporation waveguide height Z of unit (i, j) is W The transition probability The expression is:

[0012]

[0013] Step 3, perform oblique simulation on the blocks where the waveguide appears, and redefine the simulation direction at the waveguide junction to avoid the occurrence of transitions;

[0014] Step 4, calculate the three transition probability matrices of horizontal, vertical and diagonal directions;

[0015] Step 5, the horizontal and vertical extension lengths of different evaporation duct heights are estimated, and the horizontal and vertical extension length ratios of different evaporation duct heights are obtained by using the change data of the initial evaporation duct. Different evaporation duct heights are obtained with different K values. The transfer likelihoods between the evaporation duct heights are multiplied to obtain the transfer likelihood number Q of the overall evaporation duct height. When Q reaches the maximum value, the result of the K value is optimal.

[0016] Q=Q 1 …Q N-1

[0017]

[0018] Z m ,…,Z nis the value of the evaporation waveguide height corresponding to the Zth distance; R(Z i,1 =Z m ,Z j,1 =Z o ) is the non-uniform evaporation duct height. The evaporation duct height of unit (i,1) is Z m , the evaporation waveguide height of unit (j,1) is Z o The probability of is the unit of non-uniform evaporation waveguide height (i, N y ) is the height of the evaporation waveguide Z n , unit (j,N y ) is the height of the evaporation waveguide Z p The probability of Q z is the likelihood of the evaporation waveguide height transfer probability between distance Z and distance Z+1; Q is the product of the likelihoods of the transfer occurrence probability between all two adjacent distances from distance 1 to distance N;

[0019] When the transverse Markov chain is simulated along the h direction:

[0020]

[0021] When the transverse Markov chain is simulated along the h′ direction:

[0022]

[0023] When the direction of Markov chain simulation cannot be directly judged, in order to maximize the likelihood Q, R(Z 1,i =Z m ,Z 1,j =Z o )Pick and The larger value of:

[0024]

[0025] Furthermore, in step 1, the evaporation duct height is evenly divided into 40 parts within the range of 0-40 meters, and each meter is regarded as a type of change, and the set of changes in the evaporation duct height Z = {Z 1 ,Z 2 ,Z 3 ,…,Z 40}.

[0026] Furthermore, in step 4, the calculation process of the lateral transfer probability matrix is:

[0027]

[0028] In the above formula, i,j∈{1,2,...m}, is the corresponding element in the statistical horizontal transfer count matrix.

[0029] Furthermore, in step 4, the calculation process of the vertical transfer probability matrix is:

[0030]

[0031] In the above formula, i,j∈{1,2,...m}, is the corresponding element in the statistical vertical transfer count matrix.

[0032] A 2D Markov chain-based all-round non-uniform evaporation waveguide profile modeling device, the improvement of which lies in: using the above method steps to achieve.

[0033] The beneficial effects of the present invention are:

[0034] The method and device disclosed in the present invention couple one-dimensional Markov chains in multiple directions in order to better describe the spatial distribution of the evaporation duct profile, and propose a coupled Markov chain model suitable for multi-dimensional evaporation duct profile simulation. Since the distribution of the evaporation duct profile at different distances is relatively discrete, the lateral transfer probability matrix, which is one of the main input parameters of the coupled Markov chain, is difficult to obtain, and the coupled Markov chain model is difficult to simulate the interface of the evaporation duct profile parameters with different inclination directions. The present invention improves the two-dimensional Markov chain model and its input parameter evaluation method, so that the simulation effect of the model is not limited by the inclination direction of the interface and the horizontal distance sampling point data. By using coupled two-dimensional Markov chain spatial modeling, the limitation of the directional instability of the non-uniform atmospheric duct interface is overcome, and the spatial variation parameterized modeling of the full-space non-uniform atmospheric duct change is realized, which brings an effective technical solution to the complexity of modeling the random variation process of regional non-uniform atmospheric ducts.

[0035] The method and device disclosed in the present invention have the advantages of improving the two-dimensional coupled Markov chain model, proposing a coupled Markov chain model, which couples one-dimensional Markov chains in multiple directions together, and proposes a model suitable for simulating a multi-dimensional evaporation waveguide profile. Secondly, since the distribution of the evaporation waveguide profile at different distances is relatively discrete, as one of the main input parameters of the coupled Markov chain, the lateral transfer probability matrix is ​​difficult to obtain, and the coupled Markov chain model is difficult to simulate the evaporation waveguide profile parameter interface in different tilt directions. The present invention further improves the two-dimensional Markov chain model and the evaluation method of its input parameters, so that the simulation effect of the model is not limited by the tilt direction and horizontal distance of the interface sampling point data. Thereby better realizing the full-space modeling of the non-uniform evaporation waveguide profile. Through experimental analysis, it is found that the optimized coupled two-dimensional Markov spatial modeling of the non-uniform evaporation waveguide makes the simulation effect of the model not limited by the tilt direction and horizontal distance sampling point data of the interface. It can well realize the full-space discontinuous change of the non-uniform evaporation waveguide profile. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 It is a schematic flow diagram of the method of the present invention;

[0037] Figure 2 It is the simulation diagram of regional evaporation waveguide height at different K values;

[0038] Figure 3 This is a diagram of the verification results of the non-uniform evaporation waveguide simulation height. DETAILED DESCRIPTION

[0039] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0040] Embodiment 1. This embodiment discloses a method for modeling a full-range non-uniform evaporation duct profile based on a two-dimensional Markov chain. The principle is to determine the horizontal and vertical grid sizes of the modeling, and the atmospheric duct height data values ​​of the initial lateral distance sampling points, and input the atmospheric duct height data recorded at the initial distance points into the corresponding discrete cells to obtain a preliminary non-uniform atmospheric duct height area, statistically analyze and predict the state of unknown atmospheric duct variables by counting the transition probabilities between known adjacent state variables.

[0041] The fluctuation process of the evaporation duct profile can be regarded as a Markov fluctuation process. The premise of using Markov chain is that the evaporation duct height needs to meet some basic assumptions: 1. When multiple first-order Markov chains in different directions simulate the evaporation duct height for coupling, the one-dimensional Markov chains in each direction are independent of each other. 2. The transfer process of the evaporation duct height variable in the model along each direction has the first-order Markov property. 3. The one-dimensional Markov chain of the evaporation duct height change in different directions is homogeneous.

[0042] like Figure 1 As shown, the following steps are included:

[0043] Step 1, dividing the region with non-uniform evaporation waveguide height into a number of element units of equal size, wherein the evaporation waveguide height in each divided element unit remains unchanged;

[0044] In the range of 0-40 meters, the evaporation duct height is divided into 40 parts, and each meter is regarded as a type of change. The set of changes in the evaporation duct height Z = {Z 1 ,Z 2 ,Z 3 ,…,Z 40}.

[0045] Since the working principle of the Markov chain is to infer the height of the next evaporation waveguide through the value of the evaporation waveguide height of the previous element unit, when making predictions, the known elements must be used as the starting point for full-space simulation.

[0046] Step 2, divide the change area of ​​the two-dimensional non-uniform evaporation duct height into two directions, horizontally and vertically. The horizontal direction is the expansion of the 100-kilometer data detected by the radar, and there are two columns of initial values ​​in the vertical direction. There is only one simulation starting point on each unit in the same column or the same row, that is, the Markov chain of the column (row) can only be simulated along the same direction, that is, the simulated evaporation duct height can only choose the Markov chain in one direction from left to right h and from right to left h′ and the Markov chain vertically downward v for coupling simulation; first, it is assumed that the spatial transfer process in the horizontal and vertical directions of the simulated area has a first-order Markov property, and the Markov chains in the horizontal and vertical directions are independent of each other.

[0047] The Markov chain coupling is performed for the evaporation duct height in the vertical downward v direction and from left to right h direction. The evaporation duct height range type of unit (i, j) depends on the type of regional unit (i-1, j) and unit (i, j-1). If the evaporation duct height of unit (i-1, j) is Z p , the evaporation waveguide height of unit (i,j-1) is Z q , the evaporation waveguide height of unit (i, j) is Z W , ZW The conditional probability is:

[0048]

[0049] If the end point of the h direction (N x ,j) the evaporation waveguide height Z u As a constraint, the evaporation waveguide height Z of unit (i, j) is W The transition probability The expression is:

[0050]

[0051]

[0052] Step 3, according to the actual situation of the waveguide, the block in the waveguide area is simulated obliquely, and the simulation direction is re-determined at the waveguide junction, and the occurrence of transition is avoided; to ensure that the simulated data has better ductility. Therefore, in order to overcome the above shortcomings, the present invention re-determines the simulation direction at the junction of the improved two-dimensional coupled Markov chain when simulating the direction, and does not remain consistent with the previous simulation direction.

[0053] Step 4, calculate the three transition probability matrices of horizontal, vertical and diagonal directions;

[0054] The transfer probability matrix is ​​an important input parameter in the coupled Markov chain model. Due to the anisotropy of the spatial distribution, the transfer probability matrix of the coupled Markov chain model is different in the horizontal and vertical directions. The value of the transfer probability matrix will directly affect the simulation results of the non-uniform evaporation waveguide height. Therefore, reasonably estimating the height transfer probability matrix of the lateral and vertical evaporation waveguides is the prerequisite for obtaining a reasonable coupled Markov chain model.

[0055] The calculation process of the lateral transfer probability matrix is:

[0056]

[0057] In the above formula, i,j∈{1,2,...m}, is the corresponding element in the statistical horizontal transfer count matrix.

[0058] The calculation process of the vertical transfer probability matrix is:

[0059]

[0060] In the above formula, i,j∈{1,2,...m}, is the corresponding element in the statistical vertical transfer count matrix.

[0061] Step 5, the horizontal and vertical extension lengths of different evaporation duct heights are estimated. The horizontal and vertical extension length ratios of different evaporation duct heights are obtained by using the change data of the initial evaporation duct. The basic idea is similar to the maximum likelihood estimation. Different K values ​​result in different evaporation duct heights. The transfer likelihoods between the evaporation duct heights are multiplied to obtain the transfer likelihood Q of the overall evaporation duct height. When Q reaches the maximum value, the result of the K value is optimal.

[0062] Q=Q 1 …Q N-1

[0063]

[0064] Z m ,…,Z n is the value of the evaporation waveguide height corresponding to the Zth distance; R(Z i,1 =Z m ,Z j,1 =Z o ) is the non-uniform evaporation duct height. The evaporation duct height of unit (i,1) is Z m , the evaporation waveguide height of unit (j,1) is Z o The probability of , which is related to the simulation direction; is the unit of non-uniform evaporation waveguide height (i, N y ) is the height of the evaporation waveguide Z n , unit (j,N y ) is the height of the evaporation waveguide Z p The probability of is related to the simulation direction; Q z is the likelihood of the evaporation waveguide height transfer probability between distance Z and distance Z+1; Q is the product of the likelihoods of the transfer occurrence probability between all two adjacent distances from distance 1 to distance N;

[0065] When the transverse Markov chain is simulated along the h direction:

[0066]

[0067] When the transverse Markov chain is simulated along the h′ direction:

[0068]

[0069] When the direction of Markov chain simulation cannot be directly judged, in order to maximize the likelihood Q, R(Z 1,i =Z m ,Z 1,j =Zo )Pick and The larger value of:

[0070]

[0071] Figure 2 This is a simulation diagram of the regional evaporation waveguide height for different K values.

[0072] Figure 3 The comparison results of the model of the present invention and the one-dimensional Markov chain and linear interpolation methods for the changes of non-uniform atmospheric ducts are given. The average error of the linear interpolation method is 6.3 meters; while the error of the two-dimensional Markov chain simulation is 2.3 meters. In comparison, the simulation of the two-dimensional Markov chain effectively reduces the simulation error of the non-uniform evaporation duct, making the actual changes of the non-uniform evaporation duct closer to the real situation, thereby verifying the reliability of the two-dimensional Markov chain for spatial simulation.

[0073] This embodiment also discloses a 2D Markov chain-based all-round non-uniform evaporation waveguide profile modeling device, which is implemented using the above method steps.

Claims

1. A method for modeling a omnidirectional non-uniform evaporation waveguide profile based on a two-dimensional Markov chain, characterized in that: The steps include: Step 1, dividing the region with non-uniform evaporation waveguide height into a number of element units of equal size, wherein the evaporation waveguide height in each divided element unit remains unchanged; Step 2, divide the variation area of ​​the two-dimensional non-uniform evaporation duct height into two directions, horizontally and vertically. The horizontal direction is the expansion of the 100-kilometer data detected by the radar, and the vertical direction has two columns of initial values. There is only one simulation starting point on each unit in the same column or row, that is, the simulated evaporation duct height can only select the Markov chain in one direction from left to right h and from right to left h′ and the Markov chain in the vertical downward v direction for coupling simulation; The Markov chain coupling is performed on the evaporation waveguide height in the vertical downward direction v and from left to right direction h. If the evaporation waveguide height of unit (i-1, j) is Z p , the evaporation waveguide height of unit (i,j-1) is Z q , the evaporation waveguide height of unit (i,j) is Z W , Z W The conditional probability is: If the end point of the h direction (N x ,j) the evaporation waveguide height Z u As a constraint, the evaporation waveguide height Z of unit (i, j) is W The transition probability The expression is: Step 3, perform oblique simulation on the blocks where the waveguide appears, and redefine the simulation direction at the waveguide junction to avoid the occurrence of transitions; Step 4, calculate the three transition probability matrices of horizontal, vertical and diagonal directions; Step 5, the horizontal and vertical extension lengths of different evaporation duct heights are estimated, and the horizontal and vertical extension length ratios of different evaporation duct heights are obtained by using the change data of the initial evaporation duct. Different evaporation duct heights are obtained with different K values. The transfer likelihoods between the evaporation duct heights are multiplied to obtain the transfer likelihood number Q of the overall evaporation duct height. When Q reaches the maximum value, the result of the K value is optimal. Q=Q1…Q N-1 Q z =R(Z i,1 =Z m ,Z j,1 =Z o )R(Z i,2 =Z m+1 ,Z j,2 =Z o+1) …R(Zi,Ny=Z n ,Zj,Ny=Z p ) Z m ,…,Z n is the value of the evaporation waveguide height corresponding to the Zth distance; R(Z i,1 =Z m ,Z j,1 =Z o ) is the non-uniform evaporation duct height. The evaporation duct height of unit (i,1) is Z m , the evaporation waveguide height of unit (j,1) is Z o The probability of is the unit of non-uniform evaporation waveguide height (i, N y ) is the height of the evaporation waveguide Z n , unit (j,N y ) is the height of the evaporation waveguide Z t The probability of Q z is the likelihood of the evaporation waveguide height transfer probability between distance Z and distance Z+1; Q is the product of the likelihoods of the transfer occurrence probability between all two adjacent distances from distance 1 to distance N; When the transverse Markov chain is simulated along the h direction: When the transverse Markov chain is simulated along the h′ direction: When the direction of Markov chain simulation cannot be directly judged, in order to maximize the likelihood Q, R(Z 1,i =Z m ,Z 1,j =Z o )Pick and The larger value of:

2. The method for modeling a omnidirectional non-uniform evaporation waveguide profile based on a two-dimensional Markov chain according to claim 1, characterized in that: In step 1, the evaporation duct height is divided into 40 parts in the interval of 0-40 meters, and each meter is regarded as a change type, and the set of changes in the evaporation duct height Z = {Z1, Z2, Z3, ..., Z 40 }.

3. The method for modeling a 2D Markov chain-based omnidirectional non-uniform evaporation waveguide profile according to claim 1, characterized in that: In step 4, the calculation process of the lateral transfer probability matrix is: In the above formula, i,j∈{1,2,...m}, is the corresponding element in the statistical horizontal transfer count matrix.

4. The method for modeling a 2D Markov chain-based omnidirectional non-uniform evaporation waveguide profile according to claim 1, characterized in that: In step 4, the calculation process of the vertical transfer probability matrix is: In the above formula, i,j∈{1,2,...m}, is the corresponding element in the statistical vertical transfer count matrix.

5. A 2D Markov chain-based all-round non-uniform evaporation waveguide profile modeling device, characterized in that: The method steps described in claim 1 are used to achieve this.

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