A situation missing information nonlinear filling method for aerial game confrontation
By constructing a nonlinear prediction model based on Gaussian kernel mapping, the problem of incompleteness in air combat situation data was solved, enabling efficient filling of missing information and improving data quality and utilization efficiency.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- HANGZHOU EBOYLAMP ELECTRONICS CO LTD
- Filing Date
- 2024-02-19
- Publication Date
- 2026-06-26
AI Technical Summary
Existing deep reinforcement learning algorithms lack robustness to the problem of incomplete air combat situation data. Linear imputation methods are difficult to effectively represent the nonlinear relationships in air combat situation data, resulting in inaccurate accuracy in imputing missing information.
A nonlinear prediction model based on Gaussian kernel mapping is constructed. By acquiring standardized situational data and missing information, the input information in the nonlinear prediction model based on Gaussian kernel mapping is set, and the prediction coefficients are solved. The Gaussian kernel mapping model is then used to fill in the missing information.
It improves the quality and efficiency of situational data utilization, solves the problem that linear imputation methods are difficult to characterize nonlinear mapping relationships, and improves the accuracy of missing information imputation.
Smart Images
Figure CN118193962B_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of situational information processing, specifically relating to a nonlinear method for filling in missing situational information in aerial game confrontation. Background Technology
[0002] Deep reinforcement learning is a crucial technological approach for achieving intelligent aerial combat. Aerial combat is essentially an incomplete information adversarial process, resulting in incomplete situational data. Incompleteness refers to the dynamic absence of some observations at certain time steps; that is, the dimensions and timing of these missing observations cannot be known in advance by the aerial combat agent. Furthermore, another factor contributing to data incompleteness is the malfunction of airborne sensors or errors during data acquisition and transmission. However, current deep reinforcement learning algorithms lack robustness to incomplete information. For example, proximal policy optimization algorithms, employing an Actor-Critic architecture (policy network and value network), require complete observation information to output actions.
[0003] To address the incompleteness of air combat situational data, typical solutions include neighbor imputation, mean imputation, and linear regression imputation. While neighbor imputation and mean imputation are naturally suited to steady-state, slowly changing systems, they are unsuitable for the complex and rapidly changing battlefield environment of air combat scenarios. Linear regression imputation establishes a linear mapping between missing features and remaining features to fill in the missing values. However, the features in air combat situational data exhibit highly nonlinear relationships, making it difficult for this linear imputation method to effectively represent these nonlinear mappings, thus often compromising the accuracy of missing information filling. Summary of the Invention
[0004] The purpose of this invention is to address the problems raised in the background art by proposing a nonlinear method for filling in missing situational information in aerial game confrontation.
[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:
[0006] The present invention proposes a nonlinear method for filling missing situation information in aerial game confrontation, which includes acquiring standardized situation data and missing information in the situation data during the confrontation between the red and blue sides.
[0007] A nonlinear prediction model for Gaussian kernel mapping is constructed based on the missing information, and the specific form of the nonlinear prediction model for Gaussian kernel mapping is as follows:
[0008] W'=Θ T φ(B)
[0009] Where W' represents missing information, Θ represents prediction coefficients, T represents transpose, φ(·) represents a nonlinear function based on Gaussian kernel mapping, and B represents the input information of the nonlinear prediction model based on Gaussian kernel mapping;
[0010] Based on the type of missing information, the input information in the nonlinear prediction model of each Gaussian kernel mapping is set, and the prediction coefficients in the nonlinear prediction model of each Gaussian kernel mapping are solved to obtain the nonlinear prediction model of each Gaussian kernel mapping.
[0011] Finally, a nonlinear prediction model using Gaussian kernel mapping is used to predict the missing information and complete the filling of the missing information.
[0012] Preferably, the acquisition of standardized situational data and missing information in the situational data during the confrontation between the red and blue teams includes:
[0013] First, standardized situational data for both the red and blue sides are constructed separately during the confrontation. Then, K rounds of confrontation are conducted, each round containing S-step situational data, where the red side's situational data for each step includes d... r The characteristics of the blue team's situational data at each step include d b The characteristic is that the standardized situational data of the Red team in the S-step of the k-th game is denoted as follows: This represents the situational data of the Red team in the S-step situational data of the k-th game, denoted as [the j-th feature]. The standardized situational data of the Blue team in the S-step situational data of the k-th game is denoted as [the j-th feature]. Let s represent the situation data of the i-th feature in the S-step situation data of the blue team in the k-th game, where s = 1, 2, ..., S, k = 1, 2, ..., K;
[0014] Acquire standardized situational data from the confrontation between the red and blue teams, and compare the acquired situational data with the constructed data to obtain missing information.
[0015] Preferably, when the missing information is a feature missing from one step of the situation data of the red side in a game of confrontation, the corresponding nonlinear prediction model of the first Gaussian kernel mapping is constructed as follows:
[0016]
[0017] In particular, the j-th feature is missing from the situational data of the red side in the k-th game and the s-th step. This represents the situation data of the Red team in the k-th game, s-th step, after removing the j-th feature. d represents the prediction coefficient between the j-th feature in the red team's situation data at step s in game k and after removing the j-th feature. rThis represents the total number of features in the situational data of the red side at step s in the k-th game, where S represents the total number of steps for either the red or blue side in the k-th game, and K represents the total number of games played between the red and blue sides.
[0018] Preferably, the process of solving for the prediction coefficients in the nonlinear prediction model of the first Gaussian kernel mapping is as follows:
[0019] Given the first regularization coefficient C r Solve for the prediction coefficient The objective function is as follows:
[0020]
[0021] By minimizing For prediction coefficients Solving for the problem, we get:
[0022]
[0023] The dual form is
[0024]
[0025] in, and and and All of these represent intermediate parameters. Represents K×S rows d φ The dimension of the column matrix, This represents the dimension of a vector with S rows and 1 column. This represents the dimension of a K×S vector with 1 row and 1 column. This represents the set of situational data for the j-th feature across all moves in the k-th game for the Red team.
[0026] Define matrix And matrix The element in the p-th row and q-th column is denoted as and
[0027] Where m(·,·) represents the Gaussian kernel function, and σ represents the hyperparameter of the Gaussian kernel function. This represents the situational data of the Red team after removing the j-th feature from the p-th step situational data. This represents the situational data of the Red team after removing the j-th feature from the q-th step situational data. This represents the dimension of a matrix with K×S rows and K×S columns;
[0028] Will Substitute into From:
[0029]
[0030] Will right After differentiating and setting the derivative to zero, we get:
[0031]
[0032] Then, substituting formula (2) into formula (1), we obtain the solution for the prediction coefficients in the nonlinear prediction model of the first Gaussian kernel mapping:
[0033]
[0034] The nonlinear prediction model for the first Gaussian kernel mapping is then obtained as follows:
[0035]
[0036] Among them, Record Let n be a column vector, and let n be the nth element of the column vector.
[0037] The missing information of the j-th feature in the red team's situation data at step s in the k-th game is obtained through the nonlinear prediction model of the first Gaussian kernel mapping in the above formula, and then the missing information is filled in.
[0038] Preferably, when the missing information is a feature missing from one step of the situation data of the blue side in a game of confrontation, the corresponding nonlinear prediction model of the second Gaussian kernel mapping is constructed as follows:
[0039]
[0040] In particular, the i-th feature is missing from the situational data of the blue team in the k-th game and s-th step. This represents the situational data of the Blue team in the k-th game, step s, after removing the i-th feature. d represents the prediction coefficient between the i-th feature in the blue team's situational data at step s in the k-th game and after removing the i-th feature. b This represents the total number of features in the situational data of the blue side in the k-th game at step s, S represents the total number of steps for either the red or blue side in the k-th game, and K represents the total number of games played between the red and blue sides.
[0041] Preferably, the process of solving for the prediction coefficients in the nonlinear prediction model of the second Gaussian kernel mapping is as follows:
[0042] Given the second regularization coefficient C b Solve for the prediction coefficient The objective function is as follows:
[0043]
[0044] By minimizing For prediction coefficients Solving for the problem, we get:
[0045]
[0046] The dual form is
[0047]
[0048] in, and and and All of these represent intermediate parameters. Represents K×S rows d φ The dimension of the column matrix, This represents the dimension of a vector with S rows and 1 column. This represents the dimension of a K×S vector with 1 row and 1 column. This represents the set of situational data for the i-th feature across all moves in the k-th game for the blue team.
[0049] Define matrix And matrix The element in the p-th row and q-th column is denoted as and
[0050] Where m(·,·) represents the Gaussian kernel function, and σ represents the hyperparameter of the Gaussian kernel function. This represents the situational data of the Blue Team after removing the i-th feature from the p-th step situational data. This represents the situational data of the Blue Team after removing the i-th feature from the q-th step situational data. This represents the dimension of a matrix with K×S rows and K×S columns;
[0051] Will Substitute into From:
[0052]
[0053] Will right After differentiating and setting the derivative to zero, we get:
[0054]
[0055] Then, substituting formula (4) into formula (3), we obtain the solution for the prediction coefficients in the nonlinear prediction model of the second Gaussian kernel mapping:
[0056]
[0057] The nonlinear prediction model for the second Gaussian kernel mapping is then obtained as follows:
[0058]
[0059] Among them, Record Let n be a column vector, and let n be the nth element of the column vector.
[0060] The missing information of the i-th feature in the blue team's situation data at step s in the k-th game is obtained through the nonlinear prediction model of the second Gaussian kernel mapping in the above formula, and then the missing information is filled in.
[0061] Preferably, when the missing information is of the missing situation data of the blue side in one move of a game, the corresponding nonlinear prediction model with a third Gaussian kernel mapping is constructed as follows:
[0062]
[0063] Among them, the situational data of the blue team in the k-th game and the h-th step is missing, and This represents the situational data of the Blue team in the previous l steps of the k-th game, i.e. Θ b' This represents the prediction coefficient between the situation data of the blue team at step h and the situation data of the previous l steps, and d represents the prediction coefficient between the i-th feature in the h-th step situation data to be predicted by the blue team and the situation data in the previous l steps. b This represents the total number of features in the situational data of the blue side at step s in the k-th game, where S represents the total number of steps for either the red or blue side in the k-th game, and K represents the total number of games played between the red and blue sides. d φ line d b The dimension of the column matrix.
[0064] Preferably, the process of solving for the prediction coefficients in the nonlinear prediction model of the third Gaussian kernel mapping is as follows:
[0065] Given parameter l, process the blue team's situational data for each game, extract the situational data of the previous l steps before the h-th step of the blue team's situational data to be predicted, h = l+1, l+2, ..., S, and denot the situational data of the previous l steps as . It is expressed as follows:
[0066]
[0067] in, This represents the first step of the extracted situational data from the previous l steps, where f+l=h;
[0068] Simultaneously, the situational data to be predicted at step h is used as label data, denoted as...
[0069] For the blue team's situational data in the k-th round, the set of situational data for all missing steps is represented as: The missing information at each step is predicted using the corresponding previous l steps. Therefore, for the blue team's situation data in the k-th game, the set of all previous l steps is represented as follows:
[0070] For game K, the set of situation data for all missing steps is represented as: The set of all the previous l steps is represented as
[0071] Given a third regularization coefficient C b' Solve for the prediction coefficients The objective function is as follows:
[0072]
[0073] in, This represents the i-th feature of the Blue team in the f-th step of the situation data in the k-th game;
[0074] By minimizing For prediction coefficients Solving for the problem, we get:
[0075]
[0076] The dual form is
[0077]
[0078] in, and and and All of these represent intermediate parameters. Represents K×(Sl) rows d φ The dimension of the column matrix, d φ The dimension of a matrix with rows Sl and columns, This represents the dimension of a K×(Sl) row, 1 column vector;
[0079] Define matrix And matrix The element in the p-th row and q-th column is denoted as and
[0080] Where m(·,·) represents the Gaussian kernel function, and σ represents the hyperparameter of the Gaussian kernel function. express The p-th element, express The q-th element, This represents the dimension of a matrix with K×(Sl) rows and K×(Sl) columns;
[0081] Will Substitute into From:
[0082]
[0083] Will right After differentiating and setting the derivative to zero, we get:
[0084]
[0085] Then, by substituting formula (6) into formula (5), the prediction coefficients in the nonlinear prediction model of the third Gaussian kernel mapping are obtained. Solution:
[0086]
[0087] The nonlinear prediction model using the third Gaussian kernel mapping then predicts each feature missing in the h-th step of the k-th game as follows:
[0088]
[0089] Among them, Record Let n be a column vector, and let n be the nth element of the column vector.
[0090] By using a nonlinear prediction model based on the third Gaussian kernel mapping, each feature in the situational data of the blue team at step h in the k-th game is predicted, thereby completing the filling of missing information in the situational data of the blue team at step h in the k-th game.
[0091] Compared with the prior art, the beneficial effects of the present invention are as follows:
[0092] This nonlinear situational information filling method for aerial game confrontation constructs a Gaussian kernel mapping nonlinear prediction model. Based on the type of missing information, it sets the input information for each Gaussian kernel mapping nonlinear prediction model and solves for the prediction coefficients in each model, thus obtaining the nonlinear prediction model for each Gaussian kernel mapping. Finally, it uses the Gaussian kernel mapping nonlinear prediction model to predict the corresponding missing information, completing the missing information filling. This avoids data waste caused by data loss due to missing data, greatly improving the quality and utilization efficiency of situational data. It solves the problem in existing technologies where linear filling methods are difficult to effectively represent nonlinear mapping relationships, leading to inaccurate missing information filling accuracy. Attached Figure Description
[0093] Figure 1 This is a flowchart illustrating the nonlinear filling method for missing situational information in aerial game confrontation according to the present invention. Detailed Implementation
[0094] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.
[0095] It should be noted that when a component is referred to as being "connected" to another component, it can be directly connected to the other component or there may be an intervening component. Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used herein in the specification of this application is for the purpose of describing particular embodiments only and is not intended to limit the application.
[0096] like Figure 1 As shown, a nonlinear method for filling in missing situational information in aerial game confrontation includes:
[0097] Step 1: Obtain standardized situational data and missing information from the situational data during the confrontation between the red and blue teams. Specifically, this includes:
[0098] First, standardized situational data for both the red and blue sides are constructed separately during the confrontation. Then, K rounds of confrontation are conducted, each round containing S-step situational data, where the red side's situational data for each step includes d... r The characteristics of the blue team's situational data at each step include d b The characteristic is that the standardized situational data of the Red team in the S-step of the k-th game is denoted as follows: This represents the situational data of the Red team in the S-step situational data of the k-th game, denoted as the situational data of the Blue team in the S-step standardized process of the k-th game. Let s represent the situation data of the i-th feature in the S-step situation data of the blue team in the k-th game, where s = 1, 2, ..., S, k = 1, 2, ..., K;
[0099] Acquire standardized situational data from the confrontation between the red and blue teams, and compare the acquired situational data with the constructed data to obtain missing information.
[0100] It should be noted that the standardization process is dimensionless. The features of each step of the situational data for both the red and blue teams include at least longitude, latitude, altitude, velocity, acceleration, heading angle, roll angle, pitch angle, previous time step longitude, previous time step latitude, previous time step altitude, previous time step velocity, and previous time step acceleration. The number of features d for each step of the red team's situational data is... r The number of features d that can be compared with the situation data of the blue team at each step b The values can be equal or unequal; each feature of the situational data of both the red and blue sides at each step can be acquired through sensors (i.e., all the situational data of each side after standardization during the confrontation process; other methods can also be used to acquire this data, without restriction). The acquired situational data is compared with the constructed situational data to obtain missing information (the absence of corresponding situational data obtained by the sensors is considered missing information). The situational data refers to the specific numerical values of the features.
[0101] Step 2: Construct a nonlinear prediction model for Gaussian kernel mapping based on the missing information. The specific form of the nonlinear prediction model for Gaussian kernel mapping is as follows:
[0102] W'=Θ T φ(B)
[0103] Where W' represents missing information, Θ represents prediction coefficients, T represents transpose, φ(·) represents a nonlinear function based on Gaussian kernel mapping, and B represents the input information of the nonlinear prediction model based on Gaussian kernel mapping;
[0104] Step 3: Based on the type of missing information, set the input information in the nonlinear prediction model of each Gaussian kernel mapping, and solve the prediction coefficients in the nonlinear prediction model of each Gaussian kernel mapping to obtain the nonlinear prediction model of each Gaussian kernel mapping.
[0105] Step 4: Finally, use the nonlinear prediction model of Gaussian kernel mapping to predict the corresponding missing information and complete the filling of missing information.
[0106] It should be noted that this patent uses three types of missing information as examples for illustration, specifically: the missing feature of one step of the red side's situational data in a game, the missing feature of one step of the blue side's situational data in a game, and the missing situational data of one step of the blue side in a game; where the red side is our opposing team and the blue side is the opposing team, therefore the red side's missing information will not be extensive, that is, the red side will not have the missing situational data of one step in a game.
[0107] 1) When the missing information is a feature missing from one step of the situation data of the Red side in a game, the corresponding nonlinear prediction model based on the first Gaussian kernel mapping is constructed as follows (using the remaining features of the current step in the current game where the missing feature of the Red side is located to predict the missing feature):
[0108]
[0109] In particular, the j-th feature is missing from the situational data of the red side in the k-th game and the s-th step. This represents the situation data of the Red team in the k-th game, s-th step, after removing the j-th feature. d represents the prediction coefficient between the j-th feature in the red team's situation data at step s in game k and after removing the j-th feature. r This represents the total number of features in the situational data of the red side at step s in the k-th game, where S represents the total number of steps for either the red or blue side in the k-th game, and K represents the total number of games played between the red and blue sides.
[0110] The solution process for the prediction coefficients in the nonlinear prediction model of the first Gaussian kernel mapping is as follows:
[0111] Given the first regularization coefficient C r Solve for the prediction coefficient The objective function is as follows:
[0112]
[0113] By minimizing For prediction coefficients Solving for the problem, we get:
[0114]
[0115] The dual form is
[0116]
[0117] in, and and and All of these represent intermediate parameters. Represents K×S rows d φ The dimension of the column matrix, This represents the dimension of a vector with S rows and 1 column. This represents the dimension of a K×S vector with 1 row and 1 column. This represents the set of situational data for the j-th feature across all moves in the k-th game for the Red team.
[0118] Define matrix And matrix The element in the p-th row and q-th column is denoted as and
[0119] Where m(·,·) represents the Gaussian kernel function, and σ represents the hyperparameter of the Gaussian kernel function. This represents the situational data of the Red team after removing the j-th feature from the p-th step situational data. This represents the situational data of the Red team after removing the j-th feature from the q-th step situational data. This represents the dimension of a matrix with K×S rows and K×S columns;
[0120] Will Substitute into From:
[0121]
[0122] Will right After differentiating and setting the derivative to zero, we get:
[0123]
[0124] Then, substituting formula (2) into formula (1), we obtain the solution for the prediction coefficients in the nonlinear prediction model of the first Gaussian kernel mapping:
[0125]
[0126] The nonlinear prediction model for the first Gaussian kernel mapping is then obtained as follows:
[0127]
[0128] Among them, Record Let n be a column vector, and let n be the nth element of the column vector.
[0129] The missing information of the j-th feature in the red team's situation data at step s in the k-th game is obtained through the nonlinear prediction model of the first Gaussian kernel mapping in the above formula, and then the missing information is filled in.
[0130] 2) When the missing information is a feature missing from one step of the situation data of the blue side in a game, the corresponding nonlinear prediction model of the second Gaussian kernel mapping is constructed as follows (using the remaining features of the current step of the current game in which the missing feature of the blue side is located to predict the missing feature):
[0131]
[0132] In particular, the i-th feature is missing from the situational data of the blue team in the k-th game and s-th step. This represents the situational data of the Blue team in the k-th game, step s, after removing the i-th feature. d represents the prediction coefficient between the i-th feature in the blue team's situational data at step s in the k-th game and after removing the i-th feature. b This represents the total number of features in the situational data of the blue side in the k-th game at step s, S represents the total number of steps for either the red or blue side in the k-th game, and K represents the total number of games played between the red and blue sides.
[0133] The solution process for the prediction coefficients in the nonlinear prediction model of the second Gaussian kernel mapping is as follows:
[0134] Given the second regularization coefficient C b Solve for the prediction coefficient The objective function is as follows:
[0135]
[0136] By minimizing For prediction coefficients Solving for the problem, we get:
[0137]
[0138] The dual form is
[0139]
[0140] in, and and and All of these represent intermediate parameters. Represents K×S rows d φ The dimension of the column matrix, This represents the dimension of a vector with S rows and 1 column. This represents the dimension of a K×S vector with 1 row and 1 column. This represents the set of situational data for the i-th feature across all moves in the k-th game for the blue team.
[0141] Define matrix And matrix The element in row p and column qw is denoted as and
[0142] Where m(·,·) represents the Gaussian kernel function, and σ represents the hyperparameter of the Gaussian kernel function. This represents the situational data of the Blue Team after removing the i-th feature from the p-th step situational data. This represents the situational data of the Blue Team after removing the i-th feature from the q-th step situational data. This represents the dimension of a matrix with K×S rows and K×S columns;
[0143] Will Substitute into From:
[0144]
[0145] Will right After differentiating and setting the derivative to zero, we get:
[0146]
[0147] Then, substituting formula (4) into formula (3), we obtain the solution for the prediction coefficients in the nonlinear prediction model of the second Gaussian kernel mapping:
[0148]
[0149] The nonlinear prediction model for the second Gaussian kernel mapping is then obtained as follows:
[0150]
[0151] Among them, Record Let n be a column vector, and let n be the nth element of the column vector.
[0152] The missing information of the i-th feature in the blue team's situation data at step s in the k-th game is obtained through the nonlinear prediction model of the second Gaussian kernel mapping in the above formula, and then the missing information is filled in.
[0153] 3) When the missing information is the missing situation data of the blue side in one of the rounds of the game, the corresponding nonlinear prediction model of the third Gaussian kernel mapping is constructed as follows (using the situation data of the previous l steps in the current round where the situation data of the missing blue side's step is located to predict the situation data of the missing step):
[0154]
[0155] Among them, the situational data of the blue team in the k-th game and the h-th step is missing, and This represents the situational data of the Blue team in the previous l steps of the k-th game, i.e. Θ b' This represents the prediction coefficient between the situation data of the blue team at step h and the situation data of the previous l steps, and d represents the prediction coefficient between the i-th feature in the h-th step situation data to be predicted by the blue team and the situation data in the previous l steps. b This represents the total number of features in the situational data of the blue side at step s in the k-th game, where S represents the total number of steps for either the red or blue side in the k-th game, and K represents the total number of games played between the red and blue sides. d φ line d b The dimension of the column matrix.
[0156] The solution process for the prediction coefficients in the nonlinear prediction model of the third Gaussian kernel mapping is as follows:
[0157] Given parameter l, process the blue team's situational data for each game, extract the situational data of the previous l steps before the h-th step of the blue team's situational data to be predicted, h = l+1, l+2, ..., S, and denot the situational data of the previous l steps as . It is expressed as follows:
[0158]
[0159] in, This represents the first step of the extracted situational data from the previous l steps, where f+l=h;
[0160] Simultaneously, the situational data to be predicted at step h is used as label data, denoted as...
[0161] For the blue team's situational data in the k-th round, the set of situational data for all missing steps is represented as: The missing information at each step is predicted using the corresponding previous l steps. Therefore, for the blue team's situation data in the k-th game, the set of all previous l steps is represented as follows:
[0162] For game K, the set of situation data for all missing steps is represented as: The set of all the previous l steps is represented as
[0163] Given a third regularization coefficient C b' Solve for the prediction coefficients The objective function is as follows:
[0164]
[0165] in, This represents the i-th feature of the Blue team in the f-th step of the situation data in the k-th game;
[0166] By minimizing For prediction coefficients Solving for the problem, we get:
[0167]
[0168] The dual form is
[0169]
[0170] in, and and and All of these represent intermediate parameters. Represents K×(Sl) rows d φ The dimension of the column matrix, d φ The dimension of a matrix with rows Sl and columns, This represents the dimension of a K×(Sl) row, 1 column vector;
[0171] Define matrix And matrix The element in the p-th row and q-th column is denoted as and
[0172] Where m(·,·) represents the Gaussian kernel function, and σ represents the hyperparameter of the Gaussian kernel function. express The p-th element, express The q-th element, This represents the dimension of a matrix with K×(Sl) rows and K×(Sl) columns;
[0173] Will Substitute into From:
[0174]
[0175] Will right After differentiating and setting the derivative to zero, we get:
[0176]
[0177] Then, by substituting formula (6) into formula (5), the prediction coefficients in the nonlinear prediction model of the third Gaussian kernel mapping are obtained. Solution:
[0178]
[0179] The nonlinear prediction model using the third Gaussian kernel mapping then predicts each feature missing in the h-th step of the k-th game as follows:
[0180]
[0181] Among them, Record Let n be a column vector, and let n be the nth element of the column vector.
[0182] The nonlinear prediction model using the third Gaussian kernel mapping is used to predict each feature in the situation data of the blue side in the h-th step of the k-th game, thereby completing the filling of missing information in the situation data of the blue side in the h-th step of the k-th game. The missing situation information of the blue side in other steps of the k-th game is calculated in the same way and will not be described again.
[0183] This nonlinear situational information filling method for aerial game confrontation constructs a Gaussian kernel mapping nonlinear prediction model. Based on the type of missing information, it sets the input information for each Gaussian kernel mapping nonlinear prediction model and solves for the prediction coefficients in each model, thus obtaining the nonlinear prediction model for each Gaussian kernel mapping. Finally, it uses the Gaussian kernel mapping nonlinear prediction model to predict the corresponding missing information, completing the missing information filling. This avoids data waste caused by data loss due to missing data, greatly improving the quality and utilization efficiency of situational data. It solves the problem in existing technologies where linear filling methods are difficult to effectively represent nonlinear mapping relationships, leading to inaccurate missing information filling accuracy.
[0184] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.
[0185] The embodiments described above are merely specific and detailed examples of the embodiments described in this application, and should not be construed as limiting the scope of the patent application. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the scope of protection of this application. Therefore, the scope of protection of this patent application should be determined by the appended claims.
Claims
1. A nonlinear method for filling in missing situational information in aerial game confrontation, characterized in that: The nonlinear method for filling in missing situational information in aerial game confrontation includes: Acquire standardized situational data and missing information from the situational data during the confrontation between the red and blue teams; A nonlinear prediction model for Gaussian kernel mapping is constructed based on the missing information, and the specific form of the nonlinear prediction model for Gaussian kernel mapping is as follows: in, Indicates missing information. Represents the prediction coefficient. Indicates transpose. This represents a nonlinear function based on Gaussian kernel mapping. This represents the input information for a nonlinear prediction model based on Gaussian kernel mapping; Based on the type of missing information, the input information in the nonlinear prediction model of each Gaussian kernel mapping is set, and the prediction coefficients in the nonlinear prediction model of each Gaussian kernel mapping are solved to obtain the nonlinear prediction model of each Gaussian kernel mapping. Finally, the nonlinear prediction model of Gaussian kernel mapping is used to predict the corresponding missing information and complete the filling of missing information. The acquisition of standardized situational data and missing information in the situational data during the confrontation between the red and blue teams includes: First, standardized situational data for both the red and blue teams during the confrontation process are constructed separately, and then... The game is a series of matches, each containing... Step-by-step situation data, including the situation data of the Red team at each step. The characteristics of the blue team's situational data at each step include: The first characteristic, the red team in the... The Bureau's First The situational data after standardization is denoted as , Indicates that the red team is in the first place. The Bureau's First The first step in the situational data The situational data of the first characteristic, the blue team in the first... The Bureau's First The situational data after standardization is denoted as , Indicates that the blue team is in the The Bureau's First The first step in the situational data Situational data with several characteristics ; Acquire standardized situational data during the confrontation between the red and blue teams, and compare the acquired situational data with the constructed data to obtain missing information; When the missing information is a feature missing from the situational data of the red side in one move during a game of combat, the corresponding nonlinear prediction model based on the first Gaussian kernel mapping is constructed as follows: in, Indicates the red team's first Bureau No. Remove the first step from the situational data The situational data following each feature Indicates the red team's first Bureau No. The first step in the situation data The first feature and elimination Prediction coefficients between features Indicates the red team's first Bureau No. The total number of features in the stance data. Indicates the first or second position of the red or blue team. Total number of steps in the game This indicates the total number of games played between the red and blue teams; When the missing information is a feature missing from the situational data of the blue side in one step of a game, the corresponding nonlinear prediction model based on the second Gaussian kernel mapping is constructed as follows: in, Indicates the blue team's first Bureau No. Remove the first step from the situational data The situational data following each feature Indicates the blue team's first Bureau No. The first step in the situation data The first feature and elimination Prediction coefficients between features Indicates the blue team's first Bureau No. The total number of features in the stance data. Indicates the first or second position of the red or blue team. Total number of steps in the game This indicates the total number of games played between the red and blue teams.
2. The nonlinear filling method for missing situational information in aerial game confrontation as described in claim 1, characterized in that: The process of solving the prediction coefficients in the nonlinear prediction model of the first Gaussian kernel mapping is as follows: Given the first regularization coefficient Solve for the prediction coefficient The objective function is as follows: By minimizing For prediction coefficients Solving for the problem, we get: （1） The dual form is : in, ,and , ,and , , , , , , , and All of these represent intermediate parameters. express OK The dimension of the column matrix, express The dimension of a vector with 1 row and 1 column. express The dimension of a vector with 1 row and 1 column. Indicates the red team's first The first step of all the games A collection of situational data with specific characteristics; Define matrix And matrix The Middle Line number Column elements are denoted as ,and ; in, Denotes the Gaussian kernel function, and , The hyperparameters representing the Gaussian kernel function are: Indicates the red team's first Remove the first step from the situational data The situational data following each feature Indicates the red team's first Remove the first step from the situational data The situational data following each feature express OK The dimension of the column matrix; Will Substitute into From: Will right After differentiating and setting the derivative to zero, we get: （2） Then, by substituting formula (2) into formula (1), we obtain the solution for the prediction coefficients in the nonlinear prediction model of the first Gaussian kernel mapping: The nonlinear prediction model for the first Gaussian kernel mapping is then obtained as follows: Among them, Record , Let be a column vector, and let the i-th column vector contain the i-th... The elements are denoted as ; The nonlinear prediction model of the first Gaussian kernel mapping in the above equation is then used to obtain the red side's... Bureau No. The first step in the situation data The missing information of each feature is then filled in.
3. The nonlinear filling method for missing situational information in aerial game confrontation as described in claim 1, characterized in that: The solution process for the prediction coefficients in the nonlinear prediction model of the second Gaussian kernel mapping is as follows: Given the second regularization coefficient Solve for the prediction coefficient The objective function is as follows: By minimizing For prediction coefficients Solving for the problem, we get: （3） The dual form is : in, ,and , , ,and , , , , , , , , and All of these represent intermediate parameters. express OK The dimension of the column matrix, express The dimension of a vector with 1 row and 1 column. express The dimension of a vector with 1 row and 1 column. Indicates the blue team's first The first step of all the games A collection of situational data with specific characteristics; Define matrix And matrix The Middle Line number Column elements are denoted as ,and ; in, Denotes the Gaussian kernel function, and , The hyperparameters representing the Gaussian kernel function are: Indicates the blue team's first Remove the first step from the situational data The situational data following each feature Indicates the blue team's first Remove the first step from the situational data The situational data following each feature express OK The dimension of the column matrix; Will Substitute into From: Will right After differentiating and setting the derivative to zero, we get: （4） Then, by substituting formula (4) into formula (3), the solution for the prediction coefficients in the nonlinear prediction model of the second Gaussian kernel mapping is obtained: The nonlinear prediction model for the second Gaussian kernel mapping is then obtained as follows: Among them, Record , Let be a column vector, and let the i-th column vector contain the i-th... The elements are denoted as ; The nonlinear prediction model of the second Gaussian kernel mapping in the above equation is then used to obtain the blue square's first... Bureau No. The first step in the situation data The missing information of each feature is then filled in.
4. The nonlinear filling method for missing situational information in aerial game confrontation as described in claim 1, characterized in that: When the missing information is of the type that is missing situational data for one move of the blue side in a game, the corresponding nonlinear prediction model based on the third Gaussian kernel mapping is constructed as follows: Among them, the blue team's number Bureau No. The situational data is missing, and , Indicates the blue team's first Bureau No. Step forward Step situation data, i.e. , This indicates that the blue team needs to predict the number of... Step-by-step situation data and previous The predictive coefficients between the step situation data, and , This indicates that the blue team needs to predict the number of... The first step in the situation data One feature and the previous Prediction coefficients between step situation data, Indicates the blue team's first Bureau No. The total number of features in the stance data. Indicates the first or second position of the red or blue team. Total number of steps in the game This represents the total number of games played between the red and blue teams. express OK The dimension of the column matrix.
5. The nonlinear filling method for missing situational information in aerial game confrontation as described in claim 4, characterized in that: The solution process for the prediction coefficients in the nonlinear prediction model of the third Gaussian kernel mapping is as follows: Given parameters The situational data of the blue team in each game is processed to extract the blue team's prediction data. The front of the situation data Step-by-step situational data, And the previous Step situation data is recorded as , means as follows: in, Indicates the previous step of extraction The first step in the situational data, and ; Meanwhile, the number to be predicted The situational data of the step is used as label data, denoted as ; For the The situational data of the blue team, the set of situational data for all missing steps, is represented as: The missing information at each step is represented by its corresponding preceding information. To predict, therefore for the first step Blue team situation data, all previous The set of steps is represented as ; for The set of situational data for all missing steps is represented as All the previous The set of steps is represented as ; Given a third regularization coefficient Solve for the prediction coefficients The objective function is as follows: in, Indicates that the blue team is in the The Bureau's First The first step in the situational data One feature; By minimizing For prediction coefficients Solving for the problem, we get: （5） The dual form is : in, ,and , ,and , , , , , , and All of these represent intermediate parameters. express OK The dimension of the column matrix, express OK The dimension of the column matrix, express The dimension of a vector with 1 row and 1 column; Define matrix And matrix The Middle Line 1 Column elements are denoted as ,and ; in, Denotes the Gaussian kernel function, and , The hyperparameters representing the Gaussian kernel function are: express The Middle One element, express The Middle One element, express OK The dimension of the column matrix; Will Substitute into From: Will right After differentiating and setting the derivative to zero, we get: （6） Then, by substituting formula (6) into formula (5), the prediction coefficients in the nonlinear prediction model of the third Gaussian kernel mapping are obtained. Solution: Then the nonlinear prediction model of the third Gaussian kernel mapping is obtained for the first... The missing number in the game Each feature in the step is predicted as follows: Among them, Record , Let be a column vector, and let the first column vector be the first column vector. The elements are denoted as ; The nonlinear prediction model of the third Gaussian kernel mapping is used to predict the blue square's first... Bureau No. Predict each feature in the situational data to obtain the blue team's first... Bureau No. Step-by-step situational data to fill in the missing information.