Missile end point reasoning method based on Gaussian process online learning
Through the online learning method based on Gaussian process, the conditional mean function and kernel function are generated and the missile endpoint is inferred, which solves the problem of pre-determining of motion models and insufficient Markovness in the prior art, and achieves higher endpoint inference accuracy and real-time situation intelligence provision.
Patent Information
- Application Number
- CN202510328879.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-19
- Publication Date
- 2025-05-06
AI Technical Summary
The existing missile end point inference method is based on the state space model, and requires the predetermined accurate motion model. The Markov nature is too simple to fully describe complex motion, resulting in limited improvement in accuracy.
The online learning method based on Gaussian process is used to generate the conditional mean function and conditional kernel function that characterizes the missile's motion pattern. By stacking the mean vector and nuclear matrix, the time when the missile reaches each possible end point is estimated, the likelihood value of the online measurement data is calculated, and the Bayesian criterion is used to infer the actual end point of the missile.
It improves the accuracy of missile end point reasoning, can calculate the real-time probability of missile reaching each possible end point, provides real-time battlefield situation intelligence, enhances surveillance and early warning capabilities, and assists in decision-making at the upper level.
Smart Images
Figure CN119939394A_ABST
Abstract
Description
Technical Field
[0001] The invention belongs to the technical field of missile intention reasoning, and in particular relates to a missile endpoint reasoning method based on Gaussian process online learning. Background Art
[0002] In the real world, many objects are driven by intention, such as guided missiles that strike high-value objects (radar stations, ships, or important military facilities, etc.). This kind of intention information contains the future movement trend of the missile, so making full use of this information in algorithm design will certainly be of great benefit to improving tracking performance. However, except for some non-confrontational behaviors, in most scenarios, the prior knowledge about intention information is always incomplete. For example, when tracking a missile cluster that strikes multiple locations of our side in a coordinated manner, we only know that each missile has reached one of several possible destinations at a known location.
[0003] By implementing real-time missile endpoint reasoning through algorithms, it is possible to shift from conventional independent movement between missiles (missiles move independently without competition, premeditation, and clustering) to an integrated perspective that can self-learn both endpoint guidance and cluster interaction. In addition, it can provide situational intelligence information, enhance monitoring and early warning capabilities, and thus assist upper-level decision-making.
[0004] Existing endpoint inference methods are all based on the state space model framework. They all require a precise motion model to be determined in advance, and their Markov properties are too simple to fully describe complex motions, which makes the existing endpoint inference methods less intuitive and limits their accuracy. Therefore, it is necessary to study an intuitive, efficient and robust missile endpoint inference method based on a new paradigm. Summary of the invention
[0005] The technical problem to be solved by the present invention is to provide a missile endpoint inference method based on Gaussian process online learning in view of the deficiencies in the above-mentioned prior art, which can pre-identify the actual endpoint of the missile with higher accuracy than traditional methods, and can also calculate the real-time probability of the missile reaching each possible endpoint, which can provide real-time battlefield situation intelligence for the upper-level command hub, thereby gaining the initiative on the battlefield.
[0006] In order to solve the above technical problems, the technical solution adopted by the present invention is: a missile endpoint inference method based on Gaussian process online learning, the method comprising the following steps:
[0007] Step 1: Based on the possible destination and unknown arrival time of the missile, generate the conditional mean function and conditional kernel function that characterize the missile motion pattern;
[0008] Step 2: Stack the mean vectors and kernel matrices on all dimensions;
[0009] Step 3: Estimate the time it takes for the missile to reach each possible destination;
[0010] Step 4: Calculate the likelihood value of the online measurement data;
[0011] Step 5: Based on the prior probability of each possible endpoint, use the Bayesian criterion to infer the actual endpoint of the missile.
[0012] In the above-mentioned missile endpoint inference method based on Gaussian process online learning, the specific process of generating the conditional mean function and conditional kernel function characterizing the missile motion mode based on the possible endpoint and unknown arrival time of the missile in step 1 is as follows:
[0013] Step 101: In each Cartesian space coordinate dimension j, the position relationship of the missile at any time is regarded as an infinite-dimensional Gaussian distribution, whose properties are determined by the original mean function in the Gaussian process and the original kernel function κ (j) (t,t′) is defined as:
[0014]
[0015] Where t and t′ are two arbitrary moments; superscript · (j) Represents the quantity related to the specific dimension j; f (j) (t) represents the position of the missile at time t; represents a Gaussian process; represents the original mean function set a priori; κ (j) (t, t′) represents the original kernel function set a priori;
[0016] Step 102: According to each possible end point of the missile k=1,...,m, and the time it takes for the unknown missile to reach this destination There are endpoint constraints that are closely related to the missile's motion pattern Introducing it into the original mean function in the Gaussian process and the original kernel function κ (j) (t, t′), generate the conditional mean function that characterizes the missile motion pattern and conditional kernel function for:
[0017]
[0018]
[0019] in, -1 Indicates inversion; subscript · k and Representation and possible endpoint the quantity concerned;
[0020] At this time, the missile's position at time t is f (j) (t) There are new expressions:
[0021]
[0022] Step 103: According to the statistical rules of a large category of scenarios, pre-set the possible endpoints. The relevant set of hyperparameters The value of represents the conditional mean function The set of hyperparameters in , Represents the conditional kernel function The set of hyperparameters in .
[0023] In the above-mentioned missile endpoint inference method based on Gaussian process online learning, the specific process of stacking the mean vectors and kernel matrices on all dimensions in step 2 is:
[0024] Step 201: Combine all Cartesian space coordinate dimensions and for each possible end point of the missile According to the measurement model z (j) =f (j) (t)+v, Until the current time t n The accumulated online measurement data are
[0025] in, represents the measurement received by the sensor at time t, represents a real number; v represents a zero mean and a variance equal to Independent and identically distributed Gaussian noise; n represents the number of measurements; T represents transpose;
[0026] Step 202: stack the mean vectors and kernel matrices on all dimensions:
[0027]
[0028] in, Represents the mean vector of all dimensions; K tt,k represents the kernel matrix integrating all dimensions; t={t i} i＝1,...,n Indicates the time series corresponding to the online measurement data; represents the mean vector related to the time series corresponding to the online measurement data on dimension j, It indicates the quantity to the right of the vertical line that is substituted in the calculation process; represents the kernel matrix related to the time series corresponding to the online measurement data on dimension j, Indicates the quantity to be substituted into the right side of the vertical line during calculation; subscript · k , and· ·,k Indicates possible endpoint d k Related quantities; blkdiag[] represents the block diagonal.
[0029] In the above-mentioned missile endpoint inference method based on Gaussian process online learning, the specific process of estimating the time when the missile reaches each possible endpoint in step 3 is:
[0030] Step 301: for each possible end point d k , according to the standard form of multivariate Gaussian distribution, the log-likelihood function of online measurement data is:
[0031]
[0032] Wherein, log represents the natural logarithm; Represents a set of hyperparameters that integrate all dimensions; D t Refers to the actual destination of the missile, that is, as a logical identifier in the algorithm, D t =d k Indicates that the actual destination of the missile is considered to be a specific possible destination d k ;|·| represents the determinant; I 2n represents the identity matrix with dimension equal to 2n; π represents pi; σ v represents the standard deviation of the measurement noise, represents the variance of the measurement noise;
[0033] Step 302: The missile reaches the possible end point d k Time Considered as a hyperparameter, the maximum likelihood estimation method is used to maximize the above log-likelihood function to obtain the possible destination d of the missile. k Time Estimated value of And the parameters The value of is updated.
[0034] The above-mentioned missile endpoint inference method based on Gaussian process online learning uses a gradient-based optimization algorithm to perform maximum likelihood estimation and analytically finds the log-likelihood function with respect to The partial derivative of :
[0035]
[0036] Among them, tr(·) means finding the trace;
[0037] In the above-mentioned missile endpoint inference method based on Gaussian process online learning, the specific method for calculating the likelihood value of the online measurement data in step 4 is: comprehensively consider all Cartesian space coordinate dimensions, and for each possible endpoint d k , the likelihood of the online measurement data is given by the standard form of the multivariate Gaussian distribution inherent in the Gaussian process:
[0038]
[0039] Among them, p() represents the probability value; represents the probability value of the multivariate Gaussian distribution of a1 with a2 as the mean vector and a3 as the covariance matrix.
[0040] In the above-mentioned missile endpoint inference method based on Gaussian process online learning, the likelihood value of the online measurement data in step 4 is transformed from the logarithmic likelihood value of the estimated time for the missile to reach a certain possible endpoint. For each possible endpoint d k ,have:
[0041]
[0042] In the above-mentioned missile endpoint inference method based on Gaussian process online learning, the specific process of inferring the actual endpoint of the missile based on the prior probability of each possible endpoint and the Bayesian criterion in step 5 is as follows:
[0043] Step 501: Combine all Cartesian space coordinate dimensions and for each possible end point d k , since they all have the time when the missile reaches this destination Based on the Bayesian criterion, there is a joint posterior probability:
[0044]
[0045] Among them, Σ is the accumulation symbol; p(D t =d k ) indicates that the missile reaches each possible destination d k The prior probability of can be specified based on prior information such as experience or intelligence, or set to an equal probability p(D t =d k )=1 / m; For each possible endpoint d k The joint likelihood under ;
[0046] Step 502: Further converted to:
[0047]
[0048] in, Represents the likelihood value of online measurement data; It means that the actual destination of the missile is assumed to be the possible destination d k The time it takes for the missile to reach this destination is the probability of the estimated value of ;
[0049] Step 503: Get a new expression for the joint posterior probability:
[0050]
[0051] Step 504: Use the maximum a posteriori criterion to select a possible endpoint set {d1,…,d m The endpoint that maximizes the joint posterior probability is taken as the missile endpoint inference result:
[0052]
[0053] in, represents the inference result of the actual end point of the missile; p(t N ,D t =d|z) represents the joint posterior probability distribution, which is A set of k=1,...,m; argmax(a4) means finding the candidate quantity that makes a4 reach the maximum value.
[0054] The above-mentioned missile endpoint inference method based on Gaussian process online learning, between step 503 and step 504, also includes giving the missile's arrival at each possible endpoint d according to the new expression of the joint posterior probability k The real-time probability steps.
[0055] Compared with the prior art, the present invention has the following advantages:
[0056] 1. Compared with the classical algorithm, the present invention has a higher endpoint reasoning accuracy and can calculate the real-time probability of the missile reaching each possible endpoint.
[0057] 2. The present invention can identify the end point of the missile more accurately, making up for the reduced motion modeling level and state estimation accuracy due to incomplete intention information.
[0058] 3. The present invention can provide situation intelligence information, enhance monitoring and early warning capabilities, and thus assist upper-level decision-making.
[0059] 4. The present invention is a perfect algorithm that comprehensively considers the nearest neighbor principle, azimuth direction and the actual movement mode of the missile (implicit in the measurement data), which can provide real-time battlefield situation intelligence to the upper command hub, thereby gaining the initiative on the battlefield.
[0060] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS
[0061] Figure 1 It is a flowchart of the method of the present invention;
[0062] Figure 2 A schematic diagram of a strike scenario of a coordinated combat missile group according to an embodiment of the present invention;
[0063] Figure 3 The real-time endpoint reasoning results of each missile in a Monte Carlo experiment of an embodiment of the present invention;
[0064] Figure 4 A real-time endpoint inference probability graph of missile 3 in a Monte Carlo experiment according to an embodiment of the present invention;
[0065] Figure 5 This is a comparison chart of the missile endpoint inference accuracy of the embodiment of the present invention and the classic algorithm. DETAILED DESCRIPTION
[0066] In multidimensional Cartesian space, there are multiple possible endpoints of missile motion with known position information, expressed as:
[0067] f(t N ) = d t ,d t ∈{d1,...,d m}
[0068] in, represents the actual / possible end point of the missile, d (j) represents the actual / possible end point of the missile in dimension j, with the superscript · (j) represents the quantity related to the specific dimension j, Indicates the number of dimensions; {d1,...,d m} represents the set of possible endpoints with known location information, and m represents the number of possible endpoints; d t Indicates the actual end point of the missile; t N Indicates the time when the missile reaches the destination; represents the unknown function related to the missile motion integrating all dimensions;
[0069] At this point, we only know the possible destinations of the missiles {d1,...,d m}, but the actual destination of the unknown missile is d t This also means that the time t when the unknown missile reaches the actual destination N .
[0070] like Figure 1As shown, the missile endpoint inference method based on Gaussian process online learning included in the present invention includes the following steps:
[0071] Step 1: Based on the possible destination and unknown arrival time of the missile, generate the conditional mean function and conditional kernel function that characterize the missile motion pattern;
[0072] In this embodiment, the specific process of generating the conditional mean function and conditional kernel function characterizing the missile motion pattern based on the possible destination and unknown arrival time of the missile in step 1 is:
[0073] Step 101: In each Cartesian space coordinate dimension j, the position relationship of the missile at any time is regarded as an infinite-dimensional Gaussian distribution, whose properties are determined by the original mean function in the Gaussian process and the original kernel function κ (j) (t,t′) is defined as:
[0074]
[0075] Where t and t′ are two arbitrary moments; superscript · (j) Represents the quantity related to the specific dimension j; f (j) (t) represents the position of the missile at time t; represents a Gaussian process; represents the original mean function set a priori; κ (j) (t, t′) represents the original kernel function set a priori;
[0076] In this embodiment, Characterizes the position of the missile at any time t; f (j) (t′) represents the position of the missile at time t′, represents the original mean function set a priori; E[·] represents the mean;
[0077] Step 102: According to each possible end point of the missile k=1,…,m, and the unknown time for the missile to reach this destination There are endpoint constraints that are closely related to the missile's motion pattern Introducing it into the original mean function in the Gaussian process and the original kernel function κ (j) (t, t′), generate the conditional mean function that characterizes the missile motion pattern and conditional kernel function for:
[0078]
[0079] in, -1Indicates inversion; subscript · k and Representation and possible endpoint the quantity concerned;
[0080] is the cross-covariance of the function values corresponding to the test input and training input time, is the prior variance of the test input function value, The missile arrival time is set to The original mean function at the location and is the original kernel function that is set to characterize the missile position;
[0081] At this time, the missile's position at time t is f (j) (t) There are new expressions:
[0082]
[0083] Step 103: According to the statistical rules of a large category of scenarios, pre-set the possible endpoints. The relevant set of hyperparameters The value of represents the conditional mean function The set of hyperparameters in , Represents the conditional kernel function The set of hyperparameters in .
[0084] Step 2: Stack the mean vectors and kernel matrices on all dimensions;
[0085] In this embodiment, the specific process of stacking the mean vectors and kernel matrices on all dimensions in step 2 is:
[0086] Step 201: Combine all Cartesian space coordinate dimensions and for each possible end point of the missile According to the measurement model z (j) =f (j) (t)+v, Until the current time t n The accumulated online measurement data are
[0087] in, represents the measurement received by the sensor at time t, represents a real number; v represents a zero mean and a variance equal to Independent and identically distributed Gaussian noise; n represents the number of measurements; T represents transpose; f (j) (t) represents the predicted output;
[0088] Step 202: In order to jointly infer the actual end point of the missile between different dimensions, it is necessary to stack the mean vectors and kernel matrices on all dimensions:
[0089]
[0090] in, Represents the mean vector of all dimensions; K tt,k represents the kernel matrix integrating all dimensions; t={t i} i＝1,n. Indicates the time series corresponding to the online measurement data; represents the mean vector related to the time series corresponding to the online measurement data on dimension j, It indicates the quantity to the right of the vertical line that is substituted in the calculation process; represents the kernel matrix related to the time series corresponding to the online measurement data on dimension j, Indicates the quantity to be substituted into the right side of the vertical line during calculation; subscript · k , and· ·，k Indicates possible endpoint d k Related quantities; blkdiag[] represents the block diagonal.
[0091] Step 3: Estimate the time it takes for the missile to reach each possible destination;
[0092] In this embodiment, the specific process of estimating the time when the missile reaches each possible destination in step 3 is as follows:
[0093] Step 301: In order to calculate the likelihood value of the online measurement data by integrating all Cartesian space coordinate dimensions, it is necessary to first estimate the probability that the missile will reach each possible destination d k time; for each possible endpoint d k , according to the standard form of multivariate Gaussian distribution, the log-likelihood function of online measurement data is:
[0094]
[0095] Wherein, log represents the natural logarithm; Represents a set of hyperparameters that integrate all dimensions; D t Refers to the actual destination of the missile, that is, as a logical identifier in the algorithm, D t =d k Indicates that the actual destination of the missile is considered to be a specific possible destination d k ;|·| represents the determinant; I 2n represents the identity matrix with dimension equal to 2n; π represents the ratio of pi; n is the number of training inputs; σ v represents the standard deviation of the measurement noise, represents the variance of the measurement noise;
[0096] Step 302: The missile reaches the possible end point d k Time Considered as a hyperparameter, the maximum likelihood estimation method is used to maximize the above log-likelihood function to obtain the possible destination d of the missile. k Time Estimated value of And the parameters The value of is updated.
[0097] In this embodiment, a gradient-based optimization algorithm is used to perform maximum likelihood estimation, and the log-likelihood function is analytically obtained with respect to The partial derivative of :
[0098]
[0099] Among them, tr(·) means finding the trace;
[0100] Step 4: Calculate the likelihood value of the online measurement data;
[0101] In this embodiment, the specific method for calculating the likelihood value of the online measurement data in step 4 is: comprehensively consider all Cartesian space coordinate dimensions, and for each possible end point d k , the likelihood of the online measurement data is given by the standard form of the multivariate Gaussian distribution inherent in the Gaussian process:
[0102]
[0103] Among them, p() represents the probability value; represents the probability value of the multivariate Gaussian distribution of a1 with a2 as the mean vector and a3 as the covariance matrix.
[0104] In this embodiment, the likelihood value of the online measurement data in step 4 is transformed from the logarithmic likelihood value of the estimated time for the missile to reach a certain possible end point. For each possible end point d k ,have:
[0105]
[0106] Step 5: Based on the prior probability of each possible endpoint, use the Bayesian criterion to infer the actual endpoint of the missile.
[0107] In this embodiment, the specific process of inferring the actual destination of the missile based on the prior probability of each possible destination and using the Bayesian criterion in step 5 is as follows:
[0108] Step 501: Combine all Cartesian space coordinate dimensions and for each possible end point dk , since they all have the time when the missile reaches this destination Based on the Bayesian criterion, there is a joint posterior probability:
[0109]
[0110] Among them, Σ is the accumulation symbol; p(D t =d k ) indicates that the missile reaches each possible destination d k The prior probability of can be specified based on prior information such as experience or intelligence, or set to an equal probability p(D t =d k )=1 / m; For each possible endpoint d k The joint likelihood under ;
[0111] Step 502: Further converted to:
[0112]
[0113] in, Represents the likelihood value of online measurement data; It means that the actual destination of the missile is assumed to be the possible destination d k The time it takes for the missile to reach this destination is The probability of an estimated value of Obey the uniform distribution in the value space;
[0114] Step 503: Get a new expression for the joint posterior probability:
[0115]
[0116] Step 504: Use the maximum a posteriori criterion to select a possible endpoint set {d1,…,d m The endpoint that maximizes the joint posterior probability is taken as the missile endpoint inference result:
[0117]
[0118] in, represents the inference result of the actual end point of the missile; p(t N ,D t =d|z) represents the joint posterior probability distribution, which is A set of k=1,…,m; argmax(a4) means finding the candidate quantity that makes a4 reach the maximum value.
[0119] In this embodiment, between step 503 and step 504, the method further includes providing the probability that the missile reaches each possible destination d according to the new expression of the joint posterior probability. k The real-time probability steps.
[0120] In this embodiment, Figure 2 As shown in the figure, it is assumed that six missiles guided by proportional guidance cooperate to attack three fixed points. These three fixed points are the possible end points of each missile, and their position coordinates are shown in Table 1. In addition, the parameters of each missile are shown in Table 2. In this scenario, the missiles fight in coordination, so it is impossible to predict the actual end point of each missile, but only know that it will reach one of the three end points.
[0121] Table 1 Location coordinates of all possible endpoints
[0122]
[0123] Table 2 Missile group parameter settings
[0124]
[0125] In the case of unknown missile guidance mode, guidance parameters, actual arrival time and actual destination, based on the missile measurement received by the sensor, the missile destination inference method based on Gaussian process online learning of the present invention is used to perform real-time destination inference of each missile. The destination inference result under a Monte Carlo experiment is as follows: Figure 3 As shown. From the simulation results, it can be seen that:
[0126] 1) Based on the same setting, the present invention can accurately identify the actual end point of the missile a certain time in advance when facing missiles with different movement modes and different end points, which verifies the effectiveness of the present invention.
[0127] 2) As the missile approaches its actual destination, the uncertainty of the missile’s intention becomes smaller and smaller. Therefore, the inference results of the missile’s destination from the intermediate moment in this scenario are very accurate and can be robustly maintained.
[0128] The endpoint inference result of the present invention has probabilistic significance. In addition to being able to give single-point inference based on the maximum a posteriori criterion, it can also give the real-time a posteriori probability of the missile reaching each possible endpoint. For example, Figure 3 The real-time endpoint inference probability diagram of missile 3 is shown in Figure 4As shown. It can be concluded that as time goes by, the uncertainty of the missile's movement intention gradually decreases, so the posterior probability value of the actual end point gradually increases. In particular, at 3 / 5 of the total time window, the present invention believes that the posterior probability of the actual end point is >84%, and when it reaches 4 / 5 of the total time window, this posterior probability is increased to >97%. This confirms that the results in the probability sense given by the present invention are intuitive and correct.
[0129] Comparison of missile endpoint inference accuracy between the present invention and the classical algorithm Figure 5 It can be concluded that the present invention does not require any prior information about known missiles and still has the highest accuracy.
[0130] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any way. Any simple modification, change and equivalent structural change made to the above embodiment based on the technical essence of the present invention still falls within the protection scope of the technical solution of the present invention.
Claims
1. A missile endpoint inference method based on Gaussian process online learning, characterized in that: The method comprises the following steps: Step 1: Based on the possible destination and unknown arrival time of the missile, generate the conditional mean function and conditional kernel function that characterize the missile motion pattern; Step 2: Stack the mean vectors and kernel matrices on all dimensions; Step 3: Estimate the time it takes for the missile to reach each possible destination; Step 4: Calculate the likelihood value of the online measurement data; Step 5: Based on the prior probability of each possible endpoint, use the Bayesian criterion to infer the actual endpoint of the missile.
2. A missile endpoint inference method based on Gaussian process online learning according to claim 1, characterized in that: The specific process of generating the conditional mean function and conditional kernel function that characterize the missile motion pattern based on the possible destination and unknown arrival time of the missile in step 1 is: Step 101: In each Cartesian space coordinate dimension j, the position relationship of the missile at any time is regarded as an infinite-dimensional Gaussian distribution, whose properties are determined by the original mean function in the Gaussian process and the original kernel function κ (j) (t,t′) is defined as: Where t and t′ are two arbitrary moments; superscript · (j) Represents the quantity related to the specific dimension j; f (j) (t) represents the position of the missile at time t; represents a Gaussian process; represents the original mean function set a priori; κ (j) (t, t′) represents the original kernel function set a priori; Step 102: According to each possible end point of the missile and the time when the unknown missile will arrive at this destination There are endpoint constraints that are closely related to the missile's motion pattern Introducing it into the original mean function in the Gaussian process and the original kernel function κ (j) (t, t′), generate the conditional mean function that characterizes the missile motion pattern and conditional kernel function for: Among them, -1 means inversion; subscript · k and Indicates possible endpoints the quantity concerned; At this time, the missile's position at time t is f (j) (t) There are new expressions: Step 103: According to the statistical rules of a large category of scenarios, pre-set the possible endpoints. The relevant set of hyperparameters The value of represents the conditional mean function The set of hyperparameters in , Represents the conditional kernel function The set of hyperparameters in .
3. A missile endpoint inference method based on Gaussian process online learning according to claim 1, characterized in that: The specific process of stacking the mean vectors and kernel matrices on all dimensions described in step 2 is: Step 201: Combine all Cartesian space coordinate dimensions and for each possible end point of the missile According to the measurement model z (j) =f (j) (t)+v, Until the current time t n The accumulated online measurement data are in, represents the measurement received by the sensor at time t, represents a real number; v represents a zero mean and a variance equal to of independent and identically distributed Gaussian noise; n represents the number of measurements; T represents transposition; Step 202: stack the mean vectors and kernel matrices on all dimensions: in, Represents the mean vector of all dimensions; K tt,k represents the kernel matrix integrating all dimensions; t={t i } i＝1,...,n Indicates the time series corresponding to the online measurement data; represents the mean vector related to the time series corresponding to the online measurement data on dimension j, It indicates the quantity to the right of the vertical line that is substituted in the calculation process; represents the kernel matrix related to the time series corresponding to the online measurement data on dimension j, Indicates the quantity to be substituted into the right side of the vertical line during calculation; subscript · k , and Indicates possible endpoint d k Related quantities: blkdiag[·] represents the block diagonal.
4. A missile endpoint inference method based on Gaussian process online learning according to claim 1, characterized in that: The specific process of estimating the time when the missile reaches each possible destination described in step 3 is: Step 301: for each possible end point d k , according to the standard form of multivariate Gaussian distribution, the log-likelihood function of online measurement data is: Wherein, log represents the natural logarithm; Represents a set of hyperparameters that integrate all dimensions; D t Refers to the actual destination of the missile, that is, as a logical identifier in the algorithm, D t =d k Indicates that the actual destination of the missile is considered to be a specific possible destination d k ;|·| represents the determinant; I 2n represents the identity matrix with dimension equal to 2n; π represents pi; σ v represents the standard deviation of the measurement noise, represents the variance of the measurement noise; Step 302: The missile reaches the possible end point d k Time Considered as a hyperparameter, the maximum likelihood estimation method is used to maximize the above log-likelihood function to obtain the possible destination d of the missile. k Time Estimated value of And the parameters The value of is updated.
5. A missile endpoint inference method based on Gaussian process online learning according to claim 4, characterized in that: A gradient-based optimization algorithm is used to perform maximum likelihood estimation, and the log-likelihood function is analytically obtained with respect to The partial derivative of : Among them, tr(·) means finding the trace; 6. A missile endpoint inference method based on Gaussian process online learning according to claim 1, characterized in that: The specific method for calculating the likelihood value of the online measurement data in step 4 is: integrating all Cartesian space coordinate dimensions, for each possible end point d k , the likelihood of the online measurement data is given by the standard form of the multivariate Gaussian distribution inherent in the Gaussian process: Among them, p() represents the probability value; represents the probability value of the multivariate Gaussian distribution of a1 with a2 as the mean vector and a3 as the covariance matrix.
7. A missile endpoint inference method based on Gaussian process online learning according to claim 1, characterized in that: The likelihood value of the online measurement data in step 4 is transformed from the logarithmic likelihood value of the estimated time for the missile to reach a certain possible destination. For each possible destination d k ,have:
8. A missile endpoint inference method based on Gaussian process online learning according to claim 1, characterized in that: The specific process of inferring the actual destination of the missile based on the prior probability of each possible destination and using the Bayesian criterion in step 5 is as follows: Step 501: Combine all Cartesian space coordinate dimensions and for each possible end point d k , since they all have the time when the missile reaches this destination Based on the Bayesian criterion, there is a joint posterior probability: Among them, Σ is the accumulation symbol; p(D t =d k ) indicates that the missile reaches each possible destination d k The prior probability of can be specified based on prior information such as experience or intelligence, or set to an equal probability p(D t =d k )=1 / m; For each possible endpoint d k The joint likelihood under ; Step 502: Further converted to: in, Represents the likelihood value of online measurement data; It means that the actual destination of the missile is assumed to be the possible destination d k The time it takes for the missile to reach this destination is the probability of the estimated value of ; Step 503: Get a new expression for the joint posterior probability: Step 504: Use the maximum a posteriori criterion to select a possible endpoint set {d1, ..., d m The endpoint that maximizes the joint posterior probability is taken as the missile endpoint inference result: in, represents the inference result of the actual end point of the missile; p(t N ,D t =d|z) represents the joint posterior probability distribution, which is A set of k=1,...,m; argmax(a4) means finding the candidate quantity that makes a4 reach the maximum value.
9. A missile endpoint inference method based on Gaussian process online learning according to claim 1, characterized in that: Between step 503 and step 504, the method also includes giving the probability of the missile reaching each possible destination d according to the new expression of the joint posterior probability. k The real-time probability steps.