Guided missile arrival time estimation method based on Gaussian process online learning
Through the online learning method based on Gaussian process, combined with the constraints of the missile end point position, the problem of estimating the arrival time of the enemy's non-cooperative missile is solved, and the effect of accurately estimating the arrival time of the missile without control information is achieved.
Patent Information
- Application Number
- CN202510251395.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-03-04
- Publication Date
- 2025-06-10
AI Technical Summary
It is difficult to accurately estimate the arrival time of enemy non-cooperative missiles, especially in the absence of unknown control information.
The online learning method based on the Gaussian process is adopted to estimate the missile arrival time by introducing the constraints of the missile end point position. This method does not require known missile control information, and relies on dual drives of data and knowledge.
It can accurately estimate the actual arrival time of the missile at a certain time in advance, improve the accuracy of estimating the missile's motion state, provide battlefield situation intelligence, and assist upper-level decision-making.
Smart Images
Figure CN120124477A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of missile intention reasoning, and particularly relates to a method for estimating the time of arrival of a missile based on online learning of Gaussian processes. Background Art
[0002] Purpose-driven behaviors and end-point oriented movements widely exist in human activities and physical phenomena. For example, anti-radiation missiles or anti-ship missiles advance towards a predetermined impact point in the terminal guidance section. The end points of these specific behaviors contain the movement intentions of the targets, and this intention information can be used as predictive information for the target movement states, indicating that as time goes by, the uncertainty of the target movement states gradually decreases. In adversarial scenarios, for example, when tracking a missile cluster that saturates and strikes our important facilities, it is simply impossible to know in advance the actual time of arrival of each missile. At this time, by combining the received measurement data and the existing prior knowledge of the end-point positions, real-time estimation of the potential time of arrival of the missiles can not only help achieve more accurate estimation of the missile movement states, but also assist in making precise predictions in advance about the future movement patterns of the missiles. This paradigm aims to achieve a higher-level understanding of the missile movement patterns, assist in higher-level automated decision-making, and can play roles such as situation awareness, conflict avoidance, opportunity discovery, or resource allocation optimization.
[0003] Regarding the problem of estimating the time of arrival of a missile, there has been a lot of research in a field called remaining time of arrival / flight time estimation. However, the methods for estimating the time of arrival of missiles studied in this field are applied to our cooperative missiles when the control information of the missiles, such as the guidance law, orientation angle, and yaw angle, is accurately known. For non-cooperative missiles of the enemy, it is impossible to obtain the aforementioned control information more accurately or at all, resulting in the inapplicability of this type of missile time of arrival estimation method. Therefore, it is necessary to break through the traditional thinking and study a method for estimating the time of arrival of a missile without known control information. Summary of the Invention
[0004] The technical problem to be solved by the present invention is to provide a method for estimating the time of arrival of a missile based on online learning of Gaussian processes in view of the deficiencies in the above-mentioned prior art. It is driven by both data and knowledge, does not require known control information of the missile, and can still accurately estimate the actual time of arrival of the missile in advance by a certain amount of time, thereby providing the command department with the situation intelligence information of the battlefield and assisting in upper-level decision-making.
[0005] To solve the above technical problem, the technical solution adopted by the present invention is: A method for estimating the time of arrival of a missile based on online learning of Gaussian processes, the method comprising the following steps:
[0006] Step 1, set the original mean function and the original kernel function for representing the missile position;
[0007] Step 2: Set the terminal constraint according to the known missile terminal position and the unknown missile arrival time, and introduce the terminal constraint into the original mean function and the original kernel function to generate a conditional mean function and a conditional kernel function representing the motion with terminal constraint;
[0008] Step 3: Use the parameter estimation method to estimate the estimated values of the hyperparameters in the conditional mean function and the conditional kernel function;
[0009] Step 4: Stack the mean vectors and kernel matrices in each spatial dimension;
[0010] Step 5: Regard the missile arrival time as a hyperparameter in the Gaussian process, and use the parameter estimation method to estimate the estimated value of the missile arrival time embedded in the mean vector and the kernel matrix.
[0011] For the above missile arrival time estimation method based on Gaussian process online learning, the specific process of setting the original mean function and the original kernel function representing the missile position in Step 1 is as follows:
[0012] Step 101: In each spatial dimension
[0013] regard the position of the missile between any two moments as an infinite-dimensional Gaussian distribution, and its properties are completely determined by the original mean function and the original kernel function, expressed as:
[0014]
[0015] where is the number of spatial dimensions, t and t′ are any two moments; f(t) is the position of the missile at any moment t; represents the Gaussian process; is the original mean function set to represent the position of the missile at any moment t and E[·] represents the mean; κ(t, t′) is the original kernel function set to represent the missile position and f(t′) is the position of the missile at any moment t′; is the original mean function set to represent the position of the missile at any moment t′ and
[0016] For the above missile arrival time estimation method based on Gaussian process online learning, when setting the terminal constraint according to the known missile terminal position and the unknown missile arrival time in Step 2, represent the terminal constraint as f(t N ) = d, where d is the known missile terminal position, and t N is the unknown missile arrival time;
[0017] When introducing the end - point constraint into the original mean function and the original kernel function in Step 2 to generate the conditional mean function and the conditional kernel function characterizing the end - point - constrained motion, the conditional mean function is expressed as:
[0018]
[0019] where κ(t,t N ) is the cross - covariance of the function values corresponding to the test input and the training input times, κ -1 (t N ,t N ) represents the inverse of κ(t N ,t N ), κ(t N ,t N ) is the prior variance of the test - input function value, is the set original mean function characterizing the position of the missile at the missile arrival time t N and
[0020] The conditional kernel function κ N (t,t′) is expressed as:
[0021] κ N (t,t′)=κ(t,t′)-κ(t,t N )κ -1 (t N ,t N )κ(t N ,t′)
[0022] where κ(t N ,t′) is the set original kernel function characterizing the position of the missile;
[0023] The position f(t) of the missile at any time t is determined by the conditional mean function and the conditional kernel function and is expressed as:
[0024]
[0025] In the above - mentioned missile arrival - time estimation method based on Gaussian - process online learning, the original mean function in Step 1 is a compliant prior function, including the zero - mean function which is expressed as:
[0026]
[0027] The original kernel function κ(t,t′) in Step 1 is a compliant prior function, including the SE kernel function κ SE (t,t′), which is expressed as:
[0028]
[0029] Among them, σ is the amplitude hyperparameter, l is the characteristic length scale hyperparameter, and exp(·) is the exponential function with the natural constant e as the base.
[0030] In the above missile time-of-arrival estimation method based on Gaussian process online learning, the conditional mean function described in step 2 includes a conditional zero-mean function based on the zero-mean function which is expressed as: It is expressed as:
[0031]
[0032] In the above missile time-of-arrival estimation method based on Gaussian process online learning, the conditional kernel function described in step 2 includes a conditional SE kernel function κ SE (t, t′) which is expressed as: N_SE (t, t′) and is expressed as:
[0033]
[0034] In the above missile time-of-arrival estimation method based on Gaussian process online learning, when using the parameter estimation method to estimate the estimated values of the hyperparameters in the conditional mean function and the conditional kernel function, the parameter estimation method used is the maximum likelihood estimation method; the specific process of using the maximum likelihood estimation method to estimate the estimated values of the hyperparameters in the conditional mean function and the conditional kernel function is as follows:
[0035] Step 301: In each spatial dimension up to the current time t n , a total of n measurements are received according to the measurement model z k = f(t k ) + v k . Then there is a training data set D = {(t k , z k )}, a time series set t = {t k＝1,...,n}, and a measurement set z = {z k}; where t k＝1,...n, is an arbitrary sampling time not later than the current time t k , f(t k＝1,...,n ) is the predicted output, v k is Gaussian white noise with zero mean and variance equal to n ; z k is the measurement received at time t k and z k ∈ R, where R represents the set of real numbers. k and z k ∈ R, where R represents the set of real numbers. κ ∈ R, where R represents the set of real numbers.
[0036] Step 302: Give the log-likelihood function of the training data in the Gaussian process according to the standard form of the multivariate Gaussian distribution:
[0037]
[0038] where log is the logarithm with the natural constant e as the base, is the likelihood, is the set of hyperparameters, is the set of hyperparameters in the conditional mean function, Θ κ is the set of hyperparameters in the conditional kernel function; T represents the transpose; represents the mean vector of the training data and K tt is the kernel matrix of the training data and I n is the n-dimensional identity matrix; |·| represents the determinant of the matrix; π is the circumference ratio; n is the number of measurements;
[0039] Step 303: Use a gradient-based optimization algorithm to maximize the log-likelihood function given in Step 302 to obtain an estimated value of the hyperparameter set Θ, and then update Θ for subsequent steps and for hyperparameter estimation at the next sampling moment; when obtaining the maximum likelihood estimate of the hyperparameters in the conditional mean function, find the partial derivative of the log-likelihood function with respect to :
[0040]
[0041] where, represents the partial derivative;
[0042] When obtaining the maximum likelihood estimate of the hyperparameters Θ κ in the conditional kernel function, find the partial derivative of the log-likelihood function with respect to Θ κ :
[0043]
[0044] where, tr(·) is the trace of the matrix.
[0045] For the above missile time-of-arrival estimation method based on Gaussian process online learning, when finding the partial derivative of the log-likelihood function with respect to in Step 303, the conditional mean function uses the conditional zero-mean function based on the zero-mean function The conditional kernel function uses the conditional SE kernel function κ SE (t, t′) based on the SE kernel function κ N_SE (t, t′), and the hyperparameter set is The general calculation formula for each item in
[0046]
[0047] The general calculation formula for each item in
[0048]
[0049] For the above missile time - of - arrival estimation method based on Gaussian process online learning, the specific method of stacking the mean vectors and kernel matrices in each spatial dimension in step four is as follows:
[0050] Integrating each spatial dimension, the missile's end - point position is expressed as Until the current time t n The cumulative measurement set is To jointly estimate the missile time - of - arrival between different spatial dimensions, stack the mean vectors and kernel matrices in each spatial dimension:
[0051]
[0052] where blkdiag[·] is the block - diagonal; the superscript · (·) is a specific dimension; is the number of spatial dimensions.
[0053] For the above missile time - of - arrival estimation method based on Gaussian process online learning, the specific process of regarding the missile time - of - arrival as a hyper - parameter in Gaussian process and estimating the estimated value of the missile time - of - arrival embedded in the mean vector and kernel matrix using the parameter estimation method in step five is as follows:
[0054] Step 501: Integrating each spatial dimension, the log - likelihood function of the training data in Gaussian process is given according to the standard form of the multivariate Gaussian distribution:
[0055]
[0056] where log is the natural logarithm with base e, is the likelihood, is the set of hyper - parameters, is the set of hyper - parameters in the conditional mean function, Θ κ is the set of hyper - parameters in the conditional kernel function; T represents the transpose; represents the mean vector of the training data and K tt is the kernel matrix of the training data and I nis the n-dimensional identity matrix; |·| represents the determinant of a matrix; π is the ratio of a circle's circumference to its diameter; n is the number of training inputs;
[0057] Step 502: Use a gradient-based optimization algorithm to maximize the above logarithmic likelihood function, and an estimated value of the missile arrival time t N can be obtained. And update the parameter value t N for the estimated missile arrival time at the next sampling moment.
[0058] To obtain the maximum likelihood estimate of the missile arrival time t N , the partial derivative of the logarithmic likelihood function with respect to t N needs to be calculated:
[0059]
[0060] where
[0061] In the above missile arrival time estimation method based on online learning of Gaussian processes, in step 502, there are still partial derivative terms N in the partial derivative result of the logarithmic likelihood function with respect to t and that need to be expanded. When using the conditional zero-mean function and the conditional SE kernel function κ N_SE (t, t′), the hyperparameter set is then and each term in has a general calculation formula:
[0062]
[0063] The present invention has the following advantages compared with the prior art:
[0064] 1. In the modeling stage, the present invention introduces the end point information of the missile instead of through post-processing. The state evolution process is intuitive and efficient, with a higher level of motion modeling, ensuring efficient missile arrival time estimation.
[0065] 2. In the method of the present invention, as the missile approaches its end point, the accuracy of the missile arrival time estimation rapidly improves, and it can accurately estimate the actual arrival time of the missile a certain time in advance and robustly maintain this result thereafter.
[0066] 3. The method of the present invention can provide situation intelligence information, enhance surveillance and early warning capabilities, and thus assist upper-level decision-making.
[0067] 4. The method of the present invention is driven by both data and knowledge. Without the control information of known missiles, it can still accurately estimate the actual arrival time of missiles in advance by a certain period, thereby providing the command department with the situation intelligence information of the battlefield and assisting the upper-level decision-making. It can effectively deal with non-cooperative missiles of the enemy. Therefore, the present invention has strong practicability, good use effect and is convenient for popularization and use.
[0068] The technical solution of the present invention will be further described in detail below with reference to the drawings and embodiments. Brief Description of the Drawings
[0069] Figure 1 is the flowchart of the method of the present invention;
[0070] Figure 2 is the schematic diagram of the random scenario 1 of the cooperative combat missile group in the embodiment of the present invention;
[0071] Figure 3 is the schematic diagram of the random scenario 2 of the cooperative combat missile group in the embodiment of the present invention;
[0072] Figure 4 is the schematic diagram of the random scenario 3 of the cooperative combat missile group in the embodiment of the present invention;
[0073] Figure 5 is the schematic diagram of the estimated results of the average arrival time of each missile under 500 Monte Carlo experiments in the embodiment of the present invention. Detailed Embodiment
[0074] As Figure 1 shown, the method for estimating the arrival time of missiles based on online learning of Gaussian process of the present invention includes the following steps:
[0075] Step 1: Set the original mean function and the original kernel function for characterizing the missile position;
[0076] In this embodiment, the specific process of setting the original mean function and the original kernel function for characterizing the missile position in Step 1 is as follows:
[0077] Step 101: In each spatial dimension
[0078] (omitting the superscript for identifying the specific spatial dimension), the position of the missile at any time is regarded as an infinite-dimensional Gaussian distribution, and its properties are completely determined by the original mean function and the original kernel function, expressed as:
[0079]
[0080] Among them, is the number of spatial dimensions, t and t' are any two moments; f(t) is the position of the missile at any moment t; represents a Gaussian process; is the original mean function set to characterize the position of the missile at any time t and E[·] represents the mean; κ(t, t′) is the original kernel function set to characterize the position of the missile and f(t′) is the position of the missile at any time t′; is the original mean function set to characterize the position of the missile at any time t′ and
[0081] In this embodiment, the original mean function described in step one is a compliant prior function, including a zero-mean function is expressed as:
[0082]
[0083] The original kernel function κ(t, t′) described in step one is a compliant prior function, including the SE kernel function κ SE (t, t′), which is expressed as:
[0084]
[0085] where σ is the amplitude hyperparameter, l is the characteristic length scale hyperparameter, and exp(·) is the exponential function with the natural constant e as the base.
[0086] In specific implementation, the original mean function and the original kernel function κ(t, t′) are not fixed, but can be flexibly selected or set according to requirements, and can also be set to other compliant prior functions.
[0087] Step two: Set the end point constraint according to the known end point position of the missile and the unknown arrival time of the missile, and introduce the end point constraint into the original mean function and the original kernel function to generate a conditional mean function and a conditional kernel function characterizing the end point constraint motion;
[0088] In this embodiment, when setting the end point constraint according to the known end point position of the missile and the unknown arrival time of the missile in step two, the end point constraint is expressed as f(t N ) = d, where d is the known end point position of the missile, and t N is the unknown arrival time of the missile;
[0089] When introducing the end point constraint into the original mean function and the original kernel function to generate a conditional mean function and a conditional kernel function in step two, the conditional mean function is expressed as:
[0090]
[0091] Among them, κ(t, t N ) is the cross-covariance of the function values corresponding to the test input and the training input time, and κ -1 (t N , t N ) represents the inverse of κ(t N , t N ), and κ(t N , t N ) is the prior variance of the test input function value. is the set original mean function representing the position of the missile at the missile arrival time t N , and
[0092] The conditional kernel function κ N (t, t′) is expressed as:
[0093] κ N (t, t′) = κ(t, t′) - κ(t, t N )κ -1 (t N , t N )κ(t N , t′)
[0094] Among them, κ(t N , t′) is the set original kernel function representing the position of the missile;
[0095] The position f(t) of the missile at any time t is determined by the conditional mean function and the conditional kernel function, and is expressed as:
[0096]
[0097] In this embodiment, the conditional mean function described in step two includes a conditional zero-mean function based on the zero-mean function , which is expressed as:
[0098]
[0099] The conditional kernel function described in step two includes a conditional SE kernel function κ SE (t, t′) based on the SE kernel function κ(t, t′), which is expressed as: N_SE
[0100]
[0101] Step three: Use the parameter estimation method to estimate the estimated values of the hyperparameters in the conditional mean function and the conditional kernel function;
[0102]
[0102] In this embodiment, when using the parameter estimation method to estimate the estimated values of the hyperparameters in the conditional mean function and the conditional kernel function, the parameter estimation method used is the maximum likelihood estimation method; the specific process of using the maximum likelihood estimation method to estimate the estimated values of the hyperparameters in the conditional mean function and the conditional kernel function is as follows:
[0103] Step 301. In each spatial dimension
[0104] (omitting the superscript indicating the specific spatial dimension), up to the current time t n , a total of n measurements are received according to the measurement model z k =f(t k )+v k . Then there is a training data set D = {(t k ,z k )} k＝1,...,n , a time series set t = {t k} k＝1,...,n , and a measurement set z = {z k} k＝1,.n. ; where t k is an arbitrary sampling time not later than the current time t n , f(t k ) is the predicted output, v k is Gaussian white noise with zero mean and variance equal to ; z k is the measurement received at time t k and z k ∈R, where R represents the set of real numbers;
[0105] Step 302. Give the log-likelihood function of the training data in the Gaussian process according to the standard form of the multivariate Gaussian distribution:
[0106]
[0107] where log is the natural logarithm with base e,
[0108] is the likelihood, is the set of hyperparameters, is the set of hyperparameters in the conditional mean function, and each hyperparameter is Θ κ is the set of hyperparameters in the conditional kernel function, and each hyperparameter is Θ κ ; T represents the transpose; represents the mean vector of the training data and K tt is the kernel matrix of the training data and I nis the n-dimensional identity matrix; |·| represents the determinant of a matrix; π is the circumference ratio; n is the number of measurements;
[0109] Step 303: Use a gradient-based optimization algorithm to maximize the log-likelihood function given in Step 302, obtain an estimated value of the hyperparameter set Θ, and then update Θ for subsequent steps and for hyperparameter estimation at the next sampling moment; when obtaining the maximum likelihood estimate of the hyperparameter in the conditional mean function, find the partial derivative of the log-likelihood function with respect to :
[0110]
[0111] where represents the partial derivative;
[0112] When obtaining the maximum likelihood estimate of the hyperparameter Θ κ in the conditional kernel function, find the partial derivative of the log-likelihood function with respect to Θ κ :
[0113]
[0114] where tr(·) is the trace of a matrix.
[0115] In specific implementation, the parameter value of the unknown missile arrival time t N can be set in two ways: one is to directly use the missile arrival time estimated at the previous sampling moment; the other is to randomly select a value within a reasonable range. Similarly, for the hyperparameter set Θ, a similar method can also be used, that is, it can be set based on the hyperparameter estimated value at the previous sampling moment, or randomly selected within a reasonable range.
[0116] In this embodiment, when finding the partial derivative of the log-likelihood function with respect to in Step 303, the conditional mean function uses the conditional zero-mean function based on the zero-mean function The conditional kernel function uses the conditional SE kernel function κ based on the SE kernel function κ SE (t, t′), and the hyperparameter set is N_S ( E t, t′), and the general calculation formula for each item in is:
[0117]
[0118] The general calculation formula for each item in
[0119]
[0120] Step 4. Stack the mean vectors and kernel matrices in each spatial dimension;
[0121] In this embodiment, the specific method for stacking the mean vectors and kernel matrices in each spatial dimension in Step 4 is as follows:
[0122] Combining each spatial dimension, represent the missile's terminal position as until the current time t n The cumulative measurement set is In order to jointly estimate the missile arrival time between different spatial dimensions, stack the mean vectors and kernel matrices in each spatial dimension:
[0123]
[0124] where blkdiag[·] is the block diagonal; the superscript · (·) is a specific dimension; is the number of spatial dimensions.
[0125] Step 5. Treat the missile arrival time as a hyperparameter in the Gaussian process, and use the parameter estimation method to estimate the estimated value of the missile arrival time embedded in the mean vector and kernel matrix.
[0126] In this embodiment, the specific process of treating the missile arrival time as a hyperparameter in the Gaussian process and using the parameter estimation method to estimate the estimated value of the missile arrival time embedded in the mean vector and kernel matrix in Step 5 is as follows:
[0127] Step 501. Combining each spatial dimension, give the log-likelihood function of the training data in the Gaussian process according to the standard form of the multivariate Gaussian distribution:
[0128]
[0129] where log is the logarithm with the natural constant e as the base,
[0130] is the likelihood, is the set of hyperparameters, is the set of hyperparameters in the conditional mean function, and each hyperparameter is Θ κ is the set of hyperparameters in the conditional kernel function, and each hyperparameter is Θ κ ; T represents the transpose; represents the mean vector of the training data and K tt is the kernel matrix of the training data and I nis the n-dimensional identity matrix; |·| represents the determinant of a matrix; π is the ratio of a circle's circumference to its diameter; n is the number of training inputs;
[0131] Step 502: Maximize the above log-likelihood function using a gradient-based optimization algorithm to obtain the estimated value of the missile arrival time t N and update the parameter value t N for the missile arrival time estimation at the next sampling moment;
[0132] To obtain the maximum likelihood estimate of the missile arrival time t N , the partial derivative of the log-likelihood function with respect to t N needs to be calculated:
[0133]
[0134] where
[0135] In this embodiment, in step 502, there are still partial derivative terms N in the partial derivative result of the log-likelihood function with respect to t and that need to be expanded. When using the conditional zero-mean function and the conditional SE kernel function κ N_SE (t, t′), the hyperparameter set is then and each term in has a general calculation formula:
[0136]
[0137] The gradient-based optimization algorithm includes the trust-region reflection method. Its core idea is roughly the same as the quasi-Newton method, but the optimization space is constrained. When estimating the missile arrival time, since the estimated value should always be greater than the current moment, therefore, the lower bound of the parameter value of the missile arrival time t N is set to the current moment.
[0138] To verify the technical effects that the present invention can produce, the following experiment was conducted:
[0139] Assume that four missiles come from the northwest direction and successively attack our fixed facility located at [25, -28] km, and set the actual arrival times of each missile as shown in Table 1.
[0140] Table 1 Setting of the actual arrival times of each missile in the scenario
[0141]
[0142] Adopt a stochastic guidance method to generate different missile movement trajectories in each Monte Carlo experiment. Figure 2 This is a schematic diagram of the random scenario 1 of the cooperative combat missile group in this embodiment. Figure 3 This is a schematic diagram of the random scenario 2 of the cooperative combat missile group in this embodiment. Figure 4 This is a schematic diagram of the random scenario 3 of the cooperative combat missile group in this embodiment. Figure 2 、 Figure 3 and Figure 4 In, the missile trajectory is small-scale dots connected by solid lines, and the large-scale dots are the end points of the missiles.
[0143] When the guidance method, guidance parameters and actual arrival time of the missile are unknown, and only the end position of the missile is known, based on the missile measurements received by the sensor, the missile arrival time estimation method based on online learning of Gaussian process of the present invention is used to estimate the real-time arrival time of each missile. By conducting 500 Monte Carlo experiments and regarding the missile movement trajectories generated by the same parameters as shown in Table 1 as the same missile, the average arrival time estimation results of each missile can be obtained, as shown in Figure 5 shown. Figure 5 In, the abscissa is the sampling time axis of the sensor, with the unit of second; the four subgraphs respectively correspond to four missiles, the solid lines are the actual arrival times of each missile, the solid dots are the starting values of the randomly set missile arrival time parameters, and the dotted lines are the real-time missile arrival time estimation values.
[0144] From Figure 5 it can be seen that although the missile movement trajectories are different in each Monte Carlo experiment and there is a certain degree of maneuver, and different missiles have different actual arrival times, the missile arrival time estimation algorithm proposed by the present invention can still accurately estimate the actual arrival time of the missile a certain time in advance. Specifically, as time goes by, the error between the missile arrival time estimation value and the actual value gradually converges to 0, which verifies the strong self-learning ability, robustness and effectiveness of the present invention.
[0145] It can be concluded from this that the present invention can still accurately estimate the actual arrival time of the missile a certain time in advance without knowing the control information of the missile, and further provide the battlefield situation intelligence information for the command post to assist the upper-level decision-making.
[0146] The above is only a preferred embodiment of the present invention, and does not impose any limitation on the present invention. Any simple modification, change and equivalent structural change made to the above embodiment according to the technical essence of the present invention still fall within the protection scope of the technical solution of the present invention.
Claims
1. A missile arrival time estimation method based on Gaussian process online learning, characterized in that: The method comprises the following steps: Step 1: Set the original mean function and original kernel function that characterize the missile position; Step 2: Set the endpoint constraint according to the known missile endpoint position and the unknown missile arrival time, and introduce the endpoint constraint into the original mean function and the original kernel function to generate the conditional mean function and the conditional kernel function that characterize the endpoint constraint motion; Step 3: Use parameter estimation method to estimate the estimated values of hyperparameters in the conditional mean function and conditional kernel function; Step 4: Stack the mean vectors and kernel matrices in each spatial dimension; Step 5: Consider the missile arrival time as a hyperparameter in the Gaussian process, and use the parameter estimation method to estimate the estimated value of the missile arrival time embedded in the mean vector and kernel matrix.
2. A method for estimating missile arrival time based on Gaussian process online learning according to claim 1, characterized in that: The specific process of setting the original mean function and the original kernel function that characterize the missile position in step 1 is: Step 101: In each spatial dimension On the other hand, the position of the missile at any time is regarded as an infinite-dimensional Gaussian distribution, and its properties are completely determined by the original mean function and the original kernel function, which can be expressed as: in, is the number of spatial dimensions, t and t′ are two arbitrary moments; f(t) is the position of the missile at any moment t; represents a Gaussian process; is the original mean function that characterizes the position of the missile at any time t. E[·] represents the mean; κ(t, t′) is the original kernel function that characterizes the missile position. f(t′) is the position of the missile at any time t′; is the original mean function that characterizes the position of the missile at any time t′ and 3. A method for estimating missile arrival time based on Gaussian process online learning according to claim 2, characterized in that: When setting the endpoint constraint according to the known missile endpoint position and the unknown missile arrival time in step 2, the endpoint constraint is expressed as f(t N ) = d, where d is the known missile terminal position, t N is the unknown missile arrival time; In step 2, the endpoint constraint is introduced into the original mean function and the original kernel function to generate the conditional mean function and the conditional kernel function that characterize the endpoint constraint motion. The conditional mean function It is expressed as: Among them, κ(t,t N ) is the cross-covariance of the function values corresponding to the test input and training input time, κ -1 (t N ,t N ) represents the relationship between κ(t N ,t N ) to find the inverse, κ(t N ,t N ) is the prior variance of the test input function value, is the missile arrival time t N The original mean function at the location and Conditional kernel function κ N (t,t′) is expressed as: k N (t,t′)=κ(t,t′)-κ(t,t N )k -1 (t N ,t N )k(t N ,t′) Among them, κ(t N ,t′) is the original kernel function that is set to characterize the missile position; The position f(t) of the missile at any time t is determined by the conditional mean function and the conditional kernel function, which can be expressed as:
4. A method for estimating missile arrival time based on Gaussian process online learning according to claim 3, characterized in that: The original mean function described in step 1 is a compliant prior function, including a zero-mean function It is expressed as: The original kernel function κ(t, t′) described in step 1 is a compliant prior function, including the SE kernel function κ SE (t,t′), expressed as: Where σ is the amplitude hyperparameter, is the characteristic length scale hyperparameter, and exp(·) is the exponential with the natural constant e as the base.
5. A method for estimating missile arrival time based on Gaussian process online learning according to claim 4, characterized in that: The conditional mean function in step 2 includes a zero mean function based on The conditional zero mean function of It is expressed as: The conditional kernel function in step 2 includes the SE kernel function κ SE The conditional SE kernel function κ of (t,t′) N_SE (t,t′), expressed as:
6. A method for estimating missile arrival time based on Gaussian process online learning according to claim 1, characterized in that: When the parameter estimation method is used in step 3 to estimate the estimated values of the hyperparameters in the conditional mean function and the conditional kernel function, the parameter estimation method used is the maximum likelihood estimation method; the specific process of using the maximum likelihood estimation method to estimate the estimated values of the hyperparameters in the conditional mean function and the conditional kernel function is as follows: Step 301: In each spatial dimension Until the current time t n , according to the measurement model z k =f(t k )+v k Receive n measurements, then there is a training data set D = {(t k ,z k )} k＝1,...,n , the time series set t={t k } k＝1,...n, , the measurement set z = {z k } k＝1,...,n ; where t k is no later than the current time t n At any sampling time, f(t k ) is the predicted output, v k has zero mean and variance equal to Gaussian white noise; z k is time t k The received measurement and z k ∈R, R represents a real number; Step 302: The log-likelihood function of the training data in the Gaussian process is given according to the standard form of multivariate Gaussian distribution: Among them, log is the logarithm with the natural constant e as the base, For the likelihood, is a set of hyperparameters, is the set of hyperparameters in the conditional mean function, Θ κ is the set of hyperparameters in the conditional kernel function; T represents transposition; represents the mean vector of the training data and K tt is the kernel matrix of the training data and I n is the n-dimensional identity matrix; |·| represents the determinant of the matrix; π is the circumference of a circle; n is the number of measurements; Step 303: Use a gradient-based optimization algorithm to maximize the log-likelihood function given in step 302 to obtain an estimated value of the hyperparameter set Θ, and then update Θ for subsequent steps and to estimate the hyperparameters at the next sampling moment; when the hyperparameters in the conditional mean function are obtained, When the maximum likelihood estimate of is used, find the log-likelihood function about The partial derivative of : in, represents partial derivative; When the hyperparameter Θ in the conditional kernel function is obtained κ When the maximum likelihood estimate of , find the log-likelihood function about Θ κ The partial derivative of : in, tr(·) is the trace of the matrix.
7. A method for estimating missile arrival time based on Gaussian process online learning according to claim 6, characterized in that: In step 303, the log-likelihood function is calculated with respect to When the partial derivative of , the conditional mean function is based on the zero mean function The conditional zero mean function of The conditional kernel function is based on the SE kernel function κ SE The conditional SE kernel function κ of (t,t′) N_SE (t,t′), the hyperparameter set is The general formula for calculating each item in is: The general formula for calculating each item in is:
8. A method for estimating missile arrival time based on Gaussian process online learning according to claim 6, characterized in that: The specific method of stacking the mean vector and kernel matrix in each spatial dimension described in step 4 is: Combining various spatial dimensions, the missile terminal position is expressed as Until the current time t n The accumulated measurement set is In order to jointly estimate the missile arrival time across different spatial dimensions, the mean vectors and kernel matrices in each spatial dimension are stacked: Where blkdiag[·] is the block diagonal; superscript · (·) For a specific dimension; is the number of spatial dimensions.
9. A method for estimating missile arrival time based on Gaussian process online learning according to claim 1, characterized in that: In step 5, the missile arrival time is regarded as a hyperparameter in the Gaussian process, and the specific process of using the parameter estimation method to estimate the estimated value of the missile arrival time embedded in the mean vector and the kernel matrix is as follows: Step 501: Comprehensively consider all spatial dimensions and give the log-likelihood function of the training data in the Gaussian process according to the standard form of multivariate Gaussian distribution: Among them, log is the logarithm with the natural constant e as the base, For the likelihood, is a set of hyperparameters, is the set of hyperparameters in the conditional mean function, Θ κ is the set of hyperparameters in the conditional kernel function; T represents transposition; represents the mean vector of the training data and K tt is the kernel matrix of the training data and I n is the n-dimensional identity matrix; |·| represents the determinant of the matrix; π is the circumference of a circle; n is the number of training inputs; Step 502: Using a gradient-based optimization algorithm to maximize the log-likelihood function, the missile arrival time t can be obtained. N Estimated value of And for the parameter value t N Update the missile arrival time estimate at the next sampling moment; In order to obtain the missile arrival time t N The maximum likelihood estimate of t requires the log-likelihood function to be calculated with respect to t N The partial derivative of : in, 10. A method for estimating missile arrival time based on Gaussian process online learning according to claim 9, characterized in that: In step 502, the log-likelihood function is N There are still partial derivatives in the partial derivative results and Need to be expanded, when using conditional zero mean function and conditional SE kernel function κ N_SE When (t,t′), the hyperparameter set is but and Each item in has a general calculation formula: