A ballistic missile active phase tracking method and device, computer equipment and medium

Abstract

This invention provides a method, apparatus, computer equipment, and medium for tracking the active phase of a ballistic missile, belonging to the field of motion tracking. The method includes: constructing a set of modes to describe the flight of a ballistic missile during its active phase; obtaining state prediction distributions for a gravity-turning model and a three-dimensional gravity-turning model using unscented Kalman filtering; selecting the key state components most sensitive to flight mode switching through sensitivity analysis; constructing a maximum part-correlation entropy criterion based on the key state components; calculating the part-correlation entropy score of each model; constructing a mode separability metric; and determining whether the two models are currently separable. If separable, the unscented Kalman filter posterior estimation result is directly output as the tracking result; if inseparable, the state estimation results of the two models are weighted and fused as the tracking result. This improves the estimation accuracy during mode switching while enhancing the stability of the tracking result, exhibiting good engineering applicability.

Description

Technical Field

[0001] This invention belongs to the field of motion tracking, specifically relating to a ballistic missile active phase tracking method, device, computer equipment, and medium. Background Technology

[0002] The boost phase of a ballistic missile is the only flight phase where the target is continuously driven by the propulsion system. The tracking accuracy during this phase directly impacts subsequent trajectory extrapolation, intercept window construction, radar relay deployment, and the generation of initial conditions for mid- and terminal phase defense. Compared to the mid-course and reentry phases, the boost phase is characterized by multi-stage boosts, dramatic thrust variations, frequent attitude adjustments, and significant inter-stage switching. The target motion exhibits strong nonlinearity, strong time-varying characteristics, and dynamics coupled with multi-source uncertainties. In practical engineering, key physical parameters of the target during the boost phase are often difficult to obtain accurately a priori, such as engine thrust variations, inter-stage mass mutations, angle-of-attack scheduling, aerodynamic disturbances, and non-gravitational acceleration distributions caused by attitude control. Furthermore, sensor-acquired measurement data is also affected by observation noise. Therefore, high-precision continuous tracking during the boost phase has always been a significant challenge in ballistic missile defense.

[0003] Existing active phase modeling methods mainly include template modeling, kinematic modeling, dynamic modeling, multi-model methods, and machine learning methods. Specifically, template methods rely on the accuracy and completeness of the template library; once the target flight state deviates from the preset template, the estimation performance will significantly decrease. Although kinematic methods are simple to implement, they are difficult to characterize the real dynamic mechanisms brought about by the thrust, angle of attack, and multi-stage separation in the active phase, and acceleration mismatch often occurs in strong maneuvering scenarios. Single dynamic models (such as using GT or GT3 alone) have strong physical interpretability, but model mismatch is prone to occur when switching between zero and non-zero angle of attack states. Multi-model methods such as IMM can alleviate single-model mismatch through probabilistic interaction, but they usually rely on pre-constructed model transition matrices and model separability; once the mode transition prior is inaccurate or the two models are weakly separable, the model probability allocation is easily distorted. Machine learning methods learn the nonlinear mapping between the active phase flight state and observation information in a data-driven manner, and have strong adaptability to complex maneuvers, mode switching, and unknown disturbances, which can alleviate the problems caused by template mismatch and inaccurate analytical models to a certain extent. However, such methods usually rely on a large amount of high-quality training data and have problems such as insufficient physical interpretability and generalization ability limited by sample distribution. In engineering applications, they often need to be used in combination with mechanistic models or filtering methods.

[0004] Furthermore, traditional pattern recognition methods based on global likelihood or global correlation entropy are not sensitive enough to abrupt changes in the active phase triggered by local physical variables. For example, inter-stage switching and non-zero angle-of-attack maneuvers often show significant changes first in the velocity and acceleration dimensions, while the position dimension has a natural integral smoothing characteristic, resulting in a response lag for pattern recognition methods that rely purely on full-dimensional measurement probability updates or global kernel functions.

[0005] Therefore, existing ballistic missile active phase tracking methods suffer from several drawbacks during flight mode switching. These include the difficulty of a single dynamic model to account for both zero and non-zero angle of attack states, the lag in the response of full-dimensional correlation entropy to local maneuver mutations, and the distortion of model probability allocation in weakly separable stages by multi-model methods. Consequently, the accuracy of state estimation decreases, and tracking results may jump, making it difficult to achieve continuous, stable, and high-precision tracking. Summary of the Invention

[0006] To address the problems of decreased state estimation accuracy and abrupt changes in tracking results during flight mode switching in existing ballistic missile active phase tracking methods, which make it difficult to achieve continuous and stable high-precision tracking, this invention provides a ballistic missile active phase tracking method, device, computer equipment, and medium.

[0007] To achieve the above objectives, the present invention provides the following technical solution: A ballistic missile active phase tracking method, the method comprising: A set of models is constructed to describe the flight of a ballistic missile in the active phase. The set of models includes a gravity turning model for describing the zero angle of attack flight state and a three-dimensional gravity turning model for describing the non-zero angle of attack flight state. For the gravity turning model and the three-dimensional gravity turning model, the state prediction mean and prediction covariance of each model are obtained through the prediction step of unscented Kalman filtering. From the state prediction mean and state prediction covariance, the key state components most sensitive to flight mode switching are screened out through sensitivity analysis, and the partial correlation entropy score of each model is calculated based on the key state components to identify the flight mode at the current moment. The partial correlation entropy score is used to quantify the degree of matching between each candidate model and the real flight state in terms of key state components. Based on the partial correlation entropy scores of the gravity turning model and the 3D gravity turning model, a pattern separability metric is constructed, and the separability metric is compared with a preset separability threshold to determine whether the gravity turning model and the 3D gravity turning model can be reliably distinguished at the current moment; wherein, the separability threshold is used to control the aggressiveness of pattern recognition; If it is determined that the two models can be reliably distinguished, the unscented Kalman filter posterior estimation result of the model corresponding to the currently identified flight mode will be used as the tracking result; if it is determined that the two models cannot be reliably distinguished, the normalized weights will be calculated based on the partial correlation entropy scores of the two models, and the state estimation results of the two models will be weighted and fused to serve as the tracking result.

[0008] Optionally, the process of screening out the key state components most sensitive to flight mode switching through sensitivity analysis includes: A preset perturbation is applied to the flight evolution factors of the three-dimensional gravity turning model, and the normalized sensitivity measure of each state component relative to the flight evolution factors is calculated to obtain the normalized sensitivity measure values ​​of the position component and the velocity component; the flight evolution factors include the initial state, thrust parameters, mass dissipation, target latitude and longitude, and interstage time series. When the normalized sensitivity metric of the velocity component is greater than the normalized sensitivity metric of the position component, all velocity components are identified as the critical state components.

[0009] Optionally, calculating the partial correlation entropy score of each model based on the key state components includes: For any turning model, the predicted state mean and predicted covariance are obtained by unscented Kalman filtering. Based on the predicted state mean and predicted covariance, sampling points symmetrically distributed about the predicted mean are generated; All sampling points are projected onto the key state subspace composed of the key state components, and a partial correlation entropy score is calculated based on the decentralized symmetric sampling points. The partial correlation entropy score is smoothed using a sliding window of preset length to obtain a smoothed partial correlation entropy score.

[0010] Optionally, the separability metric for the construction pattern includes: The ratio of the absolute value of the difference between the smoothed partial correlation entropy scores of the gravity turning model and the three-dimensional gravity turning model to the larger score is calculated, and the ratio is used as the separability metric. When the separability metric is greater than or equal to the separability threshold, it is determined that the two objects can be reliably distinguished; when the separability metric is less than the separability threshold, it is determined that the two objects cannot be reliably distinguished.

[0011] Optionally, the step of calculating normalized weights based on the partial correlation entropy scores of the two models, and then weighting and fusing the state estimation results of the two models to output the following: Calculate the normalized weights of the two models based on their smoothed partial correlation entropy scores. The normalized weights are used to perform weighted fusion of the estimation results of the kinematic state components of each model to obtain the fused kinematic state estimate. For the estimation results of the dynamic parameters of each model, the dynamic parameter estimation results of the model with higher smoothed partial correlation entropy scores in the gravity turning model and the three-dimensional gravity turning model are retained.

[0012] Optionally, after constructing a set of patterns to describe the active phase flight of a ballistic missile, the method further includes constructing a joint measurement model of radar and dual infrared detectors for the unscented Kalman filtering: The deployment position of the forward ground-based radar in the geocentric fixed coordinate system is obtained, and the real-time position of the ballistic missile target in the geocentric fixed coordinate system is transformed to the northeast local coordinate system. The radar measurement equations including radial distance, azimuth angle and elevation angle are established. Obtain the deployment positions of the two infrared detectors in the geocentric fixed coordinate system, and establish the measurement equations for the elevation angle and azimuth angle of the target relative to each infrared detector; The radar measurement equation and the measurement equation of the dual infrared detector are unified to form a nonlinear measurement function, which is used for the measurement update of the unscented Kalman filter.

[0013] A ballistic missile active phase tracking device, the device comprising: A construction module is used to construct a set of modes for describing the active phase flight of a ballistic missile. The set of modes includes a gravity turning model for describing the zero angle of attack flight state and a three-dimensional gravity turning model for describing the non-zero angle of attack flight state. The identification module is used to obtain the state prediction mean and prediction covariance of each model through the prediction step of the gravity turning model and the three-dimensional gravity turning model respectively through the prediction step of unscented Kalman filtering; from the state prediction mean and state prediction covariance, the key state components most sensitive to flight mode switching are screened out through sensitivity analysis, and the partial correlation entropy score of each model is calculated based on the key state components to identify the flight mode at the current moment. The partial correlation entropy score is used to quantify the degree of matching between each candidate model and the real flight state in terms of key state components. The judgment module is used to construct a pattern separability metric based on the partial correlation entropy scores of the gravity turning model and the three-dimensional gravity turning model, and compare the separability metric with a preset separability threshold to determine whether the gravity turning model and the three-dimensional gravity turning model can be reliably distinguished at the current moment; wherein, the separability threshold is used to control the aggressiveness of pattern recognition; The determination module is used to determine the tracking result if the model corresponding to the currently identified flight mode is reliably distinguishable, and to use the unscented Kalman filter posterior estimate of the model as the tracking result if the model is not reliably distinguishable. If the model is determined to be unreliably distinguishable, the module calculates the normalized weights based on the partial correlation entropy scores of the two models, and then uses the weighted fusion of the state estimates of the two models as the tracking result.

[0014] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned ballistic missile active phase tracking method.

[0015] A computer device includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the aforementioned ballistic missile active phase tracking method.

[0016] The ballistic missile active phase tracking method provided by this invention has the following beneficial effects: This invention employs a simplified flight mode set composed of a gravity-based turning model and a three-dimensional gravity-based turning model, accurately describing two typical flight states: zero angle of attack and non-zero angle of attack, thus avoiding the systematic mismatch of a single model during maneuver switching. Sensitivity analysis is used to select the velocity component as the key state component, and a pattern recognition criterion is constructed based on the maximum part correlation entropy criterion, significantly improving the sensitivity to dynamic abrupt changes such as inter-stage switching and angle-of-attack mutations, while suppressing interference from non-Gaussian noise. Furthermore, a pattern separability metric and threshold decision are introduced. When the pattern is clear, the filtered result of the recognition model is directly output to ensure accuracy; when the pattern is weakly separable, the estimation results of the two models are weighted and fused to suppress jumps. Overall, this invention achieves continuous and smooth tracking throughout the entire active phase of flight, improving the estimation accuracy during mode switching while enhancing the stability of the tracking results, and exhibiting good engineering applicability. Attached Figure Description

[0017] To more clearly illustrate the embodiments and design schemes of the present invention, the accompanying drawings required for this embodiment will be briefly described below. The drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart illustrating a ballistic missile active phase tracking method according to an exemplary embodiment of the present invention.

[0019] Figure 2 This is a flowchart illustrating another ballistic missile active phase tracking method provided by the present invention according to an exemplary embodiment.

[0020] Figure 3This is a block diagram of a ballistic missile active phase tracking device according to an exemplary embodiment of the present invention. Detailed Implementation

[0021] To enable those skilled in the art to better understand and implement the technical solutions of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The following embodiments are only used to more clearly illustrate the technical solutions of the present invention and should not be construed as limiting the scope of protection of the present invention.

[0022] The technical solutions provided by the various embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0023] First, this invention provides a ballistic missile active phase tracking method, specifically as follows: Figure 1 As shown, it includes the following steps: S101. Construct a set of patterns to describe the active phase flight of a ballistic missile.

[0024] The model set includes a gravity turning model for describing zero angle-of-attack flight and a three-dimensional gravity turning model for describing non-zero angle-of-attack flight.

[0025] For example, suppose the flight process of a ballistic missile during its active phase is divided into two typical stages: the first stage (angle of attack approximately zero) and the second stage (programmed turns occur, angle of attack is non-zero). Based on this, the following set of patterns can be constructed:

[0026] Gravity Turning Model (GT Model): Used to describe the first stage of flight, the state equations are based on the assumption that non-gravitational acceleration is parallel to the velocity vector.

[0027] The 3D Gravity Turning Model (GT3 Model) is used to describe the second-stage flight state. This model allows non-gravitational acceleration to have different scaling factors in three directions, making it suitable for 3D maneuvering flight with an angle of attack.

[0028] In this way, the two models mentioned above together constitute the flight mode set, which can be switched or combined for use in actual tracking based on the identification results.

[0029] After constructing a set of patterns to describe the active phase flight of a ballistic missile, this step also constructs a joint measurement model of radar and dual infrared detectors for this unscented Kalman filter.

[0030] For example, the deployment position of the forward ground-based radar in the geocentric fixed coordinate system is obtained, and the real-time position of the ballistic missile target in the geocentric fixed coordinate system is transformed to the northeast-sky local coordinate system. A radar measurement equation including radial distance, azimuth angle, and elevation angle is established. The deployment positions of the two infrared detectors in the geocentric fixed coordinate system are obtained, and measurement equations for the elevation angle and azimuth angle of the target relative to each infrared detector are established respectively. The radar measurement equation is unified with the measurement equation of the dual infrared detectors to form a nonlinear measurement function, which is used for the measurement update of the unscented Kalman filter.

[0031] S102. For the gravity turning model and the three-dimensional gravity turning model, the state prediction mean and prediction covariance of each model are obtained through the prediction step of unscented Kalman filtering. From the state prediction mean and state prediction covariance, the key state components that are most sensitive to flight mode switching are screened out through sensitivity analysis, and the partial correlation entropy score of each model is calculated based on the key state components to identify the flight mode at the current moment.

[0032] The relevant entropy score in this part is used to quantify the degree of matching between each candidate model and the real flight state in key state components.

[0033] In this step, after obtaining the state prediction distribution, a preset perturbation is applied to the flight evolution factors of the three-dimensional gravity turning model, and the normalized sensitivity measure of each state component relative to the flight evolution factor is calculated to obtain the normalized sensitivity measure values ​​of the position component and the velocity component. The flight evolution factor includes the initial state, thrust parameters, mass dissipation, target latitude and longitude, and inter-stage time series. When the normalized sensitivity measure value of the velocity component is greater than the normalized sensitivity measure value of the position component, all velocity components are identified as the key state components.

[0034] For any turning model, the predicted state mean and predicted covariance are obtained through unscented Kalman filtering. Based on the predicted state mean and predicted covariance, sampling points with a symmetric distribution about the predicted mean are generated. All sampling points are projected onto the key state subspace composed of the key state components, and a partial correlation entropy score is calculated based on the decentralized symmetric sampling points. The partial correlation entropy score is smoothed using a sliding window of a preset length to obtain a smoothed partial correlation entropy score.

[0035] S103. Based on the partial correlation entropy scores of the gravity turning model and the three-dimensional gravity turning model, construct a pattern separability metric, and compare the separability metric with a preset separability threshold to determine whether the gravity turning model and the three-dimensional gravity turning model can be reliably distinguished at the current moment.

[0036] The separability threshold is used to control the aggressiveness of pattern recognition. This threshold can be determined using historical data. For example, the active phase flight time of a certain type of ballistic missile is 60 seconds, with 0-30 seconds being the zero angle-of-attack mode, 30-35 seconds the interstage separation transition phase, and 35-60 seconds the non-zero angle-of-attack mode. Using a ground simulation system, the method of this invention is run 100 times under typical noise conditions, recording the partial correlation entropy score difference between the two models at each time point. By statistically analyzing the correlation entropy scores during the stable flight phase (i.e., the zero angle-of-attack and non-zero angle-of-attack modes), an interval is determined based on the ratio of the absolute value of the score difference between the two models to the larger score. Based on actual needs, any value within this interval is selected as the separability threshold. For example, if 0.03 is selected as the separability threshold, at a certain stage, for the GT model and the GT3 model, based on the predicted distribution of their velocity components, the average correlation entropy of the decentralized symmetric sampling points is calculated using the Gaussian kernel function. The partial correlation entropy score of the GT model is 0.32, and the partial correlation entropy score of the GT3 model is 0.87. Since the score of the GT3 model is significantly higher than that of the GT model, it indicates that the predicted distribution of the GT3 model in the velocity subspace matches the current actual measurement better. Moreover, the calculated separability metric of the two is approximately 0.63, which is greater than 0.03. Therefore, the current flight mode is identified as a non-zero angle of attack mode, and the GT3 model is selected for subsequent state updates.

[0037] In this step, the absolute value of the difference between the smoothed partial correlation entropy scores of the gravity turning model and the three-dimensional gravity turning model is calculated, and the ratio between the larger score and the smaller score is used as the separability metric. When the separability metric is greater than or equal to the separability threshold, it is determined that the model can be reliably distinguished; when the separability metric is less than the separability threshold, it is determined that the model cannot be reliably distinguished.

[0038] S104. If it is determined that the two models can be reliably distinguished, the unscented Kalman filter posterior estimation result of the model corresponding to the currently identified flight mode is directly output. If it is determined that the two models cannot be reliably distinguished, the normalized weight is calculated based on the partial correlation entropy scores of the two models, and the state estimation results of the two models are weighted and fused to obtain the tracking result.

[0039] In this step, if the models are determined to be inseparable, the normalized weights corresponding to each model are calculated based on the smoothed partial correlation entropy scores of the two models. The normalized weights are then used to perform weighted fusion of the estimation results of the kinematic state components of each model to obtain the fused kinematic state estimates. For the estimation results of the dynamic parameters of each model, the dynamic parameter estimation results of the model with the higher smoothed partial correlation entropy score in the gravity turning model and the three-dimensional gravity turning model are retained.

[0040] It should be noted that in the aforementioned step S102 and this step, the unscented Kalman filter includes a covariance adaptive adjustment strategy based on the normalized innovation square, wherein the covariance adaptive adjustment strategy includes: calculating the normalized innovation square in the filtering process and preset an innovation threshold; when the normalized innovation square is greater than the innovation threshold, adaptively expanding the prediction covariance matrix to suppress the influence of model mismatch or anomalous measurements on state estimation.

[0041] Using the above method, a simplified flight mode set is constructed by combining a gravity-based turning model and a three-dimensional gravity-based turning model, accurately describing two typical flight states: zero angle of attack and non-zero angle of attack, thus avoiding the systematic mismatch of a single model during maneuver switching. Sensitivity analysis is used to select the velocity component as the key state component, and a pattern recognition criterion is constructed based on the maximum part correlation entropy criterion, significantly improving the sensitivity to dynamic abrupt changes such as inter-stage switching and angle-of-attack mutations, while suppressing interference from non-Gaussian noise. Furthermore, a pattern separability metric and threshold decision are introduced. When the pattern is clear, the filtered result of the recognition model is directly output to ensure accuracy; when the pattern is weakly separable, the estimation results of the two models are weighted and fused to suppress jumps. Overall, this invention achieves continuous and smooth tracking throughout the entire active phase of flight, improving the estimation accuracy during mode switching while enhancing the stability of the tracking results, and exhibiting good engineering applicability.

[0042] Based on the above method steps, the present invention also provides an embodiment for theoretical explanation, the overall process of which is as follows: Figure 2 As shown, it mainly includes 4 steps: Construct a set of GT / GT3 dynamic models and measurement models.

[0043] Flight pattern recognition is based on the largest possible correlation entropy.

[0044] The judgment is based on the separability of the model.

[0045] Based on the model's separability judgment results, joint estimation of state and parameters is performed and fused output is generated.

[0046] The first step is to build a set of GT / GT3 dynamic models.

[0047] GT model (Gravity Turning Model) -- The GT model is used to describe flight states with zero or near-zero angle of attack.

[0048] First, a physical analysis is performed on the main forces acting on a ballistic missile during its boost phase. In actual flight, the missile is primarily subjected to engine thrust. Aerodynamics Earth's gravity Control And the additional Coriolis force caused by the Earth's rotation The combined effects of these factors, and based on Newton's second law, establish the fundamental vector dynamics equations of a ballistic missile as follows:

[0049] , in, This refers to the current mass of the missile. This is the missile's position vector.

[0050] To accurately and efficiently describe this complex nonlinear system, this invention, based on the classical gravity-based turning theory, makes the following three fundamental physical assumptions for the smooth flight phase: The angle of attack during the boost phase is extremely small, almost zero; In addition to gravity, the non-gravitational net acceleration experienced by the missile (Composed of thrust, aerodynamic force, Coriolis force, etc.) Parallel to its relative velocity vector The turning of a ballistic trajectory is mainly the result of gravity.

[0051] Based on the above assumptions, the gravity curvature coefficient is defined in the geocentric fixed coordinate system (ECEF). ,satisfy The 7-dimensional state vector of the GT model is set as follows: The high-precision continuous-time physical state equations for the GT model are as follows:

[0052] ; in, This represents system noise.

[0053] The calculation formula is as follows: ; in, , These are the standard gravity parameters for Earth.

[0054] GT3 model (3D gravity turning model) -- used to describe the three-dimensional dynamic abrupt change mode of a missile during interstage separation or complex maneuvers.

[0055] When a multi-stage ballistic missile changes its flight program or switches between stages, the missile's angle of attack will change and will no longer be zero. Simultaneously, the target's three-axis dynamic characteristics exhibit severe inconsistencies, rendering the traditional single GT model assumptions inapplicable. Therefore, this invention breaks the rigid constraint that the resultant force direction is parallel to the velocity and further defines a three-dimensional non-gravitational turning coefficient matrix based on the GT model. From the ballistic missile's active phase motion model, the three-dimensional gravity turning coefficient can be determined. The physical meaning is: ; In the target tracking model, the three-dimensional gravity turning coefficient is defined as: ; Define the state vector of the GT3 model as follows: In this case, decomposing the gravitational turning coefficient into three directions of motion allows for a precise description of the three-dimensional nongravitational acceleration. Extending the three-dimensional gravitational turning coefficient to include state variables yields the following state equation:

[0056] ; in, This represents system noise.

[0057] The measurement models include measurement models built based on radar and dual infrared detectors, respectively.

[0058] First, to achieve high-precision continuous tracking of ballistic missiles in their active phase, a forward-deployed ground-based radar is used to detect the target and obtain its radial distance, azimuth, and elevation angles in the Northeastern Sky (ENU) local coordinate system. To map the position state generated by the dynamic evolution into the radar's measurement output, the following spatial nonlinear coordinate transformation and measurement mapping equations need to be constructed:

[0059] The transformation equation for converting the three-dimensional absolute position of a ballistic missile target in the geocentric fixed coordinate system (ECEF) to its relative position in the radar-centered northeastern sky (ENU) coordinate system is as follows: ; in, This represents the real-time 3D position of the target in the ECEF coordinate system. This represents the three-dimensional relative position of the target in the ENU coordinate system after transformation. Given the known precise deployment location of the forward-deployed ground-based radar in the ECEF coordinate system, this embodiment presupposes the fixed spatial coordinates of the radar as follows: (Unit: meter) The coordinate rotation matrix from the ECEF coordinate system to the ENU coordinate system is expressed as follows: ; in, and These represent the longitude and latitude of the geographical location of the forward-deployed ground-based radar, respectively, and their values ​​can be obtained from the radar's three-dimensional fixed coordinates. The unique inverse solution is determined.

[0060] Based on the relative position vector in the ENU coordinate system mentioned above A nonlinear spatial geometric measurement model for the radar system is established, and its measurement equations are as follows: ; in, , , These represent the radial distance, azimuth angle, and elevation angle of the target detected by the radar, respectively. The zero-mean Gaussian white noise sequence generated by the radar system in the three detection channels of radial distance, azimuth angle and elevation angle has a covariance matrix equal to R, which represents the inherent observation error that is unavoidable in the front-end radar detection hardware.

[0061] Secondly, a dual infrared detection system is used to detect ballistic missiles. During the missile's booster phase, the engine continuously operates, and the high-temperature, high-pressure gases generated by the complete combustion of the oxidizer and propellant can reach several thousand degrees Celsius, exhibiting a distinct infrared signature against the Earth's background. The dual infrared detection system can obtain real-time information on the missile's elevation and azimuth relative to the detectors. Assuming the infrared detectors are fixedly connected to the Earth's core:

[0062] ; In the formula: the position state of the target point is The positions of the infrared detectors in the geocentric fixed coordinate system are as follows: .

[0063] The measurement model for dual infrared detectors is as follows: ; In the formula: The elevation angle; It is the azimuth angle; Noise for elevation angle measurement; To reduce azimuth measurement noise, positioning the dual infrared detectors on either side of the target trajectory allows for better and wider-range comprehensive detection.

[0064] In summary, the measurement models for radar and dual infrared detectors can be uniformly represented as follows: ; in, Target state vector For joint measurement vectors, This corresponds to the nonlinear measurement function formed by the measurement relationship between the radar and the dual infrared detectors. This is the joint noise vector composed of the measurement noise from each detection channel.

[0065] The second step is to identify flight patterns based on the largest possible correlation entropy.

[0066] After obtaining the predicted states and their uncertainty descriptions for each candidate dynamic model, further discrimination of the current flight mode is required. To enhance the robustness of model identification under non-Gaussian noise and anomalous disturbance conditions, a correlation entropy metric based on information theory learning is introduced. Correlation entropy, through a kernel function, characterizes the local similarity between random variables. Compared to the traditional second-order error criterion, it has a stronger ability to suppress heavy-tailed noise and outliers, and has been widely used in robust filtering.

[0067] Considering the significant differences in the sensitivity of different state components to sudden maneuvers, incremental sensitivity analysis is first used to screen out the key components most sensitive to flight mode switching from the target state, with the velocity component being the preferred choice. Subsequently, a correlation entropy evaluation function is constructed only in the velocity dimension to weaken the dilution effect of low-sensitivity components on pattern recognition, thereby achieving rapid differentiation between zero angle of attack (GT) mode and non-zero angle of attack (GT3) mode.

[0068] The first step is sensitivity analysis.

[0069] Nominal Model: In the GT3 model, the state derivative at time t follows the following nonlinear ordinary differential equation: ; in, , .

[0070] This invention artificially introduces a +1% step deviation into the missile's core parameters, including initial position (Px), initial velocity (Vx), main engine thrust factor, mass dissipation rate, and target setting latitude and longitude, and analyzes the normalized sensitivity measurement formula for the disturbance propagation effect: Speed ​​sensitivity ( ): ; Position sensitivity ( ): ; Comparative analysis of graphs under the same physical mutation input shows that, when faced with the same maneuver mutation, the sensitivity curve of the velocity dimension (Sv) can produce a steep jump at the moment of mutation; while the sensitivity curve of the position dimension (Sp) is almost zero in the early stage of mutation.

[0071] The conclusion is that, when faced with the same maneuvering anomalies, the transient response sensitivity in the velocity dimension is significantly better than that in the position dimension.

[0072] Secondly, the most important part is the explanation of the relevant entropy criterion.

[0073] For any candidate model At any moment In the prediction phase, the mean of the predicted state is obtained from UKF. With predicted covariance To improve the filtering stability under complex noise and model mismatch conditions, Normalized Innovative Square (NIS) is introduced to adaptively correct the prediction covariance, and symmetric sampling points are generated based on this, which are then projected onto the critical state subspace.

[0074] Further define candidate models At any moment The partial correlation entropy score is ; in, This represents the total number of sampling points used for calculating partial correlation entropy. Indicates the width of the Gaussian kernel. Indicates the first The projection of each sampling point onto the critical state subspace Representing candidate models The predicted mean in the key state subspace. In this embodiment, the sampling points are constructed using a symmetric distribution about the predicted mean; therefore, when the state dimension of the candidate model is... Sometimes, To avoid the zero-error samples from having a dominant effect on the kernel function, some correlation entropy calculations only use decentralized symmetric sampling points, thereby enhancing the ability to characterize the discrete characteristics of the state distribution.

[0075] The larger the value, the more concentrated the prediction distribution of the candidate model is in the critical state subspace, and the stronger its consistency with the current real flight mode.

[0076] To suppress score fluctuations caused by transient noise, a length of [length missing] is used. A sliding window is used to smooth the scores: .

[0077] The third step is to make a judgment based on the separability of the model.

[0078] After obtaining the maximum relevance entropy score for each candidate dynamic model, it is still necessary to further evaluate the distinguishability between different models to avoid misjudgment during weakly separable or mode transition stages. To this end, this invention further constructs a mode separability metric:

[0079] ; This metric essentially reflects the relative differences between different candidate models in the critical state subspace: when the discrete characteristics of the predicted distributions of the two models in the velocity subspace are significantly different, the difference in the correlation entropy score increases, thus corresponding to a larger... Conversely, when the target is in a mode transition or weak maneuver phase, both models can explain the current motion characteristics well, and their relevant entropy scores tend to be similar, leading to... Smaller.

[0080] ; in, User-defined separability threshold. Based on the above separability metrics, a decision threshold is introduced. The pattern recognition results are divided into two categories: separable and inseparable. When the current flight mode is determined to be separable, the UKF posterior estimation result corresponding to the candidate model is directly output; when If the current flight mode is determined to be inseparable, the estimation results of the GT model and the GT3 model are fused and output.

[0081] The fourth step is to perform joint estimation of state and parameters and fusion output based on the model's separability judgment results.

[0082] In this step, a joint estimation algorithm for the target state and parameters is designed based on the separability judgment result of the dynamic model. When the dynamic model is separable, the unscented Kalman filter algorithm is used to jointly estimate the target state and parameters based on the currently identified dynamic model; when the dynamic model is not separable, the state and parameter estimation results under each model are fused and output to avoid large estimation errors caused by mode misuse.

[0083] The first step is state estimation under the separable pattern.

[0084] UKF constructs deterministic sampling points (Sigma points) near the state mean and covariance through unscented transformations, and then propagates them through nonlinear functions, thereby achieving a high-precision approximation of the statistics of nonlinear systems.

[0085] Set time The augmented state vector is: ; in, and These represent the target's position and velocity, respectively. Represents the dynamic parameters. The system state equation and measurement equation are as follows:

[0086] ; ; in, It is a nonlinear state transition function. It is a nonlinear measurement function. For process noise, To measure noise, the following conditions must be met: .

[0087] At any moment Given the posterior mean of the state and posterior covariance Let the state dimension be... Then the scaling parameter of UKF is defined as:

[0088] ; in, These are the parameters for the unscented transform. Based on these parameters, the following is constructed: Sigma points:

[0089] ; And the predicted mean and covariance are obtained through unscented transformation: ; in, Representative deviation term .

[0090] To improve the robustness of the filter under model mismatch and anomalous measurement conditions, an adaptive covariance adjustment strategy based on normalized innovation square (NIS) is adopted. For candidate models... Its innovation statistic is defined as:

[0091] ; This processing can adaptively amplify uncertainty when innovation anomalies increase, thereby avoiding excessive convergence of the filter and improving the stability of state and parameter estimation.

[0092] The predicted measurement statistics are further obtained through measurement function propagation, and the Kalman gain is constructed. ; This completes the joint update of state and parameters: .

[0093] Secondly, there is state estimation under the indivisible mode.

[0094] When the current flight mode is inseparable, the estimation results of the GT model and the GT3 model are fused and output, and normalized weights are constructed based on their relevant entropy scores: Thus, the fusion state estimate is obtained. This approach aims to mitigate the propagation impact of pattern misjudgment on the joint estimation of state and parameters. It should be noted that, in the case where patterns are inseparable, only kinematic state components with consistent physical meaning are fused, while the dynamic parameters retain the estimation results corresponding to the candidate patterns. This avoids estimation distortion caused by unconstrained averaging between parameters with different physical meanings.

[0095] Thus, at the modeling level, this invention employs a simplified model set composed of GT and GT3, which retains the physical interpretability of the dynamic model while also representing the characteristics of both zero and non-zero angle of attack flight states, avoiding the systematic mismatch of a single model in complex active phase scenarios. At the pattern recognition level, a flight pattern recognition method based on a combination of partial correlation entropy and sensitivity analysis is constructed, eliminating interference from sluggish state components and achieving rapid capture and low-latency response to underlying dynamical abrupt changes. At the tracking framework level, this invention introduces pattern separability analysis, coupling pattern recognition and state estimation in a coupled design. When patterns are separable, it maintains deterministic output of the recognition results; when patterns are inseparable, it employs fused output, which helps reduce estimation jumps caused by incorrect model selection and improves the stability and robustness of the tracking process.

[0096] Secondly, the present invention also provides a ballistic missile active phase tracking device, such as... Figure 3 As shown, it includes: Module 201 is used to construct a set of modes for describing the active phase flight of a ballistic missile. The set of modes includes a gravity turning model for describing the zero angle of attack flight state and a three-dimensional gravity turning model for describing the non-zero angle of attack flight state.

[0097] The identification module 202 is used to obtain the state prediction mean and prediction covariance of each model through the prediction step of unscented Kalman filtering for the gravity turning model and the three-dimensional gravity turning model, respectively; from the state prediction mean and state prediction covariance, the key state components most sensitive to flight mode switching are screened out through sensitivity analysis, and the partial correlation entropy score of each model is calculated based on the key state components to identify the flight mode at the current moment. The partial correlation entropy score is used to quantify the degree of matching between each candidate model and the real flight state in terms of key state components.

[0098] The judgment module 203 is used to construct a pattern separability metric based on the partial correlation entropy scores of the gravity turning model and the three-dimensional gravity turning model, and compare the separability metric with a preset separability threshold to determine whether the gravity turning model and the three-dimensional gravity turning model can be reliably distinguished at the current moment; wherein, the separability threshold is used to control the aggressiveness of pattern recognition.

[0099] The determination module 204 is used to determine the tracking result if it is determined that the flight mode can be reliably distinguished, and to use the unscented Kalman filter posterior estimation result of the model corresponding to the currently identified flight mode as the tracking result; if it is determined that the flight mode cannot be reliably distinguished, it calculates the normalized weight based on the partial correlation entropy scores of the two models, and uses the weighted fusion of the state estimation results of the two models as the tracking result.

[0100] The present invention also provides a computer-readable storage medium storing a computer program that can be used to execute the above-described... Figure 1 The steps of a ballistic missile active phase tracking method are provided.

[0101] This invention also provides a computer device. At the hardware level, the computer device includes a processor, an internal bus, a network interface, memory, and non-volatile memory, and may also include other hardware required for various operations. The processor reads the corresponding computer program from the non-volatile memory into memory and then executes it to achieve the above-mentioned functions. Figure 1 The steps of a ballistic missile active phase tracking method are provided.

[0102] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0103] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, as well as combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0104] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0105] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0106] It should be noted that the specific embodiments described above enable those skilled in the art to more fully understand the present invention, but do not limit the present invention in any way. Therefore, although the present invention has been described in detail in this specification, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the present invention; and all technical solutions and improvements that do not depart from the spirit and scope of the present invention are covered within the protection scope of the patent of the present invention. No reference numerals in the claims should be construed as limiting the scope of the claims.

Claims

1. A method of tracking a ballistic missile in its boost phase, characterized by, The method includes: A set of models is constructed to describe the flight of a ballistic missile in the active phase. The set of models includes a gravity turning model for describing the zero angle of attack flight state and a three-dimensional gravity turning model for describing the non-zero angle of attack flight state. For the gravity turning model and the three-dimensional gravity turning model, the state prediction mean and prediction covariance of each model are obtained through the prediction step of unscented Kalman filtering. From the state prediction mean and state prediction covariance, the key state components most sensitive to flight mode switching are screened out through sensitivity analysis, and the partial correlation entropy score of each model is calculated based on the key state components to identify the flight mode at the current moment. The partial correlation entropy score is used to quantify the degree of matching between each candidate model and the real flight state in terms of key state components. Based on the partial correlation entropy scores of the gravity turning model and the 3D gravity turning model, a pattern separability metric is constructed, and the separability metric is compared with a preset separability threshold to determine whether the gravity turning model and the 3D gravity turning model can be reliably distinguished at the current moment; wherein, the separability threshold is used to control the aggressiveness of pattern recognition; If it is determined that the two models can be reliably distinguished, the unscented Kalman filter posterior estimation result of the model corresponding to the currently identified flight mode will be used as the tracking result; if it is determined that the two models cannot be reliably distinguished, the normalized weights will be calculated based on the partial correlation entropy scores of the two models, and the state estimation results of the two models will be weighted and fused to serve as the tracking result.

2. The method of claim 1, wherein, The key state components most sensitive to flight mode switching, as identified through sensitivity analysis, include: A preset perturbation is applied to the flight evolution factors of the three-dimensional gravity turning model, and the normalized sensitivity measure of each state component relative to the flight evolution factors is calculated to obtain the normalized sensitivity measure values ​​of the position component and the velocity component; the flight evolution factors include the initial state, thrust parameters, mass dissipation, target latitude and longitude, and interstage time series. When the normalized sensitivity metric of the velocity component is greater than the normalized sensitivity metric of the position component, all velocity components are identified as the critical state components.

3. The method of claim 1, wherein, The partial correlation entropy score of each model is calculated based on the key state components, including: For any turning model, the predicted state mean and predicted covariance are obtained by unscented Kalman filtering. Based on the predicted state mean and predicted covariance, sampling points symmetrically distributed about the predicted mean are generated; All sampling points are projected onto the key state subspace composed of the key state components, and a partial correlation entropy score is calculated based on the decentralized symmetric sampling points. The partial correlation entropy score is smoothed using a sliding window of preset length to obtain a smoothed partial correlation entropy score.

4. The method of claim 3, wherein, The separability metrics for the construction pattern include: The ratio of the absolute value of the difference between the smoothed partial correlation entropy scores of the gravity turning model and the three-dimensional gravity turning model to the larger score is calculated, and the ratio is used as the separability metric. When the separability metric is greater than or equal to the separability threshold, it is determined that the two objects can be reliably distinguished; when the separability metric is less than the separability threshold, it is determined that the two objects cannot be reliably distinguished.

5. The method of claim 4, wherein, The step of calculating normalized weights based on the partial correlation entropy scores of the two models, and then weighting and fusing the state estimation results of the two models to output the following: Calculate the normalized weights of the two models based on their smoothed partial correlation entropy scores. The normalized weights are used to perform weighted fusion of the estimation results of the kinematic state components of each model to obtain the fused kinematic state estimate. For the estimation results of the dynamic parameters of each model, the dynamic parameter estimation results of the model with higher smoothed partial correlation entropy scores in the gravity turning model and the three-dimensional gravity turning model are retained.

6. The method of claim 1, wherein, After constructing a set of patterns to describe the active phase flight of a ballistic missile, the method further includes constructing a joint measurement model of radar and dual infrared detectors for the unscented Kalman filter: Obtain the deployment position of the forward ground-based radar in the geocentric fixed coordinate system, transform the real-time position of the ballistic missile target in the geocentric fixed coordinate system to the northeast local coordinate system, and establish radar measurement equations including radial distance, azimuth angle and elevation angle. Obtain the deployment positions of the two infrared detectors in the geocentric fixed coordinate system, and establish the measurement equations for the elevation angle and azimuth angle of the target relative to each infrared detector; The radar measurement equation and the measurement equation of the dual infrared detector are unified to form a nonlinear measurement function, which is used for the measurement update of the unscented Kalman filter.

7. A ballistic missile boost phase tracking apparatus, characterized by, The device includes: A construction module is used to construct a set of modes for describing the active phase flight of a ballistic missile. The set of modes includes a gravity turning model for describing the zero angle of attack flight state and a three-dimensional gravity turning model for describing the non-zero angle of attack flight state. The identification module is used to obtain the state prediction mean and prediction covariance of each model through the prediction step of the gravity turning model and the three-dimensional gravity turning model respectively through the prediction step of unscented Kalman filtering; from the state prediction mean and state prediction covariance, the key state components most sensitive to flight mode switching are screened out through sensitivity analysis, and the partial correlation entropy score of each model is calculated based on the key state components to identify the flight mode at the current moment. The partial correlation entropy score is used to quantify the degree of matching between each candidate model and the real flight state in terms of key state components. The judgment module is used to construct a pattern separability metric based on the partial correlation entropy scores of the gravity turning model and the three-dimensional gravity turning model, and compare the separability metric with a preset separability threshold to determine whether the gravity turning model and the three-dimensional gravity turning model can be reliably distinguished at the current moment; wherein, the separability threshold is used to control the aggressiveness of pattern recognition; The determination module is used to determine the tracking result if the model corresponding to the currently identified flight mode is reliably distinguishable, and to use the unscented Kalman filter posterior estimate of the model as the tracking result if the model is not reliably distinguishable. If the model is determined to be unreliably distinguishable, the module calculates the normalized weights based on the partial correlation entropy scores of the two models, and then uses the weighted fusion of the state estimates of the two models as the tracking result.

8. A computer-readable storage medium, characterized in that, The storage medium stores a computer program, which, when executed by a processor, implements the method described in any one of claims 1 to 6.

9. A computer device, comprising: The method includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the processor executes the program to implement the method described in any one of claims 1 to 6.

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