Multi-station cooperative ballistic estimation method, system, device and storage medium

Abstract

The present disclosure provides a multi-station cooperative ballistic prediction method, system, device and storage medium, which comprises: acquiring ballistic data, the ballistic data containing the position coordinates of the target at each time; initializing the state vector and covariance matrix of the extended Kalman filter according to the initial time state of the theoretical trajectory to determine the initial time ballistic state; based on the initial time ballistic state, performing incremental state prediction at a preset time step at multiple ground stations to obtain the current predicted ballistic state; after completing one incremental prediction, updating the observation value of the target at the ground station as a self-tracking station; judging whether to converge according to the updated observation value combined with a preset condition, if the convergence condition is met, the observation value is taken as the prediction result, if the convergence condition is not met, the incremental prediction is continued. This process does not require telemetry data support, and only relies on the multi-station guidance of tracking data, thereby improving the stability of multi-station cooperative tracking.

Description

Technical Field

[0001] This disclosure relates to the field of aerospace telemetry, tracking and control and spacecraft tracking technology, and in particular to a multi-station collaborative trajectory prediction method, system, equipment and storage medium. Background Technology

[0002] During rocket launches and flight tests, ground-based tracking and control networks are required to track and measure rockets in flight in real time. These networks typically consist of multiple antennas and optical measurement devices distributed across different geographical locations. Each ground station needs to accurately determine the azimuth and elevation angles of the rocket relative to its location in order to control the pointing of its antennas or optical measurement devices and effectively track the target (i.e., the rocket or satellite).

[0003] In practical applications, the following problems often exist: (1) There is a deviation between the theoretical trajectory and the actual trajectory. Before launch, a rocket's theoretical trajectory (i.e., nominal trajectory) is planned based on factors such as thrust models, aerodynamic parameters, and the Earth's gravitational field. However, due to the influence of actual flight factors such as thrust deviation, wind disturbances, and attitude control errors, the rocket's actual flight trajectory inevitably deviates from the theoretical trajectory. Over time, this deviation can accumulate to several kilometers or even tens of kilometers. If ground stations rely solely on the theoretical trajectory for pointing, the target will drift out of the antenna beam range, resulting in tracking loss.

[0004] (2) Some ground stations are unable to autonomously capture and track data. Under a multi-station joint telemetry and control system, not all ground stations can autonomously acquire and track targets during the initial stage or throughout the rocket's launch. Some ground stations may be unable to establish stable angle tracking autonomously due to factors such as long distance, low elevation angle, equipment performance limitations, or weak target signals. These ground stations require external guidance data to assist in target acquisition.

[0005] (3) Large-aperture antennas require high data accuracy. Large-aperture antennas have a smaller beam angle, and the pointing deviation of the guidance data must be controlled within the beam width range; otherwise, the target will still deviate from the beam, and guidance will fail.

[0006] (4) High real-time requirements Rockets travel at extremely high speeds (up to several kilometers per second), requiring ground station antennas to be updated in real time. The computational delay for guidance data must be controlled to the order of milliseconds to prevent the rocket from exceeding the antenna beam range.

[0007] The above method suffers from poor target tracking stability when multiple ground stations coordinate telemetry and control.

[0008] The aforementioned deficiencies are those that those skilled in the art would like to overcome. Summary of the Invention

[0009] (a) Technical problems to be solved To address the aforementioned problems in the prior art, this disclosure provides a multi-station collaborative ballistic prediction method, system, device, and storage medium, which solves the problem of poor target tracking stability during collaborative telemetry and control by multiple ground stations in the prior art.

[0010] (II) Technical Solution To achieve the above objectives, the main technical solutions adopted in this disclosure include: Firstly, this disclosure provides a multi-station collaborative ballistic prediction method, including: Acquire ballistic data, which includes the target's position coordinates at various times; Based on the initial state of the theoretical trajectory, the state vector and covariance matrix of the extended Kalman filter (EKF) are initialized to determine the initial trajectory state. Based on the initial trajectory state, incremental state prediction is performed at multiple ground stations with a preset time step to obtain the current predicted trajectory state. After completing an incremental prediction, the ground station is used as a self-tracking station to update the target's observations. The system determines whether the prediction has converged based on the updated observations and preset conditions. If the convergence conditions are met, the observations are used as the prediction results. If the convergence conditions are not met, incremental prediction continues.

[0011] In one exemplary embodiment of this disclosure, acquiring ballistic data includes: Obtain the position vectors of each data point based on the input theoretical ballistic file; If velocity is not provided, the finite difference method is used to calculate the velocity information based on the position vector. In one exemplary embodiment of this disclosure, the state vector is a multidimensional vector, including position coordinates (three-dimensional), velocity components (three-dimensional), azimuth system deviation, and elevation system deviation. Therefore, the number of dimensions of the multidimensional vector is 6 + 2N, where N is the number of ground stations and the value of N is greater than or equal to 1.

[0012] The covariance matrix includes position component uncertainty, velocity component uncertainty, and deviation component uncertainty; The determination of the ballistic state at the initial moment includes: The initial value of the deviation component of the covariance matrix is ​​set to 0; The state vector of the theoretical ballistic state at the initial moment is used as the reference.

[0013] In an exemplary embodiment of this disclosure, the step of performing incremental state prediction with a preset time step based on the initial ballistic state to obtain the current predicted ballistic state includes: Using the ballistic interpolation function, the theoretical ballistic state at the current moment is obtained as the initial ballistic state, which includes position and velocity components. Calculate the theoretical trajectory increment of the current theoretical trajectory state relative to the theoretical trajectory state of the previous time. The theoretical trajectory increment includes the motion trend of the theoretical trajectory in terms of direction and velocity over a certain time period. The corrected ballistic state estimate is obtained by superimposing the theoretical ballistic increment on the initial ballistic state. Covariance predictions are calculated for the position and velocity components in the corrected ballistic state, respectively. Update the reference state to obtain the current predicted trajectory state.

[0014] In one exemplary embodiment of this disclosure, updating the observations of the target at multiple ground stations includes: The target observation values, which are used as tracking stations, are acquired at multiple ground stations. The target observation values ​​include azimuth angle observation values ​​and elevation angle observation values. Based on the target observations, the predicted observations for each tracking station are calculated using the observation function. Calculate the Jacobian matrix of the observation function with respect to the state vector; Calculate the Kalman gain; The observation residuals are obtained by normalizing the azimuth difference values. Perform a status update; Perform covariance update; Based on the latest state and covariance of the previous ground station as the initial state of the current ground station, multiple ground stations are iteratively updated. Apply hard truncation constraints to the deviation components in the state vector.

[0015] In one exemplary embodiment of this disclosure, before the multiple ground stations acquire their respective target observations as tracking stations, the method further includes: Obtain the actual location of the tracking station; Calculate the target observation value based on the actual location.

[0016] In one exemplary embodiment of this disclosure, determining whether convergence has occurred based on the updated observations and preset conditions includes: Based on the updated observations, calculate the rate of change of the diagonal elements of the covariance matrix and take the maximum rate of change; Calculate the standard deviation of the location; The convergence is determined by comparing the maximum rate of change and the standard deviation of the location with preset conditions; the preset conditions are that the maximum rate of change is less than the convergence threshold and the standard deviation of the location is less than the preset threshold.

[0017] Determine whether to continue incremental forecasting.

[0018] Secondly, this disclosure also provides a multi-station collaborative ballistic prediction system, including: The data acquisition module is used to acquire ballistic data, which includes the target's position coordinates at various times. The initialization module is used to initialize the state vector and covariance matrix of the extended Kalman filter (EKF) based on the initial state of the theoretical trajectory, and to determine the initial trajectory state. The incremental prediction module is used to perform incremental state prediction at multiple ground stations based on the initial ballistic state at a preset time step, so as to obtain the current predicted ballistic state. The observation update module is used to update the observations of the target by using the ground station as a self-tracking station after completing an incremental prediction. The convergence judgment module is used to determine whether convergence has occurred based on the updated observations and preset conditions. If the convergence conditions are met, the observations are used as the prediction results. If the convergence conditions are not met, incremental prediction continues.

[0019] Thirdly, this disclosure also provides an electronic device, characterized in that it includes: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors perform the methods described above.

[0020] Fourthly, this disclosure also provides a computer-readable medium having a computer program stored thereon, which, when executed by a processor, implements the methods described above.

[0021] (III) Beneficial Effects The beneficial effects of this disclosure are that it provides a multi-station cooperative trajectory prediction method, system, device, and storage medium. It uses an incremental approach based on extended Kalman filtering for multi-station cooperative rocket trajectory prediction to achieve real-time estimation. This process does not require telemetry data support, relying solely on multi-station guidance from tracking data, thereby improving the stability of multi-station cooperative tracking. Attached Figure Description

[0022] Figure 1 This is a flowchart illustrating the steps of a multi-station collaborative ballistic prediction method provided in one embodiment of this disclosure; Figure 2 This is a flowchart illustrating step S110 provided in one embodiment of the present disclosure; Figure 3 This is a flowchart illustrating step S130 provided in one embodiment of the present disclosure; Figure 4 This is a schematic diagram of the process of updating the observation values ​​of the target at multiple ground stations in step S140 of an embodiment of the present disclosure; Figure 5 This is a schematic diagram of the process in step S150 of this disclosure, in which the updated observation value is combined with preset conditions to determine whether convergence has occurred. Figure 6 This is a schematic diagram of the composition of a multi-station collaborative ballistic prediction system provided in another embodiment of this disclosure; Figure 7 This is a schematic diagram of the internal structure of a computer system for an electronic device, provided in yet another embodiment of the present disclosure. Detailed Implementation

[0023] To better explain and facilitate understanding of this disclosure, the following detailed description of the disclosure is provided in conjunction with the accompanying drawings and specific embodiments.

[0024] All technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs. The terminology used herein in the specification of this disclosure is for the purpose of describing particular embodiments only and is not intended to be limiting of this disclosure. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0025] In the relevant embodiments of this disclosure, the deviation in target trajectory prediction during multi-station coordination, leading to guidance failure, is due to the following reasons: (1) Theoretical ballistic guidance Pure theoretical trajectory guidance is the simplest and most direct guidance method. Its core idea is: based on the theoretical trajectory planned in advance before launch, the predicted position of the rocket at each moment is obtained by interpolation according to the time series, and then the azimuth and elevation angles corresponding to the ground control stations are calculated to complete the antenna guidance.

[0026] Existing shortcomings: This method relies entirely on theoretical trajectories and fails to adequately account for various deviations during actual flight. As flight time increases, the positional deviation between the theoretical and actual trajectories accumulates, reaching levels ranging from several kilometers to over ten kilometers. The resulting angular errors often exceed the beamwidth of the telemetry and control antenna, ultimately leading to guidance failure. Furthermore, this method lacks the ability to correct using measured data, resulting in poor robustness.

[0027] (2) Single-station angle direct transmission method The implementation logic of the single-station angle direct transmission method is as follows: after a certain ground station achieves autonomous tracking of the target, it directly forwards the azimuth and elevation data it has measured to other ground tracking and control stations, and each station completes the guidance and pointing calculation through coordinate transformation.

[0028] Existing shortcomings: 1) Single-station angle observation only provides two observations: azimuth and elevation. It lacks distance information and cannot uniquely determine the three-dimensional spatial position of the target.

[0029] 2) The coordinate transformation process relies on the prior distance information provided by the theoretical trajectory, which will introduce systematic errors related to the deviation of the theoretical trajectory.

[0030] 3) It is impossible to integrate and utilize observation information from multiple stations, making it difficult to improve guidance accuracy through redundant information from multiple sources.

[0031] 4) It lacks filtering and smoothing capabilities, and the original observation noise will be directly transmitted to the guiding data, affecting the pointing stability.

[0032] (3) Traditional EKF ballistic filtering The Extended Kalman Filter (EKF) is a classic method for solving the state estimation of nonlinear systems. Traditional EKF ballistic filtering typically uses a dynamic model that includes factors such as thrust, aerodynamic force, and gravity as the state prediction model, and uses ground station angle observation information as measurement updates to achieve recursive estimation of the ballistic state.

[0033] Existing shortcomings: 1) It is highly dependent on the dynamic model, requiring accurate prior information such as thrust curves, aerodynamic coefficients, and atmospheric models. Model errors and parameter uncertainties directly reduce the accuracy of state prediction. Model bias is particularly significant in scenarios where aircraft parameters are not fully calibrated or information is limited.

[0034] 2) Limitations of single-station measurement updates: Most traditional EKF implementations only support measurement updates for a single ground station, making it difficult to simultaneously integrate self-tracking data from multiple stations for joint state estimation, and thus failing to fully leverage the redundancy and accuracy advantages of multi-station measurement and control.

[0035] (4) GNSS data guidance method This method receives downlink telemetry data from the rocket, extracts real-time positioning information from the Global Navigation Satellite System (GNSS), calculates the rocket's current precise position, and then generates guidance commands for various ground stations, achieving high-precision pointing of the antenna to the rocket.

[0036] The shortcomings are: This method heavily relies on the availability and resolvability of telemetry data, requiring the completion of telemetry format parsing and GNSS data extraction. Significant differences exist in the telemetry frame structure and data definitions among different launch vehicle models or flight targets, resulting in poor universality. Furthermore, due to model-specification requirements, some rockets do not disclose their telemetry parsing specifications, making it impossible to obtain GNSS positioning information. This hinders the widespread applicability of this method in multi-model, cross-platform telemetry and control missions.

[0037] To address the aforementioned technical problems, this disclosure provides a multi-station collaborative ballistic prediction method, system, device, and storage medium. It utilizes observation data from a small number of self-tracking ground stations to fuse theoretical ballistic information, thereby estimating the rocket's precise position in the Earth-centered Earth-fixed (ECEF) coordinate system in real time, and providing precise azimuth and elevation guidance data for other ground stations that have not successfully tracked the rocket autonomously.

[0038] Figure 1 This is a flowchart illustrating the steps of a multi-station collaborative ballistic prediction method provided in one embodiment of this disclosure, as follows: Figure 1 As shown, this multi-station collaborative ballistic prediction method includes the following steps: In step S110, ballistic data is acquired, wherein the ballistic data includes the target's position coordinates at each time step; In step S120, the state vector and covariance matrix of the extended Kalman filter (EKF) are initialized according to the initial state of the theoretical trajectory to determine the initial trajectory state. In step S130, based on the ballistic state at the initial moment, incremental state prediction is performed at multiple ground stations with a preset time step to obtain the current predicted ballistic state. In step S140, after completing one incremental prediction, the ground station is used as a self-tracking station to update the observations of the target. In step S150, the convergence is determined based on the updated observations and preset conditions. If the convergence conditions are met, the observations are used as the prediction results. If the convergence conditions are not met, incremental prediction continues.

[0039] Based on the above steps S110~S150, this disclosure provides a multi-station cooperative real-time rocket trajectory estimation and guidance method based on incremental extended Kalman filtering. The following is a detailed description of each step: like Figure 1 As shown, in step S110, ballistic data is acquired, which includes the target's position coordinates at each time point.

[0040] In one exemplary embodiment of this disclosure, this step mainly involves loading ballistic data.

[0041] Figure 2This is a flowchart illustrating step S110 provided in one embodiment of the present disclosure, as follows: Figure 2 As shown, the specific steps include: Step S111: Obtain the position vector of each data point based on the input theoretical ballistic file; Step S112: If velocity is not provided, the finite difference method is used to calculate velocity information based on the position vector. Since the entire filtering process requires velocity information, the finite difference method is used for trajectories where velocity is not provided to obtain the target's position and velocity at each moment, thereby combining the velocity information to determine the target's position coordinates in the Earth-centered Earth-fixed (ECEF) coordinate system at each moment.

[0042] like Figure 1 As shown, in step S120, the state vector and covariance matrix of the extended Kalman filter (EKF) are initialized according to the initial state of the theoretical trajectory to determine the initial trajectory state.

[0043] In one exemplary embodiment of this disclosure, this step involves filter initialization, using the initial state of the theoretical trajectory, i.e., an initialized state vector and an initialized covariance matrix. The initialized state vector is a multidimensional vector, including position coordinates, velocity components, azimuth system deviation, and elevation system deviation. The number of dimensions of the multidimensional vector is 6 + 2N, where N is the number of ground stations, and the value of N is greater than or equal to 1. The initialized covariance matrix is ​​a diagonal matrix, including position component uncertainty, velocity component uncertainty, and deviation component uncertainty.

[0044] This step, which involves determining the initial ballistic state, includes: The initial value of the deviation component of the covariance matrix is ​​set to 0; The state vector of the theoretical ballistic state at the initial moment is used as the reference.

[0045] like Figure 1 As shown, in step S130, based on the ballistic state at the initial moment, incremental state prediction is performed at multiple ground stations with a preset time step to obtain the current predicted ballistic state.

[0046] In one exemplary embodiment of this disclosure, this step mainly involves incremental state updates and predictions.

[0047] Figure 3 This is a flowchart illustrating step S130 provided in one embodiment of the present disclosure, as follows: Figure 3 As shown, the specific steps include: Step 131: Use the ballistic interpolation function to obtain the theoretical ballistic state at the current moment as the initial ballistic state, which includes position components and velocity components. Step 132: Calculate the theoretical trajectory increment of the theoretical trajectory state at the current moment relative to the theoretical trajectory state at the previous moment. The theoretical trajectory increment includes the motion trend of the theoretical trajectory in terms of direction and velocity within a certain time period. Step 133: Based on the initial ballistic state, superimpose the theoretical ballistic increment to obtain the corrected ballistic state estimate; Step 134: Calculate the covariance prediction for the position and velocity components in the corrected ballistic state; Step 135: Update the reference state to obtain the current predicted trajectory state.

[0048] like Figure 1 As shown, in step S140, after completing an incremental prediction, the ground station is used as a self-tracking station to update the observation values ​​of the target.

[0049] In one exemplary embodiment of this disclosure, this step mainly involves updating multi-station observations.

[0050] Figure 4 This is a schematic diagram illustrating the process of updating the target observations at multiple ground stations in step S140 of one embodiment of this disclosure, as shown below. Figure 4 As shown, the specific steps include: Step S141: Obtain target observation values ​​at multiple ground stations, each serving as a tracking station. The target observation values ​​include azimuth and elevation angle observation values. Step S142: Based on the target observation value, calculate the predicted observation value for each tracking station using the observation function; Step S143: Calculate the Jacobian matrix of the observation function with respect to the state vector; Step S144: Calculate the Kalman gain; Step S145: Normalize the azimuth difference value to obtain the observation residual; Step S146: Update the status; Step S147: Perform covariance update; Step S148: Based on the latest state and covariance of the previous ground station as the initial state of the current ground station, iteratively update multiple ground stations; Step S149: Apply hard truncation constraints to the deviation components in the state vector.

[0051] In one exemplary embodiment of this disclosure, before the multiple ground stations acquire their respective target observations as tracking stations, the method further includes: Obtain the actual location of the tracking station; Calculate the target observation value based on the actual location.

[0052] like Figure 1 As shown, in step S150, the convergence is determined based on the updated observations and preset conditions. If the convergence conditions are met, the observations are used as the prediction results. If the convergence conditions are not met, incremental prediction continues.

[0053] In one exemplary embodiment of this disclosure, this step mainly involves convergence determination.

[0054] Figure 5 This is a flowchart illustrating the process of determining convergence based on the updated observations and preset conditions in step S150 of one embodiment of the present disclosure. Figure 5 As shown, the specific steps include: Step S151: Based on the updated observations, calculate the rate of change of the diagonal elements of the covariance matrix and take the maximum rate of change. Step S152: Calculate the standard deviation of the location; The convergence is determined by comparing the maximum rate of change and the standard deviation of the location with preset conditions; the preset conditions are that the maximum rate of change is less than the convergence threshold and the standard deviation of the location is less than the preset threshold.

[0055] Step S153: Determine whether to continue incremental forecasting.

[0056] Based on the above, another embodiment of the present invention provides a multi-station cooperative real-time rocket trajectory estimation and guidance method based on incremental extended Kalman filtering, comprising the following steps: (1) System initialization The system loads theoretical ballistic data, which includes the rocket's position coordinates in the Earth-fixed coordinate system (ECEF) at various times. ECEF is a Cartesian space reference system that represents the location near the Earth (including its surface, interior, atmosphere, and surrounding outer space) as the X, Y, and Z measurements of its center of mass.

[0057] The system supports multiple input formats, including ECEF direct coordinate format, latitude-longitude-altitude (LLA) format, and launch coordinate format. WGS84 is the most common ECEF system, also known as the latitude-longitude-altitude coordinate system (longitude, latitude, and altitude, i.e., LLA coordinate system).

[0058] For ballistic files containing only position data (excluding velocity information), the velocity is automatically calculated using a differential method: The first point uses forward differencing: Formula (1) The midpoint uses central difference: Formula (2) The final point uses backward difference: Formula (3) in For the first i The position vector of each data point For the corresponding cumulative time, i The numerical range of is 0 to n.

[0059] (2) Filter initialization Initialize the state vector and covariance matrix of EKF with the initial state of the theoretical trajectory.

[0060] First, the state vector is an extended-dimensional vector, containing position, velocity, and system deviations at various ground stations: Formula (4) in For estimated values, dimensions 1-3 ( x 0 , y 0 , z 0 ) represents the ECEF position coordinates, dimensions 4-6 ( v x0 , v y0 , v z0 The velocity component is represented by the first two components, starting from the 7th dimension. Each pair of components corresponds to the azimuth system deviation of a ground station. b Az，j And elevation angle system deviation b El，j The value of N ranges from 1 to N, where N is the number of registered ground stations and is a positive integer greater than or equal to 1. For example, the 7th and 8th dimensions correspond to the azimuth system deviation of the first ground station. b Az，1 and elevation angle system deviation b El，1 ..., the azimuth system deviation of the N-1 to Nth dimensions corresponding to the last ground station b Az，N and elevation angle system deviation b El，N Therefore, by combining 3D position information, 3D velocity information, and 2N-dimensional ground station system deviations, the resulting state vector has a dimension of 6+2N.

[0061] For example, in the initial state vector, only position and velocity have values, while other deviation components are 0. Therefore, the state vector is initialized as follows: Formula (5) Secondly, after initializing the covariance matrix, the initial covariance matrix is ​​obtained. P 0 is set as a diagonal matrix. In this embodiment, the initial uncertainty of the position component is set to 1000m, the initial uncertainty of the velocity component is set to 100m / s, and the initial uncertainty of the deviation component is set to 0.03° (reflecting the prior uncertainty range of the station deviation), that is: Formula (6) For example, the initial covariance matrix Formula (7) The initial value of the deviation component is set to 0 (prior assumption of no deviation). Simultaneously, the theoretical trajectory state at the initial moment is recorded as a reference state. Formula (8) For example, the reference state is saved as follows: Formula (9) (3) Incremental state update For each time step (which can be simply referred to as a time step) k Perform the following incremental prediction: a) Obtain the theoretical ballistic state at the current moment Obtain the current time using the ballistic interpolation function. t k Corresponding theoretical ballistic state: Formula (10) For example, if the current time is t 1 At this point, the theoretical ballistic state is: Formula (11) b) Calculate the theoretical ballistic increment Calculate the change (increment) in the theoretical ballistic state at the current moment relative to the previous moment: Formula (12) This increment is used to reflect the motion trend of the theoretical trajectory during this time period, mainly referring to changes in direction and velocity.

[0062] For example, t 0 arrive t 1 The increments in position (or direction) and velocity are expressed as: Formula (13) c) Incremental state prediction The theoretical trajectory increment is superimposed on the position and velocity components of the current state estimate, rather than directly replacing them. The current state estimate can be understood as the initial state, which is then iteratively updated based on observation data. The bias components remain unchanged during the prediction step (random walk model, mean unchanged): Formula (14) Formula (15) Unlike traditional EKF ballistic filtering, which relies on an accurate dynamic model to construct state transition equations, the method provided in this embodiment only uses the increments of adjacent time steps of the theoretical trajectory as an approximate description of the motion trend, applying the increments to the current estimated state through addition. Because The data already includes correction information accumulated from all previous observation updates. Incremental prediction does not disrupt these corrections, allowing observational information to continuously accumulate during the filtering process, thus achieving a gradual approximation of the actual trajectory. This method does not require knowledge of the rocket's thrust curve, aerodynamic parameters, or other dynamic information; it only needs the theoretical trajectory position-time series planned before launch to drive the prediction.

[0063] For example, based on formulas (5) and (13), the incremental state prediction is obtained as follows:

[0064] Formula (16) d) Covariance prediction Formula (17) in F k The state transition matrix (due to the use of an incremental model), F k identity matrix I 6+2N ), Q k Let the process noise covariance matrix be denoted as , and the noise variance of its position components be denoted as . The velocity component is set to 0.1. (The velocity component has relatively low noise because the velocity change is relatively gradual.) Due to the difference in magnitude, multiplying the velocity by 0.1 gives the noise variance of the angular deviation. The deviation component is set to a minimum value. (approximately 10) -12 This only prevents the covariance from degenerating into a singular matrix, reflecting the characteristic that the deviation is approximately constant.

[0065] For example, the obtained covariance prediction is: Formula (18) e) Update reference status Formula (19) Save the current theoretical state for use in calculating the increment in the next time step. That is, the theoretical state at the current time k is used as the "previous time" for use in the next round.

[0066] For example, the updated reference state is: Formula (20) (4) Multi-station observation update For each time step, after completing one state prediction, observation updates are sequentially performed on all self-tracking stations. These self-tracking stations have multiple feed sources and are equipped with tracking receivers, enabling them to close the loop signal and ensuring accurate positioning of the self-tracking state.

[0067] a) Generate observation data For each self-tracking station j Obtain the azimuth and elevation angle observations of the target from the tracking station. In a real-world system, this data comes from the real-time tracking output of the station-end equipment. The observation data contains random measurement noise and possible system biases.

[0068] For example, suppose the actual location is: Formula (21) b) Calculate the predicted observations Predicted value based on current state Through nonlinear observation function h ()Computer station j The predicted observations. The observation model adds the geometric pointing to the station system bias: Formula (22) in h geo () represents the geometric observation function (calculating azimuth and elevation angles based on position). For the ground station in the state vector j The current deviation estimate. Ground stations j The longitude, latitude, and altitude. Observation function. h geo The implementation process of () is as follows: convert the difference between the target position and the station position in the ECEF coordinate system to the station center coordinate system with the station as the origin, and then calculate the azimuth and elevation angles.

[0069] For example, the predicted observations obtained include noise and bias: Formula (23) c) Calculate the observation Jacobian matrix The observation function is calculated using numerical differentiation. h () Jacobian matrix of the state vector: Formula (24) In the specific implementation, for each coordinate axis ( x , y , z Small perturbations are applied to each component, and partial derivatives are calculated using differential methods. Since the observed values ​​(angles) do not directly depend on velocity, the partial derivatives for the velocity component are zero. The partial derivatives of the deviation components are analytical values: the partial derivative of the azimuth deviation of the current station with respect to the azimuth observation is 1, the partial derivative of the elevation deviation with respect to the elevation observation is 1, and the partial derivatives of the remaining deviation components are 0.

[0070] Formula (25) Among them, the (6+2) j -1) column and (6+2) j The columns correspond to the stations respectively. j Azimuth system deviation b Az，j and elevation angle system deviation b El，j The value is 1, and the other deviation columns are 0.

[0071] For example, the calculated Jacobian matrix is:

[0072] Formula (26) d) Kalman gain calculation Formula (27) in R j To measure the noise covariance matrix, let it be a diagonal matrix. , To measure the standard deviation of noise.

[0073] For example, the calculated Kalman gain process is as follows: Formula (28) Formula (29) e) Observation residuals Formula (30) The `normalize()` function normalizes the azimuth difference to the range of [-180°, 180°], handling azimuth jumps across 0° / 360°. For example, 0.1 and 359.9 differ by only 0.2°, and are not considered jumps.

[0074] Formula (31) f) Status update Formula (32) For example, the calculation process for state updates is as follows: Formula (33) Based on formulas (16) and (33), the state update is calculated as follows:

[0075] Formula (34) g) Covariance Update Formula (35) For example, t 0 arrive t 1 The calculation process for covariance update is as follows:

[0076] Formula (36)

[0077] Formula (37)

[0078] Formula (38) h) Multi-station sequential iteration After completing the above steps, repeat steps b) to g) for the next self-tracking station. Each update uses the latest state and covariance from the previous station. This sequential update strategy fully utilizes the mathematical properties of EKF (i.e., sequential updates of multiple independent observations are mathematically equivalent to batch joint updates), but is simpler to implement and naturally supports asynchronous processing of data arriving at different stations at different times.

[0079] i) Deviation constraints After completing the observation updates for all stations, a hard truncation constraint is applied to the bias component in the state vector: Formula (39) Formula (40) in b max= 0.05° is the upper limit of the physical constraint on the deviation, which is determined by engineering experience in equipment calibration accuracy. This constraint prevents the deviation estimate from exceeding a reasonable range due to numerical fluctuations or initial instability, ensuring that the deviation estimate always has physical meaning.

[0080] It should be noted that ground station tracking has certain specifications. For a typical 7.5m antenna, the specification is 0.02°, which can prevent excessive deviation caused by calculation errors.

[0081] (5) Convergence judgment After each observation update, calculate the rate of change of the diagonal elements of the covariance matrix: Formula (41) Only the positional components (first 3 dimensions) are examined, and the maximum rate of change is taken: Formula (42) Calculate the standard deviation of the location: Formula (43) The process is considered stable when the following conditions are met simultaneously: the rate of change of covariance is less than the convergence threshold, and the standard deviation of the location is less than a preset value: ① Rate of change of covariance ( (Convergence threshold) ②Local Standard Deviation (For example, select the default value of 1000) When continuous N conv When all steps (requirements for consecutive convergence) satisfy the stability condition, the system is considered to have converged.

[0082] The convergent state machine contains four states: ① Initialization in progress: The filter has just started; ② Converging: A stable trend has emerged, but the requirement for consecutive iterations has not yet been met; ③ Converged: Continuous N conv Step stability; ④ Divergence: A position standard deviation exceeding 10,000m indicates that the filter is diverging.

[0083] Based on the above method, model-free state prediction based on theoretical trajectory increments does not rely on dynamic models and is driven solely by theoretical trajectory sequence data. Employing an incremental prediction method, it is applicable to various rocket tracking and control scenarios. Multi-station guidance relies solely on tracking data, requiring no telemetry data support; thus improving the stability of multi-station collaborative tracking.

[0084] Figure 6This is a schematic diagram illustrating the composition of a multi-station cooperative ballistic prediction system provided in another embodiment of this disclosure, as shown below. Figure 6 As shown, the system includes a data acquisition module 610, an initialization module 620, an incremental prediction module 630, an observation update module 640, and a convergence judgment module 650. The data acquisition module 610 acquires ballistic data, which includes the target's position coordinates at various times. The initialization module 620 initializes the state vector and covariance matrix of the Extended Kalman Filter (EKF) based on the initial state of the theoretical ballistic trajectory, determining the initial ballistic state. The incremental prediction module 630 performs incremental state predictions at multiple ground stations with a preset time step based on the initial ballistic state, obtaining the current predicted ballistic state. The observation update module 640 updates the target's observations at each ground station as a self-tracking station after completing one incremental prediction. The convergence judgment module 650 determines whether convergence has occurred based on the updated observations and preset conditions. If the convergence conditions are met, the observed values ​​are used as the prediction result; otherwise, incremental prediction continues.

[0085] The following is for reference. Figure 7 It shows a schematic diagram of the structure of a computer system 400 suitable for implementing electronic devices according to embodiments of the present application. Figure 7 The electronic device shown is merely an example and should not impose any limitation on the functionality and scope of use of the embodiments of this application.

[0086] like Figure 7 As shown, the computer system 400 includes a central processing unit (CPU) 401, which can perform various appropriate actions and processes based on programs stored in read-only memory (ROM) 402 or programs loaded from storage section 408 into random access memory (RAM) 403. The RAM 403 also stores various programs and data required for the operation of the system 400. The CPU 401, ROM 402, and RAM 403 are interconnected via a bus 404. An input / output (I / O) interface 405 is also connected to the bus 404.

[0087] The following components are connected to I / O interface 405: an input section 406 including a keyboard, mouse, etc.; an output section 407 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and speakers, etc.; a storage section 408 including a hard disk, etc.; and a communication section 409 including a network interface card such as a LAN card, modem, etc. The communication section 409 performs communication processing via a network such as the Internet. Drive 410 is also connected to I / O interface 405 as needed. Removable media 411, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., are installed on drive 410 as needed so that computer programs read from them can be installed into storage section 408 as needed.

[0088] In particular, according to embodiments of this disclosure, the processes described above with reference to the flowcharts can be implemented as computer software programs. For example, embodiments of this disclosure include a computer program product comprising a computer program carried on a computer-readable medium, the computer program containing program code for performing the methods shown in the flowcharts. In such embodiments, the computer program can be downloaded and installed from a network via communication section 409, and / or installed from removable medium 411. When the computer program is executed by central processing unit (CPU) 401, it performs the functions defined above in the system of this application.

[0089] It should be noted that the storage medium shown in this application can be a computer-readable signal medium, a computer-readable medium, or any combination thereof. A computer-readable medium can be, for example,—but not limited to—an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of a computer-readable medium may include, but are not limited to: an electrical connection having one or more wires, a portable computer disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof. In this application, a computer-readable medium can be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, apparatus, or device. In this application, a computer-readable signal medium can include a data signal propagated in baseband or as part of a carrier wave, carrying computer-readable program code. Such propagated data signals can take various forms, including but not limited to electromagnetic signals, optical signals, or any suitable combination thereof. Computer-readable signal media can also be any computer-readable medium other than a computer-readable medium, which can send, propagate, or transmit a program for use by or in connection with an instruction execution system, apparatus, or device. The program code contained on the computer-readable medium can be transmitted using any suitable medium, including but not limited to: wireless, wire, optical fiber, RF, etc., or any suitable combination thereof.

[0090] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in a block diagram or flowchart, and combinations of blocks in a block diagram or flowchart, may be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions.

[0091] The units described in the embodiments of this application can be implemented in software or hardware. The described units can also be located in a processor, and the names of these units do not necessarily limit the unit itself.

[0092] On the other hand, this disclosure also provides a storage medium, which may be included in the electronic device described in the above embodiments; or it may exist independently and not assembled into the electronic device. The storage medium carries one or more programs, which, when executed by the electronic device, cause the electronic device to include the following method steps: Acquire ballistic data, which includes the target's position coordinates at various times; Based on the initial state of the theoretical trajectory, the state vector and covariance matrix of the extended Kalman filter (EKF) are initialized to determine the initial trajectory state. Based on the initial trajectory state, incremental state prediction is performed at multiple ground stations with a preset time step to obtain the current predicted trajectory state. After completing an incremental prediction, the ground station is used as a self-tracking station to update the target's observations. The system determines whether the prediction has converged based on the updated observations and preset conditions. If the convergence conditions are met, the observations are used as the prediction results. If the convergence conditions are not met, incremental prediction continues.

[0093] It should be understood that the above description of specific embodiments of this disclosure is only for illustrating the technical approach and features of this disclosure, and is intended to enable those skilled in the art to understand the content of this disclosure and implement it accordingly. However, this disclosure is not limited to the specific embodiments described above. All changes or modifications made within the scope of the claims of this disclosure should be covered by the protection scope of this disclosure.

Claims

1. A method of multi-station cooperative ballistic prediction, characterized in that, include: Acquire ballistic data, which includes the target's position coordinates at various times; Based on the initial state of the theoretical trajectory, the state vector and covariance matrix of the extended Kalman filter (EKF) are initialized to determine the initial trajectory state. Based on the initial trajectory state, incremental state prediction is performed at multiple ground stations with a preset time step to obtain the current predicted trajectory state. After completing an incremental prediction, the ground station is used as a self-tracking station to update the target's observations. The system determines whether the prediction has converged based on the updated observations and preset conditions. If the convergence conditions are met, the observations are used as the prediction results. If the convergence conditions are not met, incremental prediction continues.

2. The method of claim 1, wherein, The acquisition of ballistic data includes: Obtain the position vectors of each data point based on the input theoretical ballistic file; If the velocity is not provided, the finite difference method is used to calculate the velocity information based on the position vector.

3. The method of claim 2, wherein: The state vector is a multidimensional vector, including position coordinates, velocity components, azimuth system deviation, and elevation system deviation. The number of dimensions of the multidimensional vector is 6 + 2N, where N is the number of ground stations and the value of N is greater than or equal to 1. The covariance matrix includes position component uncertainty, velocity component uncertainty, and deviation component uncertainty; The determination of the ballistic state at the initial moment includes: The initial value of the deviation component of the covariance matrix is ​​set to 0; The state vector of the theoretical ballistic state at the initial moment is used as the reference.

4. The method of claim 1, wherein, The step of incrementally predicting the current predicted trajectory state based on the initial trajectory state with a preset time step includes: Using the ballistic interpolation function, the theoretical ballistic state at the current moment is obtained as the initial ballistic state, which includes position and velocity components. Calculate the theoretical trajectory increment of the current theoretical trajectory state relative to the theoretical trajectory state of the previous time, wherein the theoretical trajectory increment includes the motion trend of the theoretical trajectory in terms of direction and velocity over a certain time period. The corrected ballistic state estimate is obtained by superimposing the theoretical ballistic increment on the ballistic state at the initial moment; Covariance predictions are calculated for the position and velocity components in the corrected ballistic state, respectively. Update the reference state to obtain the current predicted trajectory state.

5. The method of claim 1, wherein, The updating of target observations at multiple ground stations includes: The target observation values, which are used as tracking stations, are acquired at multiple ground stations. The target observation values ​​include azimuth angle observation values ​​and elevation angle observation values. Based on the target observations, the predicted observations for each tracking station are calculated using the observation function. Calculate the Jacobian matrix of the observation function with respect to the state vector; Calculate the Kalman gain; The observation residuals are obtained by normalizing the azimuth difference values. Perform a status update; Perform covariance update; Based on the latest state and covariance of the previous ground station as the initial state of the current ground station, multiple ground stations are iteratively updated. Apply hard truncation constraints to the deviation components in the state vector.

6. The multi-station collaborative ballistic prediction method as described in claim 5, characterized in that, Before acquiring target observations from multiple ground stations, which serve as tracking stations, the process also includes: Obtain the actual location of the tracking station; Calculate the target observation value based on the actual location.

7. The multi-station cooperative ballistic prediction method as described in any one of claims 1-6, characterized in that, The step of determining whether convergence has occurred based on updated observations and preset conditions includes: Based on the updated observations, calculate the rate of change of the diagonal elements of the covariance matrix and take the maximum rate of change; Calculate the standard deviation of the location; The convergence is determined by comparing the maximum rate of change and the standard deviation of the location with preset conditions; the preset conditions are that the maximum rate of change is less than the convergence threshold and the standard deviation of the location is less than the preset threshold. Determine whether to continue incremental forecasting.

8. A multi-station collaborative ballistic prediction system, characterized in that, include: The data acquisition module is used to acquire ballistic data, which includes the target's position coordinates at various times. The initialization module is used to initialize the state vector and covariance matrix of the extended Kalman filter (EKF) based on the initial state of the theoretical trajectory, and to determine the initial trajectory state. The incremental prediction module is used to perform incremental state prediction at multiple ground stations based on the initial ballistic state at a preset time step, so as to obtain the current predicted ballistic state. The observation update module is used to update the observations of the target by using the ground station as a self-tracking station after completing an incremental prediction. The convergence judgment module is used to determine whether convergence has occurred based on the updated observations and preset conditions. If the convergence conditions are met, the observations are used as the prediction results. If the convergence conditions are not met, incremental prediction continues.

9. An electronic device, characterized in that, include: One or more processors; Storage device for storing one or more programs; When the one or more programs are executed by the one or more processors, the one or more processors implement the method as described in any one of claims 1-7.

10. A computer-readable medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the method as described in any one of claims 1-7.

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