Strong tracking method for jumping and gliding track

Abstract

The invention belongs to the technical field of aircraft trajectory tracking, and discloses a skipping gliding trajectory strong tracking method, which comprises the following steps of: establishing a target mixed motion model, describing an unpowered section of a target skipping gliding trajectory by using a kinetic model controlled by aerodynamic force and earth gravity, and describing a powered section of the trajectory by using a uniform acceleration model; a target acceleration judgment mechanism is introduced, and conversion between a dynamic model and a uniform acceleration model is achieved; establishing an observation station observation model by using observation distance, azimuth angle and elevation angle parameters, and adding observation noise; the invention provides a high-robustness unscented Kalman filtering algorithm by using an unscented Kalman filtering algorithm based on single-row unscented transformation of # imgabs0 sigma points and adding an H infinity filtering algorithm, and the high-robustness unscented Kalman filtering algorithm can improve the tracking precision and robustness, reduce the calculation amount and accelerate the calculation speed at the same time.

Description

Technical Field

[0001] The invention belongs to the technical field of aircraft trajectory tracking, and in particular relates to a jumping gliding trajectory strong tracking method. Background Art

[0002] The trajectory of the aircraft in the gliding stage is mainly a jump-glide trajectory, and the jump-glide trajectory is divided into unpowered jump-glide and powered jump-glide. Unpowered jump-glide means that the target is only affected by aerodynamic force and earth gravity in the gliding stage; powered jump-glide means that the target is also subjected to the thrust of a type of engine for a certain period of time, making the trajectory more flexible. At present, there are few studies on the tracking of powered jump-glide trajectories, so it is necessary to study it. Maneuvering target tracking is mainly divided into two parts: target motion model and filtering algorithm. The motion model is mainly established in two ways: kinematic model and dynamic model. The kinematic model is a model that directly establishes the law of target change over time, such as uniform speed model, uniform acceleration model, uniform speed turning model, etc. The dynamic model is to derive the acceleration characteristics of each direction by mechanical analysis of the target from the perspective of target force. The motion of the powered jump-glide trajectory is complex, and the tracking party cannot know the thrust of the powered stage of the aircraft. Therefore, using a single dynamic model or the above-mentioned conventional kinematic model cannot form a more accurate target motion model. The powered jump glide trajectory is divided into an unpowered segment and a powered segment according to the force and motion state. The corresponding motion model is proposed for each segment and combined into a target hybrid motion model to better fit the actual motion state of the target. Both the target state equation and the tracking measurement equation are nonlinear equations, and nonlinear filtering algorithms need to be used. The nonlinear filtering algorithms commonly used in maneuvering target tracking mainly include generalized Kalman filtering and unscented Kalman filtering.

[0003] The above-mentioned Kalman filter algorithm is based on an accurate mathematical model and the known statistical characteristics of system process noise and measurement noise. However, in practical applications, the observer cannot obtain an accurate motion model of the target, the established target motion model is only approximate, and some prior knowledge cannot be accurately obtained, which will lead to a significant decrease in the tracking accuracy of the Kalman filter algorithm. Summary of the invention

[0004] The purpose of the present invention is to provide a method for strong tracking of jump gliding trajectories in order to improve the existing problems of poor tracking accuracy and unstable tracking of jump gliding trajectories.

[0005] The technical solution adopted by the present invention is as follows: a method for strong tracking of a jump glide trajectory, the method comprising: establishing an observation station coordinate system and a motion model of a tracked target, dividing the motion state of the tracked target into a powered stage and an unpowered stage, for the unpowered stage of the jump glide trajectory, establishing a dynamic model to describe the jump glide trajectory; for the powered stage of the jump glide trajectory, establishing a uniform acceleration model to describe the jump glide trajectory; combining the tracked target motion model into a target hybrid motion model, and judging the target acceleration, when the target acceleration reaches a set value, using a uniform acceleration model to describe the current motion state, when the target acceleration does not reach the set value, establishing an aerodynamic model to describe the target jump glide trajectory; establishing an observation station observation model; based on an unscented Kalman filtering algorithm of a single row unscented transformation, using a single row unscented change based on a single row sigma point algorithm and combined with an H-infinity filtering algorithm, after obtaining a one-step prediction of a state vector and an observation vector and a covariance matrix and a cross-correlation covariance matrix, a robust factor is introduced The state vector and covariance are corrected to obtain a strong robust unscented Kalman filter algorithm; the target state equation and observation equation are obtained through the target mixed motion model and observation model, and the target is tracked through the strong robust unscented Kalman filter algorithm.

[0006] It should be noted that one-step prediction is to predict the state at the next moment based on the state estimate and state equation at this moment.

[0007] Furthermore, the establishment of the observation station coordinate system and the motion model of the tracked target includes the following steps: setting the observation station coordinate system, with the observation station as the origin, the X-axis being the east direction of the observation station, the Y-axis being the north direction of the observation station, and the Z-axis being the vertical direction of the observation station; establishing a dynamic model based on the observation station coordinate system to describe the jumping and gliding trajectory of the target in the unpowered stage; the target is affected by aerodynamic forces, gravity and the rotation of the earth in the unpowered stage; and establishing a uniform acceleration model based on the observation station coordinate system to describe the jumping and gliding trajectory of the target in the powered stage.

[0008] Furthermore, the establishment of the dynamic model based on the observation station coordinate system includes: The target state vector under the dynamic model includes the position component, velocity component and three aerodynamic coefficients of the three axes (X, Y, and Z) of the observation station coordinate system. The three aerodynamic coefficients are modeled as a Gauss-Markov process, and the continuous state equation is:

[0009] Among them, the position components of the three axes of the coordinate system include the X-axis component , Y-axis component and the Z-axis component ; The velocity components include the X-axis velocity component , Y-axis velocity component and the Z-axis velocity component ; Aerodynamic coefficients include , , ; The target state vector under the dynamic model is, , is the component of horizontal velocity, , is the total speed, , is the atmospheric density of the target, is the Earth's gravitational constant, is the distance from the target to the center of the earth, is the Earth's rotation angular velocity, is the latitude of the observation station, is the radius of the Earth, , , The aerodynamic coefficients are , , Zero mean white noise; the function on the right side of the above continuous state equation is recorded as ; The continuous state equation is discretized, and the target state equation is approximately expressed as:

[0010] in, is the discrete time step, , For discrete moments, , The targets are , The state vector at time, for Time function The value of .

[0011] Furthermore, the uniform acceleration model is established based on the observation station coordinate system, including: The target state vector under the uniform acceleration model is set to , , and They are the uniform acceleration components of the three axes X, Y, and Z of the observation station coordinate system, and the state equation is: ; ; ; in, is the discrete time step, is a parameter related to the intensity of Gaussian white noise, for The covariance matrix of for Gaussian white noise sequence at time, for The target state vector at time .

[0012] Further, combining the tracked target motion model into a target mixed motion model includes: Set the judgment conditions for the target acceleration in the powered phase: ; ; ; ; in, , , , , , The targets are , The velocity components of the three axes X, Y, and Z in the observation station coordinate system at all times, is the discrete time step, is the acceleration component of the X axis, is the Y-axis acceleration component, is the Z-axis acceleration component, is the acceleration of the target; When the target acceleration When the above judgment conditions are met, the motion model describing the target is a uniform acceleration model; when the target acceleration When the above judgment conditions are not met, the motion model describing the target is converted into an aerodynamic model.

[0013] Furthermore, establishing the observation station observation model includes: establishing the observation station observation model in the observation station spherical coordinate system, using the observation distance , Observation azimuth , Observation elevation Indicates; observation distance is the distance from the observation station to the target, and the observation azimuth The angle between the projection of the line connecting the observation station and the target in the local horizontal plane of the observation station and the true north direction, the observation elevation angle is the angle between the line from the observation station to the target and the local horizontal plane of the observation station; Taking into account the actual engineering situation, the observation noise is introduced, and the observation equation of the observation model is: ; in, , , is the position component of the target in the observation station coordinate system, , , is Gaussian white noise.

[0014] Furthermore, the Gaussian white noise , and are independent of each other, have a mean of 0, and a constant variance.

[0015] Furthermore, the observation station tracking filtering process is expressed as a discrete nonlinear state equation: ; ; in, is the target state vector, is the observation vector, is the process noise, is the observation noise, is the state equation corresponding to the target motion model, is the observation equation corresponding to the observation model; Target state vector The length is , the observation vector Length is ; Process noise is an uncorrelated white noise vector with a mean of zero and a variance matrix of ; Observation noise is an uncorrelated white noise vector with a mean of zero and a variance matrix of ; The calculation steps of the strong robust unscented Kalman filter algorithm are: based on the single-line sigma point algorithm to generate Weight coefficient And sigma point : ; in, The values ​​are 1 to variables, is the weight coefficient; Initialize the one-element vector as: ; for ,vector for: ; Constructing sigma points : ; in, for The covariance matrix of the state vector at time instant, for The estimated value of the state vector at the moment; calculate State propagation of sigma points: ; in, is the state equation; Compute the one-step forecast and covariance matrix of the state vector: ; in, Process noise The variance matrix of For the moment, is the weight coefficient, The values ​​are 1 to variables, is the one-step prediction value of the state vector, for The covariance matrix of Process noise The variance matrix of Reconstruct the sigma point: ; in, is the one-step prediction value of the state vector, is the corresponding covariance matrix, The values ​​are 1 to variables, The vector required to construct the sigma point mentioned above; calculate Observation propagation of sigma points: ; in, is the observation equation; Compute the one-step forecast and covariance matrix of the observations: ; in, is a discrete moment, The values ​​are 1 to variables, is the weight coefficient, The observation noise The variance matrix of is the observation vector.

[0016] Furthermore, the state vector and covariance matrix correction include: ; in, For the moment, , for The state vector and corresponding covariance matrix of the one-step prediction at time, , for The observation vector and corresponding covariance matrix of the one-step forecast at time, is the state vector in The estimated value of the time, for The observation vector at time is the gain matrix, for The variance matrix corresponding to the moment-by-moment observation noise, for The cross-correlation covariance matrix between the state vector and the observation vector at the moment, is the robust factor, is the robust gain matrix, and Both can modify the state vector and the corresponding covariance.

[0017] Furthermore, the parameters The following conditions must be met: ; in The function is used to calculate the eigenvalues ​​of a matrix. For the moment, for The state vector and corresponding covariance matrix of the one-step prediction at time, for The cross-correlation covariance matrix between the state vector and the observation vector at the moment, is the robust gain matrix.

[0018] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. The present invention establishes two motion models for the tracked target of the jumping gliding trajectory, namely, a dynamic model and a uniform acceleration model, which respectively describe the motion states of the unpowered segment and the powered segment, and sets a target acceleration judgment mechanism to obtain a target hybrid motion model that can complete model conversion, so that the motion model is more in line with the target motion state.

[0019] 2. The present invention adopts a strong robust unscented Kalman filter algorithm. This method uses a strong robust unscented Kalman filter algorithm based on The single-row traceless change of the single-row sigma point algorithm of a sigma point can reduce the calculation amount of the algorithm and reduce the running speed of the algorithm without basically affecting the tracking accuracy.

[0020] 3. The present invention combines the idea of ​​H-infinity algorithm and introduces robust factor , the correction formula is obtained, and the state vector and covariance matrix in the filtering algorithm are further corrected, which improves the tracking accuracy and robustness and enhances the tracking effect of the observation station. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 It is an overall block diagram of the method of the present invention.

[0022] Figure 2 It is a calculation flow chart of the robust filtering algorithm of the jump gliding trajectory strong tracking method of the present invention.

[0023] Figure 3 Schematic diagram of the jumping and gliding trajectory and the location of the observation station in the embodiment.

[0024] Figure 4 It is a curve diagram of the height and speed change of the jumping and gliding trajectory in the embodiment.

[0025] Figure 5 Tracking position estimation deviation variation curve in the embodiment. Figure 6 Tracking speed estimation deviation variation curve in the embodiment. DETAILED DESCRIPTION

[0026] The present invention will be described in detail below in conjunction with the accompanying drawings.

[0027] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0028] like Figure 1 to Figure 2 As shown, a jump glide trajectory strong tracking method, the method comprises the following steps: Step S100: Establishing an observation station rectangular coordinate system and a motion model of the tracked target, dividing the motion state of the tracked target into a powered stage and an unpowered stage, establishing a dynamic model to describe the jump-glide trajectory in the unpowered stage; establishing a uniform acceleration model to describe the jump-glide trajectory in the powered stage of the jump-glide trajectory; Step S200: combining the tracked target motion model into a target hybrid motion model, and judging the target acceleration. When the target acceleration reaches the set value, a uniform acceleration model is used to describe the current motion state. When the target acceleration does not reach the set value, an aerodynamic model is established to describe the target jump and glide trajectory. Step S300: establishing an observation model in the spherical coordinate system of the observation station using the observation distance, observation azimuth, and observation elevation; Step S400: Based on the unscented Kalman filter algorithm of the single-row unscented transformation, the single-row unscented change based on the single-row sigma point algorithm is used in combination with the H infinity (H∞) filtering algorithm. After obtaining the one-step prediction and covariance matrix and cross-correlation covariance matrix of the state vector and observation vector, the robust factor is introduced. The state vector and covariance are modified to obtain a strong robust unscented Kalman filter algorithm; Step S500: Obtain the target state equation and observation equation through the target hybrid motion model and observation model, and track the target through the strong robust unscented Kalman filter algorithm.

[0029] Set the observation station coordinate system, with the observation station as the origin, the X axis as the east direction of the observation station, the Y axis as the north direction of the observation station, and the Z axis as the vertical direction of the observation station; A dynamic model is established based on the observation station coordinate system to describe the jumping and gliding trajectory of the target in the unpowered stage; the target is affected by aerodynamic force, gravity and the surface vision caused by the rotation of the earth in the unpowered stage; The target state vector under the dynamic model includes the position components, velocity components and three aerodynamic coefficients of the three axes of the observation station coordinate system. The three aerodynamic coefficients are modeled as a Gauss-Markov process, and the continuous state equation is:

[0030] Among them, the position components of the three axes of the coordinate system include the X-axis component , Y-axis component and the Z-axis component ; The velocity components include the X-axis velocity component , Y-axis velocity component and the Z-axis velocity component ; Aerodynamic coefficients include , , ; The target state vector under the dynamic model is , is the component of horizontal velocity, , is the total speed, , is the atmospheric density of the target, is the Earth's gravitational constant, is the distance from the target to the center of the earth, is the Earth's rotation angular velocity, is the latitude of the observation station, is the radius of the Earth, , , The aerodynamic coefficients are , , Zero mean white noise; the function on the right side of the continuous state equation is recorded as ; The continuous state equation is discretized, and the target state equation is approximately expressed as: ; in, is the discrete time step, , For discrete moments, , The targets are , The state vector at time, for Time function The corresponding value.

[0031] A uniform acceleration model is established based on the observation station coordinate system to describe the jumping and gliding trajectory of the target in the powered phase. The target state vector under the uniform acceleration model is set to , , and They are the uniform acceleration components of the three axes X, Y, and Z of the observation station coordinate system, and the state equation is: ; ; ; in, is the discrete time step, , For discrete moments, is a parameter related to the intensity of Gaussian white noise, for The covariance matrix of for Gaussian white noise sequence at time, for The target state vector at time .

[0032] Set the judgment conditions for the target acceleration in the powered phase: ; ; ; ; in, , , , , , The targets are , The velocity components of the three axes X, Y, and Z in the observation station coordinate system at all times, is the discrete time step, is the acceleration component of the X axis, is the Y-axis acceleration component, is the Z-axis acceleration component, is the acceleration of the target; When the target acceleration When the above judgment conditions are met, the motion model describing the target is a uniform acceleration model; when the target acceleration When the above judgment conditions are not met, the motion model describing the target is converted into an aerodynamic model.

[0033] The observation model of the observation station is established in the observation station spherical coordinate system: The observation model of the observation station is established in the spherical coordinate system of the observation station, using the observation distance , Observation azimuth , Observation elevation Indicates; observation distance is the distance from the observation station to the target, and the observation azimuth The angle between the projection of the line connecting the observation station and the target in the local horizontal plane of the observation station and the true north direction, the observation elevation angle is the angle between the line from the observation station to the target and the local horizontal plane of the observation station; Taking into account the actual engineering situation, the observation noise is introduced, and the observation equation of the observation model is: ; in, , , is the position component of the target in the observation station coordinate system, , , is Gaussian white noise. Gaussian white noise , and are independent of each other, have a mean of 0, and a constant variance.

[0034] The observation station tracking filtering process is expressed as a discrete nonlinear state equation: ; ; in, is the target state vector, is the observation vector, is the process noise, is the observation noise, is the state equation corresponding to the target motion model, is the observation equation corresponding to the observation model; Target state vector The length is , the observation vector Length is ; Process noise is an uncorrelated white noise vector with a mean of zero and a variance matrix of ; Observation noise is an uncorrelated white noise vector with a mean of zero and a variance matrix of ; The unscented Kalman filter algorithm based on the single-line unscented transformation is adopted and combined with the H-infinity filter algorithm to obtain a strong robust unscented Kalman filter algorithm. The calculation steps of the strong robust unscented Kalman filter algorithm are as follows: Generate based on the single-line sigma point algorithm Weight coefficient And sigma point : ; in, The values ​​are 1 to variables, is the weight coefficient; Initialize the one-element vector as: ; for ,vector for: ; Constructing sigma points : ; in, is the covariance matrix of the state vector at time k, is the estimated value of the state vector at time k; calculate State propagation of sigma points: ; in, is the state equation; Compute the one-step forecast and covariance matrix of the state vector: ; in, Process noise The variance matrix of For the moment, is the weight coefficient, The values ​​are 1 to variables, is the one-step prediction value of the state vector, for The covariance matrix of Process noise The variance matrix of Reconstruct the sigma point: ; in, is the one-step prediction value of the state vector, for The covariance matrix of The values ​​are 1 to variables, The vector required to construct the sigma point; calculate Observation propagation of sigma points: ; in, is the observation equation; Compute the one-step forecast and covariance matrix of the observations: ; in, is a discrete moment, The values ​​are 1 to variables, is the weight coefficient, The observation noise The variance matrix of is the observation vector.

[0035] The state vector and covariance matrix modifications include: ; in, For the moment, , for The state vector and corresponding covariance matrix of the one-step prediction at time, , for The observation vector and corresponding covariance matrix of the one-step forecast at time, is the state vector in The estimated value of the time, for The observation vector at time is the gain matrix, for The variance matrix corresponding to the moment-by-moment observation noise, for The cross-correlation covariance matrix between the state vector and the observation vector at the moment, is the robust factor, is the robust gain matrix, and Both can modify the state vector and the corresponding covariance. To ensure the existence of the H infinite filter, the parameter The following conditions must be met: ; in The function is used to calculate the eigenvalues ​​of a matrix. For the moment, for The state vector and corresponding covariance matrix of the one-step prediction at time, for The cross-correlation covariance matrix between the state vector and the observation vector at the moment, is the robust gain matrix.

[0036] Example like Figure 3-Figure 6 As shown, in order to verify the limitation of this implementation method, a simulation experiment is carried out in MATLAB. First, parameter setting and parameter initialization are performed: the initial longitude, latitude, altitude, and speed are input as 0°, 0°, 7000m, and 6400m / s real jump gliding trajectory data. The trajectory is as follows Figure 4 As shown; the observation station is set in the middle of the track, with longitude and latitude of 20° and 35°. The schematic diagram of the track and the observation station location is shown in Figure 3 As shown in the figure; the observation station tracking time interval is 0.1s; the observation station observation data is obtained through the observation station observation model and the real target trajectory data; the initial value of the state vector is obtained by adding normally distributed random noise to the real target trajectory value; the initial variance matrix of the state vector ; Process noise matrix of motion model ; Observation error variance matrix , it is set that when the observation distance is less than 300km and the observation elevation angle is greater than 0, the observation station can effectively track.

[0037] When the target's motion model is converted from an aerodynamic model to a uniform acceleration model, the position component and velocity component of the initial value of the uniform acceleration model state vector are provided by the corresponding values ​​in the aerodynamic model, and the acceleration component is provided by the values ​​of each acceleration component in the acceleration judgment condition. When the target's motion model is converted from a uniform acceleration model to an aerodynamic model, the position component and velocity component of the initial value of the aerodynamic model state vector are provided by the uniform acceleration model, and the initial values ​​of the three aerodynamic coefficients are set to 0.

[0038] The aerodynamic model is used as the target motion model, the target hybrid motion model and the observation station observation model proposed in this embodiment, and the robust unscented Kalman filter algorithm proposed in this embodiment are used to carry out simulation comparison experiments and analysis.

[0039] 50 Monte Carlo simulation experiments were carried out, and the position estimation deviation and velocity estimation deviation of the observation station tracking segment were calculated in the form of root mean square error. The formula is as follows: ; ; in, is the estimated deviation of the position of the tracking segment of the observation station, Estimated deviation of velocity for the tracking segment of the observation station; , , , , , are the position component and velocity component of the real target in the observation station coordinate system, , , , , , They are respectively the position component and velocity component of the tracked and estimated target in the observation station coordinate system.

[0040] The schematic diagram of the position estimation deviation and speed estimation deviation is as follows: Figure 5 and Figure 6 It can be seen that the tracking method proposed in this embodiment can still perform relatively stable tracking when the target enters the powered stage, especially in speed tracking, and will not produce tracking deviations with large changes. The running data of the tracking algorithm using different motion models is shown in Table 1: Table 1

[0041] It can be seen from Table 1 that the mean values ​​of the position and velocity estimation deviations of the target hybrid motion model adopted in this embodiment are smaller than the mean values ​​of the position and velocity estimation deviations of the aerodynamic model as the target motion model; therefore, the target hybrid motion model is more in line with the target motion state, improves the tracking accuracy and robustness, and improves the tracking effect of the observation station.

[0042] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for strong tracking of jumping and gliding trajectories, characterized in that: The method comprises: Establish the observation station coordinate system and the motion model of the tracked target, and divide the motion state of the tracked target into the powered stage and the unpowered stage. For the unpowered stage of the jump-glide trajectory, establish a dynamic model to describe the jump-glide trajectory; for the powered stage of the jump-glide trajectory, establish a uniform acceleration model to describe the jump-glide trajectory; The motion model of the tracked target is combined into a target hybrid motion model, and the target acceleration is judged. When the target acceleration reaches the set value, the uniform acceleration model is used to describe the current motion state. When the target acceleration does not reach the set value, the aerodynamic model is established to describe the target jump and glide trajectory. Establish observation model of observatory; Based on the unscented Kalman filter algorithm of single-row unscented transformation, the single-row unscented change based on the single-row sigma point algorithm is used in combination with the H-infinity filter algorithm to obtain the one-step prediction of the state vector and observation vector, the covariance matrix, and the cross-correlation covariance matrix, and then the robust factor is introduced The state vector and covariance matrix are modified to obtain a strong robust unscented Kalman filter algorithm; The target state equation and observation equation are obtained through the target hybrid motion model and observation model, and the target is tracked through the strong robust unscented Kalman filter algorithm.

2. A jumping glide trajectory strong tracking method according to claim 1, characterized in that: The establishment of the observation station coordinate system and the tracked target motion model comprises the following steps: Set the observation station coordinate system, with the observation station as the origin, the X axis as the east direction of the observation station, the Y axis as the north direction of the observation station, and the Z axis as the vertical direction of the observation station; A dynamic model is established based on the observation station coordinate system to describe the jumping and gliding trajectory of the target in the unpowered stage; the target is affected by aerodynamic force, gravity and the surface vision caused by the rotation of the earth in the unpowered stage; A uniform acceleration model is established based on the observation station coordinate system to describe the jumping and gliding trajectory of the target in the powered stage.

3. A jumping gliding trajectory strong tracking method according to claim 2, characterized in that: The establishment of the dynamic model based on the observation station coordinate system includes: The target state vector under the dynamic model includes the position components, velocity components and three aerodynamic coefficients of the three axes of the observation station coordinate system. The three aerodynamic coefficients are modeled as a Gauss-Markov process, and the continuous state equation is: Among them, the position components of the three axes of the coordinate system include the X-axis component , Y-axis component and the Z-axis component ; The velocity components include the X-axis velocity component , Y-axis velocity component and the Z-axis velocity component ; Aerodynamic coefficients include , , ; The target state vector under the dynamic model is , is the component of horizontal velocity, , is the total speed, , is the atmospheric density of the target, is the Earth's gravitational constant, is the distance from the target to the center of the earth, is the Earth's rotation angular velocity, is the latitude of the observation station, is the radius of the Earth, , , The aerodynamic coefficients are , , Zero mean white noise; the function on the right side of the continuous state equation is recorded as ; The continuous state equation is discretized, and the target state equation is approximately expressed as: ； in, is the discrete time step, , For discrete moments, , The targets are , The state vector at time, for Time function The corresponding value.

4. The jump glide trajectory strong tracking method according to claim 2 is characterized in that: The uniform acceleration model is established based on the observation station coordinate system, including: setting the target state vector under the uniform acceleration model to , , and They are the uniform acceleration components of the three axes X, Y, and Z of the observation station coordinate system, and the state equation is: ； ； ； in, is the discrete time step, , For discrete moments, is a parameter related to the intensity of Gaussian white noise, for The covariance matrix of for Gaussian white noise sequence at time, for The target state vector at time .

5. The jump glide trajectory strong tracking method according to claim 1, characterized in that: Combining the tracked target motion model into a target hybrid motion model includes: Set the judgment conditions for the target acceleration in the powered phase: ； ； ； ； in, , , , , , The targets are , The velocity components of the three axes X, Y, and Z in the observation station coordinate system at all times, is the discrete time step, is the acceleration component of the X axis, is the Y-axis acceleration component, is the Z-axis acceleration component, is the acceleration of the target; When the target acceleration When the above judgment conditions are met, the motion model describing the target is a uniform acceleration model; when the target acceleration When the above judgment conditions are not met, the motion model describing the target is converted into an aerodynamic model.

6. The jump glide trajectory strong tracking method according to claim 1, characterized in that: Establishing the observation station observation model includes: the observation station observation model is established in the observation station spherical coordinate system, using the observation distance , Observation azimuth , Observation elevation Indicates; observation distance is the distance from the observation station to the target, and the observation azimuth The angle between the projection of the line connecting the observation station and the target in the local horizontal plane of the observation station and the true north direction, the observation elevation angle is the angle between the line from the observation station to the target and the local horizontal plane of the observation station; Taking into account the actual engineering situation, the observation noise is introduced, and the observation equation of the observation model is: ； in, , , is the position component of the target in the observation station coordinate system, , , is Gaussian white noise.

7. A jumping gliding trajectory strong tracking method according to claim 6, characterized in that: The Gaussian white noise , and are independent of each other, have a mean of 0, and a constant variance.

8. The jump glide trajectory strong tracking method according to claim 1, characterized in that: The observation station tracking filtering process is expressed as a discrete nonlinear state equation: ； ； in, is the target state vector, is the observation vector, is the process noise, is the observation noise, is the state equation corresponding to the target motion model, is the observation equation corresponding to the observation model; Target state vector The length is , the observation vector Length is ; Process noise is an uncorrelated white noise vector with a mean of zero and a variance matrix of ; Observation noise is an uncorrelated white noise vector with a mean of zero and a variance matrix of ; The calculation steps of the strong robust unscented Kalman filter algorithm are: based on the single-line sigma point algorithm to generate Weight coefficient And sigma point : ； in, The values ​​are 1 to variables, is the weight coefficient; Initialize a one-element vector as: ； for ,vector for: ； Constructing sigma points : ； in, for The covariance matrix of the state vector at time instant, for The estimated value of the state vector at the moment; calculate State propagation of sigma points: ； in, is the state equation; Compute the one-step forecast and covariance matrix of the state vector: ； in, is the process noise The variance matrix of For the moment, is the weight coefficient, The values ​​are 1 to variables, is the one-step prediction value of the state vector, for The covariance matrix of is the process noise The variance matrix of Reconstruct the sigma point: ； in, is the one-step prediction value of the state vector, for The covariance matrix of The values ​​are 1 to variables, The vector required to construct the sigma point; calculate Observation propagation of sigma points: ； in, is the observation equation; Compute the one-step forecast and covariance matrix of the observations: ； in, is a discrete moment, The values ​​are 1 to variables, is the weight coefficient, The observation noise The variance matrix of is the observation vector.

9. A jumping and gliding trajectory strong tracking method according to claim 8, characterized in that: The state vector and covariance matrix correction include: ； in, For the moment, , for The state vector and corresponding covariance matrix of the one-step prediction at time, , for The observation vector and corresponding covariance matrix of the one-step forecast at time, is the state vector in The estimated value of the time, for The observation vector at time is the gain matrix, for The variance matrix corresponding to the moment-by-moment observation noise, for The cross-correlation covariance matrix between the state vector and the observation vector at the moment, is the robust factor, is the robust gain matrix, and Both can modify the state vector and the corresponding covariance.

10. A jumping gliding trajectory strong tracking method according to claim 9, characterized in that: parameter The following conditions must be met: ； in The function is used to calculate the eigenvalues ​​of a matrix. For the moment, for The state vector and corresponding covariance matrix of the one-step prediction at time, for The cross-correlation covariance matrix between the state vector and the observation vector at the moment, is the robust gain matrix.

Images