A Strong Tracking Method for Jumping Gliding Trajectory

Abstract

The present invention belongs to the technical field of aircraft trajectory tracking, and discloses a strong tracking method for a jumping and gliding trajectory. The method includes: establishing a target hybrid motion model, wherein a dynamic model controlled by aerodynamic force and earth gravity is used to describe the unpowered section of the target jumping and gliding trajectory, a uniform acceleration model is used to describe the powered section of the trajectory, and a target acceleration judgment mechanism is introduced to realize the conversion between the dynamic model and the uniform acceleration model; establishing an observation station observation model using the observation distance, azimuth angle, and elevation angle parameters, and adding observation noise; using an unscented Kalman filter algorithm based on the single-line unscented transformation of sigma points and adding an H-infinity filter algorithm to propose a strong robust unscented Kalman filter algorithm. This strong tracking method for the jumping and gliding trajectory can improve the tracking accuracy and robustness, and at the same time reduce the calculation amount and speed up the calculation speed.

Description

Technical Field

[0001] The present invention belongs to the technical field of aircraft trajectory tracking, and particularly relates to a strong tracking method for a skip-glide trajectory. Background Art

[0002] The trajectory of an aircraft in the gliding section mainly shows a skip-glide trajectory, and the skip-glide trajectory can be divided into unpowered skip-glide and powered skip-glide. In unpowered skip-glide, the target is only affected by aerodynamic force and earth gravity during the gliding section; in powered skip-glide, the target is also affected by the thrust of an engine for a certain period of time, making the trajectory more flexible. At present, there is less research on the tracking of powered skip-glide trajectories, so it is necessary to conduct research on it. Maneuvering target tracking mainly consists of two parts: the target motion model and the filtering algorithm. The motion model is mainly established in two ways: the kinematic model and the dynamic model. The kinematic model directly establishes the law model of the target's change over time, such as the uniform motion model, the uniform acceleration model, the uniform turn model, etc. The dynamic model starts from the perspective of the forces acting on the target and conducts a mechanical analysis of the target to deduce the acceleration characteristics in each direction. The motion of the powered skip-glide trajectory is complex, and the tracking party cannot know the thrust of the aircraft during the powered section. Therefore, using a single dynamic model or the above-mentioned conventional kinematic models cannot form a relatively accurate target motion model. Dividing the powered skip-glide trajectory into an unpowered section and a powered section according to the force and motion state, and proposing corresponding motion models for each section and combining them into a target hybrid motion model can better fit the actual motion state of the target. Both the target state equation and the tracking measurement equation are nonlinear equations, and a nonlinear filtering algorithm needs to be used. The commonly used nonlinear filtering algorithms in maneuvering target tracking mainly include the extended Kalman filter, the unscented Kalman filter, etc.

[0003] The above-mentioned Kalman filtering algorithm is based on an accurate mathematical model and 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, and 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 filtering algorithm. Summary of the Invention

[0004] The object of the present invention is to provide a strong tracking method for a skip-glide trajectory, aiming to improve the problems of poor tracking accuracy and unstable tracking of the existing skip-glide trajectory.

[0005] The technical solution adopted by the present invention is as follows: A strong tracking method for a jumping gliding trajectory, the method comprising: establishing an observation station coordinate system and a moving model of the target to be tracked, dividing the motion state of the target to be tracked into a powered phase and a non-powered phase, for the non-powered phase of the jumping gliding trajectory, establishing a dynamic model to describe the jumping gliding trajectory; for the powered phase of the jumping gliding trajectory, establishing a uniform acceleration model to describe the jumping gliding trajectory; combining the moving model of the target to be tracked into a target hybrid motion model, and judging the target acceleration, when the target acceleration reaches a set value, using the uniform acceleration model to describe the current motion state, when the target acceleration does not reach the set value, establishing a dynamic model to describe the target jumping gliding trajectory; establishing an observation model of the observation station; on the basis of the unscented Kalman filtering algorithm of single-line unscented transformation, using single-line unscented transformation based on the single-line sigma point algorithm and combining with the H-infinity filtering algorithm, after obtaining the one-step prediction and covariance matrix of the state vector and the observation vector, and the cross-correlation covariance matrix, introducing a robustness factor to correct the state vector and covariance, obtaining a strong robust unscented Kalman filtering algorithm; obtaining a target state equation and an observation equation through the target hybrid motion model and the observation model, and performing target tracking through the strong robust unscented Kalman filtering algorithm.

[0006] It should be noted that the one-step prediction is to predict the state of the next moment according to the state estimation value and the state equation of the current moment, etc.

[0007] Further, the establishing of the observation station coordinate system and the moving model of the target to be tracked includes the following steps: setting the observation station coordinate system, with the observation station as the origin, the X-axis being the due east direction of the observation station, the Y-axis being the due north direction of the observation station, and the Z-axis being the vertical direction of the observation station; establishing a dynamic model on the basis of the observation station coordinate system to describe the jumping gliding trajectory of the target in the non-powered phase; the target is subject to aerodynamic force, gravity, and apparent force caused by the earth's rotation in the non-powered phase; establishing a uniform acceleration model on the basis of the observation station coordinate system to describe the jumping gliding trajectory of the target in the powered phase.

[0008] Further, the establishing of the dynamic model on the basis of the observation station coordinate system includes:

[0009] The target state vector under the dynamic model includes the position components, velocity components of the three axes (X, Y, Z axes) of the observation station coordinate system, and three aerodynamic coefficients, modeling the three aerodynamic coefficients as a Gauss-Markov process, and the continuous state equation is:

[0010]

[0011] Among them, the position components of the three axes of the coordinate system include the X-axis component and the Y-axis component and the Z-axis component ; The velocity components include the X-axis velocity component , the Y-axis velocity component and the Z-axis velocity component ; The aerodynamic coefficients include , , ; Under the dynamic model, the target state vector is, , is the component of the horizontal velocity, , is the magnitude of the total velocity, , is the atmospheric density where the target is located, is the gravitational constant of the earth, is the distance from the target to the center of the earth, is the angular velocity of the earth's rotation, is the latitude of the observation station, is the radius of the earth, , , are the zero-mean white noises of the aerodynamic coefficients , , respectively; Denote the function on the right side of the equality in the above continuous state equation as ;

[0012] Discretize the continuous state equation, and the target state equation is approximately expressed as:

[0013]

[0014] where, is the discrete time step, , are the discrete moments, , are the state vectors of the target at , moments respectively, is the value of the function at the moment.

[0015] Furthermore, establish a uniform acceleration model based on the observation station coordinate system, including:

[0016] Set the target state vector under the uniform acceleration model as , , and are the uniform acceleration components along the X, Y, and Z axes of the observation station coordinate system respectively, and its state equation is:

[0017] ;

[0018] ;

[0019] ;

[0020] wherein, is the discrete time step, is the parameter related to the intensity of Gaussian white noise, is 's covariance matrix, is 's Gaussian white noise sequence at the moment, is 's target state vector at the moment.

[0021] Furthermore, combining the motion model of the target to be tracked into the target hybrid motion model includes:

[0022] Setting judgment conditions for the target acceleration in the powered phase:

[0023] ;

[0024] ;

[0025] ;

[0026] ;

[0027] wherein, , , , , , are respectively the velocity components of the target in the X, Y, and Z axial directions in the observation station coordinate system at , moments, is the discrete time step, is the X-axis acceleration component, is the Y-axis acceleration component, is the Z-axis acceleration component, is the magnitude of the target's acceleration;

[0028] When the target acceleration meets the above judgment conditions, the motion model describing the target is the uniform acceleration model; when the target acceleration does not meet the above judgment conditions, the motion model describing the target is converted to the dynamic model.

[0029] Further, establishing an observation station observation model includes: The observation station observation model is established in the spherical coordinate system of the observation station, and is represented by the observation distance , the observation azimuth , and the observation elevation angle ; The observation distance is the distance from the observation station to the target, the observation azimuth is 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 due north direction, and the observation elevation angle is the angle between the line connecting the observation station and the target and the local horizontal plane of the observation station;

[0030] Considering the actual engineering situation, observation noise is introduced, and the observation equation of its observation model is:

[0031] ;

[0032] Wherein, , , are the position components of the target in the observation station coordinate system, , , are Gaussian white noises.

[0033] Further, the Gaussian white noises , and are independent of each other, with a mean of 0 and a constant variance.

[0034] Further, the observation station tracking and filtering process is represented by a discrete non-linear state equation as:

[0035] ;

[0036] ;

[0037] Wherein, 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;

[0038] The length of the target state vector is , and the length of the observation vector is ; The process noise is an uncorrelated white noise vector with a mean of zero and a variance matrix of ; The observation noise are uncorrelated white noise vectors with zero mean and covariance matrix ;

[0039] The calculation steps of the strong robust unscented Kalman filter algorithm are as follows: Generate weight coefficients and sigma points :

[0040] ;

[0041] where is a variable that takes values from 1 to in sequence, and is the weight coefficient;

[0042] Initialize the univariate vector as:

[0043] ;

[0044] For , the vector is:

[0045] ;

[0046] Construct the sigma points :

[0047] ;

[0048] where is the covariance matrix of the state vector at , and is the estimated value of the state vector at ;

[0049] Calculate the state propagation of sigma points:

[0050] ;

[0051] where is the state equation;

[0052] Calculate the one-step prediction of the state vector and the covariance matrix:

[0053] ;

[0054] where is the variance matrix of the process noise , is the time, is the weight coefficient, is a variable that takes values from 1 to The variable is the one-step predicted value of the state vector, and is the covariance matrix of The process noise is the variance matrix;

[0055] Reconstruct the sigma points:

[0056] ;

[0057] where is the one-step predicted value of the state vector, is the corresponding covariance matrix, takes values from 1 to in sequence, is the vector required to construct the sigma points mentioned above;

[0058] Calculate the observation propagation of sigma points:

[0059] ;

[0060] where is the observation equation;

[0061] Calculate the one-step prediction of the observation and the covariance matrix:

[0062] ;

[0063] where is the discrete time, takes values from 1 to in sequence, is the weight coefficient, is the observation noise is the variance matrix, is the observation vector.

[0064] Furthermore, the correction of the state vector and the covariance matrix includes:

[0065] ;

[0066] where is the time, , are the state vector and the corresponding covariance matrix of the one-step prediction at time , are the observation vector and the corresponding covariance matrix of the one-step prediction at time is the state vector at The estimated value of the moment, is the observation vector of the moment, is the gain matrix, is the variance matrix corresponding to the observation noise at the moment, is the cross - 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 correct the state vector and the corresponding covariance.

[0067] Furthermore, the parameter satisfies the following conditions:

[0068] ;

[0069] where the function is used to calculate the matrix eigenvalues, is the moment, is the covariance matrix of the one - step prediction at the moment, is the cross - covariance matrix between the state vector and the observation vector at the moment, is the robust gain matrix.

[0070] In summary, due to the adoption of the above - mentioned technical solutions, the beneficial effects of the present invention are as follows:

[0071] 1. The present invention establishes two motion models for the tracked target with a skip - glide trajectory, namely a dynamic model and a uniform acceleration model, respectively describing the motion states of the unpowered section and the powered section, and sets up a target acceleration judgment mechanism to obtain a target hybrid motion model that can complete model conversion, making the motion model more conform to the target motion state.

[0072] 2. The present invention adopts a strong - robust unscented Kalman filtering algorithm, which uses a single - row unscented transformation of the single - row sigma - point algorithm based on sigma points on the basis of the unscented Kalman filter, and can reduce the computational complexity of the algorithm and the running speed of the algorithm on the basis of basically not affecting the tracking accuracy.

[0073] 3. The present invention combines the idea of the H - infinity algorithm, introduces the robust factor , obtains a correction formula, further corrects the state vector and the covariance matrix in the filtering algorithm, improves the tracking accuracy and robustness, and enhances the tracking effect of the observation station. BRIEF DESCRIPTION OF THE DRAWINGS

[0074] Figure 1 It is the overall block diagram of the method of the present invention.

[0075] Figure 2 It is the calculation flow chart of the robust filtering algorithm for the strong tracking method of the skip-glide trajectory of the present invention.

[0076] Figure 3 It is a schematic diagram of the skip-glide trajectory and the position of the observation station in the embodiment.

[0077] Figure 4 It is the curve graph of the height and speed change of the skip-glide trajectory in the embodiment.

[0078] Figure 5 Curve graph of the change of the tracking position estimation deviation in the embodiment.

[0079] Figure 6 Curve graph of the change of the tracking speed estimation deviation in the embodiment. Detailed implementation manners

[0080] The following will describe the present invention in detail with reference to the accompanying drawings.

[0081] In order to make the objectives, technical solutions and advantages of the present invention clearer, the present invention will be further described in detail below with reference to 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 used to limit the present invention.

[0082] As Figures 1 to 2 shown, a strong tracking method for a skip-glide trajectory, the method includes the following steps:

[0083] Step S100: Establish a rectangular coordinate system of the observation station and a motion model of the target to be tracked. Divide the motion state of the target to be tracked into a powered phase and a non-powered phase. For the non-powered phase of the skip-glide trajectory, establish a dynamic model to describe the skip-glide trajectory; for the powered phase of the skip-glide trajectory, establish a uniform acceleration model to describe the skip-glide trajectory;

[0084] Step S200: Combine the motion models of the target to be tracked into a target hybrid motion model, and judge the target acceleration. When the target acceleration reaches the set value, use the uniform acceleration model to describe the current motion state. When the target acceleration does not reach the set value, establish a dynamic model to describe the target skip-glide trajectory;

[0085] Step S300: Use the observation distance, observation azimuth angle, and observation elevation angle to establish an observation model in the spherical coordinate system of the observation station;

[0086] Step S400: Based on the unscented Kalman filter algorithm with single-line unscented transformation, use the single-line unscented transformation based on the single-line sigma-point algorithm and combine it with the H-infinity (H∞) filter algorithm. After obtaining the one-step prediction of the state vector, observation vector, covariance matrix, and cross-correlation covariance matrix, introduce a robust factor Correct the state vector and covariance to obtain a strong robust unscented Kalman filter algorithm;

[0087] Step S500: Obtain the target state equation and observation equation through the target hybrid motion model and observation model, and perform target tracking through the strong robust unscented Kalman filter algorithm.

[0088] Set up the observation station coordinate system with the observation station as the origin, the X-axis as the due east direction of the observation station, the Y-axis as the due north direction of the observation station, and the Z-axis as the vertical direction of the observation station;

[0089] Based on the observation station coordinate system, establish a dynamic model to describe the jumping glide trajectory of the target in the unpowered stage; the target is affected by aerodynamic force, gravity, and apparent force caused by the earth's rotation in the unpowered stage;

[0090] The target state vector under the dynamic model includes the position components, velocity components of the three axes of the observation station coordinate system, and three aerodynamic coefficients. Model the three aerodynamic coefficients as a Gauss-Markov process, and the continuous state equation is:

[0091]

[0092] Among them, the position components of the three axes of the coordinate system include the X-axis component , the Y-axis component , and the Z-axis component ; the velocity components include the X-axis velocity component , the Y-axis velocity component , and the Z-axis velocity component ; the aerodynamic coefficients include , , ; the target state vector under the dynamic model is , is the component of the horizontal velocity, , is the magnitude of the total velocity, , is the atmospheric density where the target is located, is the earth's gravitational constant, is the distance from the target to the earth's center, is the earth's angular velocity of rotation, is the latitude of the observation station, is the radius of the earth, , , are zero-mean white noises of aerodynamic coefficients , , respectively; denote the function on the right side of the continuous state equation as ;

[0093] Discretize the continuous state equation, and the target state equation is approximately expressed as:

[0094] ;

[0095] where is the discrete time step, , are discrete moments, , are the state vectors of the target at , moments respectively, is the value corresponding to the function at moment.

[0096] Establish a uniform acceleration model based on the observation station coordinate system to describe the jumping gliding trajectory of the target in the powered phase;

[0097] Set the target state vector under the uniform acceleration model as , , and are the uniform acceleration components along the X, Y, and Z axes of the observation station coordinate system respectively, and its state equation is:

[0098] ;

[0099] ;

[0100] ;

[0101] where is the discrete time step, , are discrete moments, is a parameter related to the intensity of Gaussian white noise, is the covariance matrix of , is the Gaussian white noise sequence at moment, is the target state vector at moment.

[0102] Set judgment conditions for the target acceleration in the powered phase:

[0103] ;

[0104] ;

[0105] ;

[0106] ;

[0107] wherein, 、 、 、 、 、 are respectively the velocity components of the target in the X, Y, and Z axial directions in the observation station coordinate system at 、 moments, is the discrete time step, is the acceleration component in the X-axis, is the acceleration component in the Y-axis, is the acceleration component in the Z-axis, is the magnitude of the acceleration of the target;

[0108] When the target acceleration meets the above judgment conditions, the motion model of the target is described as a uniform acceleration model; when the target acceleration does not meet the above judgment conditions, the motion model of the target is converted to a dynamic model.

[0109] Establish the observation model of the observation station in the spherical coordinate system of the observation station:

[0110] The observation model of the observation station is established in the spherical coordinate system of the observation station and is represented by the observation distance , the observation azimuth angle , and the observation elevation angle ; The observation distance is the distance from the observation station to the target, the observation azimuth angle is the angle between the projection of the line connecting the observation station and the target on the local horizontal plane of the observation station and the due north direction, and the observation elevation angle is the angle between the line connecting the observation station and the target and the local horizontal plane of the observation station;

[0111] Considering the actual engineering situation, observation noise is introduced, and the observation equation of its observation model is:

[0112] ;

[0113] wherein, 、 、 are the position components of the target in the observation station coordinate system, , , is Gaussian white noise. The Gaussian white noise , and are independent of each other, with a mean of 0 and a constant variance.

[0114] The tracking and filtering process of the observation station is represented by a discrete non - linear state equation as follows:

[0115] ;

[0116] ;

[0117] where, 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;

[0118] The length of the target state vector is , and the length of the observation vector is ; The process noise is an uncorrelated white noise vector with a mean of zero and a variance matrix of ; The observation noise is an uncorrelated white noise vector with a mean of zero and a variance matrix of ;

[0119] An unscented Kalman filter algorithm based on single - row unscented transform and combined with H - infinity filter algorithm is adopted to obtain a strong robust unscented Kalman filter algorithm. The calculation steps of the strong robust unscented Kalman filter algorithm are as follows: Generate weight coefficients and sigma points based on the single - row sigma - point algorithm:

[0120] ;

[0121] where, is a variable that takes values from 1 to in sequence, is the weight coefficient;

[0122] Initialize the univariate vector as:

[0123] ;

[0124] For , the vector is:

[0125] ;

[0126] Construct sigma points :

[0127] ;

[0128] wherein, is the covariance matrix of the state vector at time k, is the estimated value of the state vector at time k;

[0129] Calculate the state propagation of sigma points:

[0130] ;

[0131] wherein, is the state equation;

[0132] Calculate the one-step prediction of the state vector and the covariance matrix:

[0133] ;

[0134] wherein, is the process noise variance matrix of, is the time, is the weight coefficient, is the variable taking values from 1 to in turn, is the one-step predicted value of the state vector, is covariance matrix of, is the process noise variance matrix of;

[0135] Reconstruct sigma points:

[0136] ;

[0137] wherein, is the one-step predicted value of the state vector, is covariance matrix of, is the variable taking values from 1 to in turn, is the vector required to construct sigma points;

[0138] Calculate the observation propagation of sigma points:

[0139] ;

[0140] Among them, is the observation equation;

[0141] Calculate the one-step prediction and covariance matrix of the observation:

[0142] ;

[0143] Among them, is the discrete time, takes values in sequence from 1 to variables, is the weight coefficient, is the observation noise variance matrix of, is the observation vector.

[0144] The state vector and covariance matrix correction include:

[0145] ;

[0146] Among them, is the time, , is the state vector of the one-step prediction at time and the corresponding covariance matrix, , is the observation vector of the one-step prediction at time and the corresponding covariance matrix, is the estimated value of the state vector at time, is the observation vector at time, is the gain matrix, is the variance matrix corresponding to the observation noise at time, is the cross-correlation covariance matrix between the state vector and the observation vector at time, is the robust factor, is the robust gain matrix, and Both can correct the state vector and the corresponding covariance. To ensure the existence of the H-infinity filter, the parameter satisfies the following conditions:

[0147] ;

[0148] Among them The function is used to calculate the matrix eigenvalues, is the time, is The covariance matrix for one-step prediction of the moment, is the cross-correlation covariance matrix of the state vector and the observation vector at the moment, and

[0149] is the robust gain matrix.

[0150] As Figures 3 - 6 shown, in order to verify the finiteness of this embodiment, a simulation experiment is carried out in MATLAB. First, parameter settings and parameter initialization are performed: Input the real jump-glide trajectory data with initial longitude, latitude, altitude, and speed of 0°, 0°, 7000 m, and 6400 m / s. The trajectory situation is as Figure 4 shown; The observation station is set in the middle section of the trajectory, with longitude and latitude of 20° and 35°. The schematic diagram of the trajectory and the observation station position is as Figure 3 shown; The tracking time interval of the observation station is 0.1 s; The observation data of the observation station is obtained through the observation model of the observation station and the real target trajectory data; The initial value of the state vector is obtained by adding random noise with a normal distribution to the real target trajectory value; The initial variance matrix of the state vector ; The process noise matrix of the motion model ; The observation error variance matrix , and it is set that when the observation distance is less than 300 km and the observation elevation angle is greater than 0, the observation station can perform effective tracking.

[0151] When the motion model of the target is converted from the dynamic model to the constant acceleration model, the position component and velocity component of the initial value of the state vector of the constant acceleration model are provided by the corresponding values in the dynamic model, and the acceleration component is provided by each acceleration component value in the acceleration judgment condition. When the motion model of the target is converted from the constant acceleration model to the dynamic model, the position component and velocity component of the initial value of the state vector of the dynamic model are provided by the constant acceleration model, and the initial values of the three aerodynamic coefficients are set to 0.

[0152] Using the dynamic model as the target motion model, the target hybrid motion model proposed in this embodiment, and the observation model of the observation station, the robust unscented Kalman filter algorithm proposed in this embodiment is used to carry out simulation comparison tests and analysis.

[0153] Carry out 50 Monte Carlo simulation experiments, and calculate the position estimation deviation and velocity estimation deviation of the tracking section of the observation station in the form of root mean square error. The formula is as follows:

[0154] ;

[0155] ;

[0156] where is the position estimation deviation of the tracking segment of the observation station, is the velocity estimation deviation of the tracking segment of the observation station; , , , , , are respectively the position components and velocity components of the true target in the coordinate system of the observation station, , , , , , are respectively the position components and velocity components of the target estimated by tracking in the coordinate system of the observation station.

[0157] The schematic diagrams of the obtained position estimation deviation and velocity estimation deviation are as shown in 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 phase. Especially in terms of velocity tracking, there will be no tracking deviation with too large fluctuations. The operation data of the tracking algorithms using different motion models are shown in Table 1:

[0158] Table 1

[0159]

[0160] It can be obtained from Table 1 that both the mean values of the position and velocity estimation deviations of the target hybrid motion model adopted in this embodiment are smaller than those of the dynamic model used 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 enhances the tracking effect of the observation station.

[0161] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principle of the present invention shall be included within 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, a dynamic 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 a dynamic 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 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, 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 covariance matrix of the one-step forecast at time t, for The cross-correlation covariance matrix between the state vector and the observation vector at the moment, is the robust gain matrix.

Images