CN119937603B - A strong tracking method for jumping and gliding trajectories - Google Patents
A strong tracking method for jumping and gliding trajectories Download PDFInfo
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Abstract
The invention belongs to the technical field of aircraft track tracking and discloses a jump glide track strong tracking method, which comprises the steps of establishing a target hybrid motion model, describing an unpowered section of a target jump glide track by using a aerodynamic force and earth attraction controlled dynamics model, describing a track powered section by using a uniform acceleration model, introducing a target acceleration judging mechanism to realize conversion between the dynamics model and the uniform acceleration model, establishing an observation station observation model by using observation distance, azimuth angle and elevation angle parameters, adding observation noise, and using a model based on the uniform accelerationA strong robust unscented Kalman filtering algorithm is proposed by incorporating the single line unscented transformation of sigma points and the H-infinity filtering algorithm. This jumping gliding trajectory strong tracking method can improve tracking accuracy and robustness, while reducing computational complexity and accelerating computation speed.
Description
Technical Field
The invention belongs to the technical field of aircraft track tracking, and particularly relates to a jump glide track strong tracking method.
Background
The track of the aircraft in the glide zone is mainly represented as a jumping glide track, and the jumping glide track is divided into a power jumping glide track and a power jumping glide track. The unpowered jumping and gliding is that the target only receives aerodynamic force and earth attraction in the gliding section, and the powered jumping and gliding is that the target also receives the thrust of an engine in a certain time, so that the track is more flexible, and the track tracking of the powered jumping and gliding is less studied at present, and the development and the research are necessary. Maneuvering target tracking is mainly divided into a target motion model and a filtering algorithm. The motion model is mainly established by two modes of a kinematic model and a dynamic model. The kinematic model is a regular model for directly establishing the change of the target along with time, such as a uniform velocity model, a uniform acceleration model, a uniform velocity turning model and the like. The dynamic model is used for carrying out mechanical analysis on the target to deduce acceleration characteristics in all directions from the aspect of stress of the target. The motion of the dynamic jump glide track is complex, and the tracker cannot know the thrust of the dynamic section of the aircraft, so that a single dynamic model or the conventional kinematic model cannot be used for forming a more accurate target motion model. The dynamic jump glide track is divided into a unpowered section and a dynamic section according to the stress and the motion state conditions, and a corresponding motion model is provided for each section and combined into a target hybrid motion model, so that the actual motion state of a target can be more attached. The target state equation and the tracking measurement equation are nonlinear equations, and a nonlinear filtering algorithm is needed. The nonlinear filtering algorithm commonly used in maneuvering target tracking mainly comprises a generalized Kalman filter, an unscented Kalman filter and the like.
The Kalman filtering algorithm is based on an accurate mathematical model and the known statistical characteristics of system process noise and measurement noise, but in practical application, an observer cannot obtain an accurate target motion model, the established target motion model is only approximate, and some priori knowledge cannot be accurately obtained, so that the tracking accuracy of the Kalman filtering algorithm is obviously reduced.
Disclosure of Invention
The invention aims to solve the problems, and provides a jump glide track strong tracking method which aims to solve the problems of poor tracking precision and unstable tracking of the existing jump glide track.
The technical scheme includes that the method comprises the steps of establishing a coordinate system of an observation station and a tracked target motion model, dividing the motion state of the tracked target into a dynamic stage and a non-dynamic stage, establishing a dynamics model for describing the jump glide track in the non-dynamic stage of the jump glide track, establishing a uniform acceleration model for describing the jump glide track in the dynamic stage of the jump glide track, combining the tracked target motion model into a target mixed motion model, judging target acceleration, describing the current motion state by using the uniform acceleration model when the target acceleration reaches a set value, establishing a dynamics model for describing the target jump glide track when the target acceleration does not reach the set value, establishing an observation station observation model, using single-row non-trace change based on a sigma point algorithm and combining an H infinite filtering algorithm on the basis of a single-row Kalman filtering algorithm, and introducing a robust factor after obtaining a state vector and a one-step prediction and a covariance matrix of the observation vectorAnd obtaining a target state equation and an observation equation through a target mixed motion model and an observation model, and tracking the target through the strong robust unscented Kalman filtering algorithm.
It should be noted that the one-step prediction predicts the state at the next time based on the state estimation value and the state equation at the present time.
The method comprises the steps of setting an observation station coordinate system, setting a dynamic model on the basis of the observation station coordinate system, setting an apparent vision caused by aerodynamic force, gravity and earth rotation of the target in an unpowered stage, and setting a uniform acceleration model on the basis of the observation station coordinate system, wherein the X axis is the forward direction of the observation station, the Y axis is the north direction of the observation station and the Z axis is the vertical direction of the observation station.
Further, the establishing the dynamics model based on the coordinate system of the observation station includes:
The target state vector under the dynamic model comprises a position component, a speed component and three aerodynamic coefficients of three axes (X, Y, Z axes) of an observation station coordinate system, the three aerodynamic coefficients are modeled as a Gauss-Markov process, and a continuous state equation is as follows:
wherein the position components of the three axes of the coordinate system comprise X-axis components Component of Y axisAnd Z-axis componentThe velocity component includes an X-axis velocity componentVelocity component of Y axisAnd a Z-axis velocity componentAerodynamic coefficient comprises、、The target state vector under the dynamic model is,,As a component of the horizontal velocity,,In order to be able to achieve a total speed,,For the atmospheric density at which the target is located,Is the constant of the gravitational force of the earth,For the distance of the target to the earth's center,Is the rotational angular velocity of the earth,For the purpose of observing the latitude of the station,Is the radius of the earth's circle,、、Respectively aerodynamic coefficient、、The function on the right of the equation in the continuous state equation is recorded as;
Discretizing a continuous state equation, wherein the target state equation is approximately expressed as:
Wherein, In discrete steps of time,、Is a discrete time of day which is the time of day,、Respectively at the target、The state vector of the moment of time,Is thatTime of day functionIs a value of (2).
Further, establishing the uniform acceleration model based on the observation station coordinate system includes:
setting the target state vector under the uniform acceleration model as ,、AndThe three uniform acceleration components in the axial directions of the observation station coordinate system X, Y, Z are respectively shown in the following state equations:
;
;
;
Wherein, In discrete steps of time,As a parameter related to the intensity of white gaussian noise,Is thatIs used for the co-variance matrix of (a),Is thatA sequence of white gaussian noise at the moment in time,Is thatA time of day target state vector.
Further, combining the tracked object motion models into an object hybrid motion model includes:
Setting a judging condition for the target acceleration in the powered stage:
;
;
;
;
Wherein, 、、、、、Respectively at the target、The X, Y, Z three axial velocity components at the time under the coordinate system of the observation station,In discrete steps of time,As the X-axis acceleration component,As the component of the acceleration in the Y-axis,As a component of the acceleration in the Z-axis,The acceleration of the target is;
when the target acceleration Describing the motion model of the target as a uniform acceleration model when the judging condition is met, and judging the acceleration of the target when the motion model of the target is uniform acceleration modelAnd when the judging condition is not met, converting the motion model of the descriptive target into a dynamics model.
Further, establishing the observation station observation model comprises establishing the observation station observation model in an observation station spherical coordinate system by using the observation distanceAzimuth angle of observationElevation angle of observationRepresentation of the observation distanceTo observe the distance from the station to the target, the azimuth angle is observedFor the connection between the observation station and the target to project an angle with the northbound direction in the local horizontal plane of the observation station, elevation angle of observationTo observe the connection line from station to target an included angle of a local horizontal plane of the observation station;
In consideration of actual engineering conditions, observation noise is introduced, and an observation equation of an observation model is as follows:
;
Wherein, 、、For the position component of the object in the coordinate system of the observation station,、、Is white gaussian noise.
Further, the Gaussian white noise、AndIndependent of each other, the mean value is 0, and the variance is constant.
Further, the observation station tracking filtering process is expressed as a discrete nonlinear state equation:
;
;
Wherein, In order to be a target state vector of the object,In order to observe the vector of the light,In order for the process to be noisy,In order to observe the noise it is possible,For the state equation corresponding to the object motion model,An observation equation corresponding to the observation model;
target state vector Length of (2)Observation vectorLength ofProcess noiseThe mean value of the uncorrelated white noise vectors is zero, and the variance matrix isObservation noiseThe mean value of the uncorrelated white noise vectors is zero, and the variance matrix is;
The calculation step of the strong robust unscented Kalman filtering algorithm comprises the steps of generating based on a single-row sigma point algorithmPersonal weight coefficientSigma point:
;
Wherein, To take values of 1 toIs used for the control of the variable of (a),Is a weight coefficient;
Initializing a unitary vector as follows:
;
For the following Vector quantityThe method comprises the following steps:
;
construction of sigma points :
;
Wherein, Is as followsThe covariance matrix of the time-of-day state vector,Is thatAn estimate of the time state vector;
Calculation of State propagation of individual sigma points:
;
Wherein, Is a state equation;
calculating a one-step prediction and covariance matrix of the state vector:
;
Wherein, Is process noiseIs a matrix of variances of (a),In order to be able to take the moment of time,As the weight coefficient, the weight coefficient is used,To take values of 1 toIs used for the control of the variable of (a),Is a one-step predictor of the state vector,Is thatIs used for the co-variance matrix of (a),Is process noiseIs a variance matrix of (a);
reconstructing sigma points:
;
Wherein, Is a one-step predictor of the state vector,For the corresponding covariance matrix,To take values of 1 toIs used for the control of the variable of (a),Vectors required for constructing sigma points as mentioned above;
Calculation of Observed propagation of the individual sigma points:
;
Wherein, Is an observation equation;
calculating a one-step prediction and covariance matrix of the observation:
;
Wherein, Is a discrete time of day and is a time of day,To take values of 1 toIs used for the control of the variable of (a),As the weight coefficient, the weight coefficient is used,To observe noiseIs a matrix of variances of (a),Is an observation vector.
Further, the state vector and covariance matrix correction includes:
;
Wherein, In order to be able to take the moment of time,、Is thatThe state vector and corresponding covariance matrix of the instant one-step prediction,、Is thatThe observation vector and the corresponding covariance matrix of the instant one-step prediction,Is the state vector inAn estimate of the time of day,Is thatTime observation vector,Is a gain matrix,Is thatThe variance matrix corresponding to the moment observation noise,Is thatCross-correlation covariance matrix of state vector and observation vector at time,As a factor of the robustness (a-f),In order to have a robust gain matrix,AndBoth can correct the state vector and the corresponding covariance.
Further, parametersThe following conditions are satisfied:
;
Wherein the method comprises the steps of The function is used to calculate the matrix eigenvalues,In order to be able to take the moment of time,Is thatCovariance matrix of the time-of-day one-step prediction,Is thatCross-correlation covariance matrix of state vector and observation vector at time,Is a robust gain matrix.
In summary, due to the adoption of the technical scheme, the beneficial effects of the invention are as follows:
1. According to the method, two motion models, namely a dynamics model and a uniform acceleration model, are established for a tracked target of a jump glide track, the motion states of an unpowered section and a powered section are respectively described, and a target acceleration judging mechanism is set to obtain a target hybrid motion model capable of completing model conversion, so that the motion model is more attached to the target motion state.
2. The invention adopts a strong robust unscented Kalman filtering algorithm, and the method uses the unscented Kalman filtering algorithm based on the unscented Kalman filtering algorithmThe single-row sigma point algorithm of the single sigma points has no trace change, so that the calculated amount of the algorithm can be reduced and the running speed of the algorithm can be reduced on the basis of basically not influencing the tracking precision.
3. The invention combines the thought of H infinity algorithm and introduces a robust factorAnd a correction formula is obtained, and the state vector and the covariance matrix in the filtering algorithm are further corrected, so that the tracking precision and the robustness are improved, and the tracking effect of the observation station is improved.
Drawings
Fig. 1 is a general block diagram of the method of the present invention.
Fig. 2 is a calculation flow chart of a robust filtering algorithm of the jump glide track strong tracking method of the present invention.
Fig. 3 is a schematic diagram of a jump glide track and a station position in an embodiment.
Fig. 4 is a graph showing the height and speed of the jump glide track in the embodiment.
The tracking position estimate bias variation graph in the embodiment of fig. 5.
The tracking speed estimation bias variation graph in the embodiment of fig. 6.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
The present invention will be described in further detail with reference to the drawings and examples, in order to make the objects, technical solutions and advantages of the present invention more apparent. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
As shown in fig. 1 to 2, a jump glide track strong tracking method includes the steps of:
Step 100, establishing a rectangular coordinate system of an observation station and a motion model of a tracked object, dividing the motion state of the tracked object into a powered stage and an unpowered stage, and establishing a dynamic model for the unpowered stage of a jumping gliding track to describe the jumping gliding track;
Step 200, combining the tracked target motion model into a target hybrid motion model, judging target acceleration, describing the current motion state by using a uniform acceleration model when the target acceleration reaches a set value, and establishing a dynamics model to describe a target jumping glide track when the target acceleration does not reach the set value;
S300, establishing an observation model in an observation station spherical coordinate system by using an observation distance, an observation azimuth angle and an observation elevation angle;
step S400, on the basis of a single-row unscented Kalman filtering algorithm, using a single-row unscented variation based on a single-row sigma point algorithm and combining with an H infinity (H infinity) filtering algorithm, and introducing a robust factor after obtaining a one-step prediction and covariance matrix and a cross-correlation covariance matrix of a state vector and an observation vector Correcting the state vector and covariance to obtain a strong robust unscented Kalman filtering algorithm;
And S500, obtaining a target state equation and an observation equation through a target mixed motion model and an observation model, and tracking the target through a strong robust unscented Kalman filtering algorithm.
Setting an observation station coordinate system, wherein the observation station is taken as an origin, an X axis is taken as the forward direction of the observation station, a Y axis is taken as the north direction of the observation station, and a Z axis is taken as the vertical direction of the observation station;
establishing a dynamic model on the basis of an observation station coordinate system, wherein the dynamic model is used for describing a jumping glide track of a target in an unpowered stage;
The target state vector under the dynamic model comprises position components, speed components and three aerodynamic coefficients of three axes of an observation station coordinate system, the three aerodynamic coefficients are modeled as a Gauss-Markov process, and a continuous state equation is as follows:
wherein the position components of the three axes of the coordinate system comprise X-axis components Component of Y axisAnd Z-axis componentThe velocity component includes an X-axis velocity componentVelocity component of Y axisAnd a Z-axis velocity componentAerodynamic coefficient comprises、、The target state vector under the dynamic model is,As a component of the horizontal velocity,,In order to be able to achieve a total speed,,For the atmospheric density at which the target is located,Is the constant of the gravitational force of the earth,For the distance of the target to the earth's center,Is the rotational angular velocity of the earth,For the purpose of observing the latitude of the station,Is the radius of the earth's circle,、、Respectively aerodynamic coefficient、、The function on the right of the equation in the continuous state equation is recorded as;
Discretizing a continuous state equation, wherein the target state equation is approximately expressed as:
;
Wherein, In discrete steps of time,、Is a discrete time of day which is the time of day,、Respectively at the target、The state vector of the moment of time,Is thatTime of day functionCorresponding values.
Establishing a uniform acceleration model on the basis of an observation station coordinate system for describing a jump glide track of a target in a dynamic stage;
setting the target state vector under the uniform acceleration model as ,、AndThe three uniform acceleration components in the axial directions of the observation station coordinate system X, Y, Z are respectively shown in the following state equations:
;
;
;
Wherein, In discrete steps of time,、Is a discrete time of day which is the time of day,As a parameter related to the intensity of white gaussian noise,Is thatIs used for the co-variance matrix of (a),Is thatA sequence of white gaussian noise at the moment in time,Is thatA time of day target state vector.
Setting a judging condition for the target acceleration in the powered stage:
;
;
;
;
Wherein, 、、、、、Respectively at the target、The X, Y, Z three axial velocity components at the time under the coordinate system of the observation station,In discrete steps of time,As the X-axis acceleration component,As the component of the acceleration in the Y-axis,As a component of the acceleration in the Z-axis,The acceleration of the target is;
when the target acceleration Describing the motion model of the target as a uniform acceleration model when the judging condition is met, and judging the acceleration of the target when the motion model of the target is uniform acceleration modelAnd when the judging condition is not met, converting the motion model of the descriptive target into a dynamics model.
Establishing an observation station observation model in an observation station spherical coordinate system:
The observation model of the observation station is built in the spherical coordinate system of the observation station, and the observation distance is used Azimuth angle of observationElevation angle of observationRepresentation of the observation distanceTo observe the distance from the station to the target, the azimuth angle is observedFor the connection between the observation station and the target to project an angle with the northbound direction in the local horizontal plane of the observation station, elevation angle of observationTo observe the connection line from station to target an included angle of a local horizontal plane of the observation station;
In consideration of actual engineering conditions, observation noise is introduced, and an observation equation of an observation model is as follows:
;
Wherein, 、、For the position component of the object in the coordinate system of the observation station,、、Is white gaussian noise. White gaussian noise、AndIndependent of each other, the mean value is 0, and the variance is constant.
The observation station tracking filtering process is expressed as a discrete nonlinear state equation:
;
;
Wherein, In order to be a target state vector of the object,In order to observe the vector of the light,In order for the process to be noisy,In order to observe the noise it is possible,For the state equation corresponding to the object motion model,An observation equation corresponding to the observation model;
target state vector Length of (2)Observation vectorLength ofProcess noiseThe mean value of the uncorrelated white noise vectors is zero, and the variance matrix isObservation noiseThe mean value of the uncorrelated white noise vectors is zero, and the variance matrix is;
The unscented Kalman filtering algorithm based on single-row unscented transformation is adopted, and an H infinity filtering algorithm is combined to obtain the strong robust unscented Kalman filtering algorithm, wherein the calculation steps of the strong robust unscented Kalman filtering algorithm are that a sigma point algorithm based on single row is generatedPersonal weight coefficientSigma point:
;
Wherein, To take values of 1 toIs used for the control of the variable of (a),Is a weight coefficient;
Initializing a unitary vector as follows:
;
For the following Vector quantityThe method comprises the following steps:
;
construction of sigma points :
;
Wherein, Is the covariance matrix of the state vector at time k,An estimated value of the state vector at the moment k;
Calculation of State propagation of individual sigma points:
;
Wherein, Is a state equation;
calculating a one-step prediction and covariance matrix of the state vector:
;
Wherein, Is process noiseIs a matrix of variances of (a),In order to be able to take the moment of time,As the weight coefficient, the weight coefficient is used,To take values of 1 toIs used for the control of the variable of (a),Is a one-step predictor of the state vector,Is thatIs used for the co-variance matrix of (a),Is process noiseIs a variance matrix of (a);
reconstructing sigma points:
;
Wherein, Is a one-step predictor of the state vector,Is thatIs used for the co-variance matrix of (a),To take values of 1 toIs used for the control of the variable of (a),Vectors required to construct sigma points;
Calculation of Observed propagation of the individual sigma points:
;
Wherein, Is an observation equation;
calculating a one-step prediction and covariance matrix of the observation:
;
Wherein, Is a discrete time of day and is a time of day,To take values of 1 toIs used for the control of the variable of (a),As the weight coefficient, the weight coefficient is used,To observe noiseIs a matrix of variances of (a),Is an observation vector.
The state vector and covariance matrix correction includes:
;
Wherein, In order to be able to take the moment of time,、Is thatThe state vector and corresponding covariance matrix of the instant one-step prediction,、Is thatThe observation vector and the corresponding covariance matrix of the instant one-step prediction,Is the state vector inAn estimate of the time of day,Is thatTime observation vector,Is a gain matrix,Is thatThe variance matrix corresponding to the moment observation noise,Is thatCross-correlation covariance matrix of state vector and observation vector at time,As a factor of the robustness (a-f),In order to have a robust gain matrix,AndBoth can correct the state vector and the corresponding covariance. To ensure the existence of an H-infinity filter, parametersThe following conditions are satisfied:
;
Wherein the method comprises the steps of The function is used to calculate the matrix eigenvalues,In order to be able to take the moment of time,Is thatCovariance matrix of the time-of-day one-step prediction,Is thatCross-correlation covariance matrix of state vector and observation vector at time,Is a robust gain matrix.
Examples
In order to verify the limitation of the present embodiment, as shown in fig. 3-6, a simulation experiment is performed in MATLAB, firstly, parameter setting and parameter initialization are performed, namely, initial longitude, latitude, altitude, real jump glide track data with the speed of 0 °, 7000m and 6400m/s are input, the track condition is shown in fig. 4, the position of the observation station is set in the middle section of the track, the longitude and latitude are 20 ° and 35 °, the track and the position of the observation station are schematically shown in fig. 3, the tracking time interval of the observation station is 0.1s, the observation data of the observation station is obtained through an observation station observation model and real target track data, the initial value of the state vector is obtained by adding random noise with normal distribution to the real target track value, and the initial variance matrix of the state vectorProcess noise matrix for motion modelObservation error variance matrixWhen the observation distance is smaller than 300km and the observation elevation angle is larger than 0, the observation station can effectively track.
When the motion model of the target is converted into a uniform acceleration model by the dynamics model, the position component and the speed component of the state vector initial value of the uniform acceleration model are provided by the corresponding values in the dynamics 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 into a dynamics model from a uniform acceleration model, the position component and the speed component of the state vector initial value of the dynamics model are provided by the uniform acceleration model, and the three aerodynamic coefficient initial values are set to 0.
The dynamic model is adopted as a target motion model, the target hybrid motion model and the observation station observation model provided by the embodiment, and the robust unscented Kalman filtering algorithm provided by the embodiment is used for developing a simulation contrast test and analysis.
And (3) developing a Monte Carlo simulation experiment for 50 times, and calculating the position estimation deviation and the speed estimation deviation of the tracking section of the observation station in the form of root mean square error, wherein the formula is as follows:
;
;
Wherein, To estimate the bias for the position of the observation station tracking segment,Estimating a deviation for the speed of the observation station tracking segment;、、、、、 Respectively the position component and the speed component of the real target under the coordinate system of the observation station, 、、、、、The position component and the speed component of the target which are estimated by tracking under the coordinate system of the observation station are respectively.
The obtained position estimation deviation and velocity estimation deviation are schematically shown in fig. 5 and 6. It can be seen that the tracking method provided by the embodiment can still perform more stable tracking when the target enters the dynamic stage, and particularly in speed tracking, tracking deviation which is changed greatly cannot be generated. The running data of the tracking algorithm using the different motion models are shown in table 1:
TABLE 1
The method can obtain from the table 1 that the position and speed estimation deviation average value of the target mixed motion model adopted by the embodiment is smaller than that of the dynamic model serving as the target motion model, so that the target mixed motion model is more attached to the target motion state, the tracking precision and the robustness are improved, and the tracking effect of the observation station is improved.
The foregoing description of the preferred embodiments of the invention is not intended to be limiting, but rather is intended to cover all modifications, equivalents, and alternatives falling within the spirit and principles of the invention.
Claims (10)
1. A method for strongly tracking a jump glide trajectory, the method comprising:
Establishing an observation station coordinate system and a tracked target motion model, dividing the motion state of the tracked target into a dynamic stage and an unpowered stage, and establishing a dynamic model for describing a jumping gliding track in the unpowered stage of the jumping gliding track;
Combining the tracked target motion model into a target hybrid motion model, judging target acceleration, describing the current motion state by using a uniform acceleration model when the target acceleration reaches a set value, and establishing a dynamics model to describe a target jumping glide track when the target acceleration does not reach the set value;
Establishing an observation model of an observation station;
On the basis of a single-row unscented Kalman filtering algorithm, a single-row unscented variation based on a single-row sigma point algorithm is used and combined with an H infinity filtering algorithm to obtain a one-step prediction and covariance matrix and cross-correlation covariance matrix of state vectors and observation vectors, and then a robust factor is introduced Correcting the state vector and the covariance matrix to obtain a strong robust unscented Kalman filtering algorithm;
and obtaining a target state equation and an observation equation through the target mixed motion model and the observation model, and tracking the target through a strong robust unscented Kalman filtering algorithm.
2. The method for strongly tracking a jump glide track according to claim 1, wherein said establishing an observation station coordinate system and a tracked object motion model comprises the steps of:
Setting an observation station coordinate system, wherein the observation station is taken as an origin, an X axis is taken as the forward direction of the observation station, a Y axis is taken as the north direction of the observation station, and a Z axis is taken as the vertical direction of the observation station;
establishing a dynamic model on the basis of an observation station coordinate system, wherein the dynamic model is used for describing a jumping glide track of a target in an unpowered stage;
and establishing a uniform acceleration model on the basis of an observation station coordinate system for describing the jump glide track of the target in the dynamic stage.
3. The method for strongly tracking a jump glide track according to claim 2, wherein said establishing a kinetic model on the basis of the coordinate system of the observation station comprises:
The target state vector under the dynamic model comprises position components, speed components and three aerodynamic coefficients of three axes of an observation station coordinate system, the three aerodynamic coefficients are modeled as a Gauss-Markov process, and a continuous state equation is as follows:
wherein the position components of the three axes of the coordinate system comprise X-axis components Component of Y axisAnd Z-axis componentThe velocity component includes an X-axis velocity componentVelocity component of Y axisAnd a Z-axis velocity componentAerodynamic coefficient comprises、、The target state vector under the dynamic model is,As a component of the horizontal velocity,,In order to be able to achieve a total speed,,For the atmospheric density at which the target is located,Is the constant of the gravitational force of the earth,For the distance of the target to the earth's center,Is the rotational angular velocity of the earth,For the purpose of observing the latitude of the station,Is the radius of the earth's circle,、、Respectively aerodynamic coefficient、、The function on the right of the equation in the continuous state equation is recorded as;
Discretizing a continuous state equation, wherein the target state equation is approximately expressed as:
;
Wherein, In discrete steps of time,、Is a discrete time of day which is the time of day,、Respectively at the target、The state vector of the moment of time,Is thatTime of day functionCorresponding values.
4. The method for strongly tracking a jump glide track according to claim 2, wherein establishing the uniform acceleration model on the basis of the coordinate system of the observation station comprises setting a target state vector under the uniform acceleration model to be,、AndThe three uniform acceleration components in the axial directions of the observation station coordinate system X, Y, Z are respectively shown in the following state equations:
;
;
;
Wherein, In discrete steps of time,、Is a discrete time of day which is the time of day,As a parameter related to the intensity of white gaussian noise,Is thatIs used for the co-variance matrix of (a),Is thatA sequence of white gaussian noise at the moment in time,Is thatA time of day target state vector.
5. The method of claim 1, wherein combining the tracked object motion models into the object hybrid motion model comprises:
Setting a judging condition for the target acceleration in the powered stage:
;
;
;
;
Wherein, 、、、、、Respectively at the target、The X, Y, Z three axial velocity components at the time under the coordinate system of the observation station,In discrete steps of time,As the X-axis acceleration component,As the component of the acceleration in the Y-axis,As a component of the acceleration in the Z-axis,The acceleration of the target is;
when the target acceleration Describing the motion model of the target as a uniform acceleration model when the judging condition is met, and judging the acceleration of the target when the motion model of the target is uniform acceleration modelAnd when the judging condition is not met, converting the motion model of the descriptive target into a dynamics model.
6. The method of claim 1, wherein the step of establishing the observation model of the observation station comprises establishing the observation model of the observation station in a spherical coordinate system of the observation station by using an observation distanceAzimuth angle of observationElevation angle of observationRepresentation of the observation distanceTo observe the distance from the station to the target, the azimuth angle is observedFor the connection between the observation station and the target to project an angle with the northbound direction in the local horizontal plane of the observation station, elevation angle of observationTo observe the connection line from station to target an included angle of a local horizontal plane of the observation station;
In consideration of actual engineering conditions, observation noise is introduced, and an observation equation of an observation model is as follows:
;
Wherein, 、、For the position component of the object in the coordinate system of the observation station,、、Is white gaussian noise.
7. The method for strongly tracking a jump glide trajectory as recited in claim 6, wherein the gaussian white noise、AndIndependent of each other, the mean value is 0, and the variance is constant.
8. The method for strongly tracking a jump glide path according to claim 1 wherein,
The observation station tracking filtering process is expressed as a discrete nonlinear state equation:
;
;
Wherein, In order to be a target state vector of the object,In order to observe the vector of the light,In order for the process to be noisy,In order to observe the noise it is possible,For the state equation corresponding to the object motion model,An observation equation corresponding to the observation model;
target state vector Length of (2)Observation vectorLength ofProcess noiseThe mean value of the uncorrelated white noise vectors is zero, and the variance matrix isObservation noiseThe mean value of the uncorrelated white noise vectors is zero, and the variance matrix is;
The calculation step of the strong robust unscented Kalman filtering algorithm comprises the steps of generating based on a single-row sigma point algorithmPersonal weight coefficientSigma point:
;
Wherein, To take values of 1 toIs used for the control of the variable of (a),Is a weight coefficient;
Initializing a unitary vector as follows:
;
For the following Vector quantityThe method comprises the following steps:
;
construction of sigma points :
;
Wherein, Is thatThe covariance matrix of the time-of-day state vector,Is thatAn estimate of the time state vector;
Calculation of State propagation of individual sigma points:
;
Wherein, Is a state equation;
calculating a one-step prediction and covariance matrix of the state vector:
;
Wherein, Is process noiseIs a matrix of variances of (a),In order to be able to take the moment of time,As the weight coefficient, the weight coefficient is used,To take values of 1 toIs used for the control of the variable of (a),Is a one-step predictor of the state vector,Is thatIs used for the co-variance matrix of (a),Is process noiseIs a variance matrix of (a);
reconstructing sigma points:
;
Wherein, Is a one-step predictor of the state vector,Is thatIs used for the co-variance matrix of (a),To take values of 1 toIs used for the control of the variable of (a),Vectors required to construct sigma points;
Calculation of Observed propagation of the individual sigma points:
;
Wherein, Is an observation equation;
calculating a one-step prediction and covariance matrix of the observation:
;
Wherein, Is a discrete time of day and is a time of day,To take values of 1 toIs used for the control of the variable of (a),As the weight coefficient, the weight coefficient is used,To observe noiseIs a matrix of variances of (a),Is an observation vector.
9. The method of claim 8, wherein the state vector and covariance matrix correction comprises:
;
Wherein, In order to be able to take the moment of time,、Is thatThe state vector and corresponding covariance matrix of the instant one-step prediction,、Is thatThe observation vector and the corresponding covariance matrix of the instant one-step prediction,Is the state vector inAn estimate of the time of day,Is thatTime observation vector,Is a gain matrix,Is thatThe variance matrix corresponding to the moment observation noise,Is thatCross-correlation covariance matrix of state vector and observation vector at time,As a factor of the robustness (a-f),In order to have a robust gain matrix,AndBoth can correct the state vector and the corresponding covariance.
10. The method for strongly tracking a jump glide track according to claim 9 wherein the parameters areThe following conditions are satisfied:
;
Wherein the method comprises the steps of The function is used to calculate the matrix eigenvalues,In order to be able to take the moment of time,Is thatCovariance matrix of the time-of-day one-step prediction,Is thatCross-correlation covariance matrix of state vector and observation vector at time,Is a robust gain matrix.
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