CN115615434A - Satellite positioning failure resistant trajectory correction system and method based on 5D prediction compensation - Google Patents
Satellite positioning failure resistant trajectory correction system and method based on 5D prediction compensation Download PDFInfo
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Abstract
The invention discloses a satellite positioning failure resistant trajectory correction system and method based on 5D prediction compensation. According to the method, satellite positioning information is converted into the speed height angle, the speed direction angle, the pitch angle, the yaw angle and the axial swing angular speed of the projectile body, so that the drop point prediction is carried out by using a 5-degree-of-freedom rigid body trajectory model, the prediction accuracy is high, additional pitching and yawing attitude measurement sensors are avoided, and the cost is reduced; the accurate position deviation amount of the predicted drop point and the target point is used as a control amount, so that the projectile body flight control is realized, and the control accuracy is improved; meanwhile, aiming at satellite failure, trajectory data of a projectile in controlled flight are directly calculated by using satellite positioning information and control instruction information before failure and a 5-degree-of-freedom rigid body trajectory model and serve as compensation values of satellite positioning failure moments to participate in projectile landing point prediction, the problems of error repair and rework of a traditional algorithm are avoided, and the trajectory correction control precision of satellite signals during transient failure is improved.
Description
Technical Field
The invention relates to the technical field of correction control of simple guided munitions, in particular to a satellite positioning failure resistant trajectory correction system and method based on 5D prediction compensation.
Background
According to the traditional trajectory correction control algorithm based on the drop point prediction, when satellite positioning fails, the position and speed information of the projectile body 4 cannot be acquired, so that a correction control instruction cannot be determined, and the projectile body 4 maintains the instruction at the previous moment or performs free derotation. Maintaining the previous correction command easily causes overcorrection and reverse error correction of the projectile 4, and performing free derotation weakens the correction capability of the projectile 4, so both methods result in a reduction in trajectory correction control accuracy.
Disclosure of Invention
In view of the above, the invention provides a satellite positioning failure resistant trajectory correction system and method based on 5D prediction compensation, which can realize accurate correction control of duck-type layout high spinning projectiles under the condition of transient satellite positioning failure caused by a complex electromagnetic environment.
The invention discloses a satellite positioning failure resistant trajectory correction system based on 5D prediction compensation, which comprises: the system comprises a deviation solving module, a correction control module, an actuating mechanism, a projectile body, a trajectory measuring module, a trajectory filtering module, a drop point prediction module and an anti-satellite failure trajectory prediction compensation module;
the deviation solving module is used for solving the position deviation between the position coordinates of the target point and the position coordinates of the predicted drop point;
the correction control module obtains a roll angle control instruction gamma according to a correction control algorithm based on the position deviation amount solved by the deviation solving module C And correcting the execution period t S ；
The executing mechanism executes a roll angle control command gamma C Duration t S Time, controlling the projectile to fly;
the ballistic measurement module measures ballistic parameters of a projectile in real time based on the missile-borne satellite receiver and inputs the ballistic parameters to the ballistic filtering module;
the ballistic filtering module carries out filtering processing on the input ballistic parameters;
the drop point prediction module is used for solving a speed height angle, a speed direction angle, an axial swing angular speed, a pitch angle and a yaw angle of the projectile body based on the trajectory parameters which are output by the trajectory filtering module and subjected to filtering processing; taking ballistic parameters of the projectile body, the solved speed height angle, speed direction angle, axial swing angular velocity, pitch angle and yaw angle as input, simplifying a rigid body ballistic model by using 5 degrees of freedom, and predicting a ballistic falling point of the projectile body to obtain a predicted falling point position coordinate;
the satellite failure resistant trajectory prediction compensation module is used for correcting the roll angle control command gamma output by the control module based on the positioning failure of the trajectory measurement module C And correcting the execution period t S And the ballistic parameter filtering result of the projectile body at the previous moment, the rigid body ballistic model is simplified by using 5 degrees of freedom, and the projectile body execution roll angle control command gamma is calculated C Duration t S Ballistic parameters after time; and the calculated ballistic parameters are input to a drop point prediction module for drop point prediction after being filtered by a ballistic filtering module.
Preferably, the ballistic filtering module employs extended kalman filtering.
Preferably, the drop point prediction module is used for predicting the range O of the projectile under the ground coordinate system Oxyz (E) based on the projectile in the ballistic parameters E X E Height O E Y E And transverse offset O E Z E Velocity information v in three directions x 、v y 、v z Solving for the velocity height angle theta of the projectile a And velocity direction angle psi 2 ：
Preferably, the drop point prediction module first solves the high and low attack angles delta according to an attack angle equation between the projectile velocity axis and the projectile axis 1 Angle of attack delta 2 Then, a pitch angle and a yaw angle are obtained by combining the speed high-low angle and the speed direction angle;
the angle of attack equation between the projectile velocity axis and the projectile axis is as follows:
wherein Δ, Δ' and Δ ″ are the complex angle of attack and its first and second derivatives, respectively, and Δ = δ 1 +iδ 2 I is an imaginary unit; theta, theta,
Trajectory dip and its first and second derivatives, respectively; expression relating to aerodynamic coefficient of projectile
Where ρ is the air density, S is the characteristic area of the projectile, m is the mass of the projectile, g is the acceleration of gravity, C is the polar moment of inertia, A is the equatorial moment of inertia, l is the length of the projectile, d is the diameter of the projectile, l is the diameter of the projectile f The distance from the center of mass of the duck rudder to the center of mass of the projectile body, v is the flying speed of the projectile body,
at projectile rotation speed, gamma c Is the rolling angle of the duck rudder, c x Is the coefficient of resistance of the elastomer, c y ' is the derivative of the coefficient of lift of the projectile, m zz Is the equatorial damping moment coefficient, m y "is the second derivative of the Magnus moment coefficient, c yf Is the coefficient of the duck rudder control force, m z ' is the derivative of the static moment coefficient, m zz ' is the derivative of the equatorial damping moment coefficient;
integrating the formula (1) to obtain the high and low attack angles delta 1 Angle of attack delta 2 ；
The pitch angle is the sum of the high and low speed angles and the high and low attack angles, and the yaw angle is the sum of the speed direction angle and the direction attack angle.
Preferably, the angular velocity of axial oscillation of the projectile body
The invention also provides a satellite positioning failure resistant trajectory correction method based on 5D prediction compensation, which adopts the trajectory correction system to correct the trajectory and comprises the following steps:
step 1, calculating the position of a target point at the current moment and the position deviation amount of a predicted falling point position predicted by a falling point prediction module;
step 2, correcting the position deviation amount according to a correction control algorithm to obtain a current roll angle control instruction and a correction execution period;
step 3, the executing mechanism executes the current roll angle control instruction and continues the correction executing period to control the projectile to fly;
step 4, measuring ballistic parameters of the projectile body at the next moment based on the missile-borne satellite receiver, performing filtering processing to obtain the optimal position, speed and rotating speed of the projectile body at the next moment, and executing step 5; if the missile-borne satellite receiver fails to be positioned, turning to step 6;
step 5, based on the optimal position, speed and rotating speed of the projectile body at the next moment, solving a speed high-low angle, a speed direction angle, an axial swing angle speed, a pitch angle and a yaw angle of the projectile body at the next moment; simplifying a rigid body trajectory model based on 5 degrees of freedom, and predicting a trajectory drop point of a projectile to obtain a predicted drop point position coordinate at the next moment; the next moment is the current moment, and the step 1 is returned until the projectile body falls to the ground;
and 6, if the satellite positioning of the missile-borne satellite receiver fails, inputting the position, the speed, the rotating speed, the speed height angle, the speed direction angle, the axial swing angular velocity, the pitch angle and the yaw angle of the projectile at the current moment, simplifying a rigid body trajectory model based on 5 degrees of freedom, calculating the trajectory parameters of the projectile at the next moment after executing a current roll angle control instruction, filtering the calculated trajectory parameters at the next moment by a trajectory filtering module to serve as the optimal position, the speed and the rotating speed of the projectile at the next moment, and turning to the step 5. Has the advantages that:
according to the method, satellite positioning information is converted into the speed height angle, the speed direction angle, the pitch angle, the yaw angle and the axial swing angular speed of the projectile body, so that the drop point prediction can be performed by using a 5-degree-of-freedom rigid body trajectory model, the prediction accuracy is high, additional pitching and yawing attitude measurement sensors are avoided, and the cost is reduced; the accurate position deviation amount of the predicted drop point and the target point is used as a control amount, so that the missile flight control is realized, and the control accuracy is improved; meanwhile, aiming at the satellite failure state, the trajectory data of the projectile in controlled flight are directly calculated by using the satellite positioning information and the control instruction information before failure and using the 5-degree-of-freedom rigid body trajectory model as the compensation value of the satellite positioning failure moment to participate in the projectile drop point prediction, so that the problems of error repair and rework of the traditional algorithm are avoided, and the trajectory correction control precision of the satellite signal during transient failure can be improved.
Drawings
Fig. 1 is a schematic diagram of a trajectory correction system for satellite positioning failure resistance based on 5D prediction compensation according to the present invention.
FIG. 2 is a schematic diagram of the coordinate system and angles of the projectile.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The invention provides a trajectory correction system for resisting satellite positioning failure based on 5D prediction compensation, as shown in figure 1, comprising: the device comprises a deviation solving module 1, a correction control module 2, an actuating mechanism 3, a projectile body 4, a trajectory measuring module 5, a trajectory filtering module 6, a drop point prediction module 7 and an anti-satellite-failure trajectory prediction compensation module 8.
Wherein, the deviation solving module 1 starts controlling at a certain t after trajectory correction 0 At the moment, the range, height and lateral offset coordinates (x) of the target point T T ,y T ,z T ) And the position coordinate (x) of the predicted landing point P P ,y P ,z P ) Is calculated and the deviation amounts (Δ x, Δ y, Δ z) are input into the correction control module 2.
The correction control module 2 obtains a roll angle control command gamma related to a range and a lateral deviation amount according to a correction control algorithm f (delta x, delta z) based on the deviation amount sent by the deviation solving module C And rudder correction execution period t S . Controlling the roll angle by gamma C And rudder correction execution period t S Into the actuator 3.
The actuating mechanism 3 is a steering engine which executes a roll angle control instruction gamma C The rolling angle of the duck rudder component of the duck-type layout high spinning projectile is changed, so that correction control force in a specific direction is generated, the projectile body 4 is controlled to fly, and trajectory correction is achieved.
The trajectory measurement module 5 acquires trajectory measurement parameters such as the position, the speed and the rotating speed of the projectile body 4 in real time based on a missile-borne satellite receiver.
The trajectory filtering module 6 performs filtering processing on the trajectory measurement parameters output by the trajectory measurement module 5, and usually adopts Extended Kalman Filtering (EKF) to obtain the optimal position (x, y, z), velocity v and rotation speed at the current moment
And the filtering result is output to the drop point prediction module 7.
The drop point prediction module 7 first uses the coordinates (x, y, z), velocity v and rotational speed of the projectile 4 output by the ballistic filtering module 6
Solving for the velocity height angle theta of projectile 4 a The velocity direction angle psi 2 Angular velocity ω of axial oscillation ξ And a pitch angle
And yaw angle
Then with projectile 4
As an input, the rigid body trajectory model is simplified by 5 degrees of freedom, and the trajectory landing point of the projectile 4 is predicted to obtain the position coordinates (x) of the predicted landing point P P ,y P ,z P ) And the data is output to a deviation solving module 1, so that a complete closed-loop correction control loop is realized when the satellite positioning is normal.
Specifically, since the ballistic measurement module 5 adopts satellite positioning, the obtained ballistic measurement parameters are as follows: shot 4 range O of shot 4 under ground coordinate system Oxyz (E) E X E Height O E Y E And transverse offset O E Z E Position information (x, y, z) and velocity information (v) in three directions x ,v y ,v z ) And projectile 4 rotational speed information
Therefore, the drop point prediction module 7 needs to convert the trajectory parameters measured by the satellite to obtain the parameters required in the 5-degree-of-freedom simplified rigid body trajectory model, and then predicts the drop point of the projectile by using the 5-degree-of-freedom simplified rigid body trajectory model. The specific transformation process is as follows:
first of all, the range O measured by the ballistic measurement module 5 E X E Height O E Y E And transverse offset O E Z E Velocity information v in three directions x 、v y 、v z Solving the flying resultant velocity v of the projectile body 4 under the ground coordinate system,
velocity information v according to height and range direction of projectile 4 y 、v x Solving the velocity high and low angle theta a ，
According to the speed v of the projectile body 4 in the transverse deviation direction z And the resultant velocity v solves for the velocity direction angle psi 2 ，
In order to obtain the pitching and yawing attitude angles of the projectile body 4, firstly, an attack angle equation of the projectile body 4 is deduced, and the related expression of the attack angle and a derivative term thereof is obtained through derivation and is shown in a formula (1):
wherein Δ, Δ' and Δ ″ are the complex angle of attack and its first and second derivatives, respectively, and Δ = δ 1 +iδ 2 I is an imaginary unit; theta, theta,
Trajectory dip and its first and second derivatives, respectively; expression relating to aerodynamic coefficient of projectile
Where ρ is the air density, S is the characteristic area of the projectile, m is the mass of the projectile, g is the acceleration of gravity, C is the polar moment of inertia, A is the equatorial moment of inertia, l is the length of the projectile, d is the diameter of the projectile, l is the diameter of the projectile f The distance from the center of mass of the duck rudder to the center of mass of the projectile body, v is the flying speed of the projectile body,
is the rotational speed of the projectile, gamma c Is the rolling angle of the duck rudder, c x Is the coefficient of elastic body resistance, c y ' is the derivative of the coefficient of lift of the projectile, m zz Is the equatorial damping moment coefficient, m y Is the second derivative of the Magnus moment coefficient, c yf Coefficient of duck rudder steering force, m z ' is the derivative of the static moment coefficient, m zz ' is the derivative of the equatorial damping moment coefficient. By integrating equation (1), the high and low angles of attack delta can be solved 1 Angle of attack delta 2 。
For the high spin missile (about 100 r/s-300 r/s) in normal flight, the missile axis O xi (pointing to the head of the missile from the centroid O point of the missile) and the speed axis OX V (the point O of the center of mass of the projectile points to the speed direction of the projectile) is very small, then the included angle is delta according to the high and low attack angles 1 Angle of attack delta 2 The pitch angle of the projectile body 4 can be approximately obtained
And yaw angle
Wherein the pitch angle
Yaw angle
Thereby obtaining the pitch and yaw attitude angles of the hull 4. Because the rotation angular velocity of the high spin projectile body 4 is generally larger than the transverse swing angular velocity thereof, the axial swing angular velocity of the projectile body 4 can be simply obtained
Therefore, the position, the speed and the converted angle information acquired by the missile-borne satellite receiver are obtained
And the initial data of the simplified rigid body trajectory model with 5 degrees of freedom are used, and the high-spin projectile flight trajectory recursion is carried out by adopting a four-order Runge-Kutta numerical calculation method with fixed integral step length, so that the position prediction of the drop point of the projectile body 4 can be realized.
If the satellite positioning is normal, the trajectory measurement module 5 inputs trajectory measurement parameters measured by the missile-borne satellite receiver to the trajectory filtering module 6, and performs the drop point prediction in the drop point prediction module 7. If the satellite positioning fails and the satellite receiver cannot obtain real-time ballistic measurement parameters, the ballistic prediction compensation module 8 outputs ballistic parameter measurement compensation values to the ballistic filtering module 6 to form a complete closed loop when the satellite fails. When the satellite positioning is normal, the satellite signal receiver updates the actually measured ballistic parameters, and continues to correct the projectile body 4 by the satellite positioning data until the projectile body 4 finally falls to the ground.
The satellite failure resistant trajectory prediction compensation module 8 is used for positioning failure based on t when the trajectory measurement module 5 is used 0 The filtering result of the optimal position, speed and rotating speed at the moment is utilized to simplify a rigid body trajectory model by using 5 degrees of freedom which are the same as those of the drop point prediction module 7, and a roll angle control command gamma is carried out C And rudder execution time t S Is predicted to obtain t 0 +t S The ballistic parameters at the moment are predicted in a controlled manner; the calculation result is filtered by the trajectory filtering module 6 and then input to the drop point prediction module 7. The drop point prediction module 7 predicts the drop point of the projectile body 4 based on the trajectory parameters calculated by the satellite failure resistant trajectory prediction compensation module 8, and outputs the prediction result to the deviation solving module 1 to form a complete closed loop when the satellite fails. By adopting the satellite positioning failure resistant trajectory prediction compensation module 8, the problems of weakened correction capability, wrong correction and the like existing after satellite positioning failure by adopting a traditional drop point prediction correction control algorithm can be avoided, and the trajectory correction control precision during transient satellite positioning failure can be effectively improved.
The trajectory correction control flow of the satellite positioning failure resistant trajectory correction system based on 5D prediction compensation is as follows:
at a certain t after trajectory correction 0 At the moment, the range, height and horizontal deviation position coordinates (x) of the target point T ,y T ,z T ) And the position coordinate (x) of the predicted falling point P P ,y P ,z P ) The position deviation calculation is performed in the deviation solving module 1, and the deviation amounts (Δ x, Δ y, Δ z) are input to the correction control module 2. Predicting the drop point PPosition coordinates (x) P ,y P ,z P ) Calculated by the simplified rigid body trajectory (5D) uncontrolled drop point prediction module 7. The correction control module 2 obtains a roll angle control command gamma related to the range and the transverse deviation according to a correction control algorithm f (delta x, delta z) C And rudder correction execution period t S . Controlling the roll angle by gamma C And correcting the execution period t S The data are input into a steering engine actuating mechanism 3 and a steering engine actuating mechanism 5D controlled satellite failure resistant trajectory prediction compensation module 8. The steering engine executing mechanism 3 executes a roll angle control command gamma C The rolling angle of the duck rudder component of the duck-type layout high spinning projectile is changed, so that correction control force in a specific direction is generated, the projectile body 4 is controlled to fly, and trajectory correction is achieved. After a correction execution period t S Later, the trajectory measuring module 5 performs satellite positioning, and if the satellite positioning is normal, the projectile 4t is acquired through a satellite receiver 0 +t s And ballistic trajectory measurement parameters such as the position, the speed and the rotating speed at the moment. The measured ballistic measurement parameters are subjected to Extended Kalman (EKF) filtering in the ballistic filtering module 6 to obtain optimal position, velocity and rotation speed filtering results. The filtering result is input into a drop point prediction module 7 to predict the drop point of trajectory uncontrolled flight, and the position coordinate (x) of the predicted drop point is obtained P ,y P ,z P ) Therefore, a complete closed-loop correction control loop is realized when the satellite positioning is normal. When the satellite positioning fails, the satellite receiver cannot obtain real-time trajectory measurement parameters, and at the moment, the satellite failure resistant trajectory prediction compensation module 8 is adopted to calculate a steering engine to execute a roll angle control command gamma based on a 5-degree-of-freedom simplified rigid body trajectory model C And executing the correction execution period t S After time, the projectile has a controlled trajectory at t 0 +t S Position, speed and rotational speed at the moment of time, with calculated controlled trajectory t 0 +t S The position, the speed and the rotating speed at the moment are used as measurement compensation values of the satellite failure moment, and are input into the ballistic filtering module 6 for parameter filtering, and the drop point prediction module 7 is used for drop point prediction, so that a complete closed loop circuit when the satellite fails is formed. When the satellite positioning is normal, the satellite signal receiver updates the actually measured ballistic parameters and continues to correct the projectile body 4 until the projectile body 4 finally falls to the ground.
The invention can realize accurate correction control of duck-type layout high spinning bullets under the condition of transient satellite positioning failure caused by a complex electromagnetic environment. The invention mainly aims at simple guided ammunition which trajectory correction control is carried out by depending on satellite signals, can solve the problems of weak correction capability, error correction, back correction and the like which are easy to occur when the satellite positioning fails in the traditional drop point prediction algorithm, and has higher precision.
In one example, 200 Monte Carlo simulations were performed at 20s of random satellite signal failure, and the results using closed loop correction control were:
200 Monte Carlo uncontrolled drop points: the longitudinal density is 1/218, the transverse density is 1.52mil, cep is 163m.
The traditional correction control algorithm is adopted: the longitudinal density was 1/632, the transverse density 0.42mil, cep 53.5m.
The correction control algorithm adopted by the invention is as follows: the longitudinal concentration was 1/1174, the transverse concentration was 0.46mil, the cep was 35.3m.
Compared with the traditional algorithm for predicting the drop point, the method and the device can obviously improve the accuracy of correction control when the satellite positioning is temporarily failed.
The invention mainly aims at simple guided ammunition which trajectory correction control is carried out by depending on satellite signals, can solve the problems of weak correction capability, error correction, back correction and the like which are easy to occur when the satellite positioning fails in the traditional drop point prediction algorithm, and has higher precision.
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (6)
1. An anti-satellite positioning failure ballistic correction system based on 5D prediction compensation, comprising: the system comprises a deviation solving module (1), a correction control module (2), an actuating mechanism (3), a projectile body (4), a ballistic measuring module (5), a ballistic filtering module (6), a drop point prediction module (7) and an anti-satellite-failure ballistic prediction compensation module (8);
the deviation solving module (1) is used for solving the position deviation amount between the position coordinates of the target point and the position coordinates of the predicted drop point;
the correction control module (2) obtains a roll angle control command gamma according to a correction control algorithm based on the position deviation amount solved by the deviation solving module (1) C And correcting the execution period t S ；
The executing mechanism (3) executes a roll angle control command gamma C Duration t S Time, controlling the projectile body (4) to fly;
the ballistic measurement module (5) measures ballistic parameters of the projectile body (4) in real time based on the missile-borne satellite receiver, and inputs the ballistic parameters to the ballistic filtering module (6);
the ballistic filtering module (6) carries out filtering processing on the input ballistic parameters;
the drop point prediction module (7) is used for solving a speed height angle, a speed direction angle, an axial swinging angle speed, a pitch angle and a yaw angle of the projectile body (4) based on the ballistic parameters output by the ballistic filtering module (6) after filtering; taking ballistic parameters of the projectile body (4), the solved speed height angle, speed direction angle, axial swing angular velocity, pitch angle and yaw angle as input, utilizing 5-degree-of-freedom simplified rigid body ballistic models, and predicting the ballistic falling point of the projectile body (4) to obtain the position coordinates of the predicted falling point;
the satellite failure resistant trajectory prediction compensation module (8) is used for correcting the roll angle control command gamma output by the control module (2) based on the trajectory measurement module (5) when the trajectory measurement module (5) is positioned to fail C And correcting the execution period t S And the result of filtering the trajectory parameters of the projectile (4) at the previous moment, simplifying a rigid body trajectory model by using 5 degrees of freedom, and calculating a rolling angle control command gamma executed by the projectile (4) C Duration t S Ballistic parameters after time; and the calculated ballistic parameters are filtered by a ballistic filtering module (6) and then input to a drop point prediction module (7) for drop point prediction.
2. The satellite positioning failure resistant ballistic correction system based on 5D prediction compensation of claim 1, characterized in that the ballistic filtering module (6) employs extended kalman filtering.
3. The satellite positioning failure resistant ballistic correction system based on 5D prediction compensation of claim 1, characterized in that the drop point prediction module (7) is based on projectile range O of the projectile (4) in ballistic parameters in the ground coordinate system Oxyz (E) E X E Height O E Y E And transverse offset O E Z E Velocity information v in three directions x 、v y 、v z Solving the velocity height angle theta of the projectile body (4) a And velocity direction angle psi 2 ：
4. The satellite positioning failure resistant ballistic correction system based on 5D prediction compensation as claimed in claim 1 or 3, characterized in that the drop point prediction module (7) first solves the high and low attack angles δ according to the attack angle equation between the projectile velocity axis and the projectile axis 1 Sum direction angle of attack delta 2 Then, a pitch angle and a yaw angle are obtained by combining the speed height angle and the speed direction angle;
the angle of attack equation between the projectile velocity axis and the projectile axis is as follows:
wherein Δ, Δ' and Δ ″ are the complex angle of attack and its first and second derivatives, respectively, and Δ =δ 1 +iδ 2 I is an imaginary unit; theta, theta,
Trajectory dip and its first and second derivatives, respectively; expression relating to aerodynamic coefficient of projectile
Where ρ is the air density, S is the characteristic area of the projectile, m is the mass of the projectile, g is the acceleration of gravity, C is the polar moment of inertia, A is the equatorial moment of inertia, l is the length of the projectile, d is the diameter of the projectile, l is the diameter of the projectile f The distance from the center of mass of the duck rudder to the center of mass of the projectile body, v is the flying speed of the projectile body,
at projectile rotation speed, gamma c Is the rolling angle of the duck rudder, c x Is the coefficient of resistance of the elastomer, c y ' is the derivative of the coefficient of lift of the projectile, m zz Is the equatorial damping moment coefficient, m y "is the second derivative of the Magnus moment coefficient, c yf Coefficient of duck rudder steering force, m z ' is the derivative of the static moment coefficient, m zz ' is the derivative of the equatorial damping moment coefficient;
integrating the formula (1) to obtain the high and low attack angles delta 1 Sum direction angle of attack delta 2 ；
The pitch angle is the sum of the high and low speed angles and the high and low attack angles, and the yaw angle is the sum of the speed direction angle and the direction attack angle.
5. The anti-satellite positioning failure ballistic correction system of claim 4, wherein projectile axial swing angular velocity is based on 5D predictive compensation
6. A ballistic correction method based on 5D prediction compensation for satellite positioning failure resistance, characterized in that the ballistic correction system according to any one of claims 1-5 is used for ballistic correction, comprising:
step 1, calculating the position of a target point at the current moment and the position deviation amount of a predicted drop point position predicted by a drop point prediction module (7);
step 2, correcting the position deviation amount according to a correction control algorithm to obtain a current roll angle control instruction and a correction execution period;
step 3, the executing mechanism (3) executes the current roll angle control instruction and continues the correction executing period to control the projectile body (4) to fly;
step 4, measuring ballistic parameters of the projectile body at the next moment based on the missile-borne satellite receiver, performing filtering processing to obtain the optimal position, speed and rotating speed of the projectile body (4) at the next moment, and executing step 5; if the missile-borne satellite receiver fails to be positioned, turning to step 6;
step 5, based on the optimal position, speed and rotating speed of the projectile body (4) at the next moment, solving a speed height angle, a speed direction angle, an axial swinging angle speed, a pitch angle and a yaw angle of the projectile body (4) at the next moment; simplifying a rigid body trajectory model based on 5 degrees of freedom, and predicting a trajectory drop point of the projectile body (4) to obtain a predicted drop point position coordinate at the next moment; the next moment is the current moment, and the step 1 is returned until the projectile body falls to the ground;
and 6, if the satellite positioning of the missile-borne satellite receiver fails, inputting the position, the speed, the rotating speed, the speed height angle, the speed direction angle, the axial swinging angular velocity, the pitch angle and the yaw angle of the projectile body (4) at the current moment, simplifying a rigid body trajectory model based on 5 degrees of freedom, calculating a trajectory parameter of the projectile body (4) at the next moment after executing a current rolling angle control instruction, filtering the calculated trajectory parameter at the next moment by a trajectory filtering module (6) to serve as the optimal position, the speed and the rotating speed of the projectile body (4) at the next moment, and turning to the step 5.
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