CN105550497B - A kind of high-precision projectile correction method - Google Patents
A kind of high-precision projectile correction method Download PDFInfo
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Abstract
The invention discloses a kind of high-precision projectile correction methods, which is characterized in that including：Using the method that noise estimator is estimated and corrected to state-noise and measurement noise, utilizes noise estimator to complete the process of one-step prediction and complete the process of projectile correction based on noise estimator and fading factor.A kind of high-precision projectile correction method provided by the invention, the projectile correction method of design is during pseudo-linear optimal filter, on the one hand state value is predicted using metric data, on the other hand the influence of noise parameter estimation lax pair projectile correction result is reduced to adjust filtering gain matrix by process noise estimator and the characterisitic parameter for measuring the adaptive estimation of noise estimator and correction noise；It introduces fading factor simultaneously and is reasonably faded to outmoded data, increase the weight of new metric data, achieve the purpose that reduce filtering evaluated error, inhibition due to filtering divergence caused by system model is inaccurate and state mutation.
Description
Technical field
The present invention relates to a kind of high-precision projectile correction method, specifically one kind is related to pressing down during projectile correction
System dissipates and puies forward high-precision method, especially considers the factors such as the non-linear of model trajectory, time variation and noise jamming, it is intended to press down
System hair caused by the modeling error of model trajectory and the evaluated error of noise statistics are in ballistic data makeover process
It dissipates, improves the precision that trajectory is formed.The present invention can be effectively ensured projectile correction process stability and ballistic trajectory formed
Accuracy, the ballistic trajectory for being suitable for Gun Position Radar form system.
Background technology
Gun Position Radar carries out projectile correction using the flight parameter of the bullet obtained, forms ballistic trajectory to carry out target
Tracking.The bullet to fly in big spatial domain is influenced by various factors, such as the height of projectile flight, Mach number, aerodynamic force
The measured value and calculated value of parameter can inaccurately etc. cause the model parameter of bullet to change very greatly.In addition, during projectile correction
It can also be had a certain difference between the experience estimated value and the parameter of practical projectile flight of setting.Optimal flat using pseudo-linear
When sliding filtering algorithm carries out projectile correction, error, model trajectory description caused by model trajectory discretization and linearisation be not smart
Really, used process noise and measure noise statistical property and actual conditions deviation is big etc. that factors may all lead to state
Estimated value deviates with bullet practical flight data, causes filtering accuracy to decline, cannot be satisfied the requirement of Practical Project.Actual environment
The enchancement factors such as variation can also cause systematic procedure noise and measure noise anomalous variation, and gain square is will produce in filtering
The erroneous estimation of battle array and prediction error variance, in this case gain matrix will lose suitable weighting effect, new measurement number
It will be continuously decreased according to the adjusting correcting action to state estimation, and to filtering divergence phenomenon occur, projectile correction be caused to fail,
It can not continue to track target.
Invention content
The technical problem to be solved by the invention is to provide a kind of to state-noise and noise is measured using noise estimator
The high-precision projectile correction method estimated and corrected；Further, present invention offer is a kind of utilizing noise estimator
One-step prediction is completed, uncertain noise statistics and other random disturbances etc. in pseudo-linear optimal smoothing filtering are reduced
The high-precision projectile correction method of influence of the factor to projectile correction precision；Further, the present invention provides one kind and is based on
Noise estimator and fading factor complete projectile correction, covariance and filter of the fading factor to the one-step prediction error of state estimation
Wave gain matrix carries out adaptive adjustment, inhibits due to caused by state mutation during model trajectory is inaccurate and filtering
The high-precision projectile correction method of Divergent Phenomenon.
In order to solve the above technical problems, the technical solution adopted by the present invention is：
A kind of high-precision projectile correction method, which is characterized in that including：Using noise estimator to state-noise and amount
The method that noise is estimated and corrected is surveyed, which includes the following steps：
S01, model trajectory：
The state equation that model trajectory uses for：
In formula (1), X (t) indicates that the state of bullet, W (t) are process noises, and Γ (t) is noise driving battle array；
The measurement equation that model trajectory uses for：
Z (t)=h (X (t))+V (t) (2)
Z (t) indicates to measure variable in formula (2), and V (t) is to measure noise；
It is obtained after carrying out discretization to formula (1), formula (2)：
Xk+1=G (Xk)+Γ(Xk)Wk (3)
Zk+1=h (Xk+1)+Vk+1 (4)
S02, the calculation of initial value of projectile correction：
When being modified to ballistic trajectory, definition status vector is：
X=[x y z vx vy vz c ac] (5)
X, y and z indicate directive distance, height and the lateral deviation of bullet respectively in formula (5)；vx, vyAnd vzBullet speed is indicated respectively
Three components of degree；C and acBallistic coefficient and projectile correction coefficient are indicated respectively；
If the two initial point sampling values that radar measures shell are (x1,y1,z1) and (x2,y2,z2), thus obtain state arrow
Measure the initial valuation of XFor：
Initial prediction error variance matrix is：
In formula (7),For the variance of system random error,It is ballistic coefficient and projectile correction system
The empirical estimating value of number mean square deviation.
The invention also includes the process for completing one-step prediction using noise estimator, which includes the following steps：
S03, projectile correction：
S03-1 calculates one-step prediction smooth value：
S03-1-1 calculates relevant parameter using the prediction result of initial value and formula (7),
Calculate function of state：
X in formula (9)4r=vx-wxAnd x6r=vz-wzPractical speed of the bullet in x and z directions after by air speed influence is indicated respectively
Degree, wxAnd wzFor wind speed x and z directions component,ρ is atmospheric density,
S is that bullet maximum blocks area i.e.D is caliber, and m is Shell body quality；Cx(Ma) it is coefficient of air resistance, is Mach
The function of number Ma, g are the acceleration of gravity at height above sea level y, BZFor lateral lift acceleration；
Calculate the partial derivative of function of state
Calculate one step state transition matrix
The variance matrix of calculating process noise and the variance matrix for measuring noise：
In formula (12), (13), H indicates conjugate transposition；
S03-1-2 carries out predictive estimation：
Calculate one-step prediction estimated value：
Calculate one-step prediction error covariance：
It calculates and measures transfer matrix：
Calculate gain matrix：
S03-1-3 corrects noise using noise estimator：
The variance matrix of process noise is modified：
Variance matrix to measuring noise is modified：
In formula (18), (19), residual error newly ceasesBe calculated as：
In formula (18), (19), dk=(1- α)/(1- αk), 0 ＜ α ＜ 1 are forgetting factor；
S03-1-4 carries out self-adaptive smooth filtering：
Calculate filtering value：
S03-1-5, iterative calculation
It enablesIt repeats S03-1-1 to S03-1-5 calculating process at least three times, is so at least changed three times
It can be acquired after generationApproximation, complete one-step prediction smooth value calculating.
The invention also includes the process for completing projectile correction based on noise estimator and fading factor, which includes：
S03-2 corrects filter result using fading factor：
S03-2-1 calculates fading factor, enables fading factor
S03-2-2 carries out one-step prediction modified result,
Calculate the error co-variance matrix of the one-step prediction with fading factor
Calculate gain matrix
Calculate filtering estimated value
Calculate filtering error variance matrix
S03-3 enables k+1 → k, repeats S03-1 to S03-3 steps, completes projectile correction process.
The number of the iterative calculation is three times.
A kind of high-precision projectile correction method provided by the invention, the projectile correction method that the present invention designs are in quasi- line
Property optimal filter during, using metric data on the one hand state value is predicted, on the other hand estimated by process noise
Device and the characterisitic parameter of the adaptive estimation and correction noise of measurement noise estimator are reduced and are made an uproar to adjust filtering gain matrix
The influence of sound parameter Estimation lax pair projectile correction result；Fading factor is introduced simultaneously to carry out reasonably gradually outmoded data
Disappear, increase the weight of new metric data, by existing in real time to the covariance matrix and filtering gain matrix progress of predicting error
Line adjusts, and reaches reduction filtering evaluated error, inhibits due to filtering divergence caused by system model is inaccurate and state mutation
Purpose.
Figure of description
Fig. 1 is that the present invention is based on the projectile correction flow charts of adaptive fading factor；
Fig. 2 is Divergent Phenomenon figure of the prior art based on pseudo-linear optimal smoothing filtering algorithm projectile correction；
The simulation result diagram of high-precision projectile correction method in Fig. 3 present invention.
Specific implementation mode
The present invention is further described below in conjunction with the accompanying drawings.
As shown in FIG. 1 to 3, in order to verify the present invention the projectile correction method based on noise estimator and fading factor
Validity is selected as 1100m/s in shell initial velocity, and directive angle is selected as 25o condition Imitatings and generates radar measurement data, adopts respectively
With the ballistic trajectory correction algorithm and pseudo-linear optimal smoothing filtering algorithm of the present invention, fly to the shell that radar surveying obtains
Data are filtered analysis, and the three-dimensional artificial result of the ballistic trajectory of formation is as shown in Figure 2 and Figure 3, wherein " emulation data " are mould
Quasi- radar measurement data, " filtering data " are the ballistic trajectory of filtering estimation.As shown in Fig. 2, occurring filtering divergence in Fig. 2
Phenomenon, and in Fig. 3 diverging is effectively inhibited using the projectile correction method based on noise estimator and fading factor.
A kind of high-precision projectile correction method, which is characterized in that including：Using noise estimator to state-noise and amount
The method that noise is estimated and corrected is surveyed, which includes the following steps：
S01, model trajectory：
The state equation that model trajectory uses for：
In formula (1), X (t) indicates that the state of bullet, W (t) are process noises, and Γ (t) is noise driving battle array；
The measurement equation that model trajectory uses for：
Z (t)=h (X (t))+V (t) (2)
Z (t) indicates to measure variable in formula (2), and V (t) is to measure noise；
It is obtained after carrying out discretization to formula (1), formula (2)：
Xk+1=G (Xk)+Γ(Xk)Wk (3)
Zk+1=h (Xk+1)+Vk+1 (4)
S02, the calculation of initial value of projectile correction：
When being modified to ballistic trajectory, definition status vector is：
X=[x y z vx vy vz c ac] (5)
X, y and z indicate directive distance, height and the lateral deviation of bullet respectively in formula (5)；vx, vyAnd vzBullet speed is indicated respectively
Three components of degree；C and acBallistic coefficient and projectile correction coefficient are indicated respectively；
If the two initial point sampling values that radar measures shell are (x1,y1,z1) and (x2,y2,z2), thus obtain state arrow
Measure the initial valuation of XFor：
Initial prediction error variance matrix is：
In formula (7),For the variance of system random error,It is ballistic coefficient and projectile correction
The empirical estimating value of coefficient mean square deviation.
The invention also includes the process for completing one-step prediction using noise estimator, which includes the following steps：
S03, projectile correction：
S03-1 calculates one-step prediction smooth value：
S03-1-1 calculates relevant parameter using the prediction result of initial value and formula (7),
Calculate function of state：
X in formula (9)4r=vx-wxAnd x6r=vz-wzPractical speed of the bullet in x and z directions after by air speed influence is indicated respectively
Degree, wxAnd wzFor wind speed x and z directions component,ρ is atmospheric density,
S is that bullet maximum blocks area i.e.D is caliber, and m is Shell body quality；Cx(Ma) it is coefficient of air resistance, is Mach
The function of number Ma, g are the acceleration of gravity at height above sea level y, BZFor lateral lift acceleration；
Calculate the partial derivative of function of state
Calculate one step state transition matrix
The variance matrix of calculating process noise and the variance matrix for measuring noise：
In formula (12), (13), H indicates conjugate transposition；
S03-1-2 carries out predictive estimation：
Calculate one-step prediction estimated value：
Calculate one-step prediction error covariance：
It calculates and measures transfer matrix：
Calculate gain matrix：
S03-1-3 corrects noise using noise estimator：
The variance matrix of process noise is modified：
Variance matrix to measuring noise is modified：
In formula (18), (19), residual error newly ceasesBe calculated as：
In formula (18), (19), dk=(1- α)/(1- αk), 0 ＜ α ＜ 1 are forgetting factor；
S03-1-4 carries out self-adaptive smooth filtering：
Calculate filtering value：
S03-1-5, iterative calculation
It enablesIt repeats S03-1-1 to S03-1-5 calculating process at least three times, is so at least changed three times
It can be acquired after generationApproximation, complete one-step prediction smooth value calculating.
The invention also includes the process for completing projectile correction based on noise estimator and fading factor, which includes：
S03-2 corrects filter result using fading factor：
S03-2-1 calculates fading factor, enables fading factor
S03-2-2 carries out one-step prediction modified result,
Calculate the error co-variance matrix of the one-step prediction with fading factor
Calculate gain matrix
Calculate filtering estimated value
Calculate filtering error variance matrix
S03-3 enables k+1 → k, repeats S03-1 to S03-3 steps, completes projectile correction process.
The number of the iterative calculation is three times.
The above is only a preferred embodiment of the present invention, it should be pointed out that：For the ordinary skill people of the art
For member, various improvements and modifications may be made without departing from the principle of the present invention, these improvements and modifications are also answered
It is considered as protection scope of the present invention.
Claims (2)
1. a kind of high-precision projectile correction method, which is characterized in that including：Using noise estimator to state-noise and measurement
The method that noise is estimated and corrected, the method include the following steps：
S01, model trajectory：
The state equation that model trajectory uses for：
In formula (1), X (t) indicates that the state of bullet, W (t) are process noises, and Γ (t) is noise driving battle array；
The measurement equation that model trajectory uses for：
Z (t)=h (X (t))+V (t) (2)
Z (t) indicates to measure variable in formula (2), and V (t) is to measure noise；
It is obtained after carrying out discretization to formula (1), formula (2)：
Xk+1=G (Xk)+Γ(Xk)Wk (3)
Zk+1=h (Xk+1)+Vk+1 (4)
In formula (3), formula (4),Xk=X (t) |T=kT, T=tk+1-tkFor
Sampling interval, tkFor k-th of sampling time；Wk=W (t) |T=kT, Vk+1=V (t) |T=(k+1) T；
S02, the calculation of initial value of projectile correction：
When being modified to ballistic trajectory, definition status vector is：
X=[x y z vx vy vz c ac] (5)
X, y and z indicate directive distance, height and the lateral deviation of bullet respectively in formula (5)；vx, vyAnd vzVelocity of shot is indicated respectively
Three components；C and acBallistic coefficient and projectile correction coefficient are indicated respectively；
If the two initial point sampling values that radar measures shell are (x1,y1,z1) and (x2,y2,z2), thus obtain state vector X
Initial valuationFor：
Initial prediction error variance matrix is：
In formula (7),For the variance of system random error,It is that ballistic coefficient and projectile correction coefficient are equal
The empirical estimating value of variance；
Further include the process that one-step prediction is completed using noise estimator, which includes the following steps：
S03, projectile correction：
S03-1 calculates one-step prediction smooth value：
S03-1-1 calculates relevant parameter using the prediction result of initial valuation and formula (7),
It enables
Calculate function of state：
X in formula (9)4r=vx-wxAnd x6r=vz-wzActual speed of the bullet in x and z directions after by air speed influence, w are indicated respectivelyx
And wzFor wind speed x and z directions component,ρ is atmospheric density, and S is bullet
Ball maximum blocks area i.e.D is caliber, and m is Shell body quality；Cx(Ma) it is coefficient of air resistance, is Mach number Ma
Function, g are the acceleration of gravity at height above sea level y, BZFor lateral lift acceleration；
Calculate the partial derivative of function of state
Calculate one step state transition matrix
The variance matrix of calculating process noise and the variance matrix for measuring noise：
In formula (12), (13), H indicates conjugate transposition；
S03-1-2 carries out predictive estimation：
Calculate one-step prediction estimated value：
Calculate one-step prediction error covariance：
It calculates and measures transfer matrix：
Calculate gain matrix：
S03-1-3 corrects noise using noise estimator：
The variance matrix of process noise is modified：
Variance matrix to measuring noise is modified：
In formula (18), (19), residual error newly ceasesBe calculated as：
In formula (18), (19), dk=(1- α)/(1- αk), 0 ＜ α ＜ 1 are forgetting factor；
S03-1-4 carries out self-adaptive smooth filtering：
Calculate filtering value：
S03-1-5, iterative calculation
It enablesRepeat S03-1-1 to S03-1-5 calculating process at least three times, so carry out at least be after iteration three times
It can acquire Approximation, complete one-step prediction smooth value calculating.
2. a kind of high-precision projectile correction method according to claim 1, it is characterised in that：Further include being estimated based on noise
Gauge and fading factor complete the process of projectile correction, which includes：
S03-2 corrects filter result using fading factor：
S03-2-1 calculates fading factor, enables fading factor
In formula (22), Tr indicates to seek the mark of matrix； lk=1-dk；
S03-2-2 carries out one-step prediction modified result,
Calculate the error co-variance matrix of the one-step prediction with fading factor
Calculate gain matrix
Calculate filtering estimated value
Calculate filtering error variance matrix
S03-3 enables k+1 → k, repeats S03-1 to S03-3 steps, completes projectile correction process.
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| CN106484980B (en) * | 2016-09-29 | 2019-08-13 | 中国人民解放军军械工程学院 | A kind of fixed rudder two dimension Correction Projectiles aerodynamic coefficient method |
| CN107219519B (en) * | 2017-04-20 | 2019-12-17 | 中国人民解放军军械工程学院 | Method for fitting trajectory curve of continuous-firing gun |
| CN107194111B (en) * | 2017-06-06 | 2020-12-18 | 中北大学 | Projectile full trajectory optimization design method based on ISIGIT software |
| CN108572378A (en) * | 2018-04-10 | 2018-09-25 | 北京大学 | The adaptive filter algorithm of Signal Pretreatment in a kind of satellite navigation system |
| CN111284690B (en) * | 2018-12-07 | 2021-10-12 | 北京理工大学 | Composite range-extending aircraft capable of correcting lateral deviation |
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