CN107943079B - Online estimation method for residual flight time - Google Patents

Online estimation method for residual flight time Download PDF

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CN107943079B
CN107943079B CN201711209049.8A CN201711209049A CN107943079B CN 107943079 B CN107943079 B CN 107943079B CN 201711209049 A CN201711209049 A CN 201711209049A CN 107943079 B CN107943079 B CN 107943079B
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CN107943079A (en
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蔡远利
李红霞
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Xian Jiaotong University
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Abstract

An on-line estimation method of residual flight time adopts the measured relative distance of a bullet and respectively establishes a model by adopting a system identification method and a regression analysis method; estimating the miss distance by using the established model and the current known relative distance of the missile to obtain an estimated miss distance value, wherein the time corresponding to the estimated miss distance value is the time when the missile is predicted to intercept the target; calculating a time interval value between the estimation moment of the relative distance between the missile and the target interception moment of the predicted missile, and multiplying the time interval value by the sampling period to obtain a residual flight time estimation component of the current moment; and obtaining a residual flight time fusion estimation value by adopting a Fisher information fusion method. The residual flight time estimation algorithm provided by the invention only needs the relative distance of the bullet and the sampling period, and the relative distance of the bullet and the sampling period are obtained by measurement and are given by the guidance system, so that the method has better calculation efficiency feasibility and stronger robustness.

Description

Online estimation method for residual flight time
Technical Field
The invention belongs to the field of aircraft control, and particularly relates to an online residual flight time estimation method.
Background
The residual flight time is widely applied to the guidance of aircrafts as an important parameter of a guidance system. Especially in the process of terminal guidance of the aircraft, besides the goal hit or interception by the missile, the incidence angle, the energy consumption and the like need to be restrained. The optimal guidance law is a better and widely adopted guidance scheme at present, and the accurate estimation of the residual flight time is a key factor for realizing the guidance law and playing the role of the guidance law. Meanwhile, the residual flight time is also an important basis for judging the weapon warhead design and interception effectiveness, and the accuracy of parameter estimation directly influences the guidance performance such as control force, miss distance, capture area and the like. However, any equipment or instrument cannot directly measure this parameter. Moreover, when the distance measurement accuracy of the seeker is not high, or the radar seeker has a large error along with the measurement of the approaching angle of the projectile distance, or the distance measurement channel is disturbed by the outside, the estimation accuracy of the remaining flight time is affected due to the inaccuracy of the measurement data. Therefore, it is an urgent problem to be solved to research and provide a remaining flight time estimation algorithm with high estimation accuracy, strong robustness, high computation efficiency and high feasibility.
The conventional method for estimating the remaining time of flight is tgo＝R/Vm(where t isgoFor the remaining flight time, R is the relative distance of the eyes, VmMissile speed) and the method has better application in proportional guidance. However, when the trajectory is a curved path, the estimation algorithm generates a large estimation error. Aiming at the problem that the traditional residual flight time estimation algorithm is low in precision, a plurality of scholars provide improved algorithms on the basis.
Whang et al propose a residual time estimation method based on Kalman filtering for the proportional guidance law; in addition, a residual time estimation filter is derived for the biased proportional pilot case, but the method is not suitable for the case that the initial lead angle is large. Shin and other application guidance instruction historical information provide a remaining time estimation method, but the method has the problems of large calculation amount and large occupied memory of a computer on a missile, so that the method is not easy to be applied to an actual guidance system. Choal et al derive a class of weighted energy optimal guidance law for missiles with certain uncertainty of speed change law, predict future speed curves of the missiles, and estimate the required residual time, but the estimation accuracy of the guided missiles cannot meet the time control requirement. The Li thill and the like respectively aim at the characteristics of forward and reverse tracks for intercepting flight tracks, and a corresponding residual flight time estimation method is designed based on the predicted collision point, but the method has the problem of low estimation precision when the front angle of the missile is larger. Aiming at the problem that the estimation precision is not high when the missile lead angle is large in the residual time estimation method, Zhang Yogan and the like, a proportion guidance residual time estimation algorithm adopting segmentation solution is provided, the algorithm firstly deforms a closed loop motion equation of proportion guidance to obtain a first-order nonlinear differential equation of the missile-eye distance and the flight time relative to the lead angle, then the change interval of the lead angle is segmented properly, the increment of the lead angle is ensured to be small angle in each interval, so that the differential equation in each interval is solved by utilizing first-order Taylor expansion, and finally the residual time estimation under the large lead angle is obtained through segmentation iteration solution. Ryoo et al designed two residual time-of-flight estimation algorithms for the optimal guidance law with terminal incident angle constraints, namely method 1 and method 2. Wherein, the method 1 is the ratio of the length of the missile track to the approaching speed of the missile, and the method 2 is the ratio of the relative distance of the missile to the average approaching speed of the missile. Wherein, the convergence speed of the missile flight time curve corresponding to the residual flight time estimated value obtained by the method 2 is faster than that of the missile flight time curve corresponding to the residual flight time obtained by the method 1. Therefore, the method 2 has better estimation precision on the remaining flight time. However, the estimation method is derived by modeling the guidance model and based on the nonlinear model linearization. Therefore, the method has serious dependence on the missile on a guidance model and modeling errors and linearization errors are inevitable.
In summary, the proposed off-target analysis method has the following disadvantages:
(1) there is a severe dependence on guidance models;
(2) the missile and the target flight state need to be assumed;
(2) a large amount of guidance system performance parameters are needed to participate in operation, namely, the calculated amount is increased and the operation efficiency is not high.
Disclosure of Invention
Aiming at the problems in the prior art, the invention aims to provide the residual flight time online estimation algorithm which has no dependence on a guidance model, high operation efficiency and feasibility and strong robustness. The method specifically adopts the measured relative distance of the bullet and applies a modeling method with high calculation precision to establish a model, the miss distance is predicted by applying the model and the known relative distance of the bullet at the current moment, and the product of the interval value from the current moment to the moment corresponding to the predicted miss distance and the sampling period is the estimated value of the residual flight time at the current moment.
In order to achieve the purpose, the invention adopts the following technical scheme to realize the purpose:
a method for estimating remaining flight time on line comprises the following steps:
1) respectively establishing models by adopting the measured relative distance of the bullet eyes and adopting a system identification method and a regression analysis method;
2) estimating the miss distance by using the established model and the current known relative distance of the missile to obtain an estimated miss distance value, wherein the time corresponding to the estimated miss distance value is the time when the missile is predicted to intercept the target;
3) calculating a time interval value between the estimation moment of the relative distance between the missile and the target interception moment of the predicted missile, and multiplying the time interval value by the sampling period to obtain a residual flight time estimation component of the current moment;
4) and obtaining a fusion estimation value of the remaining flight time at the current moment by adopting a Fisher information fusion method.
The further improvement of the invention is that the measured relative distance between the bullet eyes and the system identification method and the regression analysis method are adopted to respectively establish a model in the step 1), and the specific process is as follows:
suppose that the relative distance between the bullet and the current m time can be measured and recorded from 0 time
Figure BDA0001484253960000031
Wherein m is the current time value; according to the obtained relative distance sequence of the bullets
Figure BDA0001484253960000032
Obtain the corresponding first order difference sequence and record as
Figure BDA0001484253960000033
And has a Delta Ri＝Ri+1-Ri(ii) a The model established by the jth modeling method at the mth moment is fj,m(·), wherein j ═ 1, …, n; here, the modeling method is a system identification method and a regression analysis method, and n is 2.
The further improvement of the invention is that the miss distance is estimated by using the established model and the current known relative distance of the missile in the step 2) to obtain an estimated miss distance value, the time corresponding to the estimated miss distance value is the time for predicting the interception of the missile on the target, and the specific process is as follows:
based on the above-mentioned model fj,m(. and the known relative distance R of the projectile at the current momentmEstimating the miss distance; wherein, the expression of estimating the relative distance between the bullets at the l +1 th moment by the jth modeling method at the m moment is written as
Figure BDA0001484253960000041
Wherein,
Figure BDA0001484253960000042
the j modeling method has an estimated value of the relative distance between the bullet at the m moment and the bullet at the l moment and a first-order difference
Figure BDA0001484253960000043
Nj,mPredicting an interception moment value corresponding to the j modeling method at the m moment; n is the number of modeling methods; l is the total length of the relative distance sequence of the bullets;
definition 1 if
Figure BDA0001484253960000044
Or
Figure BDA0001484253960000045
Then
Figure BDA0001484253960000046
Wherein,
Figure BDA0001484253960000047
estimating the corresponding miss distance of the jth modeling method at the mth moment;
sequence estimation of amount of off-target from definition 1
Figure BDA0001484253960000048
Is a random sequence; assuming that this random sequence follows a Gaussian distribution, i.e.
Figure BDA0001484253960000049
Due to the fact that
Figure BDA00014842539600000410
Ratio of
Figure BDA00014842539600000411
More precisely, therefore, will
Figure BDA00014842539600000412
Taking the target miss amount as an estimated value; wherein,
Figure BDA00014842539600000413
is composed of
Figure BDA00014842539600000414
The average value of (a) of (b),
Figure BDA00014842539600000415
is composed of
Figure BDA00014842539600000416
The variance of (a);
assuming an off-target magnitude of rNAnd is compared with the estimated miss distance
Figure BDA00014842539600000417
There is a relationship between
Figure BDA00014842539600000418
Wherein epsilonj,mEstimating random errors for the miss distance corresponding to the jth modeling method at the mth moment; suppose that
Figure BDA00014842539600000419
Wherein,
Figure BDA00014842539600000420
is epsilonj,mThe variance of (a);
estimated value of miss amount
Figure BDA00014842539600000421
The corresponding time is the time when the target is intercepted by the predicted missile, namely Nj,m。
The further improvement of the invention is that the time interval value of the estimation time of the relative distance between the missile and the target interception time of the predicted missile in the step 3) is calculated, and the time interval value is multiplied by the sampling period to obtain the residual flight time estimation component of the current time, and the specific process is as follows:
suppose in Nj,mThe missile intercepts the target at the moment, so that the moment m +1 to N are estimated from the relative distance of the missile eyesj,mThe time is Nj,m-m time interval values;
estimating the residual flight time corresponding to the mth time for the jth modeling methodComponent of the measurement
Figure BDA00014842539600000422
Is shown as
Figure BDA00014842539600000423
Where T is the sampling period.
The further improvement of the invention is that a Fisher information fusion method is adopted in the step 1) to obtain a fusion estimation value of the remaining flight time at the current moment, and the specific process is as follows:
estimating the component of the residual flight time corresponding to the mth moment according to the jth modeling method
Figure 1
Obtaining a residual flight time fusion estimated value at the moment m
Figure BDA0001484253960000052
Is composed of
Figure BDA0001484253960000053
Compared with the prior art, the invention has the beneficial effects that:
1. there is no dependency on the guidance model. The residual flight time estimation algorithm provided by the invention does not need various assumptions, and only needs the relative distance of the missile and the sampling period, so that the residual flight time estimation algorithm has no dependence on a guidance model.
2. Has better precision. The residual flight time estimation algorithm provided by the invention has no dependence on the guidance model, so that the modeling of the guidance model, a large number of assumptions required by the modeling and the inaccuracy of the established model are avoided, and the estimation precision of the residual flight time is ensured.
3. The method has better calculation efficiency and feasibility. The residual flight time estimation algorithm provided by the invention only needs the relative distance of the bullet and the sampling period, and the relative distance of the bullet is measured and the sampling period is given by the guidance system. Therefore, the method provided by the invention has better calculation efficiency feasibility.
4. Has strong robustness. The residual flight time estimation algorithm provided by the invention can provide a residual flight time estimation value with higher estimation precision under the condition that external interference exists in a guidance system, so that the residual flight time estimation algorithm has stronger robustness.
Drawings
FIG. 1 is a diagram of a homing guidance model;
FIG. 2 shows the target rest θMFComparing the off-target amount estimation curve with the corresponding variance curve when the off-target amount is-30 deg; wherein, (a) is a comparison graph of miss distance estimation curves, and (b) is a comparison graph of corresponding variance curves;
FIG. 3 shows the target rest θMFComparing the off-target amount estimation curve with the corresponding variance curve when the off-target amount is 30 deg; wherein, (a) is a comparison graph of miss distance estimation curves, and (b) is a comparison graph of corresponding variance curves;
FIG. 4 shows the target rest θMFComparing the residual flight time estimation curve at-30 deg;
FIG. 5 shows the target rest θMFComparing the residual flight time estimation curve at 30 deg;
FIG. 6 shows the target rest θMFComparing the missile track curve with the track angle curve at-30 deg; wherein, (a) is a missile track comparison graph, and (b) is a track angle curve comparison graph;
FIG. 7 shows the target rest θMFComparing the missile track and the track angle curve at 30 deg; wherein, (a) is a missile track comparison graph, and (b) is a track angle curve comparison graph;
FIG. 8 shows a target sine maneuver θMFComparing the off-target amount estimation curve with the corresponding method curve when the off-target amount is-30 deg; wherein, (a) is a comparison graph of miss amount estimation curves, and (b) is a comparison graph of corresponding method curves;
FIG. 9 shows a target sine maneuver θMFComparing the off-target amount estimation curve with the corresponding method curve when the off-target amount is 30 deg; wherein, (a) is a comparison graph of miss amount estimation curves, and (b) is a comparison graph of corresponding method curves;
FIG. 10 is a target sine maneuver θMF＝-30degComparing the time-of-flight residual time estimation curves;
FIG. 11 is a target sine maneuver θMFComparing the residual flight time estimation curve at 30 deg;
FIG. 12 is a target sine maneuver θMFComparing the missile track curve with the track angle curve when the missile track curve is-30 deg; wherein, (a) is a missile track curve comparison graph, and (b) is a track angle curve comparison graph;
FIG. 13 shows a target sine maneuver θMFComparing the missile track curve with the track angle curve at 30 deg; wherein, (a) is a missile track curve comparison graph, and (b) is a track angle curve comparison graph;
FIG. 14 shows a target perturbed sine maneuver θMFComparing the off-target amount estimation curve with the corresponding variance curve when the off-target amount is-30 deg; wherein, (a) is a comparison graph of miss distance estimation curves, and (b) is a comparison graph of corresponding variance curves;
FIG. 15 shows a target perturbed sine maneuver θMFComparing the off-target amount estimation curve with the corresponding variance curve when the off-target amount is 30 deg; wherein, (a) is a comparison graph of miss distance estimation curves, and (b) is a comparison graph of corresponding variance curves;
FIG. 16 shows a target perturbed sine maneuver θMFComparing the residual flight time estimation curve at-30 deg;
FIG. 17 shows a target perturbed sine maneuver θMFComparing the residual flight time estimation curve at 30 deg;
FIG. 18 shows a target perturbed sine maneuver θMFComparing the missile track curve with the track angle curve when the missile track curve is-30 deg; wherein, (a) is a missile track curve comparison graph, and (b) is a track angle curve comparison graph;
FIG. 19 shows a target perturbed sinusoidal maneuver θMFComparing the missile track curve and the track angle curve at 30 deg. Wherein, (a) is a missile track curve comparison graph, and (b) is a track angle curve comparison graph.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
1) Respectively establishing models by adopting the measured relative distance of the bullet eyes and adopting a system identification method and a regression analysis method, and specifically comprising the following steps:
suppose that the relative distance between the bullet and the current m time can be measured and recorded from 0 time
Figure BDA0001484253960000071
Where m is the current time value. According to the obtained relative distance sequence of the bullets
Figure BDA0001484253960000072
The corresponding first order difference sequence can be obtained and is marked as
Figure BDA0001484253960000073
And has a Delta Ri＝Ri+1-Ri. The model established by the jth modeling method at the mth moment is fj,m(. cndot.) wherein j is 1, …, n. Here, the modeling method is a system identification method and a regression analysis method, and n is 2.
2) Estimating the miss distance by using the established model and the current known relative distance of the missile to obtain an estimated miss distance value, wherein the time corresponding to the estimated miss distance value is the time when the missile is predicted to intercept the target; the specific process is as follows:
based on the above-mentioned model fj,m(. and the known relative distance R of the projectile at the current momentmThe amount of miss can be estimated. Wherein, the expression of the j modeling method for estimating the relative distance between the bullet and the target at the l +1 th moment at the m moment can be written as
Figure BDA0001484253960000074
Wherein,
Figure BDA0001484253960000075
the j modeling method has an estimated value of the relative distance between the bullet at the m moment and the bullet at the l moment and a first-order difference
Figure BDA0001484253960000076
Nj,mPredicting an interception moment value corresponding to the j modeling method at the m moment; n is the number of modeling methods; and L is the total length of the relative distance sequence of the bullets.
Definition 1 if
Figure BDA0001484253960000081
Or
Figure BDA0001484253960000082
Then
Figure BDA0001484253960000083
Wherein,
Figure BDA0001484253960000084
and (4) estimating the corresponding miss distance of the jth modeling method at the mth moment.
Estimated value of miss amount
Figure BDA0001484253960000085
The accuracy of the method is directly determined by the accuracy of the estimated model and the number and the accuracy of the measured relative distance values of the bullets, namely, the more the relative distance values of the bullets are, the higher the accuracy is, the higher the accuracy of the established model is, and the more the estimated value of the miss distance is.
As can be seen from definition 1, sequence estimation of amount of off-target
Figure BDA0001484253960000086
Is a random sequence. Without loss of generality, this random sequence is assumed to follow a Gaussian distribution, i.e.
Figure BDA0001484253960000087
Due to the fact that
Figure BDA0001484253960000088
Ratio of
Figure BDA0001484253960000089
More precisely, and will therefore be described hereinafter
Figure BDA00014842539600000810
And (4) taking the target miss amount as an estimated value. Wherein,
Figure BDA00014842539600000811
is composed of
Figure BDA00014842539600000812
The average value of (a) of (b),
Figure BDA00014842539600000813
is composed of
Figure BDA00014842539600000814
The variance of (c).
Assuming an off-target magnitude of rNAnd is compared with the estimated miss distance
Figure BDA00014842539600000815
There is a relationship between
Figure BDA00014842539600000816
Wherein epsilonj,mAnd estimating random errors for the miss distance corresponding to the mth modeling method at the mth moment. Without loss of generality, assume
Figure BDA00014842539600000817
Wherein,
Figure BDA00014842539600000818
is epsilonj,mThe variance of (c).
Estimated value of miss amount
Figure BDA00014842539600000819
The corresponding time is the time when the target is intercepted by the predicted missile, namely Nj,m。
The miss distance estimation value is caused by the measurement error and the modeling error of the relative distance of the bullet eyes
Figure BDA00014842539600000820
And the estimated error εj.mHas randomness. In theory, it is generally assumed for further analysis that random metrology errors and modeling errors follow a gaussian distribution, and this method of handling errors is also widely used in engineering.
As can be seen from the formula (2),
Figure BDA00014842539600000821
obeying a Gaussian distribution
Figure BDA00014842539600000822
Is established, then
Figure BDA00014842539600000823
Has a probability density function of
Figure BDA00014842539600000824
Wherein p isj(. h) is the probability density function of the j modeling method.
Since the n modeling methods are all different and independent of each other, the probability density function is combined
Figure BDA0001484253960000091
Is composed of
Figure BDA0001484253960000092
From the formula (4), Fisher information J of the amount of miss is
Figure BDA0001484253960000093
Where E [. cndot. ] represents the desired operation.
Since the miss distance prediction models established by different modeling methods have different accuracies, the miss distance estimation components obtained from the models also have different accuracies, and here, fusion of the miss distance estimation value components with different accuracies by using a Fisher information fusion method is considered so as to obtain a more accurate miss distance estimation value. From the above analysis, it can be seen that the miss fusion estimate is a function of the miss estimate, specifically
Figure BDA0001484253960000094
Wherein,
Figure BDA0001484253960000095
and fusion estimation value of the miss distance at the m moment.
Considering that Fisher information J can reflect each estimated component of the miss distance
Figure BDA0001484253960000096
Including a miss magnitude rNAnd it is desirable that the larger the degree of such inclusion is, the better, and therefore the miss amount fusion estimation value
Figure BDA0001484253960000097
Can be expressed as
Figure BDA0001484253960000098
Optimal solution of optimization problem equation (7)
Figure BDA0001484253960000099
Is composed of
Figure BDA00014842539600000911
The specific demonstration process of equation (8) is given below as follows:
as is apparent from the formulae (3) to (5),
Figure BDA00014842539600000910
can be expressed as
Figure BDA0001484253960000101
Due to the fact that
Figure BDA0001484253960000102
Is established, therefore, the formula (5) can be rewritten as
Figure BDA0001484253960000103
Order to
Figure BDA0001484253960000104
The optimal solution to this equation (7) is converted to the algebraic extremum problem of equation (10). Since the family of normal distributions is an exponential family, their integration and differentiation orders are interchangeable. Based on this theory, the algebraic extremal problem of equation (10) can be transformed into the optimization problem of equation (11), specifically
Figure BDA0001484253960000105
By bringing formula (11) into formula (12)
Figure BDA0001484253960000106
The solution of formula (13) is
Figure BDA0001484253960000111
And
Figure BDA0001484253960000112
as can be seen from the formulas (13) to (15), the optimization problem has three solutions, namely
Figure BDA0001484253960000113
And
Figure BDA0001484253960000114
however, since only have
Figure BDA0001484253960000115
Namely, it is
Figure BDA0001484253960000116
Is rNUnbiased estimation of (d). Therefore, equation (14) is the optimal solution to this optimization problem.
3) Calculating a time interval value between the estimated time of the relative distance between the missile and the target interception time of the predicted missile, and multiplying the time interval value by the sampling period to obtain the residual flight time estimated component of the current time, wherein the specific process is as follows:
from the formula (1), it is assumed that N isj,mThe missile intercepts the target at the moment, so that the moment m +1 to N are estimated from the relative distance of the missile eyesj,mThe time is Nj,m-m time interval values.
It can be seen that the residual flight time estimation component corresponding to the mth time in the jth modeling method is estimated
Figure BDA0001484253960000117
Can be expressed as
Figure BDA0001484253960000118
Where T is the sampling period.
4) Obtaining a fusion estimation value of the remaining flight time at the current moment by adopting a Fisher information fusion method, wherein the fusion estimation value comprises the following specific processes:
estimating component according to residual flight time corresponding to the mth moment by using a Fisher information fusion method according to the jth modeling method
Figure BDA0001484253960000119
Obtaining the fusion estimation value of the residual flight time at the moment m
Figure BDA00014842539600001110
Is composed of
Figure BDA00014842539600001111
In order to save the computation time and the storage space of the missile computer and improve the estimation precision of the remaining flight time of the interception segment, the estimation method needs to adopt a time-varying sampling period in practical application, namely the sampling period is reduced along with the gradual reduction of the relative distance of the missile eyes.
Simulation analysis and results
In order to better verify the characteristics of the proposed on-line estimation algorithm of the miss distance and the residual flight time, three simulation experiments are designed, specifically, a target is in a static state, sine maneuver and disturbed sine maneuver are designed, and each experiment is discussed for two cases of expected incident angles of-30 deg and 30 deg; secondly, modeling the measured relative distance sequence by using a system identification and regression analysis algorithm; thirdly, selecting the length of the relative distance data of the total bullet
Figure BDA0001484253960000121
And establishing an initial model. Finally, the nominal value of the remaining time of flight is given by the mentioned method 2 and compared with the estimated value obtained by the remaining time of flight estimation algorithm proposed here.
(1) The target is stationary
FIG. 1 is a model of a homing guidance system. In fig. 1, two sets of coordinate systems are involved, specifically, an XOZ ground coordinate system and a sight line coordinate system. The ground coordinate system is a static coordinate system fixed on the earth surface, the origin O is the intersection point of the missile initial position direction and the target initial position direction on the ground, the OX axis points to the target initial position direction, and the OZ points to the missile initial position direction; the sight line coordinate system is a moving coordinate system, and specifically, in fig. 1, the position T of the target is taken as an origin, the shot-to-eye distance is taken as a horizontal axis, the direction is from the target to the missile, and the vertical axis of the sight line coordinate system is perpendicular to the shot-to-eye distance and is upward.
M and T denote missile and target, VMVelocity of the missile, θM(t) is the track angle in the missile ground coordinate system
Figure BDA0001484253960000122
Is viewed by the missileTrack angle, n, in a linear coordinate systemcIs the missile acceleration; vTIs the target speed, β is the track angle of the target in the ground coordinate system, thetaMF(t) is the expected angle of incidence of the missile in the ground coordinate system,
Figure BDA0001484253960000123
for a desired angle of incidence of the missile in the line-of-sight coordinate system, nTIs the expected angle of incidence of the missile in the line-of-sight coordinate system. Theta (t) is the viewing angle, z (t) is the longitudinal distance of the missile in the ground coordinate system, R is the missile-eye distance,
Figure BDA0001484253960000125
is the transverse distance of the missile track in the sight line coordinate system,
Figure BDA0001484253960000124
the longitudinal distance of the missile track in the sight line coordinate system.
The corresponding motion equation of the interception problem when the target is static is
Figure BDA0001484253960000131
Wherein the optimal guidance law n with terminal incident angle constraintcIs composed of
Figure BDA0001484253960000132
The remaining time-of-flight estimation algorithm method 2(C.K.Ryoo, H.Cho, M.J.Tahk, optimal Guidance law with a final impact constraint, Journal of Guidance, Control and dynamics, 2005,28(4):724-
Figure BDA0001484253960000133
Here (x)M0,zM0) And (x)T0,zT0) Initial position coordinates of the missile and the target respectively and respectively (0m,3048m) and (12160m, 3048m), VMAnd thetaM0914.4000m/s and 90deg, respectively, and the sampling time (i.e., sampling period) is 0.001 s.
Two sets of miss distance estimation curves and corresponding variance curves under different incidence angles are given by a system identification method, a regression analysis method and a Fisher information fusion method, and are specifically shown in FIG. 2 and FIG. 3; meanwhile, fig. 4 and 5 respectively show the residual flight time estimation curves corresponding to the three algorithms under different incident angles. In order to verify the correctness of the Fisher fusion estimation algorithm on the estimation of the residual flight time, a missile track curve and a track angle curve corresponding to the residual flight time estimated by the Fisher fusion estimation algorithm under two groups of different incidence angles are respectively shown in FIGS. 6 and 7.
As can be seen from fig. 2(a) and 3(a), when the desired entrance angles are-30 deg and 30deg, the miss distance estimation curves of the three estimation algorithms all have the same trend of change; meanwhile, although the initial miss amount estimated values of the three estimation algorithms are all large, the initial miss amount estimated values are all less than 0.9m (V)M914.4000m/s, with a sampling interval of 0.001s, the missile step size is 0.9144 m). Therefore, the three estimation algorithms can effectively estimate the miss distance of the guidance system. The variance estimation curves corresponding to fig. 2(a) and 3(a) are referred to in fig. 2(b) and 3(b), respectively. As can be seen from the two graphs, the variance value corresponding to the Fisher fusion algorithm is always smaller than the variance values corresponding to the other two algorithms. Therefore, the estimated miss distance value of the Fisher fusion algorithm has good convergence characteristics and high estimation precision.
Fig. 4 and 5 show the remaining time-of-flight estimation curves for these two different desired angles of incidence. From the two graphs, the residual flight time estimation curves corresponding to the three estimation algorithms almost coincide with the respective nominal curves, and all the residual flight time estimation curves can rapidly trend to the nominal curves along with the increase of time. Therefore, when the target is in a static state, the three estimation algorithms can effectively estimate the residual flight time of the guidance system and have better accuracy. However, since the residual time-of-flight estimates obtained by system identification and regression analysis have different accuracies at different time intervals, the residual time-of-flight estimates obtained by the Fisher fusion algorithm always guarantee a bias towards estimates with higher accuracy. Therefore, the estimated value of the residual flight time of the Fisher fusion algorithm has better estimation precision. This conclusion is verified in fig. 6 and 7, specifically: and even if the expected incident angles are different, missile track curves and track angle curves corresponding to the residual flight time of the Fisher fusion estimation algorithm are almost completely superposed with the respective nominal curves.
In conclusion, when the target is in a static state, the proposed Fisher residual flight time online estimation algorithm can effectively estimate the important index of the residual flight time and has satisfactory precision. The effectiveness and the practicability of the proposed algorithm can be verified through simulation analysis.
(2) Target sine machine movement
The same homing guidance system model is considered here and the target is sinusoidally maneuvered. The equation of motion for this model is as follows
Figure BDA0001484253960000151
Wherein D1And D2Is the amount of turbulence. In the actual intercepting process, the target speed is difficult to measure accurately, and uncertainty of the parameter easily causes inaccurate modeling of the bullet motion model, and the uncertainty is regarded as the disturbance quantity of the guidance system. The effect of this perturbation on the on-line estimation of miss-throw and residual time of flight is discussed in detail in the following (3) objective perturbed sinusoidal maneuver context, where only the case where no perturbation is present is analyzed.
According to the Schwarz inequality, the optimal guidance law for maneuvering of the target and introducing the firing angle constraint can be written as
Figure BDA0001484253960000152
Wherein the target speed VTTarget acceleration n of 304.8000msT58.3078sin (3t), the other parameters are the same as (1) target still content.
FIGS. 8 and 9 show the on-line estimation curves of miss distance and the corresponding variance curves when the expected incident angles are-30 deg and 30deg, and the remaining flight time estimation curves corresponding to the above two expected incident angles are shown in FIGS. 10 and 11, respectively; meanwhile, at the two expected incidence angles, missile track curves and track angle curves corresponding to the estimated residual flight time of the Fisher fusion algorithm are compared with respective nominal curves, and the comparison is respectively shown in FIGS. 12 and 13.
As can be seen from FIGS. 8 and 9, the miss amount estimation curve and the corresponding variance curve trend substantially coincide with (1) the corresponding curve of the content in the object still when the incident angles are-30 deg and 30 deg. Meanwhile, as can be seen from fig. 8(a) and fig. 9(a), the estimated values of the miss distance obtained by the three estimation algorithms are still satisfactory, i.e., the estimated values of the miss distance are all less than 1.2m (the relative velocity between the missile and the target is 1219.2000m/s, the sampling time is 0.001s, and the relative step length is 1.2192 m). And as can be seen from fig. 8(b) and fig. 9(b), the variance value corresponding to the Fisher fusion estimation algorithm is still smaller than that of the other two algorithms, so that when the target is subjected to sine maneuver and the desired entrance angles are-30 deg and 30deg, the Fisher fusion estimation algorithm still has effectiveness and better estimation accuracy on the online estimation of the miss distance.
Furthermore, as can be seen from fig. 10, when the expected incident angle is-30 deg, the residual flight time estimated values corresponding to the three estimation algorithms at the initial time are deviated from their nominal residual flight time values, but as the time increases, the residual flight time estimated curves of the three estimation algorithms approach their nominal curves rapidly and almost coincide. Therefore, under the simulation condition, the three algorithms can carry out effective online estimation on the residual flight time. Meanwhile, as can be seen from fig. 11, when the expected incident angle is 30deg, the estimated values of the remaining flight time corresponding to the three algorithms have higher accuracy even at the initial estimated time, and can quickly approach their nominal values as time increases. Therefore, under the simulation condition, the three algorithms can effectively estimate the remaining flight time. And because the residual flight time estimated value of the Fisher information fusion algorithm is the fusion of the residual flight time estimated component values obtained by the system identification method and the regression analysis method, the residual flight time estimated value obtained by the Fisher information fusion algorithm has higher precision. The conclusion is still verified by a missile track curve and a track angle curve corresponding to the residual flight time estimated value. The missile path curves and path angle curves at an expected penetration angle of-30 deg and 30deg are compared with their respective nominal curves as shown in fig. 12 and 13. From these two figures, the missile path curve and the path angle curve can be matched with their respective nominal curves.
In conclusion, when the target is subjected to sine maneuver, the proposed Fisher fused residual flight time online estimation algorithm can effectively estimate the residual flight time and obtain satisfactory estimation precision. In addition, the validity and utility of the proposed algorithm is verified again.
(3) Target sine machine with disturbance
Considering the guidance model having the same contents as those of (1) in the stationary state and the guidance law is expression (22), the interference amounts are D11.65cos β and D2The estimated miss distance curves and their variance curves at the desired incident angles of-30 deg and 30deg are shown in fig. 14 and 15, respectively, and the corresponding estimated remaining flight time curves are shown in fig. 16 and 17, respectively, and the corresponding target track curves and track angle curves are shown in fig. 18 and 19, respectively.
From fig. 14 and 15, when the expected incident angles are-30 deg and the guidance model has disturbance, the variation trends of the miss distance estimation curve and its corresponding variance curve are consistent with (2) the corresponding curve in the target sinusoidal maneuver content. Meanwhile, under the simulation condition, the three algorithms can obtain a satisfactory miss distance estimation value and the miss distance estimation value corresponding to the Fisher information fusion method still has good estimation precision. As can be seen from fig. 16 and 17, even if there is disturbance in the guidance system, the residual flight time estimation curves obtained by the three algorithms still have a consistent variation trend with the corresponding curves in the case of no disturbance. As can be seen from fig. 18 and 19, when the expected incident angles are-30 deg and 30deg, the missile track curve and the missile track angle curve corresponding to the Fisher information fusion residual flight time estimation value can also approximate their respective nominal curves, that is, the proposed method has good robustness.
Therefore, when the guidance model has disturbance, the proposed Fisher fusion estimation algorithm can effectively and accurately estimate the important performance index of the residual flight time, and has stronger robustness.
The invention provides a novel residual flight time estimation algorithm based on data driving, aiming at the problems that the existing residual flight time estimation algorithm is high in dependence on a guidance model, multiple in parameters, low in estimation precision and the like. The algorithm does not need to model a guidance model, so that modeling errors and errors from a nonlinear system to a linear system are avoided; meanwhile, the algorithm only needs the relative distance of the missile and the target, so that the calculation efficiency is high, and the important performance index of the residual flight time can be estimated. In addition, when the guidance system has disturbance, the proposed algorithm can still effectively estimate the performance index. Algorithms proposed by a large number of simulations have high estimation precision and calculation efficiency and strong robustness and are effectively verified.

Claims (4)

1. A method for online estimation of remaining time of flight, comprising the steps of:
1) respectively establishing models by adopting the measured relative distance of the bullet eyes and adopting a system identification method and a regression analysis method;
2) estimating the miss distance by using the established model and the current known relative distance of the missile to obtain an estimated miss distance value, wherein the time corresponding to the estimated miss distance value is the time when the missile is predicted to intercept the target; the specific process is as follows: based on the above-mentioned model fj,m(. and the known relative distance R of the projectile at the current momentmEstimating the miss distance; wherein, the expression of estimating the relative distance between the bullets at the l +1 th moment by the jth modeling method at the m moment is written as
Figure FDA0002293912910000011
Wherein，
Figure FDA0002293912910000012
The j modeling method has an estimated value of the relative distance between the bullet at the m moment and the bullet at the l moment and a first-order difference
Figure FDA0002293912910000013
Nj,mPredicting an interception moment value corresponding to the j modeling method at the m moment; n is the number of modeling methods; l is the total length of the relative distance sequence of the bullets;
definition 1 if
Figure FDA0002293912910000014
Or
Figure FDA0002293912910000015
Then
Figure FDA0002293912910000016
Wherein,
Figure FDA0002293912910000017
estimating the corresponding miss distance of the jth modeling method at the mth moment;
sequence estimation of amount of off-target from definition 1
Figure FDA0002293912910000018
Is a random sequence; assuming that this random sequence follows a Gaussian distribution, i.e.
Figure FDA0002293912910000019
Due to the fact that
Figure FDA00022939129100000110
Ratio of
Figure FDA00022939129100000111
More precisely, therefore, will
Figure FDA00022939129100000112
Taking the target miss amount as an estimated value; wherein,
Figure FDA00022939129100000113
is composed of
Figure FDA00022939129100000114
The average value of (a) of (b),
Figure FDA00022939129100000115
is composed of
Figure FDA00022939129100000116
The variance of (a);
assuming an off-target magnitude of rNAnd is compared with the estimated miss distance
Figure FDA00022939129100000117
There is a relationship between
Figure FDA00022939129100000118
Wherein epsilonj,mEstimating random errors for the miss distance corresponding to the jth modeling method at the mth moment; suppose that
Figure FDA00022939129100000119
Wherein,
Figure FDA00022939129100000120
is epsilonj,mThe variance of (a);
estimated value of miss amount
Figure FDA00022939129100000121
The corresponding time is the time when the target is intercepted by the predicted missile, namely Nj,m；
3) Calculating a time interval value between the estimation moment of the relative distance between the missile and the target interception moment of the predicted missile, and multiplying the time interval value by the sampling period to obtain a residual flight time estimation component of the current moment;
4) and obtaining a fusion estimation value of the remaining flight time at the current moment by adopting a Fisher information fusion method.
2. The method for estimating remaining flight time on line according to claim 1, wherein the measured relative distance between the bullet eyes and the system identification method and the regression analysis method are adopted to respectively establish the models in the step 1), and the specific process is as follows:
suppose that the relative distance between the bullet and the current m time can be measured and recorded from 0 time
Figure FDA0002293912910000021
Wherein m is the current time value; according to the obtained relative distance sequence of the bullets
Figure FDA0002293912910000022
Obtain the corresponding first order difference sequence and record as
Figure FDA0002293912910000023
And has a Delta Ri＝Ri+1-Ri(ii) a The model established by the jth modeling method at the mth moment is fj,m(·), wherein j ═ 1, …, n; here, the modeling method is a system identification method and a regression analysis method, and n is 2.
3. The online residual flight time estimation method according to claim 1, wherein a time interval value between the estimated time of the relative distance between the missile and the target interception time of the predicted missile is calculated in step 3), and the time interval value is multiplied by the sampling period to obtain a residual flight time estimated component of the current time, and the specific process is as follows:
suppose in Nj,mThe missile intercepts the target at the moment, so that the moment m +1 to N are estimated from the relative distance of the missile eyesj,mThe time is Nj,m-m time interval values;
estimating component of residual flight time corresponding to the mth moment in the jth modeling method
Figure FDA0002293912910000024
Is shown as
Figure FDA0002293912910000025
Where T is the sampling period.
4. The method for estimating remaining time of flight online according to claim 3, wherein a Fisher information fusion method is adopted in step 1) to obtain a fusion estimation value of remaining time of flight at the current time, and the specific process is as follows:
estimating the component of the residual flight time corresponding to the mth moment according to the jth modeling method
Figure FDA0002293912910000026
Obtaining a residual flight time fusion estimated value at the moment m
Figure FDA0002293912910000027
Is composed of
Figure FDA0002293912910000028
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