CN107943079B - An Online Estimation Method of Remaining Flight Time - Google Patents

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

An Online Estimation Method of Remaining Flight Time

technical field

The invention belongs to the field of aircraft control, and in particular relates to an online estimation method for remaining flight time.

Background technique

As an important parameter of the guidance system, the remaining flight time is widely used in aircraft guidance. Especially in the terminal guidance process of the aircraft, in addition to achieving the target strike or interception of the missile, it is also necessary to restrict the incidence angle and energy consumption. The optimal guidance law is a better and widely used guidance scheme at present, and the accurate estimation of the remaining flight time is the key factor to realize this guidance law and play its role. At the same time, the remaining flight time is also an important basis for the design of the weapon warhead and the judgment of the interception effectiveness. The accuracy of the estimation of this parameter will directly affect the guidance performance such as the control force, the missed target amount and the capture area. However, any equipment and instruments cannot directly measure this parameter. Moreover, when the ranging accuracy of the seeker is not high, or there is a large error in the measurement of the approach angle of the radar seeker with the distance of the projectile, or the ranging channel is interfered by the outside world, the inaccuracy of the measurement data will affect the accuracy of the measurement. Estimation accuracy of remaining flight time. Therefore, it is an urgent problem to study and propose a remaining flight time estimation algorithm with high estimation accuracy, strong robustness, high computational efficiency and extremely feasible.

The traditional method for estimating the remaining flight time is t _go = R/V _m (where t _go is the remaining flight time, R is the relative distance of the projectile and V _m is the missile speed), and this method has better performance in proportional guidance. application. But when the ballistic trajectory is a curved path, this estimation algorithm produces a large estimation error. In view of the low accuracy of traditional remaining flight time estimation algorithms, many scholars have proposed improved algorithms on this basis.

Whang et al. proposed a residual time estimation method based on Kalman filter for the case of proportional guiding law; in addition, for the case of biased proportional guiding, a residual time estimation filter was deduced, but this method was not suitable for initial Larger front angle. Shin et al. proposed a method for estimating the remaining time by applying historical information of guidance instructions, but this method has the problem of a large amount of calculation and a lot of computer memory on the missile, so it is not easy to apply to the actual guidance system. Choal et al. deduced a class of weighted energy optimal guidance laws for missiles with certain uncertainty in the speed change law, and predicted the missile's future speed curve and estimated the remaining time required. The estimation accuracy is difficult to meet the time control requirements. Li Yuan et al. designed a corresponding residual flight time estimation method based on the predicted collision point according to the characteristics of along-orbit and reverse-orbit interception flight trajectories, but this method has the problem of low estimation accuracy when the missile lead angle is large. Aiming at the problem that the estimation accuracy of the remaining time estimation method above is not high when the missile lead angle is large, Zhang Youan et al. proposed a proportional guidance remaining time estimation algorithm using segmented solution. This algorithm first compares the closed-loop motion of proportional guidance. The equation is deformed to obtain the first-order nonlinear differential equation of the projectile distance and flight time with respect to the lead angle, and then the change interval of the lead angle is appropriately segmented, and the increment of the lead angle is guaranteed to be a small angle in each interval. , so that the first-order Taylor expansion is used to solve the differential equation in each interval, and finally, the residual time estimation under the large lead angle is obtained by subsection iterative solution. Ryoo et al. designed two remaining time-of-flight estimation algorithms for the optimal guidance law with terminal incident angle constraints, method 1 and method 2, respectively. Among them, method 1 is the ratio of the length of the missile track to the approach speed of the projectile, and method 2 is the ratio of the relative distance of the projectile to the average approach speed of the projectile. Among them, the missile flight time curve corresponding to the estimated remaining flight time obtained by method 2 converges faster than the missile flight time curve corresponding to the remaining flight time obtained by method 1. It can be seen that method 2 has better estimation accuracy for the remaining flight time. But this estimation method is derived from modeling the guidance model and linearizing the nonlinear model. Therefore, the method has a serious dependence on the guidance model of the projectile and the modeling error and linearization error are unavoidable.

To sum up, the proposed off-target quantity analysis methods have the following disadvantages:

(1) There is a serious dependence on the guidance model;

(2) It is necessary to make assumptions about the flight state of the missile and target;

(2) A large number of performance parameters of the guidance system are required to participate in the calculation, that is, the calculation amount increases and the calculation efficiency is not high.

SUMMARY OF THE INVENTION

Aiming at the problems existing in the prior art, the purpose of the present invention is to provide an online estimation algorithm for remaining flight time that is independent of the guidance model, has high computational efficiency and feasibility, and has strong robustness. The method specifically adopts the measured relative distance of the projectile and uses a modeling method with high calculation accuracy to establish a model, and uses this model and the known relative distance of the projectile at the current moment to predict the amount of misses. From the current moment to the predicted amount of misses The product of the interval value of the moment and the sampling period is the estimated value of the remaining flight time at the current moment.

To achieve the above object, the present invention adopts the following technical solutions to be realized:

An online estimation method for remaining flight time, comprising the following steps:

1) Use the measured relative distances of the projectiles and use the system identification method and regression analysis method to establish models respectively;

2) Use the established model and the currently known relative distance of the projectile to estimate the amount of misses, and obtain the estimated value of the amount of misses, and the time corresponding to the estimated value of the misses is the moment when the missile is predicted to intercept the target;

3) Calculate the time interval value between the estimated time of the relative distance of the projectile and the time when the predicted missile intercepts the target, and then multiply the time interval value by the sampling period to obtain the estimated component of the remaining flight time at the current moment;

4) Using the Fisher information fusion method, the fusion estimation value of the remaining flight time at the current moment is obtained.

A further improvement of the present invention is that in step 1), the relative distance of the projectiles measured is adopted and a system identification method and a regression analysis method are adopted to establish a model respectively, and the specific process is as follows:

其中m为当前时刻值；根据已获得的弹目相对距离序列

得到其对应的一阶差分序列，记为

且有ΔR_i＝R_i+1-R_i；第j种建模方法在第m时刻所建模型即为f_j,m(·)，其中j＝1,…,n；此处，建模方法为系统辨识方法和回归分析方法，n＝2。It is assumed that the relative distance of the projectile can be measured from time 0 to the current time m and recorded as

Where m is the current time value; according to the obtained relative distance sequence of projectiles

Get its corresponding first-order difference sequence, denoted as

And there is ΔR _i =R _i+1 -R _i ; the model built by the jth modeling method at the mth moment is f _j,m ( ), where j=1,...,n; here, the modeling The methods are system identification method and regression analysis method, n=2.

A further improvement of the present invention is that, in step 2), the established model and the currently known relative distance of the projectiles are used to estimate the amount of misses, to obtain the estimated value of the amount of misses, and the time corresponding to the estimated value of the misses is to predict that the missile will carry out the target on the target. At the time of interception, the specific process is as follows:

Based on the above-built model f _j,m ( ) and the known relative distance R _m of the projectile at the current moment, the amount of misses is estimated; among them, the jth modeling method is used for the projectile at time l+1 at time m. The expression for estimating the relative distance is written as

为第j种建模方法在m时刻对第l时刻的弹目相对距离的估计值，且有一阶差分

N_j,m为第j种建模方法在m时刻对应的预测拦截时刻值；n为建模方法个数；L为弹目相对距离序列的总长度；in,

is the estimated value of the relative distance of the projectile at the l-th time for the j-th modeling method at the m time, and has a first-order difference

N _j,m is the predicted interception time value corresponding to the jth modeling method at time m; n is the number of modeling methods; L is the total length of the relative distance sequence of the projectile;

或

则

其中，

为第j种建模方法在第m时刻对应的脱靶量估计值；Definition 1. If

or

but

in,

is the estimated value of the off-target amount corresponding to the jth modeling method at the mth time;

为随机序列；假设此随机序列服从高斯分布，即

由于

比

更精确，因此将

视为脱靶量估计值；其中，

为

的均值，

为

的方差；Obtained by definition 1, the off-target amount estimated sequence

is a random sequence; assuming that this random sequence obeys a Gaussian distribution, that is

because

Compare

more precise, so will

considered an off-target estimate; where,

for

the mean of ,

for

Variance;

之间存在如下关系Assume that the off-target value is r _N , which is the same as the off-target estimate

There is the following relationship between

其中，

为ε_j,m的方差；Among them, ε _j,m is the estimated random error of the missed target amount corresponding to the jth modeling method at the mth time;

in,

is the variance of ε _j,m ;

对应的时刻为预测导弹对目标进行拦截时刻，即N_j,m。off-target estimates

The corresponding moment is the moment when the missile is predicted to intercept the target, namely N _j,m .

A further improvement of the present invention is that in step 3), calculate the time interval value between the estimated time of the relative distance of the projectile and the time when the predicted missile intercepts the target, and then multiply the time interval value and the sampling period to obtain the estimated component of the remaining flight time at the current moment. , the specific process is as follows:

Assuming that the missile intercepts the target at time N _{j ,m,} a total of N _j,m -m time interval values are required from the estimated time m+1 to the time N j,m of the relative distance of the projectile;

表示为For the jth modeling method, the estimated component of the remaining flight time corresponding to the mth time

Expressed as

Among them, T is the sampling period.

A further improvement of the present invention is that in step 1), the Fisher information fusion method is used to obtain the fusion estimated value of the remaining flight time at the current moment, and the specific process is as follows:

得到在m时刻剩余飞行时间融合估计值

为The estimated component of the remaining flight time corresponding to the mth time according to the jth modeling method

Get the fused estimate of the remaining flight time at time m

for

Compared with the prior art, the beneficial effects of the present invention are:

1. No dependency on guidance model. The remaining flight time estimation algorithm proposed by the present invention does not need various assumptions, but only needs the relative distance of the projectile and the sampling period, so it has no dependence on the guidance model.

2. Has better precision. The remaining flight time estimation algorithm proposed by the present invention has no dependence on the guidance model, thus avoiding the modeling of the guidance model and the inaccuracy of a large number of assumptions required for modeling and the built model, thus ensuring the estimation of the remaining flight time precision.

3. It has good computational efficiency and feasibility. The remaining flight time estimation algorithm proposed by the present invention only needs the relative distance of the projectile and the sampling period, because the relative distance of the projectile is measured and the sampling period is given by the guidance system itself. Therefore, the method proposed in the present invention has better computational efficiency and feasibility.

4. Has strong robustness. The remaining flight time estimation algorithm proposed by the present invention can provide the remaining flight time estimation value with higher estimation accuracy under the condition of external interference in the guidance system, so it has strong robustness.

Description of drawings

Figure 1 is a self-homing guidance model diagram;

Fig. 2 is the comparison diagram of the off-target amount estimation curve and the corresponding variance curve when the target is stationary θ _MF =-30deg; wherein, (a) is the comparison diagram of the off-target amount estimation curve, and (b) is the corresponding variance curve comparison diagram;

Figure 3 is a comparison diagram of the off-target amount estimation curve and the corresponding variance curve when the target is stationary at θ _MF = 30deg; wherein, (a) is a comparison diagram of the off-target amount estimation curve, and (b) is a comparison diagram of the corresponding variance curve;

Fig. 4 is the remaining flight time estimation curve comparison diagram when the target is stationary θ _MF =-30deg;

Fig. 5 is the remaining flight time estimation curve comparison diagram when the target is stationary θ _MF = 30deg;

Figure 6 is a comparison diagram of the missile track and the track angle curve when the target is stationary θ _MF =-30deg; wherein, (a) is a comparison diagram of the missile track, and (b) is a comparison diagram of the track angle curve;

Figure 7 is a comparison chart of the missile track and track angle curve when the target is stationary at θ _MF = 30deg; wherein, (a) is a comparison chart of the missile track, and (b) is a comparison chart of the track angle curve;

FIG. 8 is a comparison diagram of the missed target amount estimation curve and the corresponding method curve when the target sinusoidal maneuver θ _MF =-30deg; wherein, (a) is a comparison diagram of the missed target amount estimation curve, and (b) is a comparison diagram of the corresponding method curve;

Figure 9 is a comparison diagram of the missed target amount estimation curve and the corresponding method curve when the target sinusoidal maneuver θ _MF = 30deg; wherein, (a) is a comparison diagram of the missed target amount estimation curve, and (b) is a comparison diagram of the corresponding method curve;

Figure 10 is a comparison diagram of the remaining flight time estimation curve when the target sinusoidal maneuver θ _MF =-30deg;

Figure 11 is a comparison diagram of the remaining flight time estimation curves when the target sinusoidal maneuver θ _MF = 30deg;

Figure 12 is a comparison chart of the missile track curve and the track angle curve when the target sinusoidal maneuver θ _MF =-30deg; wherein, (a) is the comparison chart of the missile track curve, and (b) is the comparison chart of the track angle curve;

Figure 13 is a comparison chart of the missile track curve and the track angle curve when the target sinusoidal maneuver θ _MF = 30deg; wherein, (a) is the comparison chart of the missile track curve, and (b) is the comparison chart of the track angle curve;

Figure 14 is a comparison chart of the missed target amount estimation curve and the corresponding variance curve when the target band perturbed sinusoidal maneuver θ _MF =-30deg; wherein, (a) is a comparison chart of the missed target amount estimation curve, and (b) is a comparison diagram of the corresponding variance curve;

Figure 15 is a comparison diagram of the missed target amount estimation curve and the corresponding variance curve when the target band disturbance sinusoidal maneuver θ _MF = 30deg; wherein, (a) is a comparison diagram of the missed target amount estimation curve, and (b) is a comparison diagram of the corresponding variance curve;

FIG. 16 is a comparison diagram of the remaining flight time estimation curves when the target band disturbance sinusoidal maneuver θ _MF =-30deg;

Figure 17 is a comparison diagram of the remaining flight time estimation curves when the target band disturbance sinusoidal maneuver θ _MF = 30deg;

Figure 18 is a comparison diagram of the missile track curve and the track angle curve when the target band disturbance sinusoidal maneuver θ _MF = -30deg; wherein, (a) is a comparison diagram of the missile track curve, (b) is a comparison diagram of the track angle curve ;

FIG. 19 is a comparison diagram of the missile track curve and the track angle curve when the target band disturbance sinusoidal maneuver θ _MF =30deg. Among them, (a) is the comparison chart of the missile track curve, and (b) is the comparison chart of the track angle curve.

Detailed ways

The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

1) Using the measured relative distance of the projectile and using the system identification method and regression analysis method to establish models respectively, the specific process is as follows:

其中m为当前时刻值。根据已获得的弹目相对距离序列

可得到其对应的一阶差分序列，记为

且有ΔR_i＝R_i+1-R_i。第j种建模方法在第m时刻所建模型即为f_j,m(·)，其中j＝1,…,n。此处，建模方法为系统辨识方法和回归分析方法，n＝2。It is assumed that the relative distance of the projectile can be measured from time 0 to the current time m and recorded as

where m is the current time value. According to the obtained relative distance sequence of projectiles

The corresponding first-order difference sequence can be obtained, denoted as

And there is ΔR _i =R _i+1 -R _i . The model built by the jth modeling method at the mth moment is f _j,m (·), where j=1,...,n. Here, the modeling method is a system identification method and a regression analysis method, and n=2.

2) Use the established model and the currently known relative distance of the projectile to estimate the amount of misses, and obtain the estimated value of the amount of misses. The time corresponding to the estimated value of the misses is the moment when the missile is predicted to intercept the target; the specific process is as follows:

Based on the above-built model f _j,m (·) and the known relative distance R _m of the projectile at the current moment, the missed target amount can be estimated. Among them, the expression for estimating the relative distance of the projectile at time l+1 by the jth modeling method at time m can be written as

为第j种建模方法在m时刻对第l时刻的弹目相对距离的估计值，且有一阶差分

N_j,m为第j种建模方法在m时刻对应的预测拦截时刻值；n为建模方法个数；L为弹目相对距离序列的总长度。in,

is the estimated value of the relative distance of the projectile at the l-th time for the j-th modeling method at the m time, and has a first-order difference

N _j,m is the predicted interception time value corresponding to the jth modeling method at time m; n is the number of modeling methods; L is the total length of the relative distance sequence of the projectile.

或

则

其中，

为第j种建模方法在第m时刻对应的脱靶量估计值。Definition 1. If

or

but

in,

is the estimated value of the off-target amount corresponding to the jth modeling method at the mth time.

的精度直接由其估计模型的精度和量测所得的弹目相对距离值的数量和精度决定，即弹目相对距离值越多且精度越高，建立的模型精度越高且对脱靶量的估计值越精确。off-target estimates

The accuracy of the model is directly determined by the accuracy of the estimated model and the number and accuracy of the relative distance values of the projectiles measured, that is, the more relative distances of the projectiles and the higher the accuracy, the higher the accuracy of the established model and the estimation of the amount of misses. The more precise the value.

为随机序列。不失一般性，假设此随机序列服从高斯分布，即

由于

比

更精确，因此在下文中将

视为脱靶量估计值。其中，

为

的均值，

为

的方差。According to Definition 1, the off-target amount estimation sequence

is a random sequence. Without loss of generality, it is assumed that this random sequence obeys a Gaussian distribution, namely

because

Compare

more precise, so in the following the

Considered an off-target estimate. in,

for

the mean of ,

for

Variance.

之间存在如下关系Assume that the off-target value is r _N , which is the same as the off-target estimate

There is the following relationship between

其中，

为ε_j,m的方差。Among them, ε _j,m is the estimated random error of the missed target amount corresponding to the jth modeling method at the mth time. Without loss of generality, suppose

in,

is the variance of εj _,m .

对应的时刻为预测导弹对目标进行拦截时刻，即N_j,m。off-target estimates

The corresponding moment is the moment when the missile is predicted to intercept the target, namely N _j,m .

和估计误差ε_j.m具有随机性。在理论上，通常为了做进一步的分析假设随机量测误差和建模误差服从高斯分布，同时这种处理误差的方法在工程上也广泛运用。Due to the measurement error and modeling error of the relative distance of the projectile, the estimated value of the miss

and the estimated error _εjm are random. In theory, it is usually assumed that random measurement errors and modeling errors obey Gaussian distribution for further analysis, and this method of dealing with errors is also widely used in engineering.

服从高斯分布即

成立，则

的概率密度函数为From formula (2), it can be known that,

obey a Gaussian distribution

established, then

The probability density function of is

Among them, p _j (·) is the probability density function of the jth modeling method.

为Since the n modeling methods are different and independent of each other, the joint probability density function

for

According to formula (4), the Fisher information J of the off-target amount is

Among them, E[·] represents the expected operation.

Since the off-target quantity prediction models established by different modeling methods have different accuracies, the off-target quantity estimated components obtained from these models also have different accuracies. Here, the Fisher information fusion method is considered to fuse the off-target quantity estimated value components of different accuracies so as to Get more precise estimates of off-targets. According to the above analysis, it can be seen that the off-target fusion estimate is a function of the off-target estimate, specifically:

为m时刻脱靶量融合估计值。in,

is the fusion estimate of off-target amount at time m.

中包含脱靶量值r_N的多少，同时希望这种包含程度越大越好，因此脱靶量融合估计值

可表示为Considering that the Fisher information J can reflect each off-target estimated component

How much of the off-target amount r _N is included in , and it is hoped that the greater the degree of inclusion, the better, so the off-target amount is fused to estimate the value

can be expressed as

为The optimal solution of the optimization problem (7)

for

The specific proof process of formula (8) will be given as follows:

可表示为From equations (3) to (5), it can be known that,

can be expressed as

成立，因此式(5)可改写为because

is established, so equation (5) can be rewritten as

make

So far, the optimal solution of equation (7) is transformed into the algebraic extreme value problem of equation (10). Since the normal distribution family is an exponential family, its integral and differential order are commutative. Based on this theory, the algebraic extreme value problem of Equation (10) can be transformed into the optimization problem of Equation (11), specifically:

Substituting equation (11) into equation (12), we can get

The solution of equation (13) is

and

和

然而由于仅有

即

是r_N的无偏估计。因此，式(14)是此优化问题的最优解。From equations (13) to (15), we can see that there are three solutions to this optimization problem, which are

and

However, since only

which is

is an unbiased estimate of r _N. Therefore, equation (14) is the optimal solution of this optimization problem.

3) Calculate the time interval value between the estimated time of the relative distance of the projectile and the time when the predicted missile intercepts the target, and then multiply the time interval value and the sampling period to obtain the estimated component of the remaining flight time at the current moment. The specific process is as follows:

From formula (1), it is assumed that the missile intercepts the target at time N _j ,m, so a total of N _j,m -m time interval values are required from time m+1 to time N _j,m to estimate the relative distance of the projectile and target.

可表示为It can be seen that for the jth modeling method, the estimated component of the remaining flight time corresponding to the mth time

can be expressed as

Among them, T is the sampling period.

4) The Fisher information fusion method is used to obtain the fusion estimated value of the remaining flight time at the current moment. The specific process is as follows:

可得在m时刻剩余飞行时间融合估计值

为Using the Fisher information fusion method, the estimated component of the remaining flight time corresponding to the mth time according to the jth modeling method

The fusion estimate of the remaining flight time at time m can be obtained

for

In order to save the computing time and storage space of the missile computer, and improve the estimation accuracy of the remaining flight time of the interception section, this estimation method needs to use a time-varying sampling period in practical applications, that is, the sampling period decreases with the relative distance of the projectile. decrease.

Simulation Analysis and Results

进行初始模型的建立。最后，剩余飞行时间的标称值由提及到的method 2给出并与此处提出的剩余飞行时间估计算法所得估计值进行对比。In order to better verify the characteristics of the proposed algorithm for online estimation of missed target amount and remaining flight time, a total of three simulation experiments are designed here. The two cases where the expected incident angle is -30deg and 30deg are discussed; secondly, the system identification and regression analysis algorithms are used to model the measured relative distance sequence; thirdly, the length of the total projectile relative distance data length is selected.

Carry out the establishment of the initial model. Finally, the nominal value of the remaining flight time is given by the mentioned method 2 and compared with the estimates obtained by the remaining flight time estimation algorithm proposed here.

(1) The target is stationary

Figure 1 shows the self-homing guidance system model. In Figure 1, two sets of coordinate systems are involved, specifically the XOZ ground coordinate system and the line-of-sight coordinate system. The ground coordinate system is a static coordinate system fixed on the surface of the earth, the origin O is the intersection of the initial position direction of the missile and the initial position direction of the target on the ground, the OX axis points to the direction of the initial position of the target, and the OZ axis points to the direction of the initial position of the missile; the line of sight coordinates The system is a moving coordinate system. In Figure 1, the target position T is taken as the origin, the projectile distance is the horizontal axis, and the direction is from the target to the missile. The vertical axis is perpendicular to the projectile distance and the direction is upward.

为导弹在视线坐标系中的航迹角，n_c为导弹加速度；V_T为目标速度，β为目标在地面坐标系中的航迹角；θ_MF(t)为导弹在地面坐标系中的期望入射角，

为导弹在视线坐标系中的期望入射角，n_T为导弹在视线坐标系中的期望入射角。θ(t)为视线角，z(t)为导弹在地面坐标系中的纵向距离，R为弹目距离，

为导弹航迹在视线坐标系的横向距离，

为导弹航迹在视线坐标系的纵向距离。M and T represent the missile and the target, V _M , is the velocity of the missile, and θ _M (t) is the track angle in the missile's ground coordinate system

is the track angle of the missile in the line-of-sight coordinate system, n _c is the missile acceleration; V _T is the target speed, β is the track angle of the target in the ground coordinate system; θ _MF (t) is the missile’s track angle in the ground coordinate system desired angle of incidence,

is the expected incident angle of the missile in the line-of-sight coordinate system, and n _T is the expected incident angle of the missile in the line-of-sight coordinate system. θ(t) is the line-of-sight angle, z(t) is the longitudinal distance of the missile in the ground coordinate system, R is the projectile distance,

is the lateral distance of the missile track in the line-of-sight coordinate system,

is the longitudinal distance of the missile track in the line-of-sight coordinate system.

When the target is stationary, the corresponding motion equation of the interception problem is:

where the optimal guidance law n _c with terminal incident angle constraints is

The remaining flight time estimation algorithm method 2 mentioned (C.K.Ryoo,H.Cho,M.J.Tahk,Optimalguidance laws with terminal impact angle constraint,Journal of Guidance,Control and Dynamic,2005,28(4):724-732.) The calculation formula is

Here (x _M0 , z _M0 ) and (x _T0 , z _T0 ) are the initial position coordinates of the missile and the target and are respectively (0m, 3048m) and (12160m, 3048m), and _{VM and θ M0 are} 914.4000m/ s and 90deg, the sampling time (ie sampling period) is 0.001s.

The estimation curves and the corresponding variance curves of the two groups of missed targets at different incident angles are given by the system identification method, the regression analysis method and the Fisher information fusion method, as shown in Figure 2 and Figure 3; at the same time, Figure 4 and Figure 5 respectively The remaining flight time estimation curves corresponding to the three algorithms under different incident angles are given. In order to verify the correctness of the estimation of the remaining flight time by the Fisher fusion estimation algorithm, Figure 6 and Figure 7 respectively show the missile track curve and track angle corresponding to the remaining flight time estimated by the Fisher fusion estimation algorithm under two groups of different incident angles. curve.

It can be seen from Figure 2(a) and Figure 3(a) that when the expected entry angle is -30deg and 30deg, the missed target quantity estimation curves of the three estimation algorithms all have the same trend of change; at the same time, although the initial The estimated values of misses are all large, but all are less than 0.9m (VM is _914.4000m /s, the sampling interval is 0.001s, and the missile step length is 0.9144m). Therefore, all three estimation algorithms can effectively estimate the miss-target amount of this guidance system. The variance estimation curves corresponding to Fig. 2(a) and Fig. 3(a) are referred to in Fig. 2(b) and Fig. 3(b), respectively. It can be seen from these two figures that the variance value corresponding to the Fisher fusion algorithm is always smaller than the corresponding variance value of the other two algorithms. It can be seen that the estimated value of the off-target amount of Fisher fusion algorithm has good convergence characteristics and high estimation accuracy.

Figures 4 and 5 present the remaining time-of-flight estimation curves for these two different expected incidence angles. It can be seen from these two figures that the remaining flight time estimation curves corresponding to the three estimation algorithms almost all coincide with their respective nominal curves, and they can all quickly tend to the nominal curves as the time increases. It can be seen that when the target is in a stationary state, these three estimation algorithms can effectively estimate the remaining flight time of the guidance system with good accuracy. However, since the estimated value of remaining flight time obtained by system identification and regression analysis has different accuracy in different time periods, the estimated value of remaining flight time obtained by Fisher fusion algorithm is always guaranteed to be biased towards the estimated value of the method with higher accuracy. It can be seen that the remaining flight time estimation value of Fisher fusion algorithm has better estimation accuracy. This conclusion is verified in Figures 6 and 7, specifically: even if the expected incidence angles are different, the missile track curve and the track angle curve corresponding to the remaining flight time of the Fisher fusion estimation algorithm are almost identical to their respective nominal curves coincide.

To sum up, when the target is stationary, the proposed Fisher remaining flight time online estimation algorithm can effectively estimate the remaining flight time, an important indicator, with satisfactory accuracy. The effectiveness and practicability of the proposed algorithm have been verified by simulation analysis.

(2) Target sinusoidal maneuver

The same model of the self-homing guidance system is considered here and the target makes a sinusoidal maneuver. The equations of motion for this model are as follows

where D ₁ and D ₂ are disturbances. In the actual interception process, it is difficult to accurately measure the target speed and the uncertainty of this parameter can easily lead to inaccurate modeling of the projectile motion model. Here, this uncertainty is regarded as the disturbance of the guidance system. The influence of this disturbance on the online estimation of the miss and remaining flight time will be discussed in detail in the following (3) Sinusoidal maneuvering with disturbance on the target, and only the case where there is no disturbance will be analyzed here.

According to Schwartz's inequality, the optimal guidance law with target maneuvering and incident angle constraints can be written as

Among them, the target speed V _T =304.8000ms, the target acceleration n _T =58.3078sin(3t), and other parameters are the same as (1) the content of the target stationary.

Figures 8 and 9 show the online estimation curve and the corresponding variance curve of the missed target amount when the expected incident angle is -30deg and 30deg. The remaining flight time estimation curves corresponding to the above two expected incident angles are shown in Figures 10 and 11, respectively At the same time, under these two expected incident angles, the comparison between the missile track curve and the track angle curve corresponding to the estimated value of the remaining flight time of the Fisher fusion algorithm and their respective nominal curves are shown in Figure 12 and Figure 13, respectively.

It can be seen from Figure 8 and Figure 9 that when the incident angle is -30deg and 30deg, the change trend of the missed target amount estimation curve and the corresponding variance curve is basically consistent with the corresponding curve of (1) the content of the target stationary. At the same time, it can be seen from Figure 8(a) and Figure 9(a) that the estimated misses obtained by the three estimation algorithms are still satisfactory, that is, the estimated misses 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, the relative step value is 1.2192m). As can be seen from Figure 8(b) and Figure 9(b), the variance value corresponding to the Fisher fusion estimation algorithm is still smaller than the other two algorithms. It can be seen that when the target performs sinusoidal maneuvers and the expected entry angle is -30deg and 30deg , Fisher fusion estimation algorithm still has effectiveness and good estimation accuracy for online estimation of off-target quantities.

In addition, it can be seen from Figure 10 that when the expected incident angle is -30deg, the estimated value of remaining flight time corresponding to the three estimation algorithms at the initial moment deviates from its nominal remaining flight time value, but as time increases, The remaining flight time estimation curves of the three algorithms all rapidly approach their nominal curves and almost coincide. It can be seen that under this simulation condition, the three algorithms can effectively estimate the remaining flight time online. At the same time, it can be seen from Figure 11 that when the expected incident angle is 30deg, the estimated value of remaining flight time corresponding to the three algorithms has high accuracy even at the initial estimation time, and can quickly approach its target value with the increase of time. value. It can be seen that under this simulation condition, the three algorithms can also effectively estimate the remaining flight time. And because the estimated value of remaining flight time of Fisher information fusion algorithm is the fusion of estimated component value of remaining flight time obtained by system identification method and regression analysis method, the estimated value of remaining flight time obtained by Fisher information fusion algorithm has high accuracy. This conclusion is still verified by the missile track curve and track angle curve corresponding to the estimated value of remaining flight time. A comparison of the missile track curves and track angle curves with their respective nominal curves at an expected entry angle of -30deg and 30deg is shown in FIGS. 12 and 13 . It can be seen from these two figures that the missile track curve and the track angle curve can be matched with their respective nominal curves.

To sum up, when the target performs sinusoidal maneuvers, the proposed Fisher fusion remaining flight time online estimation algorithm can effectively estimate the remaining flight time and obtain a satisfactory estimation accuracy. In addition, the effectiveness and practicability of the proposed algorithm have been verified again.

(3) Target Band Disturbed Sinusoidal Maneuvering

Considering the guidance model with the same content as (1) when the target is stationary and the guidance law is equation (22), the interference amounts are D ₁ =-1.65cosβ and D ₂ =0.55sinβ, respectively. Figure 14 and Figure 15 show the estimated misses and their variance curves when the expected incident angle is -30deg and 30deg, respectively. The track curve and the track angle curve are shown in Figure 18 and Figure 19, respectively.

It can be seen from Figure 14 and Figure 15 that when the expected incident angle is -30deg and 30deg and the guidance model is perturbed, the change trend of the missed target amount estimation curve and its corresponding variance curve is consistent with the corresponding curve in (2) target sinusoidal maneuvering content. At the same time, it can be seen that, under this simulation condition, the three algorithms can obtain satisfactory estimates of off-target quantities, and the estimates of off-target quantities corresponding to Fisher information fusion method still have good estimation accuracy. It can be seen from Fig. 16 and Fig. 17 that even if there is disturbance in the guidance system, the remaining flight time estimation curves obtained by the three algorithms still have the same trend as the corresponding curves without disturbance. And it can be seen from Figure 18 and Figure 19 that when the expected incident angle is -30deg and 30deg, the missile track curve and the track angle curve corresponding to the estimated value of the remaining flight time of Fisher information fusion can also approach their respective nominal curves, that is, The proposed method has good robustness.

It can be seen that when the guidance model is perturbed, the proposed Fisher fusion estimation algorithm can effectively and accurately estimate the remaining flight time, an important performance index, and has strong robustness.

Aiming at the problems that the current remaining flight time estimation algorithm is highly dependent on the guidance model, involves many parameters and has low estimation accuracy, the present invention proposes a new data-driven remaining flight time estimation algorithm. This algorithm does not need to model the guidance model, so it avoids the modeling error and the approximation error from the nonlinear system to the linearized system; at the same time, because this algorithm only needs the relative distance of the projectile, it has high computational efficiency, and An important performance indicator of remaining flight time can be estimated. In addition, when there is disturbance in the guidance system, the proposed algorithm can still effectively estimate this performance index. The algorithm proposed by a large number of simulations has high estimation accuracy, computational efficiency and strong robustness, which have been effectively verified.

Claims (4)

1. an online estimation method of remaining flight time, is characterized in that, comprises the following steps: 1) Use the measured relative distances of the projectiles and use the system identification method and regression analysis method to establish models respectively; 2) Use the established model and the currently known relative distance of the projectile to estimate the amount of misses, and obtain the estimated value of the amount of misses, and the time corresponding to the estimated value of the misses is the moment when the missile is predicted to intercept the target; the specific process is as follows: Based on the above The built model f _j,m ( ) and the known relative distance R _m of the projectile at the current moment, estimate the amount of misses; among them, the jth modeling method is relative to the projectile at the l+1th time at the m time. The expression for distance estimation is written as

in,

is the estimated value of the relative distance of the projectile at the l-th time for the j-th modeling method at the m time, and has a first-order difference

N _j,m is the predicted interception time value corresponding to the jth modeling method at time m; n is the number of modeling methods; L is the total length of the relative distance sequence of the projectile; Definition 1. If

or

but

in,

is the estimated value of the off-target amount corresponding to the jth modeling method at the mth time; Obtained by definition 1, the off-target amount estimated sequence

is a random sequence; assuming that this random sequence obeys a Gaussian distribution, that is

because

Compare

more precise, so will

considered an off-target estimate; where,

for

the mean of ,

for

Variance; Assume that the off-target value is r _N , which is the same as the off-target estimate

There is the following relationship between

Among them, ε _j,m is the estimated random error of the missed target amount corresponding to the jth modeling method at the mth time;

in,

is the variance of ε _j,m ; off-target estimates

The corresponding moment is the moment when the missile is predicted to intercept the target, namely N _j,m ; 3) Calculate the time interval value between the estimated time of the relative distance of the projectile and the time when the predicted missile intercepts the target, and then multiply the time interval value by the sampling period to obtain the estimated component of the remaining flight time at the current moment; 4) Using the Fisher information fusion method, the fusion estimation value of the remaining flight time at the current moment is obtained. 2. a kind of remaining flight time online estimation method according to claim 1, it is characterised in that in step 1), adopt the projectile relative distance of measurement and adopt system identification method and regression analysis method to build model respectively, concrete process is as follows : It is assumed that the relative distance of the projectile can be measured from time 0 to the current time m and recorded as

Where m is the current time value; according to the obtained relative distance sequence of projectiles

Get its corresponding first-order difference sequence, denoted as

And there is ΔR _i =R _i+1 -R _i ; the model built by the jth modeling method at the mth moment is f _j,m ( ), where j=1,...,n; here, the modeling The methods are system identification method and regression analysis method, n=2. 3. a kind of remaining flight time online estimation method according to claim 1, is characterized in that, in step 3), calculate the time interval value of projectile relative distance estimation moment and predicted missile to carry out interception moment to target, reuse time interval The value is multiplied by the sampling period to obtain the estimated component of the remaining flight time at the current moment. The specific process is as follows: Assuming that the missile intercepts the target at time N _{j ,m,} a total of N _j,m -m time interval values are required from the estimated time m+1 to the time N j,m of the relative distance of the projectile; For the jth modeling method, the estimated component of the remaining flight time corresponding to the mth time

Expressed as

Among them, T is the sampling period. 4. a kind of remaining flight time online estimation method according to claim 3 is characterized in that, adopt Fisher information fusion method in step 1), obtain remaining flight time fusion estimated value at current moment, and concrete process is as follows: The estimated component of the remaining flight time corresponding to the mth time according to the jth modeling method

Get the fused estimate of the remaining flight time at time m

for

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