CN111832121A - A multi-aircraft collaborative detection and guidance integration method and system - Google Patents

Abstract

The invention discloses an integrated method and system of multi-aircraft cooperative detection and guidance. The method includes: obtaining the initial lateral distance between the interceptor and the maneuvering target, the initial lateral relative velocity between the interceptor and the maneuvering target, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor; according to the initial lateral distance, The lateral relative velocity, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor are used to determine the initial state vector; the measurement information is determined according to the initial state vector and the noise of the interceptor; based on the measurement information, the estimated state vector is obtained through interactive multi-model filtering ; Determine the optimal control input according to the estimated state vector; control the line-of-sight angles of the two interceptors according to the optimal control input to realize the tracking and interception of the target. The invention introduces interactive multi-model filtering to identify the switching time and state of target maneuvering, modulates the line-of-sight separation angle of the two interceptors, enhances target detection accuracy, and realizes target tracking and interception.

Description

A multi-aircraft collaborative detection and guidance integration method and system

technical field

The invention relates to the field of target tracking, in particular to an integrated method and system of multi-aircraft cooperative detection and guidance.

Background technique

For the situation where two interceptors intercept the enemy's target that can perform the bang-bang optimal evasion maneuver. The traditional cooperative guidance law that considers two interceptors reaching the target at the same time often does not consider the influence of the relative detection configuration on the interception target accuracy, because when the multi-aircraft cooperative angle measurement method is used to further estimate the distance information, if the multi-aircraft and the target share The relative distance cannot be estimated when it is in the line, and the estimation error is larger when it is approximately collinear. Therefore, it is necessary to consider the influence of the relative detection configuration of the two interceptors on the interception accuracy in the design process of the guidance law. In addition, for the traditional KF/SF method for estimating the target state, it has low adaptability to the multi-modal motion mode for performing bang-bang maneuvers, and has a large error in the estimation accuracy of the target state.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide an integrated method and system for multi-aircraft cooperative detection and guidance, which can enhance target detection accuracy by modulating the line-of-sight separation angle of two interceptors, and achieve target tracking and interception.

For achieving the above object, the present invention provides the following scheme:

An integrated method for multi-aircraft cooperative detection and guidance, comprising:

Obtain the initial lateral distance between the interceptor and the maneuvering target, the initial lateral relative velocity between the interceptor and the maneuvering target, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor;

determining an initial state vector according to the initial lateral distance, the lateral relative velocity, the initial acceleration of the maneuvering target, and the initial acceleration of the interceptor;

determining measurement information according to the initial state vector and interceptor noise;

Based on the measurement information, an estimated state vector is obtained through interactive multi-model filtering;

According to the estimated state vector, determine the optimal control input;

The line-of-sight angles of the two interceptors are controlled according to the optimal control input, so as to realize the tracking and interception of the target.

Optionally, the estimated state vector is obtained by interactive multi-model filtering based on the measurement information, specifically including:

calculating a mixing probability according to the measurement information;

determining initial conditions according to the mixing probability;

Perform interactive multi-model filtering according to the initial conditions to obtain a likelihood function;

Update the model probability through the likelihood function;

Estimate the state vector from the updated model probabilities.

Optionally, determining the optimal control input according to the estimated state vector specifically includes:

determining a kinematic model according to the estimated state vector;

The optimal control input is determined based on the kinematic model and the remaining interception time.

Optionally, the calculation formula of the initial state vector is as follows:

为拦截器和机动目标之间的侧向相对速度，a_E为机动目标的初始加速度，a_Pi为拦截器的初始加速度。where _yi is the lateral distance between the interceptor and the maneuvering target,

is the lateral relative velocity between the interceptor and the maneuvering target, a _E is the initial acceleration of the maneuvering target, and a _Pi is the initial acceleration of the interceptor.

Optionally, the calculation formula of the remaining interception time is as follows:

Among them, t _fPiE represents the interception time, and t represents the time.

The present invention also provides a multi-aircraft collaborative detection and guidance integrated system, comprising:

The data acquisition module is used to acquire the initial lateral distance between the interceptor and the maneuvering target, the initial lateral relative velocity between the interceptor and the maneuvering target, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor;

an initial state vector determination module, configured to determine an initial state vector according to the initial lateral distance, the lateral relative velocity, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor;

determining an initial state vector determining module for determining measurement information according to the initial state vector and the noise of the interceptor;

an estimation module, based on the measurement information, to obtain an estimated state vector through interactive multi-model filtering;

an optimal control input determination module, configured to determine the optimal control input according to the estimated state vector;

The control module is used for controlling the line-of-sight angles of the two interceptors according to the optimal control input, so as to realize the tracking and interception of the target.

Optionally, the estimation module specifically includes:

a mixing probability calculation unit, configured to calculate the mixing probability according to the measurement information;

an initial condition determining unit, configured to determine an initial condition according to the mixing probability;

a likelihood function determination unit, configured to perform interactive multi-model filtering according to the initial conditions to obtain a likelihood function;

an update unit for updating the model probability through the likelihood function;

Estimation unit for estimating the state vector according to the updated model probability.

Optionally, the optimal control input determination module specifically includes:

a kinematic model determining unit, configured to determine a kinematic model according to the estimated state vector;

and an optimal control input determination unit, configured to determine the optimal control input according to the kinematic model and the remaining interception time.

Optionally, the calculation formula of the initial state vector is as follows:

为拦截器和机动目标之间的侧向相对速度，a_E为机动目标的初始加速度，a_Pi为拦截器的初始加速度。where _yi is the lateral distance between the interceptor and the maneuvering target,

is the lateral relative velocity between the interceptor and the maneuvering target, a _E is the initial acceleration of the maneuvering target, and a _Pi is the initial acceleration of the interceptor.

Optionally, the calculation formula of the remaining interception time is as follows:

Among them, t _fPiE represents the interception time, and t represents the time.

According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

The present invention determines measurement information according to the initial state vector and interceptor noise; based on the measurement information, an estimated state vector is obtained through interactive multi-model filtering; according to the estimated state vector, the optimal control input is determined; The optimal control input controls the line-of-sight angles of the two interceptors to achieve the tracking and interception of the target. The invention introduces interactive multi-model filtering to identify the switching time of the target maneuver and estimate the target state, modulate the line-of-sight separation angle of the two interceptors, enhance the target detection accuracy, and realize the target tracking and interception.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings required in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some of the present invention. In the embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative labor.

1 is a flowchart of a method for integrating multi-aircraft cooperative detection and guidance according to an embodiment of the present invention;

Figure 2 shows the engagement motion model of two interceptors and maneuvering targets;

Fig. 3 is the engagement diagram of interceptor 1 and interceptor 2 cooperatively intercepting maneuvering targets;

Figure 4 is a schematic diagram of the acceleration changes of the two interceptors;

Fig. 5 is the modulo probability change diagram of the element filter of interceptor 1;

Fig. 6 is the estimation of the acceleration of interceptor 1 by IMM filtering and KF/SF;

Fig. 7 is the position, velocity and acceleration estimation error of I interceptor 1;

Figure 8 shows the position, velocity and acceleration estimation errors of interceptor 2

FIG. 9 is a graph of the noise variation of lateral displacement measurement between the interceptor 1 and the target under different guidance laws;

Fig. 10 is a variation diagram of the line-of-sight separation angle between two interceptors under different guidance laws and estimation methods;

Figure 11 is the off-target CDF of Interceptor 1 under APN combined with IMM, the proposed guidance law combined with KF/SF and IMM;

Figure 12 is the off-target CDF of Interceptor 2 under APN combined with IMM, the proposed guidance law combined with KF/SF and IMM;

Figure 13 shows the average misses of interceptor 1 for different switching times under APN combined with IMM, the proposed guidance law combined with KF/SF and IMM;

Figure 14 shows the average misses of interceptor 2 for different switching times under APN combined with IMM, the proposed guidance law combined with KF/SF and IMM;

FIG. 15 is a structural block diagram of an integrated system for cooperative detection and guidance of multiple aircraft according to an embodiment of the present invention.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

The purpose of the present invention is to provide an integrated method and system for multi-aircraft cooperative detection and guidance, which can enhance target detection accuracy by modulating the line-of-sight separation angle of two interceptors, and achieve target tracking and interception.

In order to make the above objects, features and advantages of the present invention more clearly understood, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

As shown in Figure 1, an integrated method for multi-aircraft cooperative detection and guidance includes the following steps:

Step 101: Obtain the initial lateral distance between the interceptor and the maneuvering target, the initial lateral relative velocity between the interceptor and the maneuvering target, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor.

Step 102: Determine an initial state vector according to the initial lateral distance, the lateral relative velocity, the initial acceleration of the maneuvering target, and the initial acceleration of the interceptor. The calculation formula of the initial state vector is as follows:

为拦截器和机动目标之间的侧向相对速度，a_E为机动目标的初始加速度，a_Pi为拦截器的初始加速度。where _yi is the lateral distance between the interceptor and the maneuvering target,

is the lateral relative velocity between the interceptor and the maneuvering target, a _E is the initial acceleration of the maneuvering target, and a _Pi is the initial acceleration of the interceptor.

Step 103: Determine measurement information according to the initial state vector and the noise of the interceptor.

Step 104: Based on the measurement information, obtain an estimated state vector through interactive multi-model filtering. Specifically, it includes: calculating a mixing probability according to the measurement information; determining an initial condition according to the mixing probability; performing interactive multi-model filtering according to the initial condition to obtain a likelihood function; updating the model probability through the likelihood function ; Estimate the state vector from the updated model probabilities.

Step 105: Determine the optimal control input according to the estimated state vector. Specifically, it includes: determining a kinematic model according to the estimated state vector; and determining an optimal control input according to the kinematic model and the remaining interception time. The calculation formula of the remaining interception time is as follows:

Among them, t _fPiE represents the interception time, and t represents the time.

Step 106: Control the line-of-sight angles of the two interceptors according to the optimal control input, so as to realize the tracking and interception of the target.

The method principle of the present invention is described in detail below:

1. Problem description and establishment of relative kinematic equations

Suppose that our two interceptors intercept the enemy's target that can perform the optimal bang-bang evasion maneuver. In this case, there are two important factors to consider: First, the interceptor needs to adopt an effective estimation method to detect the random change of the target and accurately estimate the state of the target. Another is that the relative detection configuration of the two interceptors can affect the detection accuracy of the target state information.

The dynamics and kinematics models are established in the X _I -O _I -Y _I inertial coordinate system. Pi and E denote interceptor and maneuvering target, respectively. a, v, λ, r, and γ denote normal acceleration, velocity, line-of-sight angle, relative distance, and heading angle, respectively. Figure 2 shows the engagement motion model of two interceptors and maneuvering targets.

(1) Establish dynamic and kinematic models

Ignoring the effect of gravity, the engagement process between the interceptor and the maneuvering target can be expressed in the form of polar coordinates (r, λ) related to the maneuvering target, namely

为两拦截器之间的相对速度；

为两拦截器之间的视线角速率；v_Pi和v_E分别为拦截器和机动目标的速度；

和

分别为拦截器和机动目标的初始飞行路径角；λ_PiE为拦截器和机动目标之间的视线角。where:

is the relative speed between the two interceptors;

is the line-of-sight angular velocity between the two interceptors; v _Pi and v _E are the velocities of the interceptor and maneuvering target, respectively;

and

are the initial flight path angles of the interceptor and the maneuvering target, respectively; λ _PiE is the line-of-sight angle between the interceptor and the maneuvering target.

Because the direction of acceleration is always perpendicular to the direction of velocity throughout the guidance process, the velocity of the interceptor and maneuvering target is always constant. Therefore, the relationship between the normal acceleration of the aircraft and the heading angle can be expressed as

When the flight process of the two aircraft (interceptors) can be approximated as a nominal collision triangle, the above process can be linearized. In the engagement process described in Figure 2, there are two collision triangles composed of two pursuers and the maneuvering target respectively.

After linearizing the above process, the present invention can select the state vector

为拦截器Pi和机动目标E间的侧向距离，

为侧向相对速度，y_Pi和y_E分别为拦截器和机动目标相对于初始位置的侧向距离，a_E为机动目标的初始加速度，a_Pi为拦截器的初始加速度。where:

is the lateral distance between the interceptor Pi and the maneuvering target E,

is the lateral relative velocity, y _Pi and y _E are the lateral distances of the interceptor and the maneuvering target relative to the initial position, respectively, a _E is the initial acceleration of the maneuvering target, and a _Pi is the initial acceleration of the interceptor.

Assuming that the interceptor and the maneuvering target can be approximated as a first-order dynamic model, the state equation of the relative motion between the aircraft can be written as

为拦截器的指令加速度。where τ _Pi and τ _E are the overload response time constants of interceptors and maneuvering targets, respectively,

Command acceleration for the interceptor.

The matrix form of equation set (5) is

where:

A_i为系数矩阵，B_i为控制输入矩阵，C_i为外部输入矩阵，u_Pi为追击者的控制输入，且满足限制条件

为机动目标的指令加速度，w为制导过程的噪声。

A _i is the coefficient matrix, B _i is the control input matrix, C _i is the external input matrix, u _Pi is the control input of the pursuer, and the constraints are met

is the commanded acceleration of the maneuvering target, and w is the noise of the guidance process.

和

在标称碰撞三角形的假设下，航向角γ_i和视线角λ_PiE之间的偏差很小。因此，拦截器对机动目标的拦截时间是恒定的，可表示为The initial distance between the interceptor and the maneuvering target can be expressed as

and

Under the assumption of a nominal collision triangle, the deviation between the heading angle γ _i and the sight angle λ _PiE is small. Therefore, the interception time of the interceptor to the maneuvering target is constant, which can be expressed as

The present invention considers the special case of two interceptors intercepting a maneuvering target at the same time, then their interception times are equal, that is, t _fP1E =t _fP2E . Therefore, the initial distances between them are also equal, i.e.,

(2) Establish a measurement model of the aircraft

Each interceptor uses its own sensor to measure the line-of-sight angle λ _PiE . In addition, each sensor is disturbed by _vPi of Gaussian white noise, and they are independent of each other. The present invention assumes that the line-of-sight measurement noise of each interceptor obeys a distribution

As can be seen in Figure 2, during engagement, the two interceptors were able to form a baseline of measurements relative to the maneuvering target. Assuming that the interceptor can accurately measure its relative state, and they can share their respective measurement information with each other, so the relative position information between them (r, λ _PiPj ), i, j=1, 2, i≠j can get.

Therefore, through the known relative distance information r and line-of-sight angle information λ _P1P2 of the two interceptors, the relative distances between the two interceptors and the maneuvering targets can be calculated.

where:

λ _P1P2 =arctan2(y _P2 -y _P1 ,x _P2 -x _P1 ) (11)

In the formula: x _P1 and x _P2 are the coordinates of pursuer 1 and pursuer 2 on the horizontal axis, respectively, and y _P1 and y _P2 are the coordinates of pursuer 1 and pursuer 2 on the vertical axis, respectively.

Under the linearization assumption satisfying the nominal collision triangle, the lateral displacement yi perpendicular to the initial sight angle can be expressed as

y _i ≈(λ _PiE -λ _PiE0 )r _PiE (12)

r _PiE ≈v _PiE t _go (13)

In the formula: t _go is the remaining time of interception.

Combined with equation (9), the measurement equation of the interceptor can be obtained

In the formula: H＝[1 0 0 0]

It can be seen from equation (16) that when the line-of-sight separation angle |λ _PiE -λ _PjE | between the two interceptors decreases, the measurement variance of the lateral displacement _yi will increase, resulting in a decrease in the state estimation accuracy. Therefore, when designing the guidance law, it is necessary to control the line-of-sight separation angle of the two interceptors relative to the target.

(3) Establish performance indicators

Successful interception of a maneuvering target by an interceptor requires minimal terminal misses or direct hits. However, due to various factors, the interceptor cannot hit the maneuvering target with high accuracy. In particular, the method of estimating the state of maneuvering targets severely restricts the guidance accuracy of the interceptor. Because it is difficult to obtain a kill model affected by many factors in a realistic combat environment, the present invention uses a simplified kill function to evaluate the possibility of destroying the target:

In the formula: M is the terminal miss of the interceptor, and R _k is the killing range of the interceptor warhead.

The indicator of the success of interception, the missed target quantity, is affected by the random maneuvering of the target and the measurement noise of the detection process. Therefore, the missed target quantity is a random variable. The present invention generally uses the cumulative distribution function CDF (Cumulative Distribution Function) as an empirical estimate to evaluate the influence of the miss-on-target amount on the guidance accuracy, and uses it to compare the guidance performance between different guidance laws. Therefore, the present invention can judge whether the interception is successful by using the determined kill probability in advance under the given LR condition. The kill probability can be defined as

SSKP(R _k )=E{P _d (M,R _k )} (19)

In the formula: E is the mathematical expectation of the random variable of the off-target quantity. SSKP can be calculated by CDF, and its formula is

In the formula: f _M and F _M are the probability density function PDF (Probability Density Function) and CDF, respectively. The interception probability is generally taken as 0.95, and the performance indicators can be obtained:

2. Design of collaborative guidance law

The main factor considered in the design of the guidance law is that the guidance configuration of the aircraft can affect the detection accuracy of the target, that is, the line-of-sight separation angle of the two interceptors can affect the measurement variance of the relative distance. If the guidance law cannot control the line-of-sight angle, the line-of-sight separation angle between the two interceptors may become smaller, resulting in increased detection errors. Therefore, the interceptor of the present invention needs to control the line-of-sight separation angle of the guidance end so that it can meet the requirements of detection and guidance accuracy. If the interceptor with a large initial line-of-sight angle maximizes its line-of-sight angle and the other minimizes its line-of-sight angle, then the line-of-sight separation angle of the two interceptors will become larger and the estimation accuracy will be enhanced.

The present invention adopts the optimal control theory to achieve the above-mentioned purpose of cooperative guidance by taking the missed target amount and energy consumption into consideration.

(1) Objective function

Under the assumption of a nominal collision triangle, the lateral displacement of the interceptor can be approximated as

r _PiE ≈v _PiE t _go (23)

Combining equations (22) and (23), the line-of-sight angle λ _PiE can be approximated as

可建立最优控制的性能指标为import item

The performance index that can establish the optimal control is

代替

来避免在之后计算和推导公式的奇异性。当Δt→0时，

本发明使a→∞，可以得到脱靶量趋向于0的制导律。注意如果权重c_i＞0，视线角将被最小化，如果c_i＜0，视线角将被最大化。Use of the present invention

replace

to avoid singularities in calculating and deriving formulas later. When Δt→0,

In the present invention, a→∞ can be obtained, and the guidance law in which the off-target amount tends to 0 can be obtained. Note that if the weights _ci > 0, the sight angle will be minimized, and if _ci < 0, the sight angle will be maximized.

(2) Downgrade

In order to reduce the order of solving the optimization problem and obtain the analytical solution of the control input, the present invention introduces the terminal projection method to perform order reduction processing. This requires the present invention to introduce a new state variable, defined as

Z _i (t)=DΦ _i (t _f ,t)x _i (t) (26)

In the formula: Φ _i (t _f ,t) is the state transition matrix related to A _i .

Combining equation (27) and the derivative of the new state variable with respect to time, the present invention can obtain

是状态独立的，且只与所设计的控制器有关，此外，本发明将DΦ_i(t_f,t)B_i标记为

Equation (28) shows that,

is state-independent and only related to the designed controller. In addition, the present invention marks DΦ _i (t _f ,t)B _i as

Using terminal projection method to reduce the order, the objective function (25) can be represented by a new state variable

In the formula: a _i , b _i and c _i are weight coefficients, and Z _i (t _f ) is the zero-effect miss at the time of interception.

(3) Optimal controller design

The Hamiltonian function of the performance index is

In the formula: λ _Z is the adjoint vector.

The derivative of the new state variable with respect to time is state independent, which greatly simplifies the adjoint equations.

λ _Z (t _f )=a _i Z _i (t _f ) (32)

Integrating equation (31) from t _f to t and substituting equation (32) into

can be obtained from the governing equation

Substitute equation (34) into equation (28) to get

Integrating Equation (35) from t to t _f can get

where:

Therefore, Z _i (t _f ) can be solved as

Substituting Z _i (t _f ) into equation (34), the optimal controller can be solved

When a→∞, the perfect interception guidance law with interception miss amount of 0 can be obtained, namely

3. Interactive multi-model filtering for tracking target maneuvers

Interactive Multiple Model (IMM) filtering is designed to estimate hybrid system models such as the target bang-bang maneuver described above. In this system, the system dynamics model belongs to a finite set, and the models can be transferred according to a certain probability. In interactive multi-model filtering there are Kalman filters that match different models, and they run simultaneously. The input of each filter is obtained by state interaction between the filters according to the probability transition matrix. All filters compute such values at the next moment based on the model probabilities, prior state estimates, variances, likelihood functions, and probability transition matrices obtained at the previous moment. In addition, the output of interactive multi-model filtering is obtained by interactive mixing of all filters

(1) Filtering algorithm

1) Mixed probability

Conditioned on the previous measurement information z _k-1 , the probability that mode i at time k-1 affects mode j at time k can be calculated by Bayesian rule

是在k-1时刻第i个模式的条件混合概率，

为第i个模式在k-1时刻的模概率。利用总概率理论和符合马尔科夫链的概率转移矩阵，可将式(40)写成where:

is the conditional mixing probability of the ith mode at time k-1,

is the modulo probability of the i-th mode at time k-1. Using the total probability theory and the probability transition matrix conforming to the Markov chain, Equation (40) can be written as

In the formula: π _ij is the transition probability between modes.

2) Initial conditions

The initial condition of each filter that has been input interactively can be obtained from the sum of the weights of each filter related to the mixing probability, that is,

和

分别是第i个模式在k-1时刻估计的状态和方差。where:

and

are the estimated state and variance of the ith mode at time k-1, respectively.

3) Model matched filtering

和方差

Using the initial conditions of equations (41) and (42) and the new measurement information z _k , the estimated state of the jth mode at time k can be calculated

and variance

及其方差阵

可计算得到第j个滤波器的条件似然函数

该似然函数将用在之后的模概率更新过程中。According to the current filtered information

and its variance matrix

The conditional likelihood function of the jth filter can be calculated

This likelihood function will be used in subsequent modulo probability updates.

In the formula: m is the measurement number.

4) Pattern probability update

According to Bayes' rule, the modulo probability at time k can be updated

Applying the total probability theory, we can get,

(5) Hybrid estimated state and variance

Output mixed estimated state and variance after interaction

(2) Maneuvering target tracking and its model matching filter

For the bang-bang maneuver of the target, the interactive multi-model filtering is mainly used to identify the switching time of the target maneuver and estimate the state of the target. There are two main modes of bang-bang maneuvering of the target, namely the maximum positive acceleration mode and the maximum negative acceleration mode, which can be written as

为最大目标加速度指令，r表示目标的机动模式。where:

is the maximum target acceleration command, and r represents the maneuvering mode of the target.

Assuming that the transition process between maneuvering modes is a first-order Markov chain, the transition probability can be defined as

π _ij =Pr{r _k =j|r _k-1 =i},(i,j∈S) (50)

因为目标采取bang-bang机动的形式，存在两种模式，所以s＝2。where:

Since the target takes the form of a bang-bang maneuver, there are two modes, so s=2.

In the absence of external measurement information, the conversion probability matrix between modes is obtained as

In the formula: Δt is the simulation calculation step size; δ is a non-negative number not greater than 1, and the theoretical value is 0. In order to ensure that the mode conversion process is a Markov chain, a positive number close to 0 is set.

和误差方差阵

先验状态估计值

可通过式(6)给出，误差方差阵可通过下式计算，Calculate the prior state estimate at time k

and error variance matrix

prior state estimate

It can be given by equation (6), and the error variance matrix can be calculated by the following equation,

In the formula: Φ _k|k-1 is the state transition matrix from time k-1 to time k, and Q _k-1 is the discrete process noise.

及其方差阵

Calculate the innovation at time k

and its variance matrix

In the formula: H represents the measurement matrix, and R _k is the measurement noise variance matrix at time k.

状态均值

和方差阵

Calculate the filter gain at time k

state mean

and variance matrix

(3) Target maneuver detection

Since the switching time of the target bang-bang maneuver is random, the estimation process of the target maneuver is also random. Attempting to approximate this process with a deterministic quantitative model can effectively study its effect on closed-loop interception performance. In modern guidance laws designed with extensive use of target acceleration information, most of the sources of error are inaccurate estimates of acceleration. Although there are many effective and accurate estimation methods, the estimation of the acceleration will inevitably lead to a time delay in estimation, because the present invention can only obtain the orientation information of the target in practical situations. Because in the established model, the lateral displacement of the aircraft is approximately perpendicular to the line-of-sight direction, and the acceleration needs to undergo two integrations before the lateral displacement information is obtained, so this is the estimated target maneuver command. Compared with the actual command, there will be a delay s reason.

Hexner et al. pointed out a time lower bound for maneuver instruction detection independent of the estimation method. Therefore, whenever a maneuver order switch occurs, it is assumed that the IMM filtering can identify it within the time interval T _id after the maneuver order switch occurs. If the filter does not recognize a maneuver command switch within T _id time after it occurs, ie the modulo probability of the corresponding filter is always below a pre-set threshold, it will not be recognized at any time thereafter. According to the literature, T _id can be defined as

是机动切换的最小检测时间，它可以基于以下原理计算得到：当标称轨迹与目标位置之间的偏差超过测量噪声标准偏差值的两倍时，就可以检测到目标发生了机动切换。where: s _f is the tuning parameter,

is the minimum detection time for maneuvering switching, which can be calculated based on the following principle: when the deviation between the nominal trajectory and the target position exceeds twice the standard deviation value of the measured noise, the maneuvering switching of the target can be detected.

4. Simulation analysis

The present invention will perform numerical simulation verification on the proposed cooperative guidance law and IMM filtering. First, the present invention sets up simulation parameters, and preliminarily analyzes the engagement situation of the three aircraft. Then, the present invention explores the effects of cooperative guidance law and IMM filtering on maneuvering target detection and guidance performance, and introduces Monte Carlo (MC) to evaluate them. There are two main factors that affect the interceptor's guidance and detection performance: one is the detection configuration of the two interceptors during the guidance process; the other is the ability of the IMM filter to detect the target maneuver switching time. Finally, the present invention compares the proposed co-guidance law using IMM filtering with this guidance law using Kalman filtering with shaping filters (KF/SF) and the extended scale-guided guidance law (APNG) using IMM filtering Compared.

(1) Simulation parameters and combat situations

初始的侧向位移分别为

和

拦截器和目标的速度分别为v_Pi＝2000m/s和v_E＝1000m/s。忽略重力的影响，拦截器和目标的过载限制分别为

和

过载响应时间常数分别为τ_Pi＝0.2s和τ_E＝0.2s。仿真时间间隔设置为Δ＝0.001s，视线角量测噪声标准差为σ_Pi,λ＝1mrad。IMM滤波针对目标的bang-bang机动设置两种机动模式，因此需要两个元素滤波器同时运行。For the designed guidance law, the simulation parameters are set as follows: Interceptor 1 and Interceptor 2 are launched at the same time, and the initial distance to the maneuvering target is both

The initial lateral displacements are

and

The velocities of the interceptor and target are v _Pi = 2000 m/s and v _E = 1000 m/s, respectively. Neglecting the effect of gravity, the overload limits of interceptor and target are respectively

and

The overload response time constants are τ _Pi =0.2s and τ _E =0.2s, respectively. The simulation time interval is set to Δ=0.001s, and the standard deviation of the measurement noise of the line-of-sight angle is _σPi,λ =1mrad. The IMM filter sets two maneuvering modes for the target's bang-bang maneuver, thus requiring two element filters to run simultaneously.

The performance between different estimation methods and guidance laws, including the proposed co-guidance law with IMM filtering and KF/SF, and APNG with IMM filtering, respectively, is evaluated by setting 100 MC simulations with random target maneuver switching times.

Fig. 3 is an engagement diagram of interceptor 1 and interceptor 2 in cooperative interception of maneuvering targets. It can be seen from Figure 3 that the proposed cooperative guidance law can modulate the trajectory of the two interceptors to separate them from each other to increase their line-of-sight separation angle, thereby avoiding the detection error caused by the guidance configuration. Figure 4 shows the acceleration changes of the two interceptors. It can be seen from Figure 4 that the accelerations of the two interceptors do not exceed the overload limit. Combined with Figure 3 and Figure 4, because interceptor 2 does not require large-scale maneuvering, it does not require high maneuverability, while interceptor 1 and interceptor 2 should cooperate with each other to increase the line of sight separation angle between them. Therefore, compared with the initial state advantage of the interceptor 2, the interceptor 1 needs to pay a greater maneuvering cost to achieve the guidance purpose.

(2) Estimated performance evaluation

Assuming that the switching time of the maneuvering target is 1.6s, that is, the maximum acceleration maneuver in the opposite direction is performed at 1.6s, the present invention compares the estimation capabilities of IMM filtering and KF/SF, and explores the influence of the guidance configuration on the detection performance.

0.4s的检测时间是合理有效的。所有状态误差的快速收敛，特别是加速度估计误差，对终端脱靶量有很大的影响。从图6中可以看出，相比于KF/SF，IMM滤波对目标的机动切换具有更快速的响应和更精确的加速度估计性能。FIG. 5 is a graph of the modulo probability change of the element filter of the interceptor 1 . Figure 6 shows the estimation of interceptor 1 acceleration by IMM filtering and KF/SF. It can be seen from Fig. 5 that before the target maneuvering switch occurs, filter 2 has a higher modulus probability, which indicates that the maneuvering target adopts the maneuvering mode of mode 2, that is, the maximum forward acceleration mode. At about 2s, the IMM filter recognizes that the target maneuver has switched, and the target performs a maneuver switch at 1.6s to detect it at 2, which takes 0.4s, compared to the minimum detection time required. interval

A detection time of 0.4s is reasonable and effective. The rapid convergence of all state errors, especially the acceleration estimation error, has a large impact on the amount of terminal misses. As can be seen from Fig. 6, compared with KF/SF, IMM filtering has faster response and more accurate acceleration estimation performance for maneuvering switching of targets.

Figures 7 and 8 present the interceptor's position, velocity and acceleration estimation errors. It can be seen from the figure that the estimation of the acceleration by the two kinds of filtering has a large fluctuation around 2s. Referring to Fig. 6, this is caused by the time delay of the estimation of the target maneuver switching. Compared with KF/SF, IMM filtering has lower estimation error for acceleration. The accurate estimation of acceleration by the IMM filtering also enables it to accurately estimate position and velocity.

FIG. 9 is a graph showing the variation of the lateral displacement measurement noise between the interceptor 1 and the target under different guidance laws. Figure 10 is a graph of the line-of-sight separation angle variation between two interceptors under different guidance laws and estimation methods. Comparing the two figures, it can be seen that the use of APN combined with IMM will make the line-of-sight separation angle very small during the entire guidance process, which leads to a large detection error noise, because APN cannot control the line-of-sight separation between the two aircraft horn. It can be seen from Fig. 10 that the proposed guidance law can control the line of sight separation angle between the two aircraft, and can make the line of sight separation angle gradually increase. The measurement noise decreases with the increase of the line-of-sight separation angle, and finally approaches 0, which indicates that the proposed guidance law can reduce the detection errors of the two aircraft.

(3) Off-target assessment

The present invention analyzes the closed-loop interception performance of APN combined with IMM and the proposed guidance law combined with KF/SF and IMM by introducing 100 MC simulations. Figures 11 and 12 show the CDFs of the misses for the two interceptors, and Table 1 summarizes the warhead kill range required for the two interceptors to ensure a 95% kill probability. Taking Interceptor 1 as an example, compared with APN combined with IMM which requires a killing range of 9.47m and the proposed guidance law combined with KF/SF requires a killing range of 22.86m, the proposed guidance law combined with IMM only needs a killing range of 0.81m. As shown in Fig. 11 and Fig. 12, the interception performance of the proposed guidance law combined with IMM outperforms the other two guidance and estimation methods. In addition, comparing Fig. 11 and Fig. 12, the method of estimating the acceleration using the IMM makes the two interceptors have similar interception performance, and they are relatively close to the warhead kill range required to ensure a 95% kill probability. The method of using KF/SF to estimate the acceleration makes the interception performance of the two interceptors have a large difference, and their required warhead kill ranges are quite different. On the one hand, this is caused by the inaccurate estimation of the acceleration, and On the one hand this is due to the high cost of maneuvering required by Interceptor 1.

Table 1 Warhead kill range required for APN combined with IMM and the proposed guidance law combined with KF/SF and IMM to ensure 95% kill probability

Figures 13 and 14 show the average misses of the two interceptors for different switching times. It can be seen from the figure that for APN combined with IMM, when the target is concentrated in 1.5s to 4s for switching maneuvers, interception misses will be generated; for the proposed guidance law combined with KF/SF, when the target performs switching maneuvers in 1.7s to 4s will cause the interceptor 1 to produce off-target amount, and when the target performs the switching maneuver at 3.3s to 4s, it will cause the interceptor 2 to produce the off-target amount; for the proposed guidance law combined with IMM, when the target performs the switching maneuver from 3.3s to 4s, it will The interception off-target amount produced is the smallest among them, which indicates that the proposed guidance law combined with IMM has better guidance accuracy. The reason why APN combined with IMM will produce misses is that it cannot modulate the line-of-sight separation angle during the guidance process, which makes the two interceptors generate large detection errors; although the proposed guidance law combined with KF/SF avoids the inability to modulate the line-of-sight separation angle The detection error is too large, but the main reason that affects the detection accuracy is the inaccuracy of the acceleration of the target. In addition, for all guidance and estimation methods, their misses first increased and then decreased with the increase of maneuver switching time. The amount of misses increases first because the closer the target is to the guidance end for switching maneuvers, the less time is left for the interceptor to react, and the filtering delay prevents the interceptor from changing the command in time, which eventually leads to a larger amount of misses. The reason for the decrease in the amount of misses is that if the target switches maneuvers too late, the target will not have time to change directions to escape, which reduces the amount of misses again.

As shown in FIG. 15 , the present invention also provides a multi-aircraft cooperative detection and guidance integrated system, including:

The data acquisition module 1501 is used to acquire the initial lateral distance between the interceptor and the maneuvering target, the initial lateral relative velocity between the interceptor and the maneuvering target, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor.

The initial state vector determination module 1502 is configured to determine an initial state vector according to the initial lateral distance, the lateral relative velocity, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor.

The calculation formula of the initial state vector is as follows:

为拦截器和机动目标之间的侧向相对速度，a_E为机动目标的初始加速度，a_Pi为拦截器的初始加速度。where _yi is the lateral distance between the interceptor and the maneuvering target,

is the lateral relative velocity between the interceptor and the maneuvering target, a _E is the initial acceleration of the maneuvering target, and a _Pi is the initial acceleration of the interceptor.

An initial state vector determination module 1503 is configured to determine measurement information according to the initial state vector and the noise of the interceptor.

The estimation module 1504 obtains an estimated state vector through interactive multi-model filtering based on the measurement information.

Specifically, the estimation module 1504 includes:

a mixing probability calculation unit, configured to calculate the mixing probability according to the measurement information;

an initial condition determining unit, configured to determine an initial condition according to the mixing probability;

a likelihood function determination unit, configured to perform interactive multi-model filtering according to the initial conditions to obtain a likelihood function;

an update unit for updating the model probability through the likelihood function;

Estimation unit for estimating the state vector according to the updated model probability.

The optimal control input determination module 1505 is configured to determine the optimal control input according to the estimated state vector.

The optimal control input determination module 1505 specifically includes:

a kinematic model determining unit, configured to determine a kinematic model according to the estimated state vector;

and an optimal control input determination unit, configured to determine the optimal control input according to the kinematic model and the remaining interception time. The calculation formula of the remaining interception time is as follows:

Among them, t _fPiE represents the interception time, and t represents the time.

The control module 1506 is configured to control the line-of-sight angles of the two interceptors according to the optimal control input, so as to realize the tracking and interception of the target.

The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments, and the same and similar parts between the various embodiments can be referred to each other. For the system disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant part can be referred to the description of the method.

In the present invention, specific examples are used to illustrate the principles and implementations of the present invention, and the descriptions of the above embodiments are only used to help understand the method and the core idea of the present invention; There will be changes in the specific implementation manner and application scope of the idea of the invention. In conclusion, the contents of this specification should not be construed as limiting the present invention.

Claims (10)

1. a multi-aircraft collaborative detection and guidance integration method is characterized in that, comprising: Obtain the initial lateral distance between the interceptor and the maneuvering target, the initial lateral relative velocity between the interceptor and the maneuvering target, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor; determining an initial state vector according to the initial lateral distance, the lateral relative velocity, the initial acceleration of the maneuvering target, and the initial acceleration of the interceptor; determining measurement information according to the initial state vector and interceptor noise; Based on the measurement information, an estimated state vector is obtained through interactive multi-model filtering; According to the estimated state vector, determine the optimal control input; The line-of-sight angles of the two interceptors are controlled according to the optimal control input, so as to realize the tracking and interception of the target. 2. The integrated method for multi-aircraft collaborative detection and guidance according to claim 1, wherein the estimated state vector is obtained by interactive multi-model filtering based on the measurement information, specifically comprising: calculating a mixing probability according to the measurement information; determining initial conditions according to the mixing probability; Perform interactive multi-model filtering according to the initial conditions to obtain a likelihood function; Update the model probability through the likelihood function; Estimate the state vector from the updated model probabilities. 3 . The method for integrating multi-aircraft cooperative detection and guidance according to claim 1 , wherein, determining the optimal control input according to the estimated state vector, specifically comprising: 3 . determining a kinematic model according to the estimated state vector; The optimal control input is determined based on the kinematic model and the remaining interception time. 4. The multi-aircraft collaborative detection and guidance integration method according to claim 1, wherein the calculation formula of the initial state vector is as follows:

where _yi is the lateral distance between the interceptor and the maneuvering target,

is the lateral relative velocity between the interceptor and the maneuvering target, a _E is the initial acceleration of the maneuvering target, and a _Pi is the initial acceleration of the interceptor. 5. The multi-aircraft collaborative detection and guidance integration method according to claim 3, wherein the calculation formula of the remaining interception time is as follows:

Among them, t _fPiE represents the interception time, and t represents the time. 6. A multi-aircraft collaborative detection and guidance integrated system, characterized in that, comprising: The data acquisition module is used to acquire the initial lateral distance between the interceptor and the maneuvering target, the initial lateral relative velocity between the interceptor and the maneuvering target, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor; an initial state vector determination module, configured to determine an initial state vector according to the initial lateral distance, the lateral relative velocity, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor; determining an initial state vector determining module for determining measurement information according to the initial state vector and the noise of the interceptor; an estimation module, based on the measurement information, to obtain an estimated state vector through interactive multi-model filtering; an optimal control input determination module, configured to determine the optimal control input according to the estimated state vector; The control module is used for controlling the line-of-sight angles of the two interceptors according to the optimal control input, so as to realize the tracking and interception of the target. 7. The multi-aircraft collaborative detection and guidance integrated system according to claim 6, wherein the estimation module specifically comprises: a mixing probability calculation unit, configured to calculate the mixing probability according to the measurement information; an initial condition determining unit, configured to determine an initial condition according to the mixing probability; a likelihood function determination unit, configured to perform interactive multi-model filtering according to the initial conditions to obtain a likelihood function; an update unit for updating the model probability through the likelihood function; Estimation unit for estimating the state vector according to the updated model probability. 8. The multi-aircraft collaborative detection and guidance integrated system according to claim 6, wherein the optimal control input determination module specifically comprises: a kinematic model determining unit, configured to determine a kinematic model according to the estimated state vector; and an optimal control input determination unit, configured to determine the optimal control input according to the kinematic model and the remaining interception time. 9. The multi-aircraft collaborative detection and guidance integrated system according to claim 6, wherein the calculation formula of the initial state vector is as follows:

where _yi is the lateral distance between the interceptor and the maneuvering target,

is the lateral relative velocity between the interceptor and the maneuvering target, a _E is the initial acceleration of the maneuvering target, and a _Pi is the initial acceleration of the interceptor. 10. The multi-aircraft collaborative detection and guidance integrated system according to claim 8, wherein the calculation formula of the remaining interception time is as follows:

Among them, t _fPiE represents the interception time, and t represents the time.

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