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

Abstract

The present invention discloses an integrated method and system for cooperative detection and guidance of multiple aircraft. The method includes: obtaining the initial lateral distance between the interceptor and the maneuvering target, the initial lateral relative speed between the interceptor and the maneuvering target, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor; determining the initial state vector according to the initial lateral distance, the lateral relative speed, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor; determining the measurement information according to the initial state vector and the interceptor noise; obtaining the estimated state vector through interactive multi-model filtering based on the measurement information; determining the optimal control input according to the estimated state vector; controlling the line of sight angle of the two interceptors according to the optimal control input to achieve tracking and interception of the target. The present invention introduces interactive multi-model filtering to identify the switching time and state of the target maneuver, modulates the line of sight separation angle of the two interceptors, enhances the target detection accuracy, and achieves target tracking and interception.

Description

Technical Field

[0001] The present invention relates to the field of target tracking, and in particular to a method and system for integrating multi-aircraft cooperative detection and guidance. Background Art

[0002] 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 impact of the relative detection configuration on the accuracy of intercepting the target, because when using the method of multi-aircraft cooperative angle measurement to further estimate the distance information, if the multiple aircraft are collinear with the target, the relative distance cannot be estimated, and the estimation error is large when they are approximately collinear. Therefore, it is necessary to consider the impact of the relative detection configuration of the two interceptors on the interception accuracy during the design of the guidance law. In addition, for the method of estimating the target state using the traditional KF / SF, its adaptability to the multi-modal motion mode performing the bang-bang maneuver is low, and the error in the target state estimation accuracy is large. Summary of the invention

[0003] The purpose of the present invention is to provide a method and system for integrated detection and guidance of multiple aircraft, which can enhance the target detection accuracy and achieve target tracking and interception by modulating the line of sight separation angle of two interceptors.

[0004] To achieve the above object, the present invention provides the following solutions:

[0005] A multi-aircraft cooperative detection and guidance integrated method, comprising:

[0006] Obtaining an initial lateral distance between the interceptor and the maneuvering target, an initial lateral relative speed between the interceptor and the maneuvering target, an initial acceleration of the maneuvering target, and an initial acceleration of the interceptor;

[0007] determining an initial state vector according to the initial lateral distance, the lateral relative speed, the initial acceleration of the maneuvering target, and the initial acceleration of the interceptor;

[0008] Determining measurement information based on the initial state vector and interceptor noise;

[0009] Based on the measurement information, an estimated state vector is obtained through interactive multi-model filtering;

[0010] determining an optimal control input based on the estimated state vector;

[0011] The sight angles of the two interceptors are controlled according to the optimal control input to achieve tracking and interception of the target.

[0012] Optionally, obtaining an estimated state vector through interactive multi-model filtering based on the measurement information specifically includes:

[0013] Calculating a mixing probability based on the measurement information;

[0014] determining initial conditions based on the mixing probability;

[0015] Performing interactive multi-model filtering according to the initial conditions to obtain a likelihood function;

[0016] Updating the model probability by using the likelihood function;

[0017] Estimate the state vector based on the updated model probabilities.

[0018] Optionally, determining the optimal control input according to the estimated state vector specifically includes:

[0019] determining a kinematic model based on the estimated state vector;

[0020] An optimal control input is determined based on the kinematic model and the remaining interception time.

[0021] Optionally, the calculation formula of the initial state vector is as follows:

[0022]

[0023] In the formula, y i is the lateral distance between the interceptor and the maneuvering target, is the lateral relative speed between the interceptor and the maneuvering target, a E is the initial acceleration of the maneuvering target, a Pi is the initial acceleration of the interceptor.

[0024] Optionally, the calculation formula of the remaining interception time is as follows:

[0025]

[0026] Among them, t fPiE represents the interception time, and t represents the time.

[0027] The present invention also provides a multi-aircraft cooperative detection and guidance integrated system, comprising:

[0028] A data acquisition module, used to acquire an initial lateral distance between the interceptor and the maneuvering target, an initial lateral relative speed between the interceptor and the maneuvering target, an initial acceleration of the maneuvering target, and an initial acceleration of the interceptor;

[0029] an initial state vector determination module, configured to determine an initial state vector according to the initial lateral distance, the lateral relative speed, the initial acceleration of the maneuvering target, and the initial acceleration of the interceptor;

[0030] Determine an initial state vector determination module, used to determine measurement information according to the initial state vector and interceptor noise;

[0031] An estimation module, based on the measurement information, obtains an estimated state vector through interactive multi-model filtering;

[0032] An optimal control input determination module, used to determine an optimal control input according to the estimated state vector;

[0033] The control module is used to control the sight angles of the two interceptors according to the optimal control input to achieve tracking and interception of the target.

[0034] Optionally, the estimation module specifically includes:

[0035] A mixing probability calculation unit, used to calculate the mixing probability according to the measurement information;

[0036] an initial condition determination unit, configured to determine an initial condition according to the mixing probability;

[0037] A likelihood function determination unit, used for performing interactive multi-model filtering according to the initial conditions to obtain a likelihood function;

[0038] An updating unit, used for updating the model probability by using the likelihood function;

[0039] An estimation unit, used to estimate the state vector based on the updated model probability.

[0040] Optionally, the optimal control input determination module specifically includes:

[0041] A kinematic model determination unit, configured to determine a kinematic model according to the estimated state vector;

[0042] The optimal control input determination unit is used to determine the optimal control input according to the kinematic model and the remaining interception time.

[0043] Optionally, the calculation formula of the initial state vector is as follows:

[0044]

[0045] In the formula, y i is the lateral distance between the interceptor and the maneuvering target, is the lateral relative speed between the interceptor and the maneuvering target, a E is the initial acceleration of the maneuvering target, aPi is the initial acceleration of the interceptor.

[0046] Optionally, the calculation formula of the remaining interception time is as follows:

[0047]

[0048] Among them, t fPiE represents the interception time, and t represents the time.

[0049] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0050] The present invention determines measurement information based on 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, an optimal control input is determined; according to the optimal control input, the sight angles of the two interceptors are controlled to achieve tracking and interception of the target. The present invention introduces interactive multi-model filtering to identify the switching time of the target maneuver and estimate the target state, modulate the sight separation angle of the two interceptors, enhance the target detection accuracy, and achieve target tracking and interception. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0052] Figure 1 This is a flow chart of a method for integrated multi-aircraft cooperative detection and guidance according to an embodiment of the present invention;

[0053] Figure 2 Motion model for engagement between two interceptors and a maneuvering target;

[0054] Figure 3 The engagement diagram for the coordinated interception of a maneuvering target by Interceptor 1 and Interceptor 2;

[0055] Figure 4 It is a schematic diagram of the acceleration changes of the two interceptors;

[0056] Figure 5 is the modulus probability variation diagram of the element filter of interceptor 1;

[0057] Figure 6 The estimation of the interceptor 1 acceleration by IMM filtering and KF / SF;

[0058] Figure 7 is the position, velocity and acceleration estimation error of I interceptor 1;

[0059] Figure 8 Estimated errors for the position, velocity, and acceleration of interceptor 2

[0060] Fig. 9 is the noise variation diagram of the lateral displacement measurement between the interceptor 1 and the target under different guidance laws;

[0061] Fig.10 The diagram of the change of the line of sight separation angle between the two interceptors under different guidance laws and estimation methods;

[0062] Fig.11 is the miss distance CDF of interceptor 1 under APN combined with IMM, the proposed guidance law combined with KF / SF and IMM;

[0063] Fig.12 is the miss distance CDF of interceptor 2 under APN combined with IMM, the proposed guidance law combined with KF / SF and IMM;

[0064] Fig.13 is the average miss distance of interceptor 1 for different switching times under APN combined with IMM, and the proposed guidance law combined with KF / SF and IMM;

[0065] Fig.14 is the average miss distance of interceptor 2 for different switching times under APN combined with IMM, and the proposed guidance law combined with KF / SF and IMM;

[0066] Fig.15 The present invention is a block diagram of the structure of a multi-aircraft collaborative detection and guidance integrated system according to an embodiment of the present invention. DETAILED DESCRIPTION

[0067] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0068] The purpose of the present invention is to provide a method and system for integrated detection and guidance of multiple aircraft, which can enhance the target detection accuracy and achieve target tracking and interception by modulating the line of sight separation angle of two interceptors.

[0069] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments.

[0070] like Figure 1As shown, a multi-aircraft collaborative detection and guidance integration method includes the following steps:

[0071] Step 101: Obtain an initial lateral distance between the interceptor and the maneuvering target, an initial lateral relative speed between the interceptor and the maneuvering target, an initial acceleration of the maneuvering target, and an initial acceleration of the interceptor.

[0072] Step 102: Determine an initial state vector according to the initial lateral distance, the lateral relative speed, 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:

[0073]

[0074] In the formula, y i is the lateral distance between the interceptor and the maneuvering target, is the lateral relative speed between the interceptor and the maneuvering target, a E is the initial acceleration of the maneuvering target, a Pi is the initial acceleration of the interceptor.

[0075] Step 103: Determine measurement information according to the initial state vector and interceptor noise.

[0076] Step 104: Based on the measurement information, an estimated state vector is obtained through interactive multi-model filtering. Specifically, the method includes: calculating the mixing probability according to the measurement information; determining the 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; and estimating the state vector according to the updated model probability.

[0077] 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; determining 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:

[0078]

[0079] Among them, t fPiE represents the interception time, and t represents the time.

[0080] Step 106: Control the sight angles of the two interceptors according to the optimal control input to achieve tracking and interception of the target.

[0081] The method principle of the present invention is described in detail below:

[0082] 1. Problem description and establishment of relative kinematics equations

[0083] Assume that two of our interceptors intercept an enemy target that can perform the best bang-bang evasion maneuver. In this case, there are two important factors to consider: First, the interceptors need to adopt effective estimation methods to detect the random changes of the target and accurately estimate the state of the target. The other is that the relative detection configuration of the two interceptors can affect the detection accuracy of the target state information.

[0084] In X I -O I -Y I The dynamic and kinematic models are established in the inertial coordinate system. Pi and E represent the interceptor and maneuvering target respectively. a, v, λ, r and γ represent the normal acceleration, velocity, line of sight angle, relative distance and heading angle respectively. Figure 2 Shown is the engagement motion model of two interceptors and a maneuvering target.

[0085] (1) Establishing dynamic and kinematic models

[0086] 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, that is,

[0087]

[0088]

[0089] 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 speeds of the interceptor and maneuvering target, respectively; and are the initial flight path angles of the interceptor and maneuvering target respectively; PiE is the line of sight angle between the interceptor and the maneuvering target.

[0090] Since the direction of acceleration is always perpendicular to the direction of velocity during the entire guidance process, the speed of the interceptor and the maneuvering target is always constant. Therefore, the relationship between the normal acceleration and heading angle of the aircraft can be expressed as

[0091]

[0092] When the flight process of the two aircraft (interceptors) can be approximated as a nominal collision triangle, the above process can be linearized. Figure 2 In the described engagement process, there are two collision triangles formed by the two pursuers and the maneuvering target respectively.

[0093] After linearizing the above process, the present invention can select the state vector

[0094]

[0095] Where: is the lateral distance between the interceptor Pi and the maneuvering target E, is the lateral relative velocity, y Pi and E are the lateral distances of the interceptor and the maneuvering target relative to the initial position, a E is the initial acceleration of the maneuvering target, a Pi is the initial acceleration of the interceptor.

[0096] 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

[0097]

[0098] Where: τ Pi and τ E are the overload response time constants of the interceptor and maneuvering target, respectively, is the command acceleration of the interceptor.

[0099] The matrix form of equation (5) is

[0100]

[0101] Where:

[0102] 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 satisfies the constraints is the command acceleration of the maneuvering target, and w is the noise of the guidance process.

[0103] The initial distance between the interceptor and the maneuvering target can be expressed as and Under the assumption of a nominal collision triangle, the heading angle γ i and the sight angle λ PiE The deviation between them is very small. Therefore, the interception time of the interceptor for the maneuvering target is constant and can be expressed as

[0104]

[0105] The present invention considers the special case where two interceptors simultaneously intercept a maneuvering target, then their interception times are equal, that is, t fP1E =t fP2ETherefore, the initial distances between them are also equal, that is,

[0106] (2) Establishing the measurement model of the aircraft

[0107] Each interceptor uses its own sensor to measure the sight angle λ PiE In addition, each sensor is subjected to Gaussian white noise v Pi The present invention assumes that the line of sight angle measurement noise of each interceptor follows the distribution

[0108]

[0109] from Figure 2 As can be seen from the figure, during the engagement, the two interceptors can form a measurement baseline relative to the maneuvering target. Assuming that the interceptors can accurately measure their relative state and they can share their measurement information with each other, the relative position information between them (r,λ PiPj ), i,j=1,2,i≠j can be obtained.

[0110] Therefore, the relative distance information r and the sight angle information λ of the two interceptors are known. P1P2 , can calculate the relative distance between the two interceptors and the maneuvering target

[0111]

[0112] Where:

[0113]

[0114] λ P1P2 =arctan2(y P2 -y P1 ,x P2 -x P1 ) (11)

[0115] Where: x P1 and x P2 are the coordinates of pursuer 1 and pursuer 2 on the horizontal axis, y P1 and P2 are the coordinates of pursuer 1 and pursuer 2 on the vertical axis respectively.

[0116] Under the linearization assumption of the nominal collision triangle, the lateral displacement yi perpendicular to the initial line of sight angle can be expressed as

[0117] y i ≈(λ PiE -λ PiE0 )r PiE (12)

[0118] r PiE ≈v PiE t go (13)

[0119] Where: t go The remaining time for interception.

[0120]

[0121] Combined with equation (9), we can get the interceptor measurement equation:

[0122]

[0123] Where: H = [1 0 0 0]

[0124]

[0125]

[0126] From formula (16), we can see that when the line of sight separation angle between the two interceptors |λ PiE -λ PjE When | decreases, the lateral displacement y i The measurement variance will increase, resulting in a decrease in the accuracy of state estimation. 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.

[0127] (3) Establish performance indicators

[0128] The successful interception of a maneuvering target by an interceptor requires a very small terminal miss or a direct hit. However, due to the influence of various factors, the interceptor cannot hit the maneuvering target with high accuracy. In particular, the method of estimating the state of the maneuvering target seriously restricts the guidance accuracy of the interceptor. Because it is difficult to obtain a kill model affected by multiple factors in a real combat environment, the present invention uses a simplified kill function to evaluate the possibility of destroying the target:

[0129]

[0130] Where: M is the terminal miss distance of the interceptor, R k It is the killing range of the interceptor warhead.

[0131] The miss distance, which is an indicator of whether the interception is successful or not, is affected by the random maneuvers of the target and the measurement noise of the detection process. Therefore, the miss distance is a randomly changing quantity. The present invention generally uses the cumulative distribution function CDF (Cumulative Distribution Function) as an empirical estimate to evaluate the impact of the miss distance on the guidance accuracy, and uses it to compare the guidance performance between different guidance laws. Therefore, the present invention can determine whether the interception is successful by using a predetermined kill probability under given LR conditions. The kill probability can be defined as

[0132] SSKP(R k )=E{P d (M,R k )} (19)

[0133] Where: E is the mathematical expectation of the random variable of the miss distance. The SSKP can be calculated by CDF, and its formula is:

[0134]

[0135] Where: f M and F M They are probability density function PDF (Probability Density Function) and CDF respectively. The interception probability is generally taken as 0.95, and the performance index can be obtained:

[0136]

[0137] 2. Design of cooperative guidance law

[0138] The main factor considered in the guidance law design 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, then the line of sight separation angle between the two interceptors may become smaller, thereby causing the detection error to increase. Therefore, the interceptor of the present invention needs to control the line of sight separation angle at 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.

[0139] The present invention takes the miss distance and energy consumption into consideration and adopts the optimal control theory to achieve the purpose of the above-mentioned cooperative guidance.

[0140] (1) Objective function

[0141] Under the assumption of a nominal collision triangle, the lateral displacement of the interceptor can be approximated as

[0142]

[0143] r PiE ≈v PiE t go (twenty three)

[0144] Combining equations (22) and (23), the sight angle λ PiE can be approximated as

[0145]

[0146] Import Item The performance index for establishing optimal control is

[0147]

[0148] The present invention uses replace To avoid singularity in subsequent calculations and derivations of formulas. When Δt→0, The present invention makes a→∞, and can obtain a guidance law in which the miss distance tends to 0. Note that if the weight c i > 0, the sight angle will be minimized if c i <0, the sight angle will be maximized.

[0149] (2) Downscaling

[0150] 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 for order reduction. This requires the present invention to introduce a new state variable, defined as

[0151] Z i (t) = DΦ i (t f ,t)x i (t) (26)

[0152]

[0153] Where: Φ i (t f ,t) is and A i The associated state transition matrix.

[0154] Combining equation (27) and the derivative of the new state variable with respect to time, the present invention can obtain

[0155]

[0156] Formula (28) shows that is state-independent and only related to the designed controller. In addition, the present invention converts DΦ i (t f ,t)Bi Mark as

[0157] Using the terminal projection method to reduce the order, the objective function (25) can be expressed by the new state variables

[0158]

[0159] Where: a i 、b i and c i is the weight coefficient, Z i (t f ) is the zero-effective miss distance at the interception moment.

[0160] (3) Optimal controller design

[0161] The Hamiltonian function of the performance index is

[0162]

[0163] Where: Z is the adjoint vector.

[0164] The time derivatives of the new state variables are state-independent, which greatly simplifies the adjoint equation.

[0165]

[0166] λ Z (t f )=a i Z i (t f ) (32)

[0167] Transform equation (31) from t f Integrate to t, and substitute equation (32) into

[0168]

[0169] From the control equation we can get

[0170]

[0171] Substituting equation (34) into equation (28) yields

[0172]

[0173] Transform (35) from t to t f Points can be earned

[0174]

[0175] Where:

[0176] So we can solve for Z i (t f )for

[0177]

[0178] Z i (t f ) is substituted into equation (34), the optimal controller can be obtained

[0179]

[0180] When a→∞, the perfect interception guidance law with an interception miss distance of 0 can be obtained, that is,

[0181]

[0182] 3. Interactive Multi-Model Filtering for Tracking Target Maneuvers

[0183] Interactive multi-model (IMM) filtering is designed to estimate hybrid system models, such as the target bang-bang maneuver described above. In such a system, the system dynamics model belongs to a finite set, and the models can be transferred with a certain probability. In interactive multi-model filtering, there are Kalman filters matching different models, and they run simultaneously. The input of each filter is obtained by the state interaction between filters according to the probability transfer matrix. All filters calculate such values ​​at the next moment based on the model probabilities, prior state estimates, variances, likelihood functions and probability transfer matrices obtained at the previous moment. In addition, the output of interactive multi-model filtering is obtained by interactive mixing of all filters.

[0184] (1) Filtering algorithm

[0185] 1) Mixing probability

[0186] The last measurement information z k-1 The probability that mode i at time k-1 affects mode j at time k can be calculated by Bayes' rule.

[0187]

[0188] Where: is the conditional mixing probability of the ith mode at time k-1, is the modulus probability of the ith mode at time k-1. Using the total probability theory and the probability transfer matrix that conforms to the Markov chain, equation (40) can be written as

[0189]

[0190] Where: πij is the transition probability between modes.

[0191] 2) Initial conditions

[0192] The initial condition of each filter after interactive input can be obtained by the weight sum of each filter related to the mixing probability, that is,

[0193]

[0194]

[0195] Where: and are the estimated state and variance of the ith mode at time k-1 respectively.

[0196] 3) Model Matched Filtering

[0197] 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

[0198] According to the current filtering information and its variance matrix The conditional likelihood function of the jth filter can be calculated This likelihood function will be used in the subsequent modular probability update process.

[0199]

[0200] Where: m is the measurement number.

[0201] 4) Pattern probability update

[0202] According to Bayes' rule, the modulus probability at time k can be updated

[0203]

[0204] Applying the total probability theory, we can get:

[0205]

[0206] (5) Mixed estimation state and variance

[0207] After interaction, the mixed estimated state and variance are output

[0208]

[0209]

[0210] (2) Maneuvering target tracking and model matching filtering

[0211] For the bang-bang maneuver taken by the target, the interactive multi-model filter is mainly used to identify the switching time of the target maneuver and estimate the state of the target. The bang-bang maneuver of the target mainly has two modes, namely the maximum positive acceleration mode and the maximum negative acceleration mode, which can be written as

[0212]

[0213] Where: is the maximum target acceleration command, and r represents the maneuvering mode of the target.

[0214] Assuming that the transition process between maneuver modes is a first-order Markov chain, the transition probability can be defined as

[0215] π ij =Pr{r k =j|r k-1 =i},(i,j∈S) (50)

[0216] Where: Because the target adopts the form of bang-bang maneuver, there are two modes, so s=2.

[0217] When there is no external measurement information, the transition probability matrix between modes is obtained as follows:

[0218]

[0219] Where: Δt is the simulation calculation step; δ is a non-negative number not greater than 1, and its theoretical value is 0. In order to ensure that the mode conversion process is a Markov chain, it is set to a positive number close to 0.

[0220] Calculate the prior state estimate at time k and the error variance matrix Prior state estimate It can be given by formula (6), and the error variance matrix can be calculated by the following formula:

[0221]

[0222] Where: Φ k|k-1 is the state transfer matrix from time k-1 to time k, Q k-1 is the discrete process noise.

[0223] Calculate the new information at time k and its variance matrix

[0224]

[0225]

[0226] Where: H represents the measurement matrix, R k is the measurement noise variance matrix at time k.

[0227] Calculate the filter gain at time k State mean and variance matrix

[0228]

[0229]

[0230]

[0231] (3) Target maneuver detection

[0232] Since the switching time of the target bang-bang maneuver is random, the estimation process of the target maneuver is also random. Trying to use a certain quantitative model to approximate this process can effectively study its impact on the closed-loop interception performance. In modern guidance laws designed by widely using target acceleration information, most of the error sources are caused by inaccurate estimates of acceleration. Although there are many effective and accurate estimation methods, the estimation of acceleration will inevitably produce time delays in the estimation, because in actual situations, the present invention can only obtain the azimuth information of the target. Because in the established model, the lateral displacement of the aircraft is approximately perpendicular to the line of sight, and before the lateral displacement information is obtained, the acceleration needs to undergo two integrations, so this is the reason why the estimated target maneuver command will be delayed compared to the actual command.

[0233] Hexner et al. proposed a lower bound on the time of maneuver command detection that is independent of the estimation method. Therefore, no matter when the maneuver command switch occurs, it is assumed that the IMM filter can detect the time interval T after the maneuver command switch occurs. id If the filter is T id If it is not recognized within the time, that is, the modulus probability of the corresponding filter is always lower than the pre-set threshold, then it will not be recognized at any time thereafter. According to the literature, T id Can be defined as

[0234]

[0235]

[0236] Where: s f is the tuning parameter, is the minimum detection time of maneuver 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 of the measurement noise, it can be detected that the target has maneuvered.

[0237] 4. Simulation analysis

[0238] The present invention will conduct numerical simulation verification on the proposed collaborative guidance law and IMM filter. First, the present invention sets the simulation parameters and preliminarily analyzes the engagement situation of three aircraft. Then, the present invention explores the influence of the collaborative guidance law and IMM filter on the detection and guidance performance of maneuvering targets, and introduces Monte Carlo (MC) to evaluate them. There are two main factors that affect the guidance and detection performance of interceptors: one is the detection configuration of the two interceptors during the guidance process; the other is the detection ability of the IMM filter for the target maneuver switching time. Finally, the present invention compares the proposed collaborative guidance law using IMM filtering with the guidance law using Kalman filtering with shaping filter (KF / SF) and the extended proportional guidance law (APNG) using IMM filtering.

[0239] (1) Simulation parameters and combat situations

[0240] According to the designed guidance law, the simulation parameters are set as follows: Interceptor 1 and Interceptor 2 are launched simultaneously, and the initial distance to the maneuvering target is The initial lateral displacements are and The speeds of the interceptor and target are v Pi =2000m / s and v E =1000m / s. Ignoring the effect of gravity, the overload limits of the interceptor and target are and The overload response time constants are τ Pi = 0.2s and τ E =0.2s. The simulation time interval is set to Δ=0.001s, and the standard deviation of the line of sight angle measurement noise is σ Pi,λ = 1mrad. The IMM filter sets two maneuvering modes for the target's bang-bang maneuver, so two element filters need to run simultaneously.

[0241] The performance of different estimation methods and guidance laws, including the proposed cooperative guidance law using IMM filtering and KF / SF respectively, and APNG using IMM filtering, are evaluated by setting 100 MC simulations with random target maneuver switching times.

[0242] Figure 3 This is a picture of the engagement of interceptor 1 and interceptor 2 working together to intercept a maneuvering target. Figure 3It can be seen that the proposed cooperative guidance law can modulate the trajectories of the two interceptors to separate them from each other to increase their line-of-sight separation angle, thereby avoiding detection errors caused by the guidance configuration. Figure 4 is the acceleration change of the two interceptors, from Figure 4 It can be seen that the acceleration of the two interceptors did not exceed the overload limit. Figure 3 and Figure 4 Since Interceptor 2 does not need large-scale maneuvers, its requirements for maneuverability are not high. Interceptor 1 needs to cooperate with Interceptor 2 to increase the line of sight separation angle between them. Therefore, compared with the initial state advantage of Interceptor 2, Interceptor 1 needs to pay a greater maneuvering cost to achieve the guidance purpose.

[0243] (2) Estimation performance evaluation

[0244] 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 impact of the guidance configuration on the detection effectiveness.

[0245] Figure 5 This is the modulus probability variation diagram of the element filter of interceptor 1. Figure 6 is the IMM filter and KF / SF estimate of the interceptor 1 acceleration. Figure 5 It can be seen that before the target maneuver switch occurs, filter 2 has a higher modulus probability, which means that the maneuvering target adopts mode 2, that is, the maximum forward acceleration mode. At about 2 seconds, the IMM filter recognizes that the target maneuver has switched, and the target switches from executing the maneuver at 1.6 seconds to detecting it at 2 seconds, which takes 0.4 seconds, which is much shorter than the required minimum detection time interval. The detection time of 0.4s is reasonable and effective. The fast convergence of all state errors, especially the acceleration estimation error, has a great impact on the terminal miss distance. Figure 6 It can be seen that compared with KF / SF, IMM filtering has a faster response and more accurate acceleration estimation performance for the maneuvering switching of the target.

[0246] Figure 7 and Figure 8 The interceptor position, velocity and acceleration estimation errors are given. As can be seen from the figure, both filters produce large fluctuations in the estimation of acceleration around 2s. Figure 6 , which is caused by the time delay in estimating the target maneuver switching. Compared with KF / SF, IMM filtering has a lower estimation error for acceleration. The accurate estimation of acceleration by IMM filtering also enables it to accurately estimate position and velocity.

[0247] Fig. 9 The diagram shows the noise variation of the lateral displacement measurement between the interceptor 1 and the target under different guidance laws. Fig.10 The following is a graph showing the change in the line of sight separation angle between the two interceptors under different guidance laws and estimation methods. By comparing the two figures, it can be seen that the use of the APN combined with the IMM method will make the line of sight separation angle very small during the entire guidance process, which leads to a large detection error noise. This is because the APN cannot control the line of sight separation angle between the two aircraft. Fig.10 It can be seen that the proposed guidance law can control the line of sight separation angle between the two aircraft and can gradually increase the line of sight separation angle. The measurement noise decreases with the increase of the line of sight separation angle and approaches 0 in the end, which shows that the proposed guidance law can reduce the detection error of the two aircraft.

[0248] (3) Off-target amount assessment

[0249] 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. Fig.11 and Fig.12 The CDF of the miss distance of the two interceptors is shown, 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 the kill range of 9.47m required for APN combined with IMM and the kill range of 22.86m required for the proposed guidance law combined with KF / SF, the kill range of the proposed guidance law combined with IMM is only 0.81m. Fig.11 and Fig.12 As shown in , the proposed guidance law combined with IMM has better interception performance than the other two guidance and estimation methods. Fig.11 and Fig.12 The method of using IMM to estimate acceleration makes the two interceptors have similar interception performance, and the warhead damage ranges required to ensure a 95% kill probability are relatively close. However, the method of using KF / SF to estimate acceleration makes the interception performance of the two interceptors have a large difference, and the warhead damage ranges required by them are quite different. On the one hand, this is caused by the inaccurate estimation of acceleration, and on the other hand, this is because the maneuvering cost required by interceptor 1 is large.

[0250] Table 1 Warhead damage range required to ensure 95% kill probability for APN combined with IMM, proposed guidance law combined with KF / SF and IMM

[0251]

[0252] Fig.13 and Fig.14is the average miss amount of the two interceptors for different switching times. As can be seen from the figure, for APN combined with IMM, when the target is concentrated in 1.5s to 4s for switching maneuvers, the interception miss amount will be generated; for the proposed guidance law combined with KF / SF, when the target is switching maneuvers from 1.7s to 4s, it will cause interceptor 1 to have a miss amount, and when the target is switching maneuvers from 3.3s to 4s, it will cause interceptor 2 to have a miss amount; for the proposed guidance law combined with IMM, when the target is switching maneuvers from 3.3s to 4s, it will cause an interception miss amount, and the interception miss amount generated is the smallest among them, which shows that the proposed guidance law combined with IMM has better guidance accuracy. The reason why APN combined with IMM will produce miss amount is that it cannot modulate the line of sight separation angle during the guidance process, which makes the two interceptors produce large detection errors; although the proposed guidance law combined with KF / SF avoids the excessive detection error caused by the inability to modulate the line of sight separation angle, the main reason affecting its detection accuracy is the inaccurate acceleration of the target. In addition, for all guidance and estimation methods, their miss distances increase first and then decrease as the maneuver switching time increases. The miss distance increases first because the closer the target is to the guidance terminal for switching maneuvers, the less time the interceptor has to react. The filter delay makes it impossible for the interceptor to change the command in time, which ultimately leads to a large miss distance. The reason why the miss distance then decreases is that if the target switches maneuvers too late, the target will not have time to change direction and escape, which reduces the miss distance again.

[0253] like Fig.15 As shown, the present invention also provides a multi-aircraft cooperative detection and guidance integrated system, comprising:

[0254] The data acquisition module 1501 is used to acquire the initial lateral distance between the interceptor and the maneuvering target, the initial lateral relative speed between the interceptor and the maneuvering target, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor.

[0255] The initial state vector determination module 1502 is used to determine the initial state vector according to the initial lateral distance, the lateral relative speed, the initial acceleration of the maneuvering target and the initial acceleration of the interceptor.

[0256] The calculation formula of the initial state vector is as follows:

[0257]

[0258] In the formula, y i is the lateral distance between the interceptor and the maneuvering target, is the lateral relative speed between the interceptor and the maneuvering target, a E is the initial acceleration of the maneuvering target, a Pi is the initial acceleration of the interceptor.

[0259] An initial state vector determination module 1503 is configured to determine measurement information according to the initial state vector and interceptor noise.

[0260] The estimation module 1504 obtains an estimated state vector through interactive multiple model filtering based on the measurement information.

[0261] The estimation module 1504 specifically includes:

[0262] A mixing probability calculation unit, used to calculate the mixing probability according to the measurement information;

[0263] an initial condition determination unit, configured to determine an initial condition according to the mixing probability;

[0264] A likelihood function determination unit, used for performing interactive multi-model filtering according to the initial conditions to obtain a likelihood function;

[0265] An updating unit, used for updating the model probability by using the likelihood function;

[0266] An estimation unit, used to estimate the state vector based on the updated model probability.

[0267] The optimal control input determination module 1505 is used to determine the optimal control input according to the estimated state vector.

[0268] The optimal control input determination module 1505 specifically includes:

[0269] A kinematic model determination unit, configured to determine a kinematic model according to the estimated state vector;

[0270] The optimal control input determination unit is used 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:

[0271]

[0272] Among them, t fPiE represents the interception time, and t represents the time.

[0273] The control module 1506 is used to control the sight angles of the two interceptors according to the optimal control input to achieve tracking and interception of the target.

[0274] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the 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 parts can be referred to the method part.

[0275] The present invention uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only used to help understand the method and core ideas of the present invention. At the same time, for those skilled in the art, according to the ideas of the present invention, there will be changes in the specific implementation methods and application scope. In summary, the content of this specification should not be understood as limiting the present invention.

Claims

1. A method for integrated detection and guidance of multiple aircraft, characterized in that: include: Obtaining an initial lateral distance between the interceptor and the maneuvering target, an initial lateral relative speed between the interceptor and the maneuvering target, an initial acceleration of the maneuvering target, and an initial acceleration of the interceptor; determining an initial state vector according to the initial lateral distance, the lateral relative speed, 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: In the formula, y i is the lateral distance between the interceptor and the maneuvering target, is the lateral relative speed between the interceptor and the maneuvering target, a E is the initial acceleration of the maneuvering target, a Pi is the initial acceleration of the interceptor; Determining measurement information based on the initial state vector and interceptor noise; Based on the measurement information, an estimated state vector is obtained through interactive multi-model filtering, specifically including: Calculating a mixing probability based on the measurement information; determining initial conditions based on the mixing probability; Performing interactive multi-model filtering according to the initial conditions to obtain a likelihood function; Updating the model probability by using the likelihood function; Estimate the state vector based on the updated model probability; Determining an optimal control input according to the estimated state vector specifically includes: determining a kinematic model based on the estimated state vector; determining an optimal control input based on 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, t represents the time; Controlling the sight angles of the two interceptors according to the optimal control input to achieve tracking and interception of the target specifically includes: Ignoring the effect of gravity, the engagement process between the interceptor and the maneuvering target is expressed in the form of polar coordinates (r, λ) related to the maneuvering target, that is, 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 speeds of the interceptor and maneuvering target, respectively; and are the initial flight path angles of the interceptor and maneuvering target respectively; PiE is the line of sight angle between the interceptor and the maneuvering target.

2. A multi-aircraft cooperative detection and guidance integrated system, characterized in that: include: A data acquisition module, used to acquire an initial lateral distance between the interceptor and the maneuvering target, an initial lateral relative speed between the interceptor and the maneuvering target, an initial acceleration of the maneuvering target, and an 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 speed, 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: In the formula, y i is the lateral distance between the interceptor and the maneuvering target, is the lateral relative speed between the interceptor and the maneuvering target, a E is the initial acceleration of the maneuvering target, a Pi is the initial acceleration of the interceptor; Determine an initial state vector determination module, used to determine measurement information according to the initial state vector and interceptor noise; The estimation module obtains an estimated state vector through interactive multi-model filtering based on the measurement information, specifically comprising: A mixing probability calculation unit, used to calculate the mixing probability according to the measurement information; an initial condition determination unit, configured to determine an initial condition according to the mixing probability; A likelihood function determination unit, used for performing interactive multi-model filtering according to the initial conditions to obtain a likelihood function; An updating unit, used for updating the model probability by using the likelihood function; an estimation unit, for estimating a state vector according to the updated model probability; The optimal control input determination module is used to determine the optimal control input according to the estimated state vector, specifically comprising: A kinematic model determination unit, configured to determine a kinematic model according to the estimated state vector; an optimal control input determination unit, configured to determine 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, t represents the time; The control module is used to control the sight angles of the two interceptors according to the optimal control input to achieve tracking and interception of the target, specifically including: Ignoring the effect of gravity, the engagement process between the interceptor and the maneuvering target is expressed in the form of polar coordinates (r, λ) related to the maneuvering target, that is, 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 speeds of the interceptor and maneuvering target, respectively; and are the initial flight path angles of the interceptor and maneuvering target respectively; PiE is the line of sight angle between the interceptor and the maneuvering target.

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