Online robust identification method and system of missile aerodynamic parameters based on variational inference

Abstract

The invention discloses an online robust identification method and system for aerodynamic parameters of a missile based on variational inference, comprising: constructing an aerodynamic parameter estimation problem of a ballistic missile whose process noise obeys a Gaussian-Student's t mixed distribution: constructing a system equation according to a missile dynamics model and a measurement model, modeling the process noise as a Gaussian-Student's t mixed distribution, obtaining a probability model corresponding to the aerodynamic parameter estimation problem of the ballistic missile, and linearizing the system equation; designing a robust extended Kalman filtering method considering outliers in the process noise based on a variational inference technology, relying on a real-time input vector and a measurement vector of a missile system, approximately inferring a posterior distribution of a hidden variable, and obtaining aerodynamic parameters of the missile; the invention can improve the robustness and estimation accuracy of the algorithm when outliers exist in the process noise, and is helpful to realize accurate estimation of aerodynamic parameters of the missile.

Description

Technical Field

[0001] The present invention relates to the field of automatic control technology, and more specifically to an online robust identification method and system for missile aerodynamic parameters based on variational inference. Background Art

[0002] The process of estimating the specific values ​​of the control system model parameters based on the input vector and measurement vector of the control system is called parameter estimation. Robust estimation refers to a type of estimation algorithm with good robustness. Parameter estimation is an important technology in the field of automatic control. In engineering practice, the design of various model-based controllers and the selection of their algorithm parameters require the accurate system model and model parameters of the controlled object. Providing accurate model parameters will help ensure that the controller can achieve good control effects. With the development of control theory and aerospace technology, the models of various types of controlled missiles are currently more complex; and missiles often operate in various interference environments, which puts higher requirements on the accuracy and robustness of parameter estimation.

[0003] In recent years, the problem of missile model parameter estimation has received extensive attention, and various estimation methods have been proposed. For example, aerodynamic parameter identification based on the Newton-Raphson iteration formula [Liang Ming. Aerodynamic parameter identification and trajectory simulation of a certain type of aircraft [J]. Shanghai Aerospace (Chinese and English), 2022, 39(05): 140-146.] This method aims at the estimation of aerodynamic parameters in the 6-DOF missile dynamics model. It uses the Newton-Raphson iteration formula to identify aerodynamic parameters, but it is an offline identification method and requires data collection for a period of time before identification can begin; missile aerodynamic parameter estimation based on recursive least squares [Zang Jianwen, Bi Xiaoye, Jin Zhao, etc. Global aircraft aerodynamic parameter identification method based on angle of attack partitioning [J]. Systems Engineering and Electronics, 2023, 45(11): 3588-3596.] This method realizes online estimation of aerodynamic parameters and can estimate aerodynamic parameters in real time while obtaining input and measurement data, but does not consider the influence of process noise, especially the influence of outliers that may be contained in process noise.

[0004] Therefore, how to realize online estimation of missile aerodynamic parameters while improving the robustness and accuracy of aerodynamic parameter estimation is a problem that technical personnel in this field need to solve urgently. Summary of the invention

[0005] In view of this, the present invention provides an online robust identification method and system for missile aerodynamic parameters based on variational inference, which has solved some of the technical problems mentioned in the background technology.

[0006] In order to achieve the above object, the present invention adopts the following technical solution:

[0007] An online robust identification method for missile aerodynamic parameters based on variational inference includes the following steps:

[0008] S1. Construct the aerodynamic parameter estimation problem of ballistic missile with process noise obeying Gaussian-Student's t mixed distribution: Construct the system equation according to the missile dynamics model and measurement model, model the process noise as Gaussian-Student's t mixed distribution, obtain the probability model corresponding to the aerodynamic parameter estimation problem of ballistic missile, and linearize the system equation;

[0009] S2. Based on the variational inference technology, a robust extended Kalman filter method with outliers in the process noise is designed. Relying on the real-time input vector and measurement vector of the missile system, the posterior distribution of the latent variables is approximately inferred to obtain the aerodynamic parameters of the missile.

[0010] Preferably, the input vector in step S2 includes missile thrust and rudder angle, and the measurement vector includes missile motion state measurement data.

[0011] Preferably, for step S1:

[0012] The constructed system equation is:

[0013] x k =f(x k-1 ,θ,u k-1 )+w k

[0014] z k =h(x k ,θ,u k )+v k

[0015] Among them, x k 、u k 、z k are the missile state, system input, and system measurement at the kth moment, respectively. c (·) is, h c (·) is, w k is the process noise, v k is the measurement noise, θ is the column vector of aerodynamic coefficients;

[0016] The Gaussian-Student's t mixed distribution for process noise modeling, that is, the probability model corresponding to the missile aerodynamic parameter estimation problem, is:

[0017]

[0018]

[0019] p(λk )=G(λ k |υ k / 2,υ k / 2)

[0020] Among them, f k =f(x k-1 ,θ,u k-1 ), variable y k ∈{0, 1}, N(·) represents Gaussian distribution, G(·) represents Gamma distribution, Q k represents the nominal noise covariance matrix, υ k represents the degree of freedom parameter, π k represents the mixture probability that needs to be estimated online.

[0021] Preferably, the specific method for obtaining the probability model corresponding to the problem of estimating the aerodynamic parameters of a ballistic missile is:

[0022] Assume that the measurement noise v k Subject to zero mean, covariance matrix R k If is a Gaussian distribution, the measurement likelihood is modeled as:

[0023] p(z k |x k ,θ)=N(z k |h k , R k )

[0024] Among them, h k =h(x k ,θ,u k );

[0025] The disturbance w k Modeled as Gaussian-Student's t distribution, that is, the probability distribution p(x k |x k-1 ,θ) is Gaussian-Student,st distribution, and the mixed probability that needs to be estimated online is defined as π k , then given x k-1 , θ and π k When x k The conditional probability density function is:

[0026] p(x k |π k-1 ,θ,π k )=π k N(x k |f k , Q k )+(1-π k )St(xk |f k , Q k , k )

[0027] St(x k |f k , Q k , k )=∫N(x k |f k , Q k / λ k )G(λ k |υ k / 2,υ k / 2)dλ k

[0028] Assume that the mixing probability π k The prior distribution of is:

[0029] p(π k )=Beta(π k |e0,1-e0)

[0030] Among them, e0 is the artificially given prior mixing probability;

[0031] Write the Gaussian-Student's t distribution in hierarchical form, that is, the Gaussian-Student,st mixture distribution for modeling process noise;

[0032] definition The joint estimate of the state and parameters at the previous moment is assumed to be:

[0033]

[0034] Preferably, step S2 specifically includes:

[0035] S21. Initialize the robust extended Kalman filter: select the state estimate at the initial moment and its error covariance matrix P xx，0|0 , select the initial parameter estimation times and its error covariance matrix P θθ，0 , select the algorithm parameter Q k , R k ,e0,υ,ε k , N;

[0036] S22. Get the missile system input vector u k and the measurement vector z k :The system input vector of the missile is obtained from the controller, and the measurement vector is obtained through the real-time data of the navigation device, angle of attack sensor and sideslip angle sensor carried by the missile;

[0037] S23. Solution of approximate posterior of latent variables: define augmented state, set of latent variables and set of observed variables, obtain joint probability distribution according to probability model, and obtain approximate posterior distribution of latent variables with the help of relevant conclusions of variational inference;

[0038] S24. Use fixed point iteration to solve, define the maximum number of fixed point iterations and set the termination condition until the fixed point iteration is terminated to obtain an approximate optimal solution;

[0039] S25. Determine whether to terminate parameter identification. If not, return to step S22.

[0040] Preferably, the specific content of the latent variable approximate posterior solution in step S23 is:

[0041] Defining augmented states Hidden variable set Observation variable set

[0042] According to mean field theory, the probability distribution is used to approximate the posterior

[0043] With the help of the relevant conclusions of variational inference, the objective function of the optimization problem is constructed:

[0044] min KL(q(Φ k )||p(Φ k |z 1：k ))

[0045] Where KL(·||·) represents KL divergence;

[0046] The solution to the optimization problem satisfies:

[0047]

[0048] Among them, Δ k is the hidden variable set Φ k The elements in Removing Δ k After Φ k The remaining set of elements, is independent of Δ k The constant, Relative expectations;

[0049] According to the probability model, the joint probability distribution p(Φ k |z 1：k ) is:

[0050] p(Φ k |z 1：k)=p(z 1：k-1 )p(z k |x k ,θ)p(x k |x k-1 ,θ,λ k ,y k )p(y k |π k )p(λ k )

[0051] ×p(π k )p(x k-1 ,θ|z 1：k-1 )

[0052] Based on the coupling of variational parameters, the approximate optimal solution is solved using fixed point iteration;

[0053] Let (i) represent the i-th fixed point iteration, and the approximate posterior of the augmented state is:

[0054]

[0055] in,

[0056]

[0057]

[0058]

[0059] Among them, I is the unit matrix;

[0060]

[0061]

[0062]

[0063] P xζ，k|k-1 =F k P ζζ，k-1|k-1

[0064]

[0065] n z 、n x The measurement vector z is k and the state vector x k , n z Line n x Column zero matrix;

[0066] Using the conclusion of variational inference, the approximate posterior distribution of the latent variable is obtained as follows:

[0067]

[0068]

[0069] in, is the normalization constant;

[0070]

[0071]

[0072]

[0073] Hidden variable π k The approximate posterior distribution of is:

[0074]

[0075] in,

[0076]

[0077]

[0078] Hidden variable λ k The approximate posterior distribution of is:

[0079]

[0080] in,

[0081]

[0082]

[0083] The expectation calculation method that appears in the approximate posterior is:

[0084]

[0085]

[0086]

[0087]

[0088]

[0089] Among them, ψ(·) is the Digamma function.

[0090] Preferably, for step S24, the specific content of the estimation algorithm iteration is:

[0091]

[0092]

[0093] in,

[0094]

[0095] Define the maximum number of fixed point iterations as N, and set the termination condition as:

[0096]

[0097] Among them, ε k is a set algorithm parameter;

[0098] The fixed point iteration terminates when the termination condition is met or the maximum number of iterations is reached;

[0099] Then order,

[0100]

[0101]

[0102] An online robust identification system of missile aerodynamic parameters based on variational inference, based on the online robust identification method of missile aerodynamic parameters based on variational inference, comprises a problem construction module and a robust estimation module;

[0103] A problem construction module is used to construct the aerodynamic parameter estimation problem of a ballistic missile with process noise obeying Gaussian-Student's t mixed distribution. Specifically, a system equation is constructed according to the missile dynamics model and the measurement model, the process noise is modeled as a Gaussian-Student's t mixed distribution, the probability model corresponding to the aerodynamic parameter estimation problem of the ballistic missile is obtained, and the system equation is linearized;

[0104] The robust estimation module is used to design a robust extended Kalman filter method based on variational inference technology that takes into account process noise with outliers. It relies on the real-time input vector and measurement vector of the missile system to approximately infer the posterior distribution of latent variables and obtain the missile aerodynamic parameters.

[0105] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements an online robust identification method for missile aerodynamic parameters based on variational inference.

[0106] A processing terminal comprises a memory and a processor. The memory stores a computer program that can be run on the processor. When the processor executes the computer program, an online robust identification method for missile aerodynamic parameters based on variational inference is implemented.

[0107] Through the above technical scheme, it can be known that compared with the prior art, the present invention discloses an online robust identification method and system for missile aerodynamic parameters based on variational inference. Firstly, considering that the process noise to which the missile is subjected may have outliers, the process noise is modeled as a Gaussian-Student's t mixed distribution, and then a probability model based on which the missile state and aerodynamic parameter joint estimation problem is solved is constructed. The variational inference technique is used to obtain the approximate posterior distribution parameters of all hidden variables in the probability model, and finally the robust estimation of the missile parameters is realized, which can improve the robustness and estimation accuracy of the algorithm when the process noise has outliers. The simulation results show that the present invention can realize the accurate estimation of the missile aerodynamic parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0108] 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 or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0109] Figure 1 A schematic diagram of an online robust identification method for missile aerodynamic parameters based on variational inference provided by the present invention;

[0110] Figure 2 A flow chart of the robust extended Kalman filtering method provided by the present invention;

[0111] Figure 3 A schematic diagram of an error curve of aerodynamic parameters of a missile provided by the present invention. DETAILED DESCRIPTION

[0112] 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.

[0113] Taking the estimation of ballistic missile dynamic parameters as an example, an embodiment of the present invention discloses an online robust identification method of missile aerodynamic parameters based on variational inference, comprising the following steps:

[0114] S1. Construct the aerodynamic parameter estimation problem of ballistic missile with process noise obeying Gaussian-Student's t mixed distribution: Construct the system equation according to the missile dynamics model and measurement model, model the process noise as Gaussian-Student's t mixed distribution, obtain the probability model corresponding to the aerodynamic parameter estimation problem of ballistic missile, and linearize the system equation;

[0115] S2. Based on the variational inference technology, a robust extended Kalman filter method with outliers in the process noise is designed. Relying on the real-time input vector and measurement vector of the missile system, the posterior distribution of the latent variables is approximately inferred to obtain the aerodynamic parameters of the missile.

[0116] In order to further implement the above technical solution, the input vector in step S2 includes missile thrust and rudder deflection angle, and the measurement vector includes missile motion state measurement data.

[0117] In order to further implement the above technical solution, for step S1:

[0118] The 6-DOF ballistic missile dynamics model is:

[0119]

[0120]

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127]

[0128]

[0129] Among them, V x 、V y 、V z are the three-axis speeds, ω x ,ω y ,ω z is the angular velocity, γ is the attitude angle, h is the flight altitude, M R is the thrust eccentric moment, g = 9.80655-3.068×10 -6h is the acceleration due to gravity, J x , J y , J z is the moment of inertia;

[0130] N x 、N y 、N z The expressions are:

[0131]

[0132]

[0133]

[0134] Among them, m is the missile mass, R is the missile thrust;

[0135] Define the rudder deflection angle δ x , δ y , δ z , then X t , Y t , Z t They are:

[0136] X t =C x Q

[0137] Y t =C y Q

[0138] Z t =C z Q

[0139]

[0140]

[0141]

[0142] Where S is the reference area, W x , W y , W z is the component of wind speed in the missile body coordinate system;

[0143]

[0144]

[0145]

[0146] Among them, W xd and W zd is the component of wind speed in the ground coordinate system;

[0147] Then, the model of the aerodynamic coefficient is expressed as:

[0148] C x =C x0 +C x1 α 2

[0149]

[0150]

[0151]

[0152]

[0153]

[0154] Where l is the reference length of the aircraft, b A is the mean aerodynamic chord length, angle of attack Side slip angle c x0 , C x1 , C y0 , C z0 , m x0 , m y0 , m z0 , and is the aerodynamic coefficient that needs to be identified, and the 22 parameters form a 22-dimensional column vector θ;

[0155] Use vector x to represent the state of the missile:

[0156]

[0157] The system inputs for the missile are:

[0158] u=[R,δ x , δ y , δ z ] T ;

[0159] The measurements form a vector z:

[0160]

[0161] The resulting system equation is:

[0162]

[0163] z=h c (x, θ, u)

[0164] Among them, the function f c (·) and h c The specific expression of (·) is determined by the above model;

[0165] The continuous system is discretized and the process noise w is considered k and measurement noise v k , then the constructed system equation is specifically:

[0166] x k =f(x k-1 ,θ,u k-1 )+w k

[0167] z k =h(x k ,θ,u k )+v k

[0168] Among them, x k 、u k 、z k are the missile state, system input, and system measurement at the kth moment, respectively. c (·) is, h c (·) is, w k is the process noise, v k is the measurement noise, θ is the column vector of aerodynamic coefficients;

[0169] The Gaussian-Student's t mixed distribution for process noise modeling, that is, the probability model corresponding to the missile aerodynamic parameter estimation problem, is:

[0170]

[0171]

[0172] p(λ k )=G(λ k |υ k / 2,υ k / 2)

[0173] Among them, f k =f(x k-1 ,θ,u k-1 ), variable y k ∈{0, 1}, N(·) represents Gaussian distribution, G(·) represents Gamma distribution, Q k represents the nominal noise covariance matrix, υ krepresents the degree of freedom parameter, π k represents the mixture probability that needs to be estimated online.

[0174] In order to further implement the above technical solution, the specific method for obtaining the probability model corresponding to the problem of estimating the aerodynamic parameters of a ballistic missile is as follows:

[0175] Assume that the measurement noise v k Subject to zero mean, covariance matrix R k If is a Gaussian distribution, the measurement likelihood is modeled as:

[0176] p(z k |x k ,θ)=N(z k |h k , R k )

[0177] Among them, h k =h(x k ,θ,u k );

[0178] The external dynamic disturbances to the missile can be assumed to obey Gaussian distribution, but they may also obey heavy-tailed distribution due to the interference of outliers with large amplitudes in certain periods of time. k Modeled as Gaussian-Student, st distribution, that is, probability distribution p(x k |x k-1 ,θ) is Gaussian-Student,st distribution, and the mixed probability that needs to be estimated online is defined as π k , then given x k-1 , θ and π k When x k The conditional probability density function is:

[0179] p(x k |x k-1 ,θ,π k )=π k N(x k |f k , Q k )+(1-π k )St(x k |f k , Q k , k )

[0180] St(x k |f k , Q k , k )=∫N(x k |fk , Q k / λ k )G(λ k |υ k / 2,υ k / 2)dλ k

[0181] Assume that the mixing probability π k The prior distribution of is:

[0182] p(π k )=Beta(π k |e0,1-e0)

[0183] Among them, e0 is the artificially given prior mixing probability;

[0184] Write the Gaussian-Student's t distribution in stratified form, i.e., a Gaussian-Student's t mixture distribution for modeling process noise;

[0185] definition The joint estimate of the state and parameters at the previous moment is assumed to be:

[0186]

[0187] The specific content of the linearized system equation is:

[0188] Estimate the state equation at the previous moment Linearize it, and we get:

[0189]

[0190] in, is the predicted state, F x，k and F θ，k is the Jacobian matrix;

[0191]

[0192]

[0193]

[0194] Definition F k =[F x，k F θ，k ];

[0195] The measurement equation predicts the current moment Linearize it, and we get:

[0196]

[0197] in, is the predicted measurement, H x，k and H θ，k is the Jacobian matrix;

[0198]

[0199]

[0200]

[0201] Definition H k =[H x，k H θ，k ].

[0202] In order to further implement the above technical solution, step S2 specifically includes:

[0203] S21. Initialize the robust extended Kalman filter: select the state estimate at the initial moment and its error covariance matrix P xx，0|0 , select the initial parameter estimate and its error covariance matrix P θθ，0 , select the algorithm parameter Q k , R k ,e0,υ,ε k , N;

[0204] S22. Get the missile system input vector u k and the measurement vector z k :The system input vector of the missile is obtained from the controller, and the measurement vector is obtained through the real-time data of the navigation device, angle of attack sensor and sideslip angle sensor carried by the missile;

[0205] S23. Approximate posterior solution for latent variables: Define the augmented state, the set of latent variables and the set of observed variables, obtain the joint probability distribution according to the probability model, and use the relevant conclusions of variational inference to obtain the approximate posterior distribution of the latent variables;

[0206] S24. Use fixed point iteration to solve, define the maximum number of fixed point iterations and set the termination condition until the fixed point iteration is terminated to obtain an approximate optimal solution;

[0207] S25. Determine whether to terminate parameter identification. If not, return to step S22.

[0208] In order to further implement the above technical solution, the specific content of the hidden variable approximate posterior solution in step S23 is:

[0209] Defining augmented states Hidden variable set Observation variable set

[0210] According to mean field theory, the probability distribution is used to approximate the posterior

[0211] With the help of the relevant conclusions of variational inference, the objective function of the optimization problem is constructed:

[0212] min KL(q(Φ k )||p(Φ k |z 1：k ))

[0213] Where KL(·||·) represents KL divergence;

[0214] The solution to the optimization problem satisfies:

[0215]

[0216] Among them, Δ k is the hidden variable set Φ k The elements in Removing Δ k After Φ k The remaining set of elements, is independent of Δ k The constant, Relative expectations;

[0217] According to the probability model, the joint probability distribution p(Φ k |z 1：k ) is:

[0218] p(Φ k |z 1：k )=p(z 1：k-1 )p(z k |x k ,θ)p(x k |x k-l ,θ,λ k ,y k )p(y k |π k )p(λ k )

[0219] ×p(π k )p(x k-1 ,θ|z 1：k-1 )

[0220] Based on the coupling of variational parameters, the approximate optimal solution is solved using fixed point iteration;

[0221] Let (i) represent the i-th fixed point iteration, and the approximate posterior of the augmented state is:

[0222]

[0223] in,

[0224]

[0225]

[0226]

[0227] Among them, I is the unit matrix;

[0228]

[0229]

[0230]

[0231] P xξ，k|k-1 =F k P ζζ，k-1|k-1

[0232]

[0233] n z 、n x The measurement vector z is k and the state vector x k , n z Line n x Column zero matrix;

[0234] Using the conclusion of variational inference, the approximate posterior distribution of the latent variable is obtained as follows:

[0235]

[0236]

[0237] in, is the normalization constant;

[0238]

[0239]

[0240]

[0241] Hidden variable π k The approximate posterior distribution of is:

[0242]

[0243] in,

[0244]

[0245]

[0246] Hidden variable λ k The approximate posterior distribution of is:

[0247]

[0248] in,

[0249]

[0250]

[0251] The expectation calculation method that appears in the approximate posterior is:

[0252]

[0253]

[0254]

[0255]

[0256]

[0257] Among them, ψ(·) is the Digamma function.

[0258] In order to further implement the above technical solution, for step S24, the specific content of the estimation algorithm iteration is:

[0259]

[0260]

[0261] in,

[0262]

[0263] Define the maximum number of fixed point iterations as N, and set the termination condition as:

[0264]

[0265] Among them, ε k is a set algorithm parameter;

[0266] The fixed point iteration terminates when the termination condition is met or the maximum number of iterations is reached;

[0267] Then order,

[0268]

[0269]

[0270] In another embodiment, MATLAB 2023b is used as simulation software to compare the robust extended Kalman filter of the present invention considering process noise with outliers with the traditional extended Kalman filter method;

[0271] The aerodynamic parameter settings of the 6-DOF missile used in the simulation are shown in the following table:

[0272]

[0273] The simulation sampling period Δt = 0.1 seconds, the duration is 30 seconds, and a total of 10 simulations are performed;

[0274] The measurement noise used in the simulation is zero-mean Gaussian noise, and the covariance matrix is:

[0275] R k =1×10 -5 15 ;

[0276] The process noise w to which the missile state vector is subjected k Set to:

[0277]

[0278] Among them, the nominal process noise covariance matrix Q k =1×10 -5 I 10 , wp means probability, p1 = 0.01, p2 = 0.05;

[0279] The system input settings are:

[0280]

[0281] The algorithm parameters of the extended Kalman filter are set as: Q k =1×10 -5 I 10 , R k =1×10 -5 I 10 ;

[0282] The parameters of the robust extended Kalman filter are set as: Q k =1×10 -5 I 10 , R k =1×10 -5 I 10 , e0=0.5,υ=5,ε k =10-6 , N = 30;

[0283] The initial estimates of the states and parameters of the two extended Kalman filters are the same and are all set to 0;

[0284] Parameter error RMSE θ for:

[0285]

[0286] Where T=10 means the number of simulations is 10 times, θ is the true value of the parameter, is the estimated value of the parameter at the kth moment in the tth simulation;

[0287] Parameter error RMSE θ The iteration curve is as follows Figure 3 As shown, it can be seen that the robust extended Kalman filter of the present invention that takes into account the outliers in the process noise can achieve better accurate estimation effect.

[0288] An online robust identification system of missile aerodynamic parameters based on variational inference, based on an online robust identification method of missile aerodynamic parameters based on variational inference, including a problem construction module and a robust estimation module;

[0289] A problem construction module is used to construct the aerodynamic parameter estimation problem of a ballistic missile with process noise obeying Gaussian-Student's t mixed distribution. Specifically, a system equation is constructed according to the missile dynamics model and the measurement model, the process noise is modeled as a Gaussian-Student's t mixed distribution, the probability model corresponding to the aerodynamic parameter estimation problem of the ballistic missile is obtained, and the system equation is linearized;

[0290] The robust estimation module is used to design a robust extended Kalman filter method based on variational inference technology that takes into account process noise with outliers. It relies on the real-time input vector and measurement vector of the missile system to approximately infer the posterior distribution of latent variables and obtain the missile aerodynamic parameters.

[0291] A computer-readable storage medium stores a computer program, which, when executed by a processor, implements an online robust identification method for missile aerodynamic parameters based on variational inference.

[0292] A processing terminal comprises a memory and a processor. The memory stores a computer program that can be run on the processor. When the processor executes the computer program, an online robust identification method for missile aerodynamic parameters based on variational inference is implemented.

[0293] 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 device 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.

[0294] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. An online robust identification method for missile aerodynamic parameters based on variational inference, characterized in that: The following steps are involved: S1. Construct the aerodynamic parameter estimation problem of ballistic missiles with process noise obeying Gaussian-Student'st mixed distribution: Construct the system equations according to the missile dynamics model and measurement model, model the process noise as Gaussian-Student'st mixed distribution, obtain the probability model corresponding to the missile aerodynamic parameter estimation problem, and linearize the system equations; S2. Based on the variational inference technology, a robust extended Kalman filter method with outliers in the process noise is designed. Relying on the real-time input vector and measurement vector of the missile system, the posterior distribution of the latent variables is approximately inferred to obtain the aerodynamic parameters of the missile; The input vector in step S2 includes the missile thrust and the rudder deflection angle, and the measurement vector includes the missile motion state measurement data; For step S1: The constructed system equation is: x k =f(x k-1 ,θ,u k-1 )+w k z k =h(x k ,θ,u k )+v k Among them, x k 、u k 、z k are the missile state, system input, and system measurement at the kth moment, respectively. k is the process noise, v k is the measurement noise, θ is the column vector of aerodynamic coefficients; Function f c (·) and h c (·) The expression is represented by the vector x representing the state of the missile The missile's system input u = [R, δ x , δ y , δ z ] T , the measured values ​​form a vector And the resulting system equations and z = h c (x, θ, u) is determined, where V x 、V y 、V z are the three-axis speeds, ω x ,ω y ,ω z is the angular velocity, θ, γ is the attitude angle, h is the flight altitude, R is the missile thrust, δ x , δ y , δ z is the rudder deflection angle, α is the angle of attack, and β is the sideslip angle; The Gaussian-Student's t mixed distribution for process noise modeling, that is, the probability model corresponding to the missile aerodynamic parameter estimation problem, is: p(λ k )=G(λ k |u k / 2,u k / 2) Among them, f k =f(x k-1 ,θ,u k-1 ), variable y k ∈{0, 1}, N(·) represents Gaussian distribution, G(·) represents Gamma distribution, Q k represents the nominal noise covariance matrix, υ k represents the degree of freedom parameter, π k represents the mixing probability that needs to be estimated online; The specific method to obtain the probability model corresponding to the problem of estimating the aerodynamic parameters of ballistic missiles is: Assume that the measurement noise v k Subject to zero mean, covariance matrix R k If is a Gaussian distribution, the measurement likelihood is modeled as: p(z k |x k ,θ)=N(z k |h k ,R k ) among them, h k =h(x k ,θ,u k ); The disturbance w k Modeled as Gaussian-Student'st distribution, that is, probability distribution p(x k |x k-1 , θ) is Gaussian-Student'st distribution, and the mixed probability that needs to be estimated online is defined as π k , then given x k-1 , θ and π k When x k The conditional probability density function is: p(x k |x k-1 ,θ,π k )=π k N(x k |f k ,Q k )+(1-π k )St(x k |f k ,Q k ,υ k ) St(x k |f k ,Q k ,υ k )=∫N(x k |f k ,Q k / λ k )G(λ k |υ k / 2,υ k / 2)dλ k Assume that the mixing probability π k The prior distribution of is: p(π k )=Beta(π k |e0, 1-e0) Among them, e0 is the artificially given prior mixing probability; Write the Gaussian-Student's t distribution in stratified form, which is a Gaussian-Student's t mixture distribution for modeling process noise; definition The joint estimate of the state and parameters at the previous moment is assumed to be: Step S2 specifically includes: S21. Initialize the robust extended Kalman filter: select the state estimate at the initial moment and its error covariance matrix P xx，0|0 , select the initial parameter estimate and its error covariance matrix P θθ，0 , select the algorithm parameter Q k , R k ,e0,υ,ε k , N; S22. Get the missile system input vector u k and the measurement vector z k :The system input vector of the missile is obtained from the controller, and the measurement vector is obtained through the real-time data of the navigation device, angle of attack sensor and sideslip angle sensor carried by the missile; S23. Solution of approximate posterior of latent variables: define augmented state, set of latent variables and set of observed variables, obtain joint probability distribution according to probability model, and obtain approximate posterior distribution of latent variables with the help of relevant conclusions of variational inference; S24. Use fixed point iteration to solve, define the maximum number of fixed point iterations and set the termination condition until the fixed point iteration is terminated to obtain an approximate optimal solution; S25. Determine whether to terminate parameter identification, if not, return to step S22; The specific content of the hidden variable approximate posterior solution in step S23 is: Defining augmented states Hidden variable set Observation variable set According to mean field theory, the probability distribution is used to approximate the posterior With the help of the relevant conclusions of variational inference, the objective function of the optimization problem is constructed: min KL(q(Φ k )||p(Φ k |z 1：k )) Where KL(·||·) represents KL divergence; The solution to the optimization problem satisfies: Among them, Δ k is the hidden variable set Φ k The elements in Removing Δ k After Φ k The remaining set of elements, is independent of Δ k The constant, Relative expectations; According to the probability model, the joint probability distribution p(Φ k |z 1：k ) is: p(Φ k |z 1：k )=p(z 1：k-1 )p(z k |x k ,θ)p(x k |x k-1 ,θ,λ k y k )p(y k |π k )p(λ k )×p(π k )p(x k-1 ,θ|z 1：k-1 ) Based on the coupling of variational parameters, the approximate optimal solution is solved using fixed point iteration; Let (i) represent the i-th fixed point iteration, and the approximate posterior of the augmented state is: in, Among them, I is the unit matrix; P xζ，k|k-1 =F k P ζζ，k1|k-1 n z 、n x The measurement vector z is k and the state vector x k , n z Line n x Column zero matrix; Using the conclusion of variational inference, the approximate posterior distribution of the latent variable is obtained as follows: in, is the normalization constant; Hidden variable π k The approximate posterior distribution of is: in, Hidden variable λ k The approximate posterior distribution of is: in, The expectation calculation method that appears in the approximate posterior is: Where ψ(·) is the Digamma function; For step S24, the specific content of the estimation algorithm iteration is: in, Define the maximum number of fixed point iterations as N, and set the termination condition as: Among them, ε k is a set algorithm parameter; The fixed point iteration terminates when the termination condition is met or the maximum number of iterations is reached; Then order, 2. An online robust identification system for missile aerodynamic parameters based on variational inference, characterized in that: An online robust identification method for missile aerodynamic parameters based on variational inference according to claim 1, comprising a problem construction module and a robust estimation module; A problem construction module is used to construct the aerodynamic parameter estimation problem of a ballistic missile with process noise obeying Gaussian-Student's t mixed distribution. Specifically, a system equation is constructed according to the missile dynamics model and the measurement model, the process noise is modeled as a Gaussian-Student's t mixed distribution, the probability model corresponding to the aerodynamic parameter estimation problem of the ballistic missile is obtained, and the system equation is linearized; The robust estimation module is used to design a robust extended Kalman filter method based on variational inference technology that takes into account process noise with outliers. It relies on the real-time input vector and measurement vector of the missile system to approximately infer the posterior distribution of latent variables and obtain the missile aerodynamic parameters.

3. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for online robust identification of missile aerodynamic parameters based on variational inference as described in claim 1 is implemented.

4. A processing terminal, comprising a memory and a processor, wherein the memory stores a computer program that can be run on the processor, characterized in that: When the processor executes the computer program, the on-line robust identification method of missile aerodynamic parameters based on variational inference as claimed in claim 1 is implemented.

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