ATR engine control system state estimation method based on adaptive robust UKF

Abstract

The invention discloses an ATR engine control system state estimation method based on adaptive robust UKF. The method comprises the steps that a nonlinear discrete model of an ATR engine control system is established; the time updating process comprises the steps of initializing an engine state quantity and a state error covariance matrix, selecting a sampling point, constructing a state quantity of the sampling point, and predicting an estimated value of the engine state quantity and the error covariance matrix; the measurement updating process comprises the steps of updating the state quantity of the sampling point, converting the updated state quantity of the sampling point, calculating an engine output quantity estimated value and a covariance matrix through unscented transformation, and calculating a state-measurement cross covariance matrix; calculating a Kalman gain matrix process through a maximum correlation entropy criterion; and updating a state estimation and covariance matrix process. The method can solve the problems that an existing nonlinear system state estimation method is insufficient in robustness in a complex noise environment, sensitive to abnormal measurement values, difficult to cope with the influence of non-Gaussian noise and the like.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of ATR engine control, and particularly relates to an ATR engine control system state estimation method based on adaptive robust UKF. BACKGROUND

[0002] An ATR (Air Turbo-Rocket) engine is a hybrid propulsion system with high thrust-to-weight ratio and strong adaptability, which is widely used in aerospace and military fields. Due to its unique structure and performance, the ATR engine often operates in complex environments, requiring accurate real-time monitoring and control of its state to ensure the safety and stability of the system. However, the operating state of the ATR engine is highly nonlinear, and its operating environment is variable, and it is also affected by high noise interference and measurement errors. Traditional filtering methods are difficult to ensure high-precision state estimation in complex noise environments. In addition, existing filters usually use fixed parameters and cannot adaptively adjust according to real-time noise conditions, resulting in insufficient robustness and adaptability in actual applications. The current Kalman filter and its derivative methods in dealing with complex nonlinear system state estimation, the noise assumption is too ideal (usually assuming that the noise is Gaussian distribution), in the actual non-Gaussian noise and abnormal data situation, the filter performance is greatly reduced, which cannot meet the high-precision state estimation demand of ATR engine.

[0003] In order to cope with the above challenges, researchers have proposed some improvement schemes, such as adaptive filter and robust filter, aiming to improve the robustness and adaptability of the filter to complex noise. However, these methods still have problems such as inflexible parameter adjustment, large amount of calculation and inability to handle high-dimensional complex system state estimation. Therefore, there is an urgent need for an ATR engine state estimation method that can adaptively cope with complex noise environment and sensor error value influence, and has good robustness while maintaining high precision. SUMMARY

[0004] The purpose of the present application is to provide an ATR engine control system state estimation method based on adaptive robust UKF, to solve the problems of insufficient robustness of existing nonlinear system state estimation methods in complex noise environment, sensitivity to abnormal measurement values, and difficulty in coping with non-Gaussian noise.

[0005] In order to achieve the above task, the present application adopts the following technical solutions:

[0006] An ATR engine control system state estimation method based on adaptive robust UKF, comprising:

[0007] establishing a nonlinear discrete model of the ATR engine control system, including establishing a state space model for the ATR engine control system, determining specific parameters of engine state quantities, engine input quantities and engine output quantities, discretizing the state space model and calculating a noise covariance matrix;

[0008] a time update process, including initializing engine state quantities and state error covariance matrices, selecting a sampling point and constructing a state quantity of the sampling point, predicting an engine state quantity estimate value and an error covariance matrix;

[0009] a measurement update process, including updating a state quantity of the sampling point, converting the updated state quantity of the sampling point by using a measurement equation function, calculating an engine output quantity estimate value and a covariance matrix by using an unscented transformation, and calculating a cross-covariance matrix of state-measurement;

[0010] a process of calculating a Kalman gain matrix by using a maximum correlation entropy criterion, including defining a pseudo-measurement matrix, converting a nonlinear engine output quantity into a linear form by using the pseudo-measurement matrix, defining a cost function, and solving a Kalman filter gain matrix based on the cost function;

[0011] a process of updating state estimates and covariance matrices, including updating an engine state quantity estimate value and updating a state error covariance matrix.

[0012] Further, the method further comprises:

[0013] a robust state estimator design process; first, a robust state estimator batch regression form is designed, and by rewriting it into a compact form, an observation vector, a regression matrix, an error vector and an error covariance matrix are obtained; a robust scale of a residual vector is minimized, including defining a robust scale estimator and constructing a weight function to solve the robust scale estimator.

[0014] Further, a Gaussian kernel function with σ y as a kernel bandwidth is constructed, which is used to define a cost function; the expression form of the kernel bandwidth σ y is as follows:

[0015]

[0016] wherein y(k) is an engine output quantity, y(k|k-1) represents an engine output quantity estimate value predicted at k-1 time for k time; R(k) is a measurement noise covariance matrix at k time, and a superscript -1 represents a matrix inversion; ||t M =(t T Mt) 1 / 2 .

[0017] Further, the sampling point is selected and the state quantity of the sampling point is constructed, including:

[0018]

[0019] where χ i (k-1|k-1) represents the state quantity of the i-th sampling point at the k-1 time, i = 0, 1,..., 2n; (·) i represents the i-th column or i-th row of the matrix in the parentheses; P(k-1) represents the state estimation value at the k-1 time, the state error covariance matrix; n is the system state dimension, λ is a complex scaling factor, λ = α 2 (n+ε)-n; 0 < α < 1, ε is a scaling factor;

[0020] Solve by singular value decomposition method

[0021] Further, the cost function is as follows:

[0022]

[0023] where α' and β' are adjustable weight coefficients, is a Gaussian kernel function with σ y as the core bandwidth; x(k) represents the engine state quantity, represents the state estimation value at the k-1 time; P(k|k-1) is the error covariance matrix of the k-1 time prediction of the k time, y(k) is the engine output quantity, represents the engine output quantity estimation value of the k-1 time prediction of the k time, H(k) is a pseudo-measurement matrix.

[0024] Further, the Kalman filter gain matrix is solved based on the cost function, which is as follows:

[0025]

[0026] where represents the partial derivative, and ξ is an intermediate variable, and the expression is as follows:

[0027]

[0028] Take α' = 1, Substituting the above formula gives:

[0029]

[0030] After arrangement, we get:

[0031]

[0032] where is the Kalman filter gain matrix, and the expression is as follows:

[0033]

[0034] Further, the robust state estimator is expressed as:

[0035]

[0036] wherein, x(k) represents the engine state quantity, represents the state estimation value at k-1 time; is a measurement noise sequence, I is a unit matrix; y(k) is an engine output quantity, represents the engine output quantity estimation value predicted at k-1 time for k time; H(k) is a pseudo measurement matrix;

[0037] The robust state estimator is rewritten in the following compact form:

[0038]

[0039] wherein, the observation vector the regression matrix the error vector and the error covariance matrix is:

[0040]

[0041] wherein E(·) represents the expectation operation, is the measurement noise matrix after the unscented transformation, and P(k|k-1) is the error covariance matrix predicted at k-1 time for k time;

[0042] If the robust scale of the residual vector can be minimized, the state estimation result is robust, that is:

[0043]

[0044] wherein, is the engine state quantity estimation value at k time, is a robust scale estimator; is a residual vector, r i (x(k)) is the i-th residual component in the residual vector, i=1,2,...,m; m is the dimension of the observation vector .

[0045] Further, the robust scale estimator is constructed as follows:

[0046]

[0047] where δ∈[0,1], the function ρ(·) is a bounded even function satisfying

[0048] Robust scale estimator By iteration:

[0049]

[0050] where, is the relative standard residual, and the weight function is:

[0051]

[0052] where, is the i-th component of the observation vector .

[0053] A terminal device comprising a processor, a memory, and a computer program stored in the memory; when the processor executes the computer program, the adaptive robust UKF-based ATR engine control system state estimation method is realized.

[0054] A computer readable storage medium, the medium stores a computer program; when the computer program is executed by a processor, the adaptive robust UKF-based ATR engine control system state estimation method is realized.

[0055] Compared with the prior art, the present application has the following technical features:

[0056] 1. The present application adopts an adaptive filter kernel bandwidth adjustment mechanism, which can adaptively adjust according to the change of noise in the environment, and is suitable for complex environments with mixed Gaussian and non-Gaussian noise.

[0057] 2. The present application combines the maximum correlation entropy criterion, improves the ability of the filter in processing high-order moment characteristics of nonlinear systems, and improves the accuracy of state estimation, especially in the case of variable noise environment.

[0058] 3. The present application introduces a robust S estimator, effectively isolates the influence of abnormal measurement data, and ensures that the filter can still provide stable state estimation results even when the sensor fails or measures abnormally, ensuring the safe operation of the engine under extreme conditions.

[0059] 4. The present application uses batch processing regression form and optimization iteration algorithm, reduces the computational burden, and at the same time maintains high estimation accuracy and fast response performance.

[0060] ​5. The application is particularly suitable for the atmospheric and out-of-atmospheric working modes of ATR engines, and can effectively estimate the state in turbojet mode and rocket mode, and meet the state monitoring requirements of the engine in various operating environments. BRIEF DESCRIPTION OF DRAWINGS

[0061] Figure 1 is a structural schematic diagram of an ATR engine;

[0062] Figure 2 is a flowchart of the method of the application. DETAILED DESCRIPTION

[0063] 1. Working principle of an ATR engine.

[0064] A single-component liquid propellant ATR engine, as shown in Figure 1 Unlike the combustion chamber of a turbojet engine, the ATR engine uses the gas generator component in a rocket engine, so it can be regarded as a combination of a turbojet engine and a rocket engine. The working principle of the ATR engine is as follows: in the gas generator, the single-component liquid propellant is catalytically decomposed into high-temperature and high-pressure fuel-rich gas, the fuel-rich gas flows through the turbine to drive the turbine component, which in turn drives the compressor to work on the external air entering through the air inlet, the pressurized high-pressure air enters the mixing chamber through the outer duct, mixes with the fuel-rich gas at the turbine outlet, and chemically combusts in the combustion chamber to generate high-temperature and high-pressure gas, and finally the high-temperature and high-pressure gas is fully expanded in the tail nozzle and discharged at high speed to generate thrust.

[0065] Compared with a conventional turbojet engine, the ATR engine separates the air flow path through the compressor from the high-temperature and high-pressure gas flow path through the turbine, so that the turbine inlet parameters are not affected by the free flow, thereby realizing the decoupling of the compressor air flow path and the turbine gas flow path in terms of thermal parameters. This special structure and working mode enables the ATR engine to have better hypersonic performance.

[0066] Figure 1 The names of the ATR engine components and the definitions of the section numbers are given, and the names of the section numbers are shown in Table 1.

[0067] Table 1 Names of ATR engine section numbers

[0068]

[0069] 2. Adaptive robust UKF design.

[0070] As shown in Figure 2 , the ATR engine control system state estimation method based on the adaptive robust UKF provided by the application comprises the following steps:

[0071] Step 1, establishing a nonlinear discrete model of the ATR engine control system, including the following sub-steps:

[0072] Step 1.1, establishing a state space model for the ATR engine control system:

[0073]

[0074] wherein the parameter superscript dot represents the differential of the parameter, the number of dots is the differential order thereof, and the same applies below; x is the engine state quantity, u is the engine input quantity, y is the engine output quantity, n, m, p are respectively the number of state quantities, the number of internal input quantities, the number of external input quantities and the number of output quantities of the state space model, and n < m < p, f(·) represents a state nonlinear function, and g(·) represents a measurement nonlinear function.

[0075] Step 1.2, determining the specific parameters of the engine state quantity, the engine input quantity and the engine output quantity.

[0076]

[0077] wherein the superscript T on (·) represents transposition, and the same applies below; N1 is the low-pressure rotor speed, N2 is the high-pressure rotor speed, W F is the main fuel flow, A8 is the tail nozzle throat area, T t7 is the combustor outlet total temperature, SM c is the compressor surge margin.

[0078] Step 1.3, discretizing the state space model.

[0079] x(k) = f k-1 (x(k-1), u(k)) + w(k-1)

[0080] y(k) = g k (x(k), u(k)) + v(k)

[0081] wherein x(k), y(k), u(k) are the discretized representations of the engine state quantity x, the engine output quantity y and the engine input quantity u at time k, f k-1 (·), g k (·) are the discretized representations of the state nonlinear function at time k-1 and the measurement nonlinear function at time k, x(k-1) is the engine state quantity at time k-1, w(k-1) is the system process noise at time k-1, and v(k) is the system measurement noise at time k.

[0082] Step 1.4, calculating the noise covariance matrix:

[0083] E[w(k-1)wT (k-1)] = Q(k-1)

[0084] E[v(k)v T (k)] = R(k)

[0085] where Q(k-1) is the system process noise covariance matrix at time k-1, R(k) is the measurement noise covariance matrix at time k, E[·] denotes the expectation of the variable, and the superscript T denotes the transpose.

[0086] Step 2, time update process, including the following sub-steps:

[0087] Step 2.1, variable initialization:

[0088]

[0089] where x0is the engine state quantity at the initial time, is the engine state quantity estimate at the initial time, and P0is the state error covariance matrix at the initial time; in this scheme, the superscript ∧ denotes the estimate of the parameter.

[0090] Step 2.2, select 2n+1 sampling points, and construct the state quantity of the sampling points:

[0091]

[0092] where χ i (k-1|k-1) represents the state quantity of the i-th sampling point at time k-1, i = 0, 1,..., 2n; (·)i represents the i-th column or i-th row of the matrix in the parentheses; for example is the i-th column or i-th row of P(k-1) represents the state estimate and state error covariance matrix at time k-1; n is the system state dimension, and λ is a complex scaling factor, given by:

[0093] λ = α 2 (n+ε)-n

[0094] where the parameter α determines the degree of distribution of the sampling points, and is usually selected as 0 < α < 1; ε is a scaling factor, and is usually set to 3-n.

[0095] Solve The cholesky decomposition method is usually used, but the cholesky decomposition method requires that the matrix is positive definite. Due to uncertain noise and numerical solution truncation error and other factors in the engine state estimation process, the positive definiteness of the covariance matrix cannot be met, so that the decomposition fails, and the filter performance will quickly decrease. The present application solves the square root of the covariance matrix through the singular value decomposition (SVD) method, avoiding the problem of solution failure caused by positive definiteness, thereby ensuring the reliability of state estimation.

[0096] Step 2.3, the engine state quantity estimation value at time k and the error covariance matrix are predicted:

[0097]

[0098]

[0099] In the formula, P(k|k-1) is the engine state quantity estimation value at time k-1 predicted at time k, and the error covariance matrix χ i (k|k-1) represents the state quantity predicted at time k-1 at time k at the i-th sampling point, respectively, the state estimation value and the error covariance weight coefficient corresponding to the i-th sampling point, and the expression is:

[0100]

[0101] In the formula, β is a parameter related to the prior knowledge distribution of the engine state quantity x(k) at time k, and is generally set to 2 under Gaussian distribution.

[0102] Step 3, the measurement update process, including the following sub-steps:

[0103] Step 3.1, the state quantity of the sampling point is updated using the state estimation value and the error covariance matrix predicted at time k-1 at time k:

[0104]

[0105] Step 3.2, the updated state quantity of the sampling point is converted using the measurement equation function:

[0106] γ i (k|k-1)=h k (χ i (k|k-1)), i=0...2n

[0107] In the formula, h k (·) is the measurement equation function, γ i (k|k-1) represents the converted state quantity of the sampling point.

[0108] Step 3.3. Calculate the engine output quantity estimate and the covariance matrix by the unscented transformation:

[0109]

[0110] where, denotes the engine output quantity estimate predicted at time k from time k-1, P yy (k) denotes the covariance matrix, and R(k) is the measurement noise covariance matrix at time k.

[0111] Step 3.4. Calculate the cross-covariance matrix P xy (k) between the state and the measurement:

[0112]

[0113] Step 4. Calculate the Kalman gain matrix process by the maximum correlation entropy criterion, including the following sub-steps:

[0114] Step 4.1. Define the pseudo-measurement matrix as:

[0115] H(k) = (P -1 (k|k-1)P xy (k)) T

[0116] where the parameter superscript -1 denotes inversion, such as P -1 (k|k-1) denotes the inverse matrix of P(k|k-1), and the same below; P(k|k-1) is the error covariance matrix predicted at time k from time k-1.

[0117] Theorem 1 (Statistical linear regression theorem) For a given nonlinear function approximation linearization y = g(x) ≈ Ax + c, where A is the variable coefficient matrix and c is the constant term, the coefficient solution of the minimum weighted error sum of squares is:

[0118]

[0119] where, are the means of x and y, P xy is the cross-covariance matrix of x and y, and P xx is the covariance matrix of x.

[0120] and the mean and the variance P ee of the error term e = y - Ax - c satisfy:

[0121]

[0122] where P yy is the covariance matrix of y, is the mean of c.

[0123] Step 4.2, according to theorem 1, the nonlinear engine output is converted into linear form by using pseudo-measurement matrix:

[0124]

[0125] where, is the measurement noise sequence, N(·) represents Gaussian distribution, is the measurement noise matrix after unscented transformation, and its expression is:

[0126]

[0127] Step 4.3, define the cost function:

[0128] The correlation entropy is a measure of the local similarity of two random variables, which can contain the high-order moment characteristics of the variables. At present, this method has been successfully applied to linear and nonlinear filtering, and has shown its advantages in dealing with non-Gaussian signals. Considering two joint density functions F X,Y(x,y) (x,y)

[0129] V(X,Y)=E[κ(X,Y)]=∫κ(x,y)dF X,Y (x,y)

[0130] where E represents the expectation operator, and κ(·,·) represents a positive definite bounded Mercer kernel function, which is given by:

[0131]

[0132] where e=x-y is the random variable error, and σ>0 is the kernel function bandwidth.

[0133] In many practical cases, the joint density function of random variables cannot be accurately obtained, and the correlation entropy function is approximated by a set of limited data samples and sample mean estimators:

[0134]

[0135] where N is the sample number, e(i)=x(i)-y(i), is the sample data taken from F X,Y (x,y) , by which it can be found that the Gaussian correlation entropy is positive definite and bounded, and only when X=Y, the formula reaches the maximum value. When the Taylor expansion is performed on the Gaussian kernel function, we can get:

[0136]

[0137] It can be seen from the analysis that the correlation entropy is a weighted sum of all even moments of the random variable X-Y, and when a suitable kernel bandwidth is selected, the correlation entropy can capture the high-order moment characteristics of the variable. For Gaussian signals, the mean and covariance are sufficient to describe the overall distribution characteristics of the signals, so the traditional Kalman filter and its derivative methods that meet the minimum mean square error criterion can achieve optimal estimation of Gaussian systems. However, when there is a non-Gaussian signal in the system state or measurement equation, the maximum correlation entropy criterion will be more suitable for processing high-order information, thereby improving the state estimation accuracy.

[0138] Given an error data sequence The cost function of the maximum correlation entropy is defined as:

[0139]

[0140] Suppose x is the vector parameter to be estimated by the adaptive system, and the parameter estimation problem based on the maximum correlation entropy criterion can be converted into the following optimization problem:

[0141]

[0142] In the formula, represents the optimal estimation of the state, and Ω represents the feasible set of the parameter.

[0143] Inspired by the maximum correlation entropy criterion, the application defines a weighted combination cost function including the state and the measurement output error. The system noise is processed by the weighted least squares method, and the sensor measurement noise with non-Gaussian is processed by the maximum correlation entropy criterion, aiming to capture the high-order moment characteristics of the sensor noise as much as possible through the maximum correlation entropy criterion, and improve the estimation accuracy under non-Gaussian noise.

[0144] The cost function is defined as follows:

[0145]

[0146] In the formula, α' and β' are adjustable weight coefficients, and ||t|| is the Euclidean norm of the error vector t. M =(t T Mt) 1 / 2 , for example:

[0147] is a Gaussian kernel function with σ y as the kernel bandwidth.

[0148] The Gaussian kernel bandwidth σ yThe filter performance is greatly influenced, and the kernel bandwidth is still selected according to experience and trial and error method at present, so the filter does not have self-adaptability and robustness when the working environment changes greatly or the noise characteristics change.The application proposes a method for adaptively adjusting the bandwidth of the kernel function according to the error between the actual measurement value and the estimated value, and the adaptive law can adaptively adjust the filter robustly, and can ensure that the filter has good filtering performance when the environmental noise characteristics change greatly, and the expression is as follows:

[0149]

[0150] Based on the problem description of the maximum correlation entropy criterion, the engine state quantity estimated value at the k moment can be converted into the following optimization problem:

[0151]

[0152] When the partial derivative of the cost function is zero, the state is the optimal state solution.

[0153] Step 4.4, based on the cost function to solve the Kalman filter gain matrix:

[0154]

[0155] In the formula, Indicates the partial derivative, and ξ is an intermediate variable, and the expression is as follows:

[0156]

[0157] Take α'=1, Substituting the above formula gives:

[0158]

[0159] After arrangement, it is:

[0160]

[0161] In the formula, Is the Kalman filter gain matrix, and the expression is as follows:

[0162]

[0163] Step 5, the robust state estimator design process, including the following sub-steps:

[0164] Step 5.1, set the robust state estimator batch processing regression form:

[0165]

[0166] In the formula, Is the measurement noise sequence, and I is the unit matrix.

[0167] The robust state estimator can be rewritten in a compact form as follows:

[0168]

[0169] where the observation vector The regression matrix The error vector and the error covariance matrix is:

[0170]

[0171] where E(·) denotes the expectation operation, is the measurement noise matrix after the unscented transformation.

[0172] The state estimation result is robust if the robust scale of the residual vector is minimized, i.e.,

[0173]

[0174] where is the engine state estimation at time k, is a robust scale estimator. The minimization of the robust scale estimator can ensure the isolation of abnormal measurement values (engine output y); for example, the estimator of the least squares median (LMS) will minimize the median of the absolute residual; the weighted least squares estimator (WLS) will minimize the standard deviation of the residual; is the residual vector, r i is the i-th residual component in the residual vector, i = 1, 2, …, m; m is the dimension of the observation vector .

[0175] Step 5.2, define the robust scale estimator of the robust state estimator to minimize the robust scale of the residual vector.

[0176]

[0177] where δ ∈ [0, 1], and the function ρ(·) is a bounded even function satisfying .

[0178] The robust scale estimator is generally solved by iteration:

[0179]

[0180] where is the relative standard residual, and the weight function is:

[0181]

[0182] in, is the observation vector The i-th component of .

[0183] In one embodiment of the present invention, the selected ρ(·) function is a bisquare function, which is defined as follows:

[0184]

[0185] Where c is the generalized relative residual threshold.

[0186] Step 5.3, calculate the weight function as:

[0187]

[0188] The robust state estimator is thus obtained and applied to the front end of the adaptive UKF filter. The reweighting function of the above robust scale estimator is used to perform robust scale correction on the residual vector, thereby isolating the influence of abnormal measurement values.

[0189] The robust scaling in the traditional standard deviation form corresponds to an unbounded ρ function estimator, namely And δ = 1, this method will use an equal weight for all observations This method weights all observations, reducing robustness to outliers. This method, however, reweights all observations, assigning a weight of 1 to normal observations and a weight less than 1 to outliers. The further the outlier observation is from the normal value, the smaller its weight becomes, down to 0, thus isolating it. Minimizing the robustness scale of the robust state estimator's residuals has been shown to produce highly accurate robust estimation results.

[0190] Step 6, updating the state estimate and covariance matrix process, includes the following sub-steps:

[0191] Step 6.1, update the estimated value of engine state:

[0192]

[0193] In the formula, ε is an intermediate variable, and the parameter subscript t represents the result of the t-th iteration of the parameter, for example Indicates the result obtained at the tth iteration The solution of the state variable matrix is ​​essentially a fixed point iterative equation, which can generally be solved by iteration. When the accuracy requirements are met, the iterative solution is approximately the state estimation solution. In order to meet the algorithm recursive form and reduce the computational burden, the present invention adopts a single iteration method. Approximately replacing x(k), the intermediate variable ξ can be simplified to:

[0194]

[0195] At this time can be approximated as shown in the following formula:

[0196]

[0197] wherein, There is another expression form, the proof process is shown in theorem 1:

[0198]

[0199] Step 6.2, state error covariance matrix update:

[0200]

[0201] Theorem 1 when the Gaussian kernel bandwidth σ y Tends to infinity, the filter converges to the standard UKF filter.

[0202] Proof: the above filter derivation process is completely consistent with the standard UKF in the time update step, only need to prove

[0203] When σ y →∞, x(k) and P(k) in the measurement update step are the same as the update algorithm in the standard UKF.

[0204] Lemma 2 if the square matrix A is invertible, the square matrix C is invertible, and the matrix A+BCD is invertible, then

[0205] (A+BCD) -1 =A -1 -A -1 B(C -1 +DA -1 B)DA -1

[0206] Consider the formula

[0207] Take A=P -1 (k|k-1), B=ξH T (k), Satisfy the reversible condition of lemma 2, so based on lemma 2 can be obtained:

[0208]

[0209] Assume A=I, B=I, D=H(k)P(k|k-1)ξH T (k), using lemma 2 in reverse can be obtained:

[0210]

[0211] The formula is also Formula Another form of the Kalman gain matrix

[0212] When σ y →∞, ξ→1, and H(k) and Substituting the above formula gives:

[0213]

[0214] It can be seen that the Kalman gain matrix in the formula is calculated in the same way as the standard UKF gain matrix Consider the state covariance matrix P(k):

[0215]

[0216] Substituting and into the above formula gives:

[0217]

[0218] Based on Formula It can be seen that Substituting the above formula gives:

[0219]

[0220] The covariance matrix is calculated in the same way as the standard UKF covariance matrix Therefore, according to the above proof process, when σ y →∞, the adaptive UKF filter proposed in this paper converges to the standard UKF filter.

[0221] Theorem 1 is proved.

[0222] When there is a sudden large outlier or shot noise in the system measurement, i.e., ||y(k)|| ∞ →∞, there is ξ→0, and P(k) = P(k|k-1). The filter can keep the state at the previous time in time, and has a certain robustness to the noise.

[0223] The above examples are only used to illustrate the technical solutions of the present application, and not to limit them; although the present application has been described in detail with reference to the foregoing examples, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing examples, or make equivalent replacements for some technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application, and should be included in the protection scope of the present application.​

Claims

1. A state estimation method for an ATR engine control system based on an adaptive robust UKF, characterized in that: include: Establishing a nonlinear discrete model of the ATR engine control system, including establishing a state-space model for the ATR engine control system, determining specific parameters of engine state variables, engine input variables, and engine output variables, discretizing the state-space model, and calculating the noise covariance matrix; The time update process includes initializing the engine state quantity and state error covariance matrix, selecting sampling points and constructing the state quantity of the sampling points, and predicting the estimated value of the engine state quantity and the error covariance matrix; The measurement update process includes updating the state quantity of the sampling point, converting the state quantity of the updated sampling point using the measurement equation function, calculating the engine output estimate and covariance matrix through untraceable transformation, and calculating the state-measurement cross covariance matrix; The process of calculating the Kalman gain matrix by the maximum correlation entropy criterion includes defining a pseudo-measurement matrix, converting the nonlinear engine output into a linear form using the pseudo-measurement matrix, defining a cost function, and solving the Kalman filter gain matrix based on the cost function; The process of updating the state estimation and covariance matrix includes updating the engine state quantity estimation value and the state error covariance matrix.

2. The state estimation method of ATR engine control system based on adaptive robust UKF according to claim 1 is characterized in that: The method further comprises: Robust state estimator design process; first design the batch regression form of the robust state estimator, and rewrite it into a compact form to obtain the observation vector, regression matrix, error vector and error covariance matrix; minimize the robust scale of the residual vector, including defining a robust scale estimator and constructing a weight function to solve the robust scale estimator.

3. The state estimation method of ATR engine control system based on adaptive robust UKF according to claim 1, characterized in that: Constructed with σ y is the Gaussian kernel function of the kernel bandwidth, which is used to define the cost function; the kernel bandwidth σ y The expression is as follows: Where y(k) is the engine output, represents the estimated value of the engine output at time k-1 for the prediction at time k; R(k) is the measurement noise covariance matrix at time k, and the superscript -1 indicates the matrix inversion; ||t|| M =(t T Mt) 1 / 2 .

4. The state estimation method of an ATR engine control system based on an adaptive robust UKF according to claim 1, characterized in that: Select sampling points and construct the state of the sampling points, including: Where, χ i (k-1|k-1) represents the state of the i-th sampling point at time k-1, i = 0, 1, ..., 2n; (·)i represents the i-th column or i-th row of the matrix in the brackets; P(k-1) represents the state estimate and state error covariance matrix at time k-1; n is the system state dimension, λ is the composite scaling factor, λ = α 2 (n+ε)-n; 0<α<1, ε is the scaling factor; Solve by singular value decomposition method 5. The state estimation method of ATR engine control system based on adaptive robust UKF according to claim 1, characterized in that: The cost function is as follows: Where α′ and β′ are adjustable weight coefficients, is σ y is the Gaussian kernel function with kernel bandwidth; x(k) represents the engine state quantity, represents the state estimation value at time k-1; P(k|k-1) is the error covariance matrix of the prediction at time k-1 for time k, y(k) is the engine output, It represents the estimated value of the engine output predicted at time k at time k-1, and H(k) is the pseudo measurement matrix.

6. The state estimation method of ATR engine control system based on adaptive robust UKF according to claim 1, characterized in that: Solve the Kalman filter gain matrix based on the cost function, as follows: Where, Indicates partial derivative, ξ is the intermediate variable, and the expression is as follows: Take α′=1, Substituting into the above formula we get: Arranged: Where, is the Kalman filter gain matrix, which is expressed as follows:

7. The state estimation method of ATR engine control system based on adaptive robust UKF according to claim 2, characterized in that: The robust state estimator is expressed as: Where, x(k) represents the engine state, represents the estimated state value at time k-1; is the measurement noise sequence, I is the unit matrix; y(k) is the engine output, represents the estimated value of the engine output at time k-1 predicted for time k; H(k) is the pseudo measurement matrix; The robust state estimator is rewritten into the following compact form: Among them, the observation vector Regression matrix Error vector And the error covariance matrix is: Where E(·) represents the expectation operation, is the measurement noise matrix after unscented transformation, P(k|k-1) is the error covariance matrix of the prediction at time k-1 for time k; If the robust scale of the residual vector can be minimized, the state estimation result is robust, that is: Where, is the estimated value of the engine state at time k, is a robust scale estimator; is the residual vector, r i (x(k)) is the i-th residual component in the residual vector, i = 1, 2, ..., m; m is the observation vector The dimension of .

8. The state estimation method of ATR engine control system based on adaptive robust UKF according to claim 7, characterized in that: The robust scale estimator is constructed as follows: Where δ∈[0,1], function ρ(·) satisfies Bounded even function of ; Robust scale estimator Solve by iteration: Where, is the relative standard residual, and the weight function is: in, is the observation vector The i-th component of .

9. A terminal device comprising a processor, a memory, and a computer program stored in the memory; characterized in that: When the processor executes the computer program, the state estimation method of the ATR engine control system based on the adaptive robust UKF according to any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium storing a computer program; wherein: When the computer program is executed by a processor, the state estimation method of an ATR engine control system based on an adaptive robust UKF according to any one of claims 1 to 8 is implemented.

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