Modeling method and system for non-cooperative target observation and readable storage medium

Abstract

The embodiment of the invention provides a modeling method and system for non-cooperative target observation and a readable storage medium, and the method comprises the steps: employing multiple measurement devices of a non-cooperative target observation system to observe a non-cooperative target, constructing a multi-station nonlinear observation model of the non-cooperative target based on an EMBET estimation method, introducing a non-parametric variable, and carrying out the modeling of the non-cooperative target. Forming a multi-station nonlinear semi-parameter model based on the uncertain error component; constructing a regularization matrix based on the influence factors of the influence error and enabling the regularization matrix to have uniqueness, and optimizing the multi-station nonlinear semi-parameter model based on the uncertain error component by adopting an optimal regularization matrix set formed by the regularization matrix with uniqueness to obtain an optimized semi-parameter model; and solving the position of the non-cooperative target observed by the multiple measurement devices by using the optimized semi-parameter model to obtain the position of the non-cooperative target. The positioning precision is improved, the observation system error is accurately identified, and a theoretical basis is provided for complex error modeling and identification of a non-cooperative target.

Description

Technical Field

[0001] The present invention relates to the field of non-cooperative target observation, and in particular to a modeling method, system and readable storage medium for non-cooperative target observation. Background Art

[0002] Target tracking and positioning refers to the theory, technology and methods of extracting the target's motion state from observation information under a unified time and space reference. High-precision target positioning is the premise and key to the implementation of tasks in the fields of strategic deployment, military strikes, space resource detection and development, etc.

[0003] With the expansion of application needs in weapon attack and defense and space detection, the high mobility, cross-regional, multi-task characteristics and the lack of prior information on non-cooperative targets make it difficult to determine the target's motion state. The observation system has the characteristics of high dynamics, nonlinearity, complex variability and uncertainty, which leads to unclear mechanisms and complex and uncertain forms of non-cooperative target observation errors. The error model is difficult to accurately construct and the error parameters are difficult to effectively estimate, which has become a bottleneck restricting the high-precision positioning of non-cooperative targets.

[0004] Currently, the observation system error modeling and estimation methods mainly include parametric methods, non-parametric methods and semi-parametric methods.

[0005] The non-parametric method eliminates the assumption on the form of the model function and converts the prior information such as continuity into constraints, thereby controlling the state solution characteristics and avoiding the risks brought by representation errors. However, it fails to effectively utilize the prior information that can be effectively modeled in the target motion.

[0006] The semi-parametric method combines parametric models with non-parametric components, has stronger adaptability and interpretability, and has been widely studied and applied in measurement data processing. Estimation methods such as parametric approximation, two-step estimation, and robust estimation have been developed. The selection of parameters such as the regularization matrix in the model is an important factor affecting the accuracy of semi-parametric estimation, which usually depends on practical experience or post-data analysis. The main methods of constructing the regularization matrix include spline function fitting, time series characteristics, prior variance, and distance optimization. However, in the non-cooperative target multi-station observation system, the observation error is complex and changeable. The above construction method does not consider the error influencing factors, and the fixed regularization matrix is ​​difficult to accurately describe the error characteristics of the multi-station system, resulting in a decrease in positioning accuracy. It is necessary to study the online adaptive design method of the regularization matrix in combination with the error influencing factors of the multi-station observation system. Summary of the invention

[0007] The embodiments of the present invention provide a modeling method, system and readable storage medium for non-cooperative target observation, which can solve the technical problem in the prior art that "error influencing factors are not considered, and a fixed regularization matrix is ​​difficult to accurately describe the error characteristics of a multi-station system, resulting in a decrease in positioning accuracy."

[0008] To achieve the above objectives, in a first aspect, an embodiment of the present invention provides a modeling method for non-cooperative target observation, comprising:

[0009] A non-cooperative target is observed by using multiple measurement devices of a non-cooperative target observation system, and a multi-station nonlinear observation model of the non-cooperative target is constructed based on an EMBET estimation method, wherein the multi-station nonlinear observation model includes a modelable system error, and non-parametric variables are introduced into the multi-station nonlinear observation model. The non-parametric variables are used to describe the observation system error and / or model error that cannot be modeled, so as to form a multi-station nonlinear semi-parametric model based on uncertain error components;

[0010] Determine the factors affecting the estimation accuracy of the multi-station nonlinear semi-parametric model based on the uncertain error component: regularization matrix, construct a regularization matrix based on the influencing factors affecting the error and make the regularization matrix unique, the unique regularization matrix has l-point smoothing invariance and elementary transformation invariance, use the optimal regularization matrix set constructed by the unique regularization matrix to optimize the multi-station nonlinear semi-parametric model based on the uncertain error component, and obtain an optimized semi-parametric model;

[0011] An optimized multi-station nonlinear semi-parametric model is used to solve the position of the non-cooperative target observed by multiple measurement devices, and the position of the non-cooperative target is obtained.

[0012] In a second aspect, an embodiment of the present invention provides a modeling system for non-cooperative target observation, including:

[0013] An observation model construction unit is used to observe a non-cooperative target using multiple measurement devices of a non-cooperative target observation system, and to construct a multi-station nonlinear observation model of the non-cooperative target based on an EMBET estimation method, wherein the multi-station nonlinear observation model includes a modelable system error, and non-parametric variables are introduced into the multi-station nonlinear observation model. The non-parametric variables are used to describe the observation system error and / or model error that cannot be modeled, so as to form a multi-station nonlinear semi-parametric model based on uncertain error components;

[0014] A model optimization unit is used to determine the factors that affect the estimation accuracy of the multi-station nonlinear semi-parametric model based on uncertain error components: a regularization matrix is ​​constructed based on the factors that affect the error and the regularization matrix is ​​unique. The unique regularization matrix has l-point smoothing invariance and elementary transformation invariance. The multi-station nonlinear semi-parametric model based on uncertain error components is optimized using an optimal regularization matrix set constructed by a unique regularization matrix to obtain an optimized semi-parametric model.

[0015] The solving unit is used to solve the position of the non-cooperative target observed by multiple measurement devices by using an optimized semi-parametric model to obtain the position of the non-cooperative target.

[0016] In a third aspect, an embodiment of the present invention provides a computer-readable storage medium, which stores one or more programs. When the one or more programs are executed by a computer device, the computer device executes the modeling method of non-cooperative target observation mentioned above.

[0017] The above technical solution has beneficial effects: it can improve positioning accuracy, accurately identify observation system errors, and provide a theoretical basis for complex error modeling and identification of non-cooperative targets. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] 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 some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0019] Figure 1 is a flow chart of a modeling method for non-cooperative target observation according to an embodiment of the present invention;

[0020] Figure 2 is a structural diagram of a modeling system for non-cooperative target observation according to an embodiment of the present invention;

[0021] Figure 3 is a schematic diagram of a space target observation system according to an embodiment of the present invention;

[0022] Figure 4 It is a fusion estimation method based on a hybrid semi-parametric model according to an embodiment of the present invention;

[0023] Figure 6 is a hybrid semi-parametric model based on model likelihood values ​​according to an embodiment of the present invention;

[0024] Figure 5 is an example of a multi-station ranging and positioning system according to an embodiment of the present invention;

[0025] Figure 7 It is the complex error sampling data based on the mixed effect of multiple influencing factors in the embodiment of the present invention;

[0026] Figure 8 It is a comparison of the results of various methods under complex periodic errors of the embodiment of the present invention;

[0027] Fig. 9 It is a comparison of the results of various methods under the complex FBM error of the embodiment of the present invention;

[0028] Fig.10 is the estimation accuracy of each algorithm in the optimization process of the embodiment of the present invention;

[0029] Fig.11 It is a comparison of the estimation results of each algorithm after weight optimization in the embodiment of the present invention. DETAILED DESCRIPTION

[0030] 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.

[0031] like Figure 1 As shown, in combination with an embodiment of the present invention, a modeling method for non-cooperative target observation is provided, comprising:

[0032] S101: observe a non-cooperative target using multiple measurement devices of a non-cooperative target observation system, construct a multi-station nonlinear observation model of the non-cooperative target based on an EMBET estimation method, wherein the multi-station nonlinear observation model includes a modelable system error, introduce non-parametric variables into the multi-station nonlinear observation model, describe the non-modelable observation system error and / or model error through the non-parametric variables, and form a multi-station nonlinear semi-parametric model based on uncertain error components;

[0033] S102: determining factors affecting the estimation accuracy of the multi-station nonlinear semi-parametric model based on uncertain error components: a regularization matrix, and constructing a regularization matrix based on the factors affecting the error and making the regularization matrix unique, the regularization matrix with uniqueness has l-point smoothing invariance and elementary transformation invariance, and optimizing the multi-station nonlinear semi-parametric model based on uncertain error components using an optimal regularization matrix set constructed by the regularization matrix with uniqueness to obtain an optimized semi-parametric model;

[0034] S103: using an optimized semi-parametric model to solve the position of the non-cooperative target observed by multiple measurement devices to obtain the position of the non-cooperative target.

[0035] like Figure 2 As shown, in combination with an embodiment of the present invention, a modeling system for non-cooperative target observation is provided, including:

[0036] An observation model construction unit 21 is used to observe a non-cooperative target using multiple measurement devices of a non-cooperative target observation system, and to construct a multi-station nonlinear observation model of the non-cooperative target based on an EMBET estimation method, wherein the multi-station nonlinear observation model includes a modelable system error, and non-parametric variables are introduced into the multi-station nonlinear observation model. The non-parametric variables are used to describe the observation system error and / or model error that cannot be modeled, so as to form a multi-station nonlinear semi-parametric model based on uncertain error components;

[0037] The model optimization unit 22 is used to determine the factors that affect the estimation accuracy of the multi-station nonlinear semi-parametric model based on the uncertain error component: a regularization matrix, and construct a regularization matrix based on the influencing factors that affect the error and make the regularization matrix unique. The unique regularization matrix has l-point smoothing invariance and elementary transformation invariance. The multi-station nonlinear semi-parametric model based on the uncertain error component is optimized by using an optimal regularization matrix set constructed by a unique regularization matrix to obtain an optimized semi-parametric model.

[0038] The solving unit 23 is used to solve the position of the non-cooperative target observed by multiple measurement devices by using an optimized semi-parametric model to obtain the position of the non-cooperative target.

[0039] Preferably, in S101, a non-cooperative target is observed by using multiple measurement devices of a non-cooperative target observation system, and a multi-station nonlinear observation model of the non-cooperative target is constructed based on an EMBET estimation method, wherein the multi-station nonlinear observation model includes a modelable system error, including the following:

[0040] The non-cooperative target is observed by multiple measurement devices in the non-cooperative target observation system, and a multi-station nonlinear observation model of the non-cooperative target is constructed based on the EMBET estimation method:

[0041]

[0042] In the formula, The system state includes the modelable system error, e is the random error, y is the observed value of m measurement devices, and f(·) is the A function whose functional form and parameters are known.

[0043] The above technical means are also specific embodiments of the observation model building unit 21.

[0044] Preferably, the multi-station nonlinear semi-parametric model based on uncertain error components includes a point-by-point semi-parametric model, wherein the point-by-point semi-parametric model does not make time series assumptions on the system state and non-parametric components, the system state and non-parametric components at different times are unrelated, and the system state and non-parametric components at each time are estimated independently;

[0045] In S101, non-parametric variables are introduced into the multi-station nonlinear observation model, and the non-parametric variables are used to describe the observation system errors and / or model errors that cannot be modeled, so as to form a multi-station nonlinear semi-parametric model based on uncertain error components, including:

[0046] Non-parametric variables are introduced into the multi-station nonlinear observation model. The non-parametric components are used to describe the unmodelable system errors or model errors in the multi-station nonlinear observation model corresponding to the m measurement devices at a certain time, forming a point-by-point semi-parametric model. The point-by-point semi-parametric model is expressed as:

[0047]

[0048] In the formula, s represents the non-parametric component, is the covariance matrix of the random error e, and P is the weight matrix of the observation y; the residual of the point-by-point semiparametric model is calculated, and the residual of the point-by-point semiparametric model of formula (2) is expressed as:

[0049]

[0050] The normal equation of formula (3) is:

[0051]

[0052] Where J represents the Jacobian matrix;

[0053] Due to the introduction of non-parametric components, the coefficient matrix of the normal equation (4) is semi-positive definite and irreversible. The compensated least squares criterion is used to correct the normal equation (4), thereby correcting equation (3):

[0054]

[0055] In formula (4), the factors affecting the estimation accuracy of the multi-station nonlinear semi-parametric model based on uncertain error components are: smoothing factor α and regularization matrix R; a Lagrangian function is constructed to solve formula (5), and the constructed Lagrangian function is expressed as:

[0056]

[0057] make get:

[0058]

[0059] From formula (7), we can get:

[0060]

[0061]

[0062] in, is the Jacobian matrix, abbreviated as J; the system state estimation value and non-parametric estimation value obtained by solving equation (5) are:

[0063]

[0064] Among them, S is the intermediate quantity, the superscript k represents the kth iteration, and I represents the large unit matrix.

[0065] The above technical means are also specific embodiments of the observation model building unit 21.

[0066] Preferably, the multi-station nonlinear semi-parametric model based on uncertain error components also includes a semi-parametric model based on spline representation, the semi-parametric model based on spline representation makes time series assumptions on the system state and non-parametric components, assumes that the system state and the semi-parametric components satisfy the spline function within a period of time, and jointly estimates the system state and non-parametric components within a period of time;

[0067] In S101, non-parametric variables are introduced into the multi-station nonlinear observation model, and the non-parametric variables are used to describe the observation system errors and model errors that cannot be modeled, so as to form a multi-station nonlinear semi-parametric model based on uncertain error components, including:

[0068] When the non-cooperative target is observed by the multi-measurement equipment of the non-cooperative target observation system, it is assumed that the system state and non-parametric components within a period of time conform to the spline function and are added to the multi-station nonlinear observation model of the non-cooperative target to form a semi-parametric model based on spline representation. The semi-parametric model based on spline representation is expressed as:

[0069]

[0070] Among them, the observed value y i =[y i1 ,y i2 ,…,y im ] T , represents the observed value of the 1st, 2nd, ..., mth measuring device at the i-th moment, e i is the m-dimensional random error, the nonparametric component s(t i )=[s1(t i ),s2(t i ),…,s m (t i )] T ,s l (t i ),l=1,2,…,m describes the observed quantity y il The unmodeled systematic errors and / or model errors of the observed quantity y il Yesi l components of i t i Observed value y at time i The weight matrix of , the system state β is the polynomial coefficient or spline polynomial coefficient of the non-cooperative target in this time period;

[0071] The semiparametric model based on spline representation is i Time residual V i =[V i1 ,V i2 ,…,V im ] T It is expressed as:

[0072]

[0073] Due to the introduction of non-parametric components, the coefficient matrix of the normal equation (4) is semi-positive definite and irreversible. The compensated least squares criterion is used to correct the normal equation (4), thereby correcting equation (13) as follows:

[0074]

[0075] According to the properties of the semi-parametric model based on spline representation, such as continuity and differentiability at the observation nodes, equation (14) can be obtained:

[0076]

[0077] Where F and G are sparse matrices determined by the observation sampling interval, which are constructed to solve equation (15) and construct the Lagrangian function:

[0078]

[0079] In the formula, the factors affecting the estimation accuracy of the multi-station nonlinear semi-parametric model based on uncertain error components are: smoothing factor α and regularization matrix R, R = FG -1 F T , P=diag(P1,P2,…,P n ), s=(s T (t1),s T (t2),…,s T (t n )) T ,

[0080] By finding the minimum value of formula (16), we can obtain:

[0081]

[0082] From formula (17), we can get:

[0083]

[0084]

[0085] The system state estimation value and non-parametric estimation value obtained by solving equation (15) are:

[0086]

[0087] Among them, S is the intermediate quantity, the superscript k represents the kth iteration, and I represents the large unit matrix.

[0088] The above technical means are also specific embodiments of the observation model building unit 21.

[0089] Preferably, in S102, a regularization matrix is ​​constructed based on the influencing factors affecting the error and is made unique. The unique regularization matrix has l-point smoothing invariance and elementary transformation invariance, including:

[0090] For the point-by-point semiparametric model, the optimal regularization matrix set is constructed based on the factors affecting the error. One error has one regularization matrix set. The set of factors affecting the error of the measured element is A = {a1, a2, ...}, where a i , i = 1, 2, ... represents the influencing factors of the measurement error. The measuring station where the measuring equipment is located has the influencing factors of the measurement error a i The set of values ​​under is M i ={X 01 (a i ),X 02 (a i ),…,X 0m (a i )}, then the influencing factor of the measurement error is a i The measurement error of station j is determined to be X 0j (a i ),j=1,2,…,m, and this mapping relationship is recorded as:

[0091] X 0j (a i ) → g i (X 0j (a i ))

[0092] where g i (·) is the influence factor of observation error on measurement error a i Functional form; M i is an ordered set, there exists a set M i The binary relation H(a i), i = 1, 2, ..., satisfying reflexivity, antisymmetry, and transitivity, using sequence pairs <M i ,H(a i )> is expressed as, at this time, the influencing factor of the measurement error is called a i is an ordered factor;

[0093] The influencing factors of the measurement error are a i The optimal regularization matrix set M determined by i is O(a i ),make:

[0094]

[0095] Let g i (X 00 (a i ))=0, then the symmetric matrix R i1 for

[0096]

[0097] Where p and q represent the p-th row and q-th column of the matrix respectively;

[0098] According to formula (41), R i2 and R i3 the specific form of

[0099] R ik , (k=1,2,3) describes the function type of s through the functional relationship between two adjacent points. The value of each regularization matrix in the regularization matrix set corresponds to the weight of the measurement error. The functional relationship and weight between the components of the non-parametric components are described by the regularization matrix set. The compensated least squares criterion is used to make R ik ∈O(a i ),(k=1,2,3); and the optimal regularization matrix set O(a i ) has the following two characteristics:

[0100] (1) l-point smoothing invariance: This means that no matter how many adjacent non-parametric components are smoothed, the regularized matrix obtained is in the optimal regularized matrix set;

[0101] (2) Invariance under elementary transformations: Any element in the optimal regularized matrix set still belongs to the optimal regularized matrix set after an elementary transformation of the matrix.

[0102] The above technical means are also specific embodiments of the model optimization unit 22 .

[0103] Preferably, the modeling method for non-cooperative target observation further includes:

[0104] The semi-parametric model based on spline representation has a unique regularization matrix, and the corresponding optimal regularization matrix set is constructed in combination with the error influencing factor set A={a1, a2, ...}.

[0105] The above technical means are also specific embodiments of the model optimization unit 22 .

[0106] Preferably, in S102, the multi-station nonlinear semi-parametric model based on uncertain error components is optimized by using an optimal regularization matrix set formed by a unique regularization matrix to obtain an optimized semi-parametric model, including:

[0107] The geometric dilution of precision (GDOP) is the observation error magnification factor, and formula (46) is used as the objective function of weight optimization:

[0108]

[0109] in, is the precision estimate, m p is the number of parameters to be estimated, where the parameters to be estimated refer to the components in the system state;

[0110] Introduce the likelihood value of the semi-parametric model at each moment, the semi-parametric model includes: a point-by-point semi-parametric model and a semi-parametric model based on spline representation, to form a hybrid semi-parametric model based on model likelihood value, M is the number of hybrid semi-parametric models, generally M≥r; Λ j,k ,j=1,2,…,M is the likelihood value of each model at time k, and the calculation method of the likelihood value at time k is:

[0111]

[0112] Among them, r is the intermediate variable;

[0113] By introducing the likelihood value at the current moment, the weights of each regularization matrix in the optimal regularization matrix set at the next moment are adaptively adjusted, so that the weight of each semi-parametric model is close to the mixed semi-parametric model with the largest likelihood value, thereby converging to the optimal weight of the model at the current stage, adapting to the different requirements of the mixed weights of errors at different stages. One stage includes multiple moments.

[0114] Assume that the mixed semiparametric model with the maximum likelihood value at the current moment is:

[0115] Λ q,k =max{Λ 1,k ,Λ 2,k ,…,Λ M,k} (43)

[0116] Then at the next moment, the mixed weight of the error is adjusted as follows:

[0117]

[0118] Where μ is a random number in the interval [0,1].

[0119] The above technical means are also specific embodiments of the model optimization unit 22 .

[0120] Preferably, in S102, the multi-station nonlinear semi-parametric model based on uncertain error components is optimized by using an optimal regularization matrix set formed by a unique regularization matrix to obtain an optimized semi-parametric model, including:

[0121] (1) Constructing the optimal regularization matrix

[0122] After constructing the optimal regularization matrix set according to formula (42), the number of hybrid semi-parametric models M is set, k=1, and the proportion of each factor affecting the error in the observed error is initialized. The proportion represents the weight of each regularization matrix in the optimal regularization matrix set, so that the weight of each regularization matrix satisfies:

[0123]

[0124] (2) Regularization matrix for interactive mixing

[0125] Calculate factor mixture values ​​based on weights The mixed regularization matrices are constructed by formula (42) to form a mixed semi-parametric model 1, 2, ..., M;

[0126] (3) Hybrid semi-parametric estimation

[0127] Determine the components α within the smoothing factor α by using the generalized cross-verification method or the L-curve method j,k , the system state estimation value and non-parametric estimation value at the current moment are obtained through equation (11) or (20) respectively

[0128] (4) Multi-model information fusion

[0129] According to formula (46), the estimation accuracy of M hybrid semi-parametric models is calculated, and the estimated value of the system state at the current moment is obtained by optimal weighted fusion of each hybrid semi-parametric model. The optimal weighted fusion method of each hybrid semi-parametric model is:

[0130]

[0131] (5) Weight Adaptive Optimization

[0132] Let k = k + 1, calculate the likelihood value of each hybrid semi-parametric model according to formula (48), and then adaptively optimize the weight according to formulas (49) and (51); proceed to step (2) until k = N; the likelihood value of the hybrid semi-parametric model includes the current model information and model jump information, the current information refers to the likelihood value of each hybrid semi-parametric model at the current moment, and the model jump information refers to the change in the likelihood value of each hybrid semi-parametric model. If the real weights of the factors affecting the error change, the model jumps; the change in the likelihood value of the model is fed back to the weight of each regularization matrix at the next moment, and the weight is adaptively optimized according to the proportion of factors affecting the error at each stage;

[0133] The optimized semi-parametric model is obtained.

[0134] The above technical means are also specific embodiments of the model optimization unit 22 .

[0135] In combination with an embodiment of the present invention, a computer-readable storage medium is provided, which stores one or more programs. When the one or more programs are executed by a computer device, the computer device executes any of the aforementioned non-cooperative target observation modeling methods.

[0136] The beneficial technical effects achieved by the embodiments of the present invention are as follows:

[0137] The multi-station complex error uncertainty modeling and estimation method based on the hybrid semi-parametric model achieves high-precision target estimation and accurate error identification. In the non-cooperative target observation system, the errors are complex and changeable, the error model is uncertain, and the parameterized model has representation errors. Therefore, point-by-point and spline multi-station semi-parametric models of non-cooperative targets are constructed.

[0138] The traditional regularization matrix does not take into account the influencing factors of the error and cannot accurately describe the error characteristics of the multi-station system. Therefore, a regularization matrix construction method based on multiple factors is proposed, and its l-point smoothing invariance and elementary transformation invariance are proved.

[0139] On this basis, the model likelihood information is introduced, and a hybrid semi-parametric model based on weight online adaptive optimization is designed. Compared with the traditional semi-parametric model, the optimality of the regularization matrix and the optimization efficiency are enhanced.

[0140] It can improve positioning accuracy, accurately identify observation system errors, and provide a theoretical basis for complex error modeling and identification of non-cooperative targets.

[0141] The above technical solution of the embodiment of the present invention is described in detail below in conjunction with specific application examples. For technical details not introduced during the implementation process, please refer to the relevant description in the previous text.

[0142] In the prior art, the error mechanism of non-cooperative target observation systems is unclear, the form is complex and uncertain, and it is difficult to accurately model the parameters, which restricts the high-precision positioning of the target. The embodiment of the present invention proposes a target uncertainty error modeling and estimation method based on hybrid semi-parametric statistics, and constructs a regularization matrix (RM) method. Experiments and numerical simulation experiments show that it can accurately identify the source, form and change of uncertainty errors, and achieve high-precision target positioning.

[0143] 1. Regarding the problem of non-cooperative target positioning and tracking based on multi-station observation, the steps of the embodiment of the present invention are summarized as follows:

[0144] In order to solve the problem of reduced positioning accuracy caused by model representation errors in parameter models, a multi-station nonlinear observation model of uncertainty error components was constructed, and the nonlinear compensation least squares method of the point-by-point semi-parametric model and the semi-parametric model based on spline representation was studied, and the theoretical properties of its solution were proved.

[0145] Aiming at the problem that traditional regularization matrix cannot accurately estimate the multi-station system error, a regularization matrix construction method based on multiple factors is proposed, and the l-point smoothing invariance and elementary transformation invariance of the optimal regularization matrix set are proved. Then, a state fusion estimation method based on the hybrid semi-parametric model is designed.

[0146] Aiming at the problem that traditional optimization algorithms have strong randomness and unstable optimization results in weight optimization of various factors in hybrid semi-parametric models, a weight adaptive optimization method based on model likelihood is proposed. By introducing the current information and jump information of the model, online adaptive optimization of weights is realized, which improves the global optimality and optimization efficiency of the regularization matrix.

[0147] 2. Multi-station nonlinear observation model based on uncertainty error components (i.e., a multi-station nonlinear observation model containing error terms, where the error terms are part of the multi-station nonlinear observation model and are in the form of error models)

[0148] In non-cooperative target observation systems, such as Figure 3 As shown in the figure, equipment observation error and observation geometry are important factors affecting target positioning accuracy. When the configuration of the measurement equipment and the target meets the extreme condition of the geometric precision factor, the inaccuracy of observation error modeling and estimation becomes an important reason restricting the high-precision positioning of non-cooperative targets.

[0149] EMBET is the most commonly used unified estimation method, which usually models the multi-station nonlinear observation model without error terms into a certain function form such as linear, periodic, quadratic and exponential:

[0150]

[0151] In the formula, is the system state (which contains modelable system errors), e is the random error, y is the observed value of m measurement devices, The form above (the form refers to the function form of f(·), such as linear, quadratic, cubic, etc.) and the function whose parameters are known. Through nonlinear parameter estimation methods such as Gauss-Newton and Levenberg-Marquardt, a stable optimal estimate in the sense of least squares can be obtained. The optimal estimate is the optimal estimate of the parameter β to be estimated, which represents the solution of the non-cooperative target observation system, that is, the parameter estimate of β.

[0152] In order to characterize the system errors and model representation errors that cannot be accurately modeled, nonparametric components are introduced into the above non-cooperative target observation system, and a multi-station nonlinear semiparametric model based on uncertain error components is constructed. According to whether the system state and nonparametric components are assumed to be time series, it is divided into a point-by-point semiparametric model and a semiparametric model based on spline representation. The point-by-point semiparametric model does not make time series assumptions on the system state and nonparametric components, that is, the system state and nonparametric components at different times are unrelated, and the system state and nonparametric components at each time are estimated independently. The semiparametric model based on spline representation makes time series assumptions on the system state and nonparametric components, assuming that the system state and semiparametric components satisfy the spline function within a period of time and are related, and the system state and nonparametric components within a period of time can be jointly estimated; the time series assumption is applicable to the case where there is certain prior information about the target. Using the prior information to make time series assumptions on the system state and nonparametric components can improve the estimation accuracy.

[0153] 2.1 Point-by-point semiparametric modeling and estimation

[0154] In the point-by-point semi-parametric model, the non-parametric component describes the unmodelable systematic error or model error in the multi-station nonlinear observation model corresponding to the m-station measurement at a certain time. The observation equation (point-by-point semi-parametric model) is:

[0155]

[0156] Where s represents the non-parametric component, which represents the unmodelable system error or model error, that is, the error model, is the covariance matrix of the random error e, R m represents an m-dimensional real number set, and P is the weight matrix of the observation y. The residual of the point-by-point semiparametric model of equation (2) is expressed as:

[0157]

[0158] The normal equation of formula (3) is

[0159]

[0160] Where J represents the Jacobian matrix.

[0161] Due to the introduction of non-parametric components, the coefficient matrix of the normal equation (4) is semi-positive definite and irreversible. Therefore, the compensated least squares criterion is used to correct the normal equation (4), thereby correcting equation (3):

[0162]

[0163] Where α and R are the given smoothing factor and regularization matrix. The Lagrangian function (6) is constructed to solve equation (5), but it cannot replace equation (5). The constructed Lagrangian function is:

[0164]

[0165] make get:

[0166]

[0167] From the above formula (7), we can get:

[0168]

[0169]

[0170] in, is the Jacobian matrix, abbreviated as J. Then, the system state estimation value and non-parametric estimation value obtained by solving equation (5) are:

[0171]

[0172] Among them, S is the intermediate quantity, the superscript k represents the kth iteration, and I represents the large unit matrix.

[0173] In the multi-station nonlinear observation model, part of it is about the system state, and part of it is about the error (non-parametric component). Since the error (non-parametric estimate) needs to be estimated, the system state (system state estimate) must be estimated at the same time.

[0174] value).

[0175] 2.2 Semiparametric Modeling and Estimation Based on Spline Representation

[0176] In the non-cooperative target observation system, certain assumptions are made on the system state and non-parameter components of the non-cooperative target observation system over a period of time. The certain assumption is that the system state and non-parameters conform to the spline function over a period of time. A semi-parametric model based on spline representation can be established as a multi-station nonlinear observation model:

[0177]

[0178] In the formula, the observed value y i =[y i1 ,y i2 ,…,y im ] T , represents the observed value of the 1st, 2nd, ..., mth measuring device at the i-th moment, is the system state, and the system error that can be modeled, e i is the m-dimensional random error, the nonparametric component s(t i )=[s1(t i ),s2(t i ),…,s m (t i )] T ,s l (t i ),l=1,2,…,m describes the observed quantity y il The unmodeled systematic errors and model errors of the observed quantity y il Yes i The l component of P i t i Observed value y at time i The weight matrix of the system state β is the polynomial coefficient or spline polynomial coefficient of the non-cooperative target in this time period.

[0179] The semiparametric model based on spline representation is i Time residual V i =[V i1 ,V i2 ,…,V im ] T It is expressed as:

[0180]

[0181] Due to the introduction of non-parametric components, the coefficient matrix of the normal equation (4) is semi-positive definite and irreversible. Therefore, the compensated least squares criterion is used to correct the normal equation (4), thereby correcting equation (13) to:

[0182]

[0183] According to the properties of the semi-parametric model based on spline representation, such as continuity and differentiability at the observation nodes, equation (14) can be obtained:

[0184]

[0185] Where F and G are sparse matrices determined by the observation sampling interval, and their proof is discussed in Section 3. Construct the Lagrangian function constructed by solving equation (15):

[0186]

[0187] In the formula, the factors affecting the estimation accuracy of the multi-station nonlinear semi-parametric model based on uncertain error components are: smoothing factor α and regularization matrix R, R = FG -1 F T , P=diag(P1,P2,…,P n ), s=(s T (t1),s T (t2),…,s T (t n )) T ,

[0188] By finding the minimum value of formula (16), we can obtain:

[0189]

[0190] From formula (17), we can get:

[0191]

[0192]

[0193] Then, the system state estimation value and non-parametric estimation value obtained by solving equation (15) are:

[0194]

[0195] Among them, S is the intermediate quantity, the superscript k represents the kth iteration, and I represents the large unit matrix.

[0196] 2.3 Analysis of semi-parametric model estimation accuracy

[0197] The semi-parametric model (including point-by-point semi-parametric model and spline-based semi-parametric model) cancels the assumption of the form of the non-parametric partial function, because any form of model has model representation error. The semi-parametric model does not assume the form of the non-parametric partial function, which suppresses the model representation error and makes the semi-parametric model closer to the objective reality, thereby suppressing the influence of the model representation error on the target positioning accuracy. The properties of its solution are discussed as follows:

[0198] In the above semi-parametric model, when rank(RJ) = t, the system state estimate and non-parametric estimate can be uniquely obtained by equation (11) or (20), and when That is, when H is semi-positive, the estimated value obtained by using the semi-parametric model is better than the estimated value obtained by using the parametric model in terms of mean square error, that is,

[0199]

[0200] M is an intermediate quantity, and the subscript pe represents the parameter estimate. It is a parametric model Proof: According to the extreme value condition of the Lagrangian function, the normal equation of the above semi-parametric model (the normal equation (4) is transformed into the normal equation after considering the compensated least squares principle) is:

[0201]

[0202] Considering P>0, If the above formula is established and At the same time, When rank(RJ) = t, if and only if and When rank(RJ) = t, the system state estimate and non-parametric estimate can be obtained uniquely by equation (11) or (20). The system state is the unknown parameter of the system. The parameter to be estimated is the position and velocity of the target in the non-cooperative target observation system.

[0203] The mean square error is defined as:

[0204]

[0205] Among them, E stands for expectation.

[0206] The mean square error measures the accuracy of the system state estimate. This breaks down into:

[0207]

[0208] Where D represents the variance.

[0209] tr(·) represents the trace of the matrix in (). From formula (7), we can get:

[0210]

[0211] Let G = (J T PJ) -1 J T P, then therefore

[0212]

[0213]

[0214] in, represents the covariance of the random error e.

[0215] From formula (24), we can get

[0216]

[0217] Similarly, the mean square error of the system state estimation value of the semi-parametric model can be obtained as

[0218]

[0219] Therefore, the difference between the two equations (28) and (29) above is:

[0220]

[0221] Right now The proposition is established.

[0222] 3. Regularization matrix construction method based on factors affecting error

[0223] In the semi-parametric model estimation accuracy analysis, it can be seen from formula (28) that the smoothing factor α and the regularization matrix R are important factors affecting the semi-parametric model estimation accuracy, because only these two parameters need to be determined in advance and can be adjusted. Different values ​​affect the final solution of the semi-parametric model. The smoothing factor α can be obtained by the generalized cross-validation function constructed by the residual and the signal norm. and noise norm vn(α)=V T The L curve constructed by PV (which is the existing technology) is determined by other methods. The regularization matrix R describes the functional relationship and weights between the non-parametric components. The traditional semi-parametric estimation determines R based on experience or prior information, without considering the influencing factors of the observation error (i.e., the systematic error) during the target motion process, and cannot correctly reflect the complex observation errors in the actual measurement process, and does not effectively reduce the model representation error.

[0224] In the semi-parametric models (2) and (12), the regularization matrix is ​​an important factor affecting the estimation accuracy of the semi-parametric models.

[0225] To solve the above problems, we need to construct a regularization matrix R. First, we prove the uniqueness of the regularization matrix R of the semiparametric model based on spline representation, because the semiparametric model based on spline representation can uniquely determine the regularization matrix R, so there is no need to construct the regularization matrix R. A single point-by-point semiparametric model cannot uniquely determine R, so we need to construct the regularization matrix R of the point-by-point semiparametric model based on the factors that affect the error, and prove the optimality of this construction method. Then, we propose a hybrid semiparametric model and design a weight optimization method for the problem of complex and changeable factors affecting the error.

[0226] The properties and construction methods of the regularization matrix are discussed in two cases below.

[0227] 3.1 Uniqueness of the Regularization Matrix R of the Semiparametric Model Based on Spline Representation

[0228] The spline function is used to constrain the motion state and non-parameters of the non-cooperative target at a certain stage. The uniqueness of its regularization matrix can be proved by using the properties of the spline function. The time period [a, b] is divided into: Δ: a<t1<t2<…<t n <b, let us assume that a component s(t) of the nonparametric component is i ,t i+1 ] can be expressed as:

[0229]

[0230] Note s(t i )=s i , according to the continuity of s″(t) at the nodes:

[0231]

[0232] Where h is the sampling time interval.

[0233] Furthermore, formula (31) can be expressed as:

[0234]

[0235] Since s′(t) is continuous at the node, that is, s′(t i +0) = s′(t i -0), so from formula (33) we can get:

[0236]

[0237] From this we can know that: F T s=Gc (76)

[0238] Where: s=(s1,s2,…,s n ) T ,c=(c2,c3,…,c n-1 ) T , F and G are as follows:

[0239]

[0240]

[0241] Note that s″′(t) is in each subinterval [t i ,t i+1 ] is a constant, that is Then the formula (14) corresponding to the compensated least squares criterion is:

[0242]

[0243] From formula (32), we can know

[0244]

[0245] From formula (35), we can know

[0246]

[0247] Therefore, this estimation method based on the semiparametric model represented by splines can uniquely determine the regularization matrix R;

[0248] Common factors affecting measurement errors include sight line distance, timing error, station location error, environmental factors, angle difference, etc. According to the unique regularization matrix R, combined with the error influencing factor set A = {a1, a2, ...}, the corresponding optimal regularization matrix set is constructed.

[0249] 3.2 Regularization matrix construction based on factors affecting error

[0250] The regularization matrix R reflects the function type of the non-parametric component, i.e., the model error. Therefore, the selection of the regularization matrix is ​​largely determined by the influencing factors of the non-cooperative target observation system error. Common factors affecting the measurement error include sight line distance, timing error, station error, environmental factors, angle difference, etc. In the following, for the point-by-point semi-parametric model, the optimal regularization matrix set is constructed based on the factors affecting the error. One error has one regularization matrix set.

[0251] The set of factors affecting the error of the measurement element is A = {a1, a2, ...}, where a i , i = 1, 2, ... represents the influencing factors of the measurement error. The measuring station where the measuring equipment is located has the influencing factors of the measurement error a i The set of values ​​under is M i ={X 01 (a i ),X 02 (a i ),…,X 0m (a i )}, then the influencing factor of the measurement error is a i The measurement error of station j is determined to be X 0j (a i ),j=1,2,…,m, and this mapping relationship is recorded as

[0252] X 0j (a i ) → g i(X 0j (a i ))

[0253] where g i (·) is the influence factor of observation error on measurement error a i The function form of is generally linear, quadratic, exponential, etc. There exists a set M i The binary relation H(a i ), i = 1, 2, ..., satisfying reflexivity, antisymmetry, and transitivity, that is, M i For an ordered set, use the ordered pair <M i ,H(a i )>, at this time, the influencing factor of the measurement error is called a i is an ordered factor. That is, the influencing factor of the measurement error a i The observation errors of different devices can be sorted. In non-cooperative target observation systems, the factors affecting the measurement errors are generally ordered factors. The traditional regularization matrix does not use this information and cannot effectively reduce the model representation error.

[0254] The influencing factors of the measurement error are a i The optimal regularization matrix set M determined by i is O(a i ),make

[0255]

[0256] Let g i (X 00 (a i ))=0, then the symmetric matrix R i1 for

[0257]

[0258] Wherein, p and q represent the p-th row and q-th column of the matrix respectively.

[0259] Similarly, from formula (41), we can get R i2 and R i3 The specific form of R ik , (k=1,2,3) describes the function type of s through the functional relationship between two adjacent points. The value of each regularization matrix in the regularization matrix set corresponds to the weight of the non-parametric component, that is, the measurement error. The functional relationship and weight between the components of the non-parametric component are described by the regularization matrix set. Due to the use of the compensated least squares criterion, R ik ∈O(a i ),(k=1,2,3). And the optimal regularization matrix set O(a i ) has the following two characteristics:

[0260] 1) l-point smoothing invariance. The above R ik , (k = 1, 2, 3) corresponds to the sum of the squares of the differences between two adjacent non-parametric components. Similarly, it can be expanded to three-point smoothing:

[0261]

[0262] Then R i ∈O(a i ), which can be extended to l≤m point smoothing

[0263] l points refers to the number of points used. Formula (41) uses s j-1 、s j These two points are two-point smoothing; formula (43) uses s j-1 、s j 、s j+1 These three points are three-point smoothing. The meaning of l-point smoothing invariance is that no matter which points (several adjacent non-parametric components) are smoothed to obtain the regularized matrix, they are all in the optimal regularized matrix set.

[0264] 2) Invariance under elementary transformations. in, is an elementary transformation matrix for arbitrary row and column exchange. The meaning of elementary transformation invariance is that any element in the optimal regularized matrix set (i.e. any regularized matrix) still belongs to the optimal regularized matrix set after the elementary transformation of the matrix.

[0265] The advantages of these two characteristics are that the elements in the optimal regularization matrix set still belong to the optimal regularization matrix set after l-point smoothing or elementary transformation, and the elements in the optimal regularization matrix set are all optimal and consistent. Proof:

[0266] 1) Based on the compensated least squares criterion, the regularized matrix is ​​smoothed at l points The functional relationship between the adjacent l non-parametric components accurately reflects the weights of the s components, so we have

[0267] 2) Depend on

[0268]

[0269] Knowable The mean square error of the system state estimate is obtained as follows:

[0270]

[0271] Let α′=α / λ, then This is equivalent to the above minimization problem, so λR i ∈O(a i ).

[0272] In this section, in the non-cooperative target tracking and positioning scenario, due to the random variability of the non-cooperative target's motion state and the diversity of the measurement model, the error influencing factors are complicated and the error form is uncertain. The regularization matrix constructed based on a single factor cannot achieve accurate estimation of the observation error. Therefore, a set of influencing factors of the error is constructed, and a hybrid semi-parametric model is formed through the interaction of the corresponding regularization matrix set.

[0273] 4. State estimation algorithm based on hybrid semi-parametric model

[0274] According to the error influencing factor set A = {a1, a2, ...}, the corresponding regularization matrix set is constructed, combined with the regularization matrix set constructed in 3.2, and a hybrid semi-parametric model is formed through the interaction of the model (each regularization matrix corresponds to a point-by-point semi-parametric model or a semi-parametric model based on spline representation), thereby obtaining the system state estimation value and non-parametric estimation value. Figure 4 shown.

[0275] Figure 4 In the above equation, the optimal regularization matrix is ​​constructed by equation (42), and the system state and non-parametric estimation are obtained by (11) or (20). The smoothing factor α is determined by the generalized cross-validation method or the L-curve method. The mixed regularization matrix is ​​not a simple weighting of each regularization matrix, but a mixed value of the factors is calculated by weighting Then, it is constructed by formula (42). i It can be optimized iteratively through the optimization algorithm according to the estimation accuracy. Since the true state of the non-cooperative target is difficult to obtain, considering that the geometric precision factor (GDOP) is the observation error magnification factor, the following formula is used as the objective function of the weighted optimization problem:

[0276]

[0277] In the formula is the precision estimate, m p is the number of parameters to be estimated (the number of components in the system state).

[0278] If the gradient descent method is used to optimize the weights,

[0279]

[0280] It can be seen from equations (11) and (42) that the amount of gradient calculation is large and the weight optimization efficiency is low. When the heuristic algorithm is applied to the weight optimization problem of the interactively formed hybrid semi-parametric model, due to the randomness of the search, there are problems such as unstable optimization results, easy to fall into the local optimal solution, and low convergence efficiency. On the other hand, in addition to the diversity of the measurement system, the movement of non-cooperative targets has the characteristics of multi-stage, large span and random and changeable, which leads to complex and changeable error sources. The weights of various factors change all the time. The weights obtained based on global precision optimization are fixed and cannot meet the needs of high-precision positioning. Therefore, it is necessary to find an adaptive online adjustment method for weights. The likelihood value information of the semi-parametric model at each moment is introduced, and the algorithm is adjusted as follows:

[0281] Figure 6 is a mixed semiparametric model based on the model likelihood value, M is the number of mixed semiparametric models, and in general, M ≥ r. j,k ,j=1,2,…,M is the likelihood value of each model at time k, and the calculation method is:

[0282]

[0283] Among them, r is the intermediate variable.

[0284] By introducing the likelihood value of the mixed semi-parametric model at the current moment, the weights of each regularization matrix at the next moment are adaptively adjusted so that the weight of each semi-parametric model is close to the mixed semi-parametric model with the largest likelihood value, thereby converging to the optimal weight of the model at the current stage and adapting to the different requirements of error mixing weights at different stages. One stage includes multiple moments.

[0285] Assume that the mixed semi-parametric model with the maximum likelihood value at the current moment is:

[0286] Λ q,k =max{Λ 1,k ,Λ 2,k ,…,Λ M,k} (90)

[0287] Then at the next moment, the mixed weight is adjusted as follows:

[0288]

[0289] In the formula, μ is a random number in the interval [0,1]. That is, the weight of each hybrid semiparametric model is close to the model weight with the largest likelihood value. The step size depends on the likelihood value of the semiparametric model and the likelihood value of the optimal hybrid semiparametric model. The larger the gap, the larger the step size, which improves the convergence efficiency of the algorithm. μ is conducive to making each hybrid semiparametric model jump out of the local optimal solution, thereby enhancing the global optimality of the algorithm.

[0290] The specific implementation process of the algorithm is as follows:

[0291] (1) Constructing the optimal regularization matrix

[0292] First, according to the observation model and target motion characteristics, a set of influencing factors of the error is constructed, and the corresponding factor values ​​of each station are calculated. i (·) form, and construct the optimal regularization matrix according to formula (42). Set the number of models M, set k = 1, and initialize the proportion of the influencing factors of each error in the observed error, that is, the weight of each regularization matrix, so that it satisfies:

[0293]

[0294] (2) Regularization matrix for interactive mixing

[0295] Calculate factor mixture values ​​based on weights Then, the mixed regularization matrices are constructed through formula (42) to form a mixed semi-parametric model 1,2,…,M.

[0296] (3) Hybrid semi-parametric estimation

[0297] Determine the components α within the smoothing factor α by using the generalized cross-verification method or the L-curve method j,k , and then use equation (11) or (20) to get the current state estimate and non-parametric estimate Non-parametric variables represent the unmodelable errors of the observation system of each station at the current moment.

[0298] (4) Multi-model information fusion

[0299] According to formula (46), the estimation accuracy of M hybrid semi-parametric models is calculated, and the current system state estimation value with higher accuracy is obtained by optimal weighted fusion of each hybrid semi-parametric model. The optimal weighted fusion method is:

[0300]

[0301] (5) Weight Adaptive Optimization

[0302] Let k = k + 1, calculate the likelihood of each hybrid semiparametric model according to equation (48), and then adaptively optimize the weights according to equations (49) and (51). Go to step (2) until k = N.

[0303] During the motion of non-cooperative targets, the observation system error is generated by the interaction of various factors, and the proportion of each factor changes all the time. Therefore, the weight adaptive optimization method based on the likelihood value of the model is adopted. The model contains the current information of the model (that is, the likelihood value of each mixed semi-parametric model at the current moment) and the model jump information (that is, the change of the likelihood value of each mixed semi-parametric model, and the change represents the jump). If the real weights of the factors affecting the error change, that is, the model jumps, the change of the likelihood value of the model is fed back to the weights of each regularization matrix at the next moment. The weights are adaptively optimized according to the proportion of the factors affecting the error at each stage, and the error sources of multiple stations, the proportion of each error factor and the error form are accurately identified to improve the estimation accuracy. Therefore, the weights are adaptively optimized according to the observation information at each moment, and there is no need to set the iteration stop condition, so the optimization efficiency and robustness of the method are improved.

[0304] In summary, regarding the completeness of the factor set, due to the lack of prior information of non-cooperative targets and the possible coupling between different factors, a model set with too many factors increases the computational complexity. Usually, according to the measurement system and actual measurement scenario of the observation system, as well as the production background of the observation equipment, factors with a more significant impact on the station error are selected to form a factor set, and then the optimal regularization matrix set that can accurately describe the type and form of multi-station errors is generated.

[0305] 5. Simulation test and analysis

[0306] In order to verify the effectiveness of the proposed multi-station hybrid semi-parametric model and weight adaptive optimization method, a non-cooperative target positioning experiment was carried out based on the target GPS trajectory, station relative position information and observation information in the actual multi-station ranging and positioning system, combined with complex observation error simulation data.

[0307] In order to verify the systematic error identification capability of the multi-station hybrid semi-parametric model, the simulation is based on observation data of complex error forms considering multiple error factors. Constant, periodic, semi-parametric, polynomial periodic systematic error models and hybrid semi-parametric models are constructed respectively, and their systematic errors and state estimation accuracy are compared.

[0308] The target motion state is divided into multiple stages, and the proportion of each error influencing factor in the system error is different in different stages. In the hybrid semi-parametric model, the particle swarm algorithm, genetic algorithm, simulated annealing algorithm and adaptive weight optimization algorithm based on model likelihood are used to optimize the weights of each error factor. The optimization efficiency, optimization results, error identification results and state estimation accuracy of each algorithm are compared. Finally, the influence of the number of models M on the performance of the algorithm such as accuracy and efficiency is considered.

[0309] 5.1 Simulation test scenario

[0310] Convert GPS target trajectory and station position into relative coordinates, such as Figure 5 As shown in the figure, the ranging and positioning system with n=6 measuring stations is shown. After the parameter significance test, the target trajectory approximately satisfies the cubic polynomial, and the system state is the target position X=(x, y, z) T satisfy

[0311]

[0312] In the formula, a i ,b i (i=1,2,3) are polynomial coefficients, t is the sampling time. The experiment intercepts n=80 data uniformly sampled in t∈[0.7s,1.5s].

[0313] Considering the mixed effects of various influencing factors during the target movement process, the different complex errors of each station are formed, including the sight line distance (the distance between the station and the target), the distance change rate, and the station timing error (priori information can be obtained from static tests). The error amplitude is determined according to the factor values ​​of each station. On the other hand, the error form is also an important factor affecting the positioning accuracy. The error identification ability of the periodic error and fractal Brownian motion (FBM) error test model is used respectively, such as Figure 7 As shown, where S represents the station. Brownian motion {B(t), t≥0} satisfies B(0)=0, B(t) has stable independent increments, B(t)~N(0,σ 2 t). Fractal Brownian motion B H (t), 0<H<1 and more generally fractal geometry is a mathematical model proposed by Mandelbrot and Ness:

[0314]

[0315] Where H is the Hurst index that describes the long memory of the time series. H (t) is a generalization of B(t). Its increments are stable, self-similar, and self-correlated within any time window, and can be used to simulate the time trajectory of noise with fractal characteristics.

[0316] 5.2 Experimental verification of the multi-station hybrid semi-parametric model

[0317] The observation information is generated using the GPS target trajectory and the relative position of the measuring station as shown in formula (51), and the periodic error and FBM error based on multiple factors are added respectively, and the random error is set to e~N(0,0.01·I). The constant value error model (CVEM), periodic error model (PEM), semi-parametric error model (SPEM), polynomial periodic error model (PPEM) and hybrid semi-parametric error model (HSPEM) are constructed respectively, where the smoothing parameter α in SPEM and HSPEM is determined according to the generalized cross verification method (GCV), and the regularization matrix in SPEM is determined by the traditional time series characteristic method, that is, it satisfies The HSPEM is determined by a construction method based on multiple factors. The state estimation error, observation value estimation (OC) residual and system error identification of each model are as follows: Figure 8 and Fig. 9 shown.

[0318] from Figure 8 and Fig. 9 The following results and analyses can be obtained:

[0319] (1) In the two complex error cases, the changing trends of GCV(α) are consistent. This is because when α increases, αs T As the proportion of Rs increases, the nonparametric components of each station become smoother, thus more consistent with the actual error and reducing the representation error.

[0320] (2) The HSPEM positioning error considering multiple factors presents zero mean, while the positioning errors of CVEM, PEM, SPEM and PPEM are significantly periodic and non-stationary. The positioning error of the proposed method is significantly smaller than that of the traditional parameter estimation method and the semi-parametric method.

[0321] (3) In terms of total position accuracy and measurement residual, HSPEM is also significantly better than traditional methods. It can also be seen from Table 1 that the proposed method significantly improves the positioning accuracy, while the traditional semi-parametric estimation method has limited accuracy improvement compared to the parametric method. Therefore, for non-cooperative targets with complex errors, multiple factors should be considered to construct the regularization matrix.

[0322] (4) The CVEM, PEM, SPEM and PPEM methods cannot accurately identify the systematic errors of the measuring stations, while the HSPEM method can accurately identify the systematic errors of each measuring station in complex situations.

[0323] Table 1 Estimation accuracy of each method under two complex errors

[0324]

[0325]

[0326] 5.2 Experimental verification of adaptive weight optimization method

[0327] The sources of error in the target motion process are complex and changeable. The regularization matrix should be set considering multiple influencing factors. How to determine the weights of each factor of non-cooperative targets is a key issue of HSPEM, which directly determines the estimation accuracy of the system. Under the HSPEM framework, the target motion process is divided into two stages. The proportions of the sight line distance, distance change rate, and station timing errors in the two stages are p and p, respectively. (1) =(0.2,0.1,0.7) and p (2) =(0.2, 0.6, 0.2). Particle swarm algorithm (PSO), genetic algorithm (GA), simulated annealing algorithm (SA) and adaptive optimization algorithm based on model likelihood (MLAO) are used to optimize the weights of each factor, and the parameter settings are shown in Table 2.

[0328] Table 2 Parameter settings of each algorithm

[0329]

[0330] During the optimization process, the objective functions of PSO, GA and SA are shown in Equation (44), and the maximum number of iterations is set to 200. The optimization method of MLAO is Equations (46)-(48). Therefore, the number of iterations of MLAO is the number of sampling points of the target motion. The estimation accuracy of each algorithm during the optimization process is shown in Fig.10 (a). The weight of each error influencing factor and the optimization time obtained by each algorithm optimization are shown in Table 3. Setting different numbers of hybrid semi-parametric models M, the results are shown in Fig.10 (b).

[0331] Table 3 Optimization weights and optimization time of each algorithm

[0332] <![CDATA[p (1) ]]> <![CDATA[p (2) ]]> t(s) True Value [0.2,0.1,0.7] [0.2,0.6,0.2] - PSO [0.1958,0.7811,0.0231] [0.1958,0.7811,0.0231] 2390.23 GA [0.2018,0.7706,0.0275] [0.2018,0.7706,0.0275] 5952.77 SA [0.2754,0.5666,0.1580] [0.2754,0.5666,0.1580] 19595.98 MLAO(M=100) [0.1969,0.1026,0.7005] [0.2179,0.6313,0.1508] 895.74 MLAO (M=60) [0.1766,0.1098,0.7137] [0.2181,0.6519,0.1300] 212.32 MLAO(M=20) [0.1640,0.1255,0.7105] [0.2214,0.6415,0.1370] 70.87

[0333] The hybrid semi-parametric estimation method with corresponding weights is used respectively. The state estimation accuracy and system error identification are shown in Fig.11 As shown in Table 4. Based on the above results, the following conclusions can be drawn:

[0334] (1) PSO, GA and SA algorithms optimize weights according to the global accuracy of the trajectory. The weight optimization falls into the local minimum, the error is large, and the changes in the factors affecting the error cannot be identified. The constant error weight leads to low positioning accuracy, and the above algorithms have more parameters in the weight optimization problem, and the optimization efficiency is low.

[0335] (2) The MLAO algorithm can accurately and quickly converge to the optimal error factor weights at each stage and can accurately identify the model jump moment. Fig.10As shown in (a), the model jumps at the 41st sampling point, that is, the proportion of error factors changes, resulting in a short-term increase in positioning accuracy and then rapid convergence. The positioning accuracy in the second stage is lower than that in the first stage because the observation error in the second stage is larger.

[0336] (3) The larger the number of models M in the MLAO algorithm, the better the global optimality of the algorithm, but the optimization efficiency will be reduced. The smaller M is, the larger the "spike" when the model jumps.

[0337] (4) The positioning errors of the second stage of PSO, GA and SA algorithms are relatively small. This is because the observation error in the second stage is large and accounts for a large proportion in the optimization objective function. The positioning accuracy of the above algorithms is low and the error identification is inaccurate. The MLAO algorithm adaptively adjusts the weights, identifies the source of the error, accurately identifies the error form, and significantly improves the positioning accuracy.

[0338] In summary, in a non-cooperative target observation system with complex errors, the hybrid semi-parametric model based on the MLAO algorithm can accurately identify the source and form of errors, adaptively optimize the weights of error factors in stages, improve the optimization efficiency and global optimality, and significantly improve positioning accuracy.

[0339] Table 4 Comparison of the accuracy of each algorithm after weight optimization

[0340] <![CDATA[σ x (m)]]> <![CDATA[σ y (m)]]> <![CDATA[σ z (m)]]> σ(m) PSO 0.3934 0.2020 0.5026 0.6695 GA 0.3537 0.1945 0.9007 0.9870 SA 0.3384 0.1894 0.9897 1.0630 MLAO 0.0124 0.0074 0.3016 0.3019

[0341] The beneficial technical effects achieved by the embodiments of the present invention are as follows:

[0342] The multi-station complex error uncertainty modeling and estimation method based on the hybrid semi-parametric model achieves high-precision target estimation and accurate error identification. In the non-cooperative target observation system, the errors are complex and changeable, the error model is uncertain, and the parameterized model has representation errors. Therefore, point-by-point and spline multi-station semi-parametric models of non-cooperative targets are constructed.

[0343] The traditional regularization matrix does not take into account the influencing factors of the error and cannot accurately describe the error characteristics of the multi-station system. Therefore, a regularization matrix construction method based on multiple factors is proposed, and its l-point smoothing invariance and elementary transformation invariance are proved.

[0344] On this basis, the model likelihood information is introduced, and a hybrid semi-parametric model based on weight online adaptive optimization is designed. Compared with the traditional semi-parametric model, the optimality of the regularization matrix and the optimization efficiency are enhanced.

[0345] Simulation experiments demonstrate the effectiveness of the model and method, which can improve positioning accuracy, accurately identify observation system errors, and provide a theoretical basis for complex error modeling and identification of non-cooperative targets.

[0346] It should be understood that the specific order or hierarchy of steps in the disclosed process is an example of an exemplary method. Based on design preferences, it should be understood that the specific order or hierarchy of steps in the process can be rearranged without departing from the scope of protection of the present disclosure. The attached method claims present the elements of the various steps in an exemplary order and are not intended to be limited to the specific order or hierarchy described.

[0347] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A modeling method for non-cooperative target observation, characterized in that: include: A non-cooperative target is observed by using multiple measurement devices of a non-cooperative target observation system, and a multi-station nonlinear observation model of the non-cooperative target is constructed based on an EMBET estimation method, wherein the multi-station nonlinear observation model includes a modelable system error, and non-parametric variables are introduced into the multi-station nonlinear observation model. The non-parametric variables are used to describe the observation system error and / or model error that cannot be modeled, so as to form a multi-station nonlinear semi-parametric model based on uncertain error components; Determine the factors affecting the estimation accuracy of the multi-station nonlinear semi-parametric model based on the uncertain error component: regularization matrix, construct a regularization matrix based on the influencing factors affecting the error and make the regularization matrix unique, the unique regularization matrix has l-point smoothing invariance and elementary transformation invariance, use the optimal regularization matrix set constructed by the unique regularization matrix to optimize the multi-station nonlinear semi-parametric model based on the uncertain error component, and obtain an optimized semi-parametric model; The optimized semi-parametric model is used to solve the position of the non-cooperative target observed by multiple measurement devices and obtain the position of the non-cooperative target.

2. The modeling method for non-cooperative target observation according to claim 1, characterized in that: A non-cooperative target is observed by using multiple measurement devices of a non-cooperative target observation system, and a multi-station nonlinear observation model of the non-cooperative target is constructed based on the EMBET estimation method. The multi-station nonlinear observation model includes a modelable system error, including: The non-cooperative target is observed by multiple measurement devices in the non-cooperative target observation system, and a multi-station nonlinear observation model of the non-cooperative target is constructed based on the EMBET estimation method: In the formula, is the system state, which contains modelable system errors, e is the random error, y is the observed value of m measurement devices, and f(·) is the Functions of the form above are functions whose form and parameters are known.

3. The modeling method for non-cooperative target observation according to claim 2, characterized in that: The multi-station nonlinear semi-parametric model based on uncertain error components includes a point-by-point semi-parametric model, wherein the point-by-point semi-parametric model does not make time series assumptions on the system state and non-parametric components, the system state and non-parametric components at different times are unrelated, and the system state and non-parametric components at each time are estimated independently; Introducing non-parametric variables into the multi-station nonlinear observation model, describing observation system errors and / or model errors that cannot be modeled by the non-parametric variables, and forming a multi-station nonlinear semi-parametric model based on uncertain error components, including: Non-parametric variables are introduced into the multi-station nonlinear observation model. The non-parametric components are used to describe the unmodelable system errors or model errors in the multi-station nonlinear observation model corresponding to the m measurement devices at a certain time, forming a point-by-point semi-parametric model. The point-by-point semi-parametric model is expressed as: In the formula, s represents the non-parametric component, is the covariance matrix of the random error e, and P is the weight matrix of the observation y; the residual of the point-by-point semiparametric model is calculated, and the residual of the point-by-point semiparametric model of formula (2) is expressed as: The normal equation of formula (3) is: Where J represents the Jacobian matrix; Due to the introduction of non-parametric components, the coefficient matrix of the normal equation (4) is semi-positive definite and irreversible. The compensated least squares criterion is used to correct the normal equation (4), thereby correcting equation (3): In formula (4), the factors affecting the estimation accuracy of the multi-station nonlinear semi-parametric model based on uncertain error components are: smoothing factor α and regularization matrix R; a Lagrangian function is constructed to solve formula (5), and the constructed Lagrangian function is expressed as: make get: From formula (7), we can get: in, is the Jacobian matrix, abbreviated as J; the system state estimation value and non-parametric estimation value obtained by solving equation (5) are: Among them, S is the intermediate quantity, the superscript k represents the kth iteration, and I represents the large unit matrix.

4. The modeling method for non-cooperative target observation according to claim 3, characterized in that: The multi-station nonlinear semi-parametric model based on uncertain error components also includes a semi-parametric model based on spline representation, wherein the semi-parametric model based on spline representation makes time series assumptions on the system state and the non-parametric component, assumes that the system state and the semi-parametric component satisfy the spline function within a period of time, and jointly estimates the system state and the non-parametric component within a period of time; Introducing non-parametric variables into the multi-station nonlinear observation model, describing the observation system errors and model errors that cannot be modeled through the non-parametric variables, and forming a multi-station nonlinear semi-parametric model based on uncertain error components, including: When the non-cooperative target is observed by the multi-measurement equipment of the non-cooperative target observation system, it is assumed that the system state and non-parametric components within a period of time conform to the spline function and are added to the multi-station nonlinear observation model of the non-cooperative target to form a semi-parametric model based on spline representation. The semi-parametric model based on spline representation is expressed as: Among them, the observed value y i =[y i1 ,y i2 ,…,y im ] T , represents the observed value of the 1st, 2nd, ..., mth measuring device at the i-th moment, e i is the m-dimensional random error, the nonparametric component s(t i )=[s1(t i ),s2(t i ),…,s m (t i )] T ,s l (t i ),l=1,2,…,m describes the observed quantity y il The unmodeled systematic errors and / or model errors of the observed quantity y il Yes i l components of i t i Observed value at time -y i The weight matrix of , the system state β is the polynomial coefficient or spline polynomial coefficient of the non-cooperative target in this time period; The semiparametric model based on spline representation is i Time residual V i =[V i1 ,V i2 ,…,V im ] T It is expressed as: Due to the introduction of non-parametric components, the coefficient matrix of the normal equation (4) is semi-positive definite and irreversible. The compensated least squares criterion is used to correct the normal equation (4), thereby correcting equation (13) as follows: According to the properties of the semi-parametric model based on spline representation, such as continuity and differentiability at the observation nodes, equation (14) can be obtained: Where F and G are sparse matrices determined by the observation sampling interval, which are constructed to solve equation (15) and construct the Lagrangian function: In the formula, the factors affecting the estimation accuracy of the multi-station nonlinear semi-parametric model based on uncertain error components are: smoothing factor α and regularization matrix R, R = FG -1 F T , P=diag(P1,P2,…,P n ), s=(s T (t1),s T (t2),…,s T (t n )) T , By finding the minimum value of formula (16), we can obtain: From formula (17), we can get: The system state estimation value and non-parametric estimation value obtained by solving equation (15) are: Among them, S is the intermediate quantity, the superscript k represents the kth iteration, and I represents the large unit matrix.

5. The modeling method for non-cooperative target observation according to claim 4, characterized in that: Based on the factors affecting the error, a regularization matrix is ​​constructed and made unique. The unique regularization matrix has l-point smoothing invariance and elementary transformation invariance, including: For the point-by-point semiparametric model, the optimal regularization matrix set is constructed based on the factors affecting the error. One error has one regularization matrix set. The set of factors affecting the error of the measured element is A = {a1, a2, ...}, where a i , i = 1, 2, ... represents the influencing factors of the measurement error. The measuring station where the measuring equipment is located has the influencing factors of the measurement error a i The set of values ​​under is M i ={X 01 (a i ),X 02 (a i ),…,X 0m (a i )}, then the influencing factor of the measurement error is a i The measurement error of station j is determined to be X 0j (a i ),j=1,2,…,m, and this mapping relationship is recorded as: X 0j (a i )→g i (X 0j (a i )) where g i (·) is the influence factor of observation error on measurement error a i Functional form; M i is an ordered set, there exists a set M i The binary relation H(a i ), i = 1, 2, ..., satisfying reflexivity, antisymmetry, and transitivity, using sequence pairs <M i ,H(a i )> is expressed as, at this time, the influencing factor of the measurement error is called a i is an ordered factor; The influencing factors of the measurement error are a i The optimal regularization matrix set M determined by i is O(a i ),make: Let g i (X 00 (a i ))=0, then the symmetric matrix R i1 for Where p and q represent the p-th row and q-th column of the matrix respectively; According to formula (41), R i2 and R i3 the specific form of R ik , (k=1,2,3) describes the function type of s through the functional relationship between two adjacent points. The value of each regularization matrix in the regularization matrix set corresponds to the weight of the measurement error. The functional relationship and weight between the components of the non-parametric components are described by the regularization matrix set. The compensated least squares criterion is used to make R ik ∈O(a i ),(k=1,2,3); and the optimal regularization matrix set O(a i ) has the following two characteristics: (1) l-point smoothing invariance: This means that no matter how many adjacent non-parametric components are smoothed, the regularized matrix obtained is in the optimal regularized matrix set; (2) Invariance under elementary transformations: Any element in the optimal regularized matrix set still belongs to the optimal regularized matrix set after an elementary transformation of the matrix.

6. The modeling method for non-cooperative target observation according to claim 5, characterized in that: Also includes: The semi-parametric model based on spline representation has a unique regularization matrix, and the corresponding optimal regularization matrix set is constructed in combination with the error influencing factor set A={a1, a2, ...}.

7. The modeling method for non-cooperative target observation according to claim 6, characterized in that: The multi-station nonlinear semi-parametric model based on uncertain error components is optimized by using an optimal regularization matrix set formed by a unique regularization matrix to obtain an optimized semi-parametric model, including: The geometric dilution of precision (GDOP) is the observation error magnification factor, and formula (46) is used as the objective function of weight optimization: in, is the precision estimate, m p is the number of parameters to be estimated, where the parameters to be estimated refer to the components in the system state; Introduce the likelihood value of the semi-parametric model at each moment, the semi-parametric model includes: a point-by-point semi-parametric model and a semi-parametric model based on spline representation, to form a hybrid semi-parametric model based on model likelihood value, M is the number of hybrid semi-parametric models, generally M≥r; Λ j,k ,j=1,2,…,M is the likelihood value of each model at time k, and the calculation method of the likelihood value at time k is: Among them, r is the intermediate variable; By introducing the likelihood value at the current moment, the weights of each regularization matrix in the optimal regularization matrix set at the next moment are adaptively adjusted, so that the weight of each semi-parametric model is close to the mixed semi-parametric model with the largest likelihood value, thereby converging to the optimal weight of the model at the current stage, adapting to the different requirements of the mixed weights of errors at different stages. One stage includes multiple moments. Assume that the mixed semiparametric model with the maximum likelihood value at the current moment is: L q,k =max{Λ 1,k ,L 2,k ,…,L M,k } (20) Then at the next moment, the mixed weight of the error is adjusted as follows: Where μ is a random number in the interval [0,1].

8. The modeling method for non-cooperative target observation according to claim 7, characterized in that: The multi-station nonlinear semi-parametric model based on uncertain error components is optimized by using an optimal regularization matrix set formed by a unique regularization matrix to obtain an optimized semi-parametric model, including: (1) Constructing the optimal regularization matrix After constructing the optimal regularization matrix set according to formula (42), the number of hybrid semi-parametric models M is set, k=1, and the proportion of each factor affecting the error in the observed error is initialized. The proportion represents the weight of each regularization matrix in the optimal regularization matrix set, so that the weight of each regularization matrix satisfies: (2) Regularization matrix for interactive mixing Calculate factor mixture values ​​based on weights The mixed regularization matrices are constructed by formula (42) to form a mixed semi-parametric model 1, 2, ..., M; (3) Hybrid semi-parametric estimation Determine the components α within the smoothing factor α by using the generalized cross-verification method or the L-curve method j,k , the system state estimation value and non-parametric estimation value at the current moment are obtained through equation (11) or (20) respectively (4) Multi-model information fusion According to formula (46), the estimation accuracy of M hybrid semi-parametric models is calculated, and the estimated value of the system state at the current moment is obtained by optimal weighted fusion of each hybrid semi-parametric model. The optimal weighted fusion method of each hybrid semi-parametric model is: (5) Weight Adaptive Optimization Let k = k + 1, calculate the likelihood value of each hybrid semi-parametric model according to formula (48), and then adaptively optimize the weight according to formulas (49) and (51); proceed to step (2) until k = N; the likelihood value of the hybrid semi-parametric model includes the current model information and model jump information, the current information refers to the likelihood value of each hybrid semi-parametric model at the current moment, and the model jump information refers to the change in the likelihood value of each hybrid semi-parametric model. If the real weights of the factors affecting the error change, the model jumps; the change in the likelihood value of the model is fed back to the weight of each regularization matrix at the next moment, and the weight is adaptively optimized according to the proportion of factors affecting the error at each stage; The optimized semi-parametric model is obtained.

9. A modeling system for non-cooperative target observation, characterized in that: include: An observation model construction unit is used to observe a non-cooperative target using multiple measurement devices of a non-cooperative target observation system, and to construct a multi-station nonlinear observation model of the non-cooperative target based on an EMBET estimation method, wherein the multi-station nonlinear observation model includes a modelable system error, and non-parametric variables are introduced into the multi-station nonlinear observation model. The non-parametric variables are used to describe the observation system error and / or model error that cannot be modeled, so as to form a multi-station nonlinear semi-parametric model based on uncertain error components; A model optimization unit is used to determine the factors that affect the estimation accuracy of the multi-station nonlinear semi-parametric model based on uncertain error components: a regularization matrix is ​​constructed based on the factors that affect the error and the regularization matrix is ​​unique. The unique regularization matrix has l-point smoothing invariance and elementary transformation invariance. The multi-station nonlinear semi-parametric model based on uncertain error components is optimized using an optimal regularization matrix set constructed by a unique regularization matrix to obtain an optimized semi-parametric model. The solving unit is used to solve the position of the non-cooperative target observed by multiple measurement devices by using an optimized semi-parametric model to obtain the position of the non-cooperative target.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores one or more programs, which, when executed by a computer device, enable the computer device to execute the modeling method for non-cooperative target observation according to any one of claims 1 to 8.

Images