SINS initial alignment model precision evaluation method and system based on koopman operator theory

Abstract

The application provides a SINS initial alignment model precision evaluation method and system based on Koopman operator theory, and the method comprises the following steps: obtaining initial alignment data of an inertial navigation system and performing pretreatment; constructing a Davenport matrix of an initial alignment model of the SINS at each discrete time according to the pretreated initial alignment data, and obtaining a system state vector according to independent elements of the Davenport matrix; predicting the system state vector by using a Koopman operator and a DMD approximation derivation, and obtaining a system predicted state; calculating a prediction error according to the predicted state and a real state at a corresponding time, and evaluating the precision of the initial alignment model of the SINS according to the prediction deviation. The application effectively avoids the interference of factors such as sensor noise, environmental disturbance and vehicle vibration on the evaluation conclusion, and improves the accuracy of the evaluation result.

Description

Technical Field

[0001] This application relates to the field of inertial navigation technology, and in particular to a method for evaluating the accuracy of the initial alignment model of SINS based on Koopman operator theory. Background Technology

[0002] Initial alignment of a strapdown inertial navigation system (SINS) is a fundamental step in achieving high-precision navigation solutions. It involves constructing a reasonable mathematical model and processing the output data from the inertial devices to obtain initial attitude information. The structural accuracy of the initial alignment model directly determines the alignment accuracy, thus affecting the overall performance of the navigation system.

[0003] In engineering practice, the initial alignment model of SINS is usually based on nonlinear dynamics and is often simplified through small-angle assumptions or local linearization methods. However, under conditions of large misalignment angles, vibration disturbances, or complex working conditions, the linearization errors and structural incompleteness of such models will gradually become apparent, thus affecting the alignment accuracy.

[0004] Currently, traditional evaluation methods for the initial alignment model performance of SINS primarily rely on the alignment results themselves, often using indicators such as the magnitude of the alignment output attitude error, convergence speed, or root mean square error as evaluation criteria—a type of indirect evaluation. However, the initial alignment process of SINS is susceptible to the coupled effects of various external factors, such as measurement noise, carrier vibration, environmental interference, and sensor noise. Traditional indirect evaluation methods cannot effectively distinguish between the model's own structural errors and errors caused by external disturbances, resulting in evaluation results that fail to accurately reflect the true structural performance of the initial alignment model. Furthermore, traditional indirect evaluation methods do not specifically assess the internal mathematical structure of the initial alignment model, failing to quantify its dynamic descriptive capabilities at the model's essential level.

[0005] Therefore, how to directly evaluate the rationality of the initial alignment model structure and its dynamic description capability while minimizing the impact of external disturbances, and provide a reliable basis for model optimization and system design, has become an urgent problem to be solved. Summary of the Invention

[0006] In view of the above problems, this application provides a method and system for evaluating the accuracy of the initial alignment model of SINS based on Koopman operator theory, so as to solve the problem that the accuracy of the alignment model is difficult to be directly and accurately evaluated during the initial alignment process of existing inertial navigation systems.

[0007] In a first aspect, embodiments of this application provide a method for evaluating the accuracy of a SINS initial alignment model based on Koopman operator theory, including: Acquire initial alignment data for the inertial navigation system; The Davenport matrix of the initial alignment model of SINS is constructed at each discrete time based on the initial alignment data, and the system state vector is obtained based on the Davenport matrix. The predicted system state is obtained by predicting the system state vector based on the Koopman operator. The prediction error is calculated based on the predicted and actual states of the system, and the accuracy of the initial alignment model of SINS is evaluated based on the prediction deviation. Navigation solutions are calculated based on the initial alignment model of the SINS that has passed evaluation.

[0008] Further, the step of constructing the Davenport matrix of the initial alignment model of SINS at each discrete time based on the initial alignment data, and obtaining the system state vector based on the Davenport matrix, includes: The initial time attitude matrix is ​​obtained based on the initial alignment data. The initial reference vector is determined based on the initial time attitude matrix and the initial observation vector of the initial alignment model of SINS. The initial observation vector and the initial reference vector are normalized to obtain the observation unit vector and the reference unit vector; Using the QUEST method, the Davenport matrix for each discrete time step is constructed based on multiple vector pairs consisting of observed unit vectors and reference unit vectors. Based on the elements in the Davenport matrix, construct the system state vector of the initial alignment model of SINS.

[0009] Furthermore, the prediction of the system state vector based on the Koopman operator to obtain the predicted system state includes: Multiple system state vectors are collected at equal intervals to construct a snapshot matrix X of the system state and a time shift matrix X′ of the snapshot matrix; Singular value decomposition and rank truncation are performed on the snapshot matrix X to retain the subspace that reflects the dominant dynamics of the system, resulting in the truncated form of the snapshot matrix X. Based on the truncated form of the snapshot matrix, the low-dimensional linear advancement matrix is ​​obtained according to the Koopman operator. Based on a low-dimensional linear advancement matrix, the system state is predicted to obtain the predicted system state.

[0010] Furthermore, the prediction of the system state based on the low-dimensional linear advancement matrix to obtain the predicted system state includes: Projecting the system state vector at any discrete moment onto a low-dimensional coordinate system yields the dimensionality-reduced low-dimensional system state vector. Based on the low-dimensional system state vector, the predicted system state at the next moment is obtained.

[0011] Furthermore, obtaining the predicted system state at the next moment based on the low-dimensional system state vector includes: The low-dimensional system state vector at the current discrete moment is advanced, and the predicted system state at the next moment is obtained through full-dimensional reconstruction.

[0012] Furthermore, obtaining the predicted system state at the next moment based on the low-dimensional system state vector includes: The low-dimensional system state vector at the current discrete moment is predicted in p steps, and the predicted state of the system is obtained based on the prediction result of the (p-1)th step in the p-th step. In each step of prediction, the predicted state of the system at this step is obtained by reconstructing the low-dimensional system state vector in full dimensions.

[0013] Furthermore, based on the low-dimensional linear advancement matrix, the system state is predicted to obtain the predicted system state, which also includes: The low-dimensional linear propagation matrix is ​​decomposed into eigenvector matrix and eigenvalue matrix, and the DMD mode matrix of the system is constructed based on the eigenvector matrix. Based on the system's DMD mode matrix, and by performing equivalent evolution based on the DMD mode matrix and eigenvalue matrix, the predicted state of the system is obtained.

[0014] Further, the step of calculating the prediction error based on the system's predicted state and actual state, and evaluating the accuracy of the initial alignment model of SINS based on the prediction deviation, includes: The prediction error is obtained by comparing the predicted state of the system at each time step with the actual state at the corresponding time step. The root mean square error and maximum deviation are calculated based on the prediction error. The degree of deviation between the predicted state and the actual state of the system is determined based on the root mean square error and maximum deviation. The accuracy of the initial alignment model of SINS is evaluated based on the degree of deviation.

[0015] Secondly, embodiments of this application provide a SINS initial alignment model accuracy evaluation system based on Koopman operator theory, the system comprising: The acquisition module is used to acquire the initial alignment data of the inertial navigation system and perform preprocessing. The construction module is used to construct the Davenport matrix of the initial alignment model of SINS at each discrete time based on the preprocessed initial alignment data, and to obtain the system state vector based on the independent elements of the Davenport matrix. The prediction module is used to predict the system state vector using the Koopman operator and DMD approximation to obtain the predicted system state. The evaluation module is used to calculate the prediction error based on the predicted state and the actual state at the corresponding time, and to evaluate the accuracy of the initial alignment model of SINS based on the prediction deviation.

[0016] The specific beneficial effects are as follows: First, by introducing the Koopman operator theory, this invention maps the inherently nonlinear system dynamics during the initial alignment process of an inertial navigation system to a high-dimensional observable function space, thereby constructing a global linear description of the alignment model; Second, based on the dynamic mode decomposition method, data-driven modeling of the measured state time series is performed to form a finite-dimensional Koopman approximation operator, which is then used to predict the system state. By comparing the deviation between the Koopman predicted state and the actual state, the ability of the initial alignment model to describe the actual dynamic behavior of the system is directly evaluated. At the same time, the singular value decomposition truncation mechanism is used to effectively separate the dominant dynamics of the system from noise, vibration and external disturbances, so that the evaluation results can focus on the model structural error itself.

[0017] In summary, this invention effectively avoids interference from sensor noise, environmental disturbances, and vehicle vibrations on the evaluation conclusions by directly evaluating the initial alignment model. Under different operating conditions such as static, engine operation, and strong human-induced disturbances, it can clearly reveal the changing trend and failure boundary of the model's predictive ability, providing a quantitative basis for model optimization. At the same time, it breaks through the limitations of traditional small-angle linearization analysis, preserves the complete dynamic characteristics of the system, improves the accuracy and engineering reference value of the evaluation results, and has good practicality and prospects for widespread application. Attached Figure Description

[0018] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the description of the embodiments of this application will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 This is a flowchart of the method proposed in this invention; Figure 2 This is a comparison of the predicted and actual states of the sixth state under static conditions in the experimental case. Figure 3 This is a comparison of the predicted and actual states of the sixth state under the engine operating conditions in the experimental case. Figure 4 This is a comparison between the predicted and actual states of the sixth state in the experimental case, where the engine is running and personnel are getting on and off the vehicle. Figure 5 This refers to the state prediction error under static conditions in the experimental case. Figure 6 This refers to the state prediction error under the engine operating conditions in the experimental case. Figure 7 This refers to the state prediction error under the condition of engine operation and personnel getting on and off the vehicle in the experimental case. Figure 8 These are the heading alignment results and RMSE under static conditions in the experimental case. Figure 9 These are the heading alignment results and RMSE under engine operating conditions in the experimental case. Figure 10 This refers to the heading alignment results and RMSE under the conditions of engine operation and personnel getting on and off the vehicle in the experimental case. Detailed Implementation

[0020] Exemplary embodiments of this application will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of this application are shown in the drawings, it should be understood that this application may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of this application and to fully convey the scope of this application to those skilled in the art.

[0021] Combination Figure 1 This application provides a method for evaluating the accuracy of the initial alignment model of SINS based on Koopman operator theory, which includes the following steps: Step 1: Acquire the initial alignment data of the inertial navigation system; In this embodiment, the inertial navigation system first acquires data during the initial alignment phase to obtain initial alignment data. The alignment data includes the raw IMU output data of the gyroscope and accelerometer, as well as the SINS initial attitude, velocity, and position data calculated by the SINS during the alignment process using the decoded raw IMU output data.

[0022] Step 2: Construct the Davenport matrix of the initial alignment model of SINS at each discrete time based on the initial alignment data, and obtain the system state vector based on the Davenport matrix, which is used as the evaluation object; Optionally, step 2 includes the following sub-steps: Step 201: Obtain the initial time attitude matrix based on the initial alignment data, and determine the initial reference vector based on the initial time attitude matrix and the initial observation vector of the initial alignment model of SINS. Specifically, first, the basic relationship between the observation vector and the reference vector in the initial alignment model of SINS is determined: (1) in, This represents the initial attitude matrix from the vehicle coordinate system to the navigation coordinate system. Indicates the initial time. The carrier coordinate system (b system). Indicates the initial time. The navigation coordinate system (n-system). This represents the initial observation vector constructed from inertial devices (such as accelerometer force, etc.). This represents the reference vector in the navigation coordinate system constructed by gravity / Earth's rotation, etc. Secondly, in the general dynamic case, we take: (2) (3) in, Indicates time The carrier coordinate system This represents the specific force vector in the b-frame as measured by the accelerometer. Indicates time navigation coordinate system Represents acceleration in the n-frame. Represents the velocity in the n-system. This represents the Earth's rotational angular velocity in the n-frame. This represents the expression of the transport angular velocity in the n-frame relative to the Earth-fixed coordinate system. This represents the gravity vector in the n-frame. Indicates the initial time. At the time The attitude matrix in the carrier coordinate system, Indicates the initial time. At the time The attitude matrix in the navigation coordinate system; When the carrier is in a static or slightly vibrating state (approximately) , When ), the initial reference vector will simplify to: (4) Step 202: Normalize the initial observation vector and the initial reference vector to obtain the observation unit vector and the reference unit vector; To eliminate the scaling effect, the reference vector and observation vector are normalized: (5) in, This represents the normalized observation unit vector. This represents the normalized reference unit vector. Denotes the Frobenius norm; Step 203: Using the QUEST method, construct the Davenport matrix for each discrete time step based on multiple vector pairs consisting of observed unit vectors and reference unit vectors; Specifically, for the k-th discrete time ( , Given a sampling time interval, n sets of observed unit vectors / reference unit vectors form vector pairs ( ), where i = 1, 2, ..., n, i represents the index, construct the QUEST intermediate quantity: (6) (7) (8) (9) in, This represents the intermediate matrix at the k-th discrete time. This represents a symmetric matrix at the k-th discrete time. This represents the vector at the k-th discrete time. This represents the scalar at the k-th discrete time. Represents the weighting coefficient, and , This represents the unit vector of the i-th observation group at the k-th discrete time. This represents the i-th set of reference unit vectors at the k-th discrete time. Represents the trace of a matrix; The above , , , These are all QUEST intermediate values. Based on these QUEST intermediate values, the Davenport matrix can be obtained: (10) in, The Davenport matrix represents the state of the initial alignment model of SINS at the k-th discrete time, and is used to characterize the mathematical structure of the model at that discrete time. It is a 3×3 matrix. It is a 3x1 matrix; Step 204: Construct the system state vector of the initial alignment model of SINS based on the elements in the Davenport matrix; because Since it is a symmetric matrix with zero trace property, row and column elements in the matrix can be selected as states to reduce dimensionality.

[0023] In this embodiment, The independent elements are combined to form a 9-dimensional system state vector. : (11) in, Represents the Davenport matrix The element in the i-th row and j-th column; The above system state vector The "observable state" of the internal structure of the initial alignment model of SINS will serve as the core object of Koopman / DMD evaluation.

[0024] Based on state vectors at multiple discrete time points To obtain the complete state-time series It is used to reflect the evolution of the internal state of the initial alignment model over time.

[0025] Step 3: Predict the system state vector based on the Koopman operator to obtain the predicted system state; First, the basic definition of the Koopman operator is given: Consider discrete-time nonlinear systems: (12) in, , Represents a nonlinear mapping; For any observable function (or vector-valued observable functions), Koopman operator The definition of is: (13) Since the key property of the Koopman operator is linearity, for any scalar , With observable function , Then we have: (14) Therefore, although the original system is nonlinear, its propulsion operator in the observable space is a linear operator.

[0026] Secondly, the observable function is chosen as the identity mapping. That is, by directly approximating in the state space, the Koopman advance corresponds to the linear approximation of the state as follows: (15) in, Let be the finite-dimensional linear operator to be estimated, i.e., the full-dimensional linear advancement matrix.

[0027] Based on the definition of the Koopman operator above, step 3 further includes the following sub-steps: Step 301: Collect m system state vectors at equal intervals, and construct a snapshot matrix X of the system state and a time shift matrix X′ of the snapshot matrix; Specifically, the constructed state sequence Arrange the time series in chronological order, transform the transition time series into matrix form, and construct the snapshot matrix X and its time shift matrix X′: , (16) Where m is the number of snapshots (sample point summary). It consists of the first m-1 system state vectors. X and X′ are the result of shifting X one position to the right along the time axis, providing the data basis for subsequent dynamic mode decomposition and Koopman operator approximation.

[0028] Ideally, the following conditions are met: (17) By performing a least-squares fit on the above equation, we can obtain: (18) in, Describing the Frobenius norm, This indicates the Moore-Penrose pseudo-inverse.

[0029] Step 302: Perform singular value decomposition and rank truncation on the snapshot matrix X, retaining the subspace that reflects the dominant dynamics of the system, to obtain the truncated representation of the snapshot matrix X. Then, construct a low-dimensional Koopman operator based on the truncated representation of the snapshot matrix to obtain a low-dimensional linear advancement matrix. When the dimension is high or the noise is strong, direct construction The numerical values ​​may be unstable and computationally intensive, therefore SVD dimensionality reduction is employed. Specifically, the snapshot matrix is ​​first processed... Perform singular value decomposition: (19) in, and Let them represent the left singular matrix and the right singular matrix, respectively. represents a singular value matrix, and * represents the conjugate transpose; Take the previous one One principal singular value and its corresponding singular vector ( ), to obtain the snapshot matrix Truncation form: (20) in, and Let these represent the truncated left singular matrix and right singular matrix, respectively. Represents the truncated singular value matrix. Indicates the truncation order / approximate rank; Furthermore, in this embodiment, the choice of the truncation rank r achieves a balance between dominant dynamic preservation and noise / external disturbance suppression. From SVD, we can obtain: (twenty one) in, , , Indicates the truncated portion.

[0030] This invention, by constructing the following low-dimensional linear advancement matrix using only the dominant subspace, can, to some extent, reduce the impact of measurement noise and non-stationary external disturbances on operator estimation, making the evaluation index more reflective of the inherent error of the initial alignment model structure.

[0031] Specifically, based on the time shift matrix X′, the left side of equation (17) is multiplied by and utilize The low-dimensional linear advancement matrix can be obtained. : (twenty two) Next, based on the low-dimensional linear advancement matrix The system state vector can then be predicted to obtain the predicted state of the system, and then proceed directly to step 303. Step 303: Based on the low-dimensional linear advancement matrix, predict the system state to obtain the predicted system state; In this embodiment, the system state vector at any discrete time k is first... (Real state) projected onto a low-dimensional coordinate system: (twenty three) in, Represents the low-dimensional system state vector after dimensionality reduction at discrete time k; Furthermore, it can be derived from Reconstruction.

[0032] Next, the constructed low-dimensional linear advancement matrix is ​​used... (Koopman approximate linear operator) performs one-step or multi-step prediction of the system state vector to obtain the predicted state of the system; where: 1) One-step prediction: Based on the low-dimensional linear advancement matrix, advance the low-dimensional system state vector at the current discrete moment, and obtain the predicted system state at the next moment through full-dimensional reconstruction. ; (twenty four) in, This represents the predicted state vector of a low-dimensional system at discrete time k+1. This represents the system's predicted state vector at discrete time k+1; 2) Multi-step prediction: Based on the p-th power of the low-dimensional linear advancement matrix, the low-dimensional system state vector at the current discrete moment is advanced in p steps, and the predicted system state at the next moment is obtained through full-dimensional reconstruction. ; (25) in, This represents the predicted state vector of a low-dimensional system at discrete time k+p. This represents the system's predicted state vector at discrete time k+p, where p represents the number of steps. Let represent the low-dimensional linear advancement matrix at step p; Optionally, in order to reflect the main evolution mode of the internal state of the initial alignment model, the system state can be predicted by constructing the DMD mode matrix of the system, i.e., proceed to step 304 below. Step 304: Perform eigenvalue decomposition on the low-dimensional linear propagation matrix to obtain the eigenvector matrix, construct the DMD mode matrix of the system based on the eigenvector matrix, and obtain the predicted state of the system based on the DMD mode matrix.

[0033] First, the low-dimensional Koopman approximate linear operator (i.e., the low-dimensional linear advancement matrix) constructed from equation (22) is... Perform eigenvalue decomposition: (26) in, Represents the eigenvalue matrix. Represents the eigenvector matrix; Then based on the eigenvector matrix Calculate the DMD mode matrix of the system state to characterize the dominant dynamic characteristics of the system; the corresponding DMD modes (full-dimensional reconstruction) are: (27) in, The DMD mode matrix (i.e., the finite-dimensional representation of the Koopman eigenmodes) is used to intuitively reflect the main evolution patterns of the internal state of the initial alignment model, providing supplementary basis for model characteristic analysis.

[0034] Then, based on the DMD mode matrix and eigenvalue matrix Perform equivalent evolution to obtain the predicted state of the system. Furthermore, the system predicts states in modal form: (28) in, This represents the coefficient vector obtained by fitting the initial value (e.g., by least squares solution). ) Step 4: Calculate the prediction error based on the system's predicted state and actual state, and evaluate the accuracy of the initial alignment model of SINS based on the prediction deviation; Optionally, step 4 includes the following sub-steps: Step 401: Obtain the prediction error based on the difference between the predicted state of the system at each time step and the actual state at the corresponding time step; Specifically, the prediction error at each time step for: (29) in, The predicted state of the system at the k-th discrete time. Let be the system state (i.e., the true state) at the k-th discrete time. Step 402: Calculate the root mean square error and maximum deviation based on the prediction error. Use the root mean square error and maximum deviation as quantitative indicators to determine the degree of deviation between the predicted state and the actual state of the system, and evaluate the accuracy of the initial alignment model of SINS based on the degree of deviation. The formula for calculating the root mean square error (RMSE) is as follows:

[0035] Where N is the length of the sequence to be evaluated; The formula for calculating the maximum deviation is:

[0036] in, This represents the maximum deviation.

[0037] Finally, using the root mean square error (RMSE) and maximum deviation as quantitative indicators, the degree of deviation between the "Koopman predicted dynamics" and the "actual dynamics" can be characterized. The smaller the deviation, the better the structure of the initial alignment model describes the system's intrinsic dynamics. When the deviation increases significantly with the increase of the operating condition disturbance, it can be determined that the initial alignment model has unmodeled factors or incomplete structure under that operating condition, thus providing a basis for correcting the initial alignment model.

[0038] Experimental Case: To further verify the performance of the proposed method, the system state prediction results of the initial alignment model under different operating conditions (such as stationary, engine running, strong disturbance, etc.) are given, such as... Figures 2-10As shown in the figure, when the initial alignment model prediction deviation is small, it indicates a more complete model structure, and the attitude error (such as heading error) obtained from the initial alignment is more likely to achieve higher accuracy. When the prediction deviation increases significantly, it indicates that external disturbances or unmodeled nonlinear factors have exceeded the descriptive capability boundary of the current model, thus suggesting the need to introduce more complete disturbance modeling or improve the alignment model structure. As can be seen from the figure, the evaluation method proposed in this application can objectively and quantitatively evaluate the accuracy, applicability, and robustness of the initial alignment model without depending on the quality of the alignment results, thereby significantly improving the relevance and reliability of the model analysis.

[0039] Example 2: This application also provides a SINS initial alignment model accuracy evaluation system based on Koopman operator theory, including: The acquisition module is used to acquire the initial alignment data of the inertial navigation system and perform preprocessing. The construction module is used to construct the Davenport matrix of the initial alignment model of SINS at each discrete time based on the preprocessed initial alignment data, and to obtain the system state vector based on the independent elements of the Davenport matrix. The prediction module is used to predict the system state vector using the Koopman operator and DMD approximation to obtain the predicted system state. The evaluation module is used to calculate the prediction error based on the predicted state and the actual state at the corresponding time, and to evaluate the accuracy of the initial alignment model of SINS based on the prediction deviation.

[0040] Although preferred embodiments of the embodiments of this application have been described, those skilled in the art, once they have learned the basic inventive concept, can make other changes and modifications to these embodiments.

[0041] Finally, it should be noted that in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or terminal device that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or terminal device. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or terminal device that includes said element.

[0042] This document uses specific examples to illustrate the principles and implementation methods of this application. The descriptions of the above embodiments are only for the purpose of helping to understand the methods and core ideas of this application. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this application. Therefore, the content of this specification should not be construed as a limitation of this application.

Claims

1. A method for evaluating the accuracy of a SINS initial alignment model based on Koopman operator theory, characterized in that, include: Acquire initial alignment data for the inertial navigation system; The Davenport matrix of the initial alignment model of SINS is constructed at each discrete time based on the initial alignment data, and the system state vector is obtained based on the Davenport matrix. The predicted system state is obtained by predicting the system state vector based on the Koopman operator. The prediction error is calculated based on the predicted and actual states of the system, and the accuracy of the initial alignment model of SINS is evaluated based on the prediction deviation. Navigation solutions are calculated based on the initial alignment model of the SINS that has passed evaluation.

2. The method according to claim 1, characterized in that, The process of constructing the Davenport matrix of the initial alignment model of SINS at each discrete time based on the initial alignment data, and obtaining the system state vector based on the Davenport matrix, includes: The initial time attitude matrix is ​​obtained based on the initial alignment data. The initial reference vector is determined based on the initial time attitude matrix and the initial observation vector of the initial alignment model of SINS. The initial observation vector and the initial reference vector are normalized to obtain the observation unit vector and the reference unit vector; Using the QUEST method, the Davenport matrix for each discrete time step is constructed based on multiple vector pairs consisting of observed unit vectors and reference unit vectors. Based on the elements in the Davenport matrix, construct the system state vector of the initial alignment model of SINS.

3. The method according to claim 2, characterized in that, The prediction of the system state vector based on the Koopman operator to obtain the predicted system state includes: Multiple system state vectors are collected at equal intervals to construct a snapshot matrix X of the system state and a time shift matrix X′ of the snapshot matrix; Singular value decomposition and rank truncation are performed on the snapshot matrix X to retain the subspace reflecting the dominant dynamics of the system, resulting in the truncated form of the snapshot matrix X. Based on the truncated form of the snapshot matrix, the low-dimensional linear advancement matrix is ​​obtained according to the Koopman operator. Based on a low-dimensional linear advancement matrix, the system state is predicted to obtain the predicted system state.

4. The method according to claim 3, characterized in that, The prediction of the system state based on the low-dimensional linear advancement matrix, to obtain the predicted system state, includes: Projecting the system state vector at any discrete moment onto a low-dimensional coordinate system yields the dimensionality-reduced low-dimensional system state vector. Based on the low-dimensional system state vector, the predicted system state at the next moment is obtained.

5. The method according to claim 4, characterized in that, The process of obtaining the predicted system state at the next moment based on the low-dimensional system state vector includes: The low-dimensional system state vector at the current discrete moment is advanced, and the predicted system state at the next moment is obtained through full-dimensional reconstruction.

6. The method according to claim 4, characterized in that, The process of obtaining the predicted system state at the next moment based on the low-dimensional system state vector includes: Perform the following steps on the low-dimensional system state vector at the current discrete moment: p Step prediction, and the first p Step by step p The predicted state of the system is obtained based on the prediction results of step -1. At each prediction step, the predicted state of the system at that step is obtained by reconstructing the low-dimensional system state vector in full dimension.

7. The method according to claim 4, characterized in that, Based on a low-dimensional linear advancement matrix, the system state is predicted to obtain the predicted system state, which also includes: The low-dimensional linear propagation matrix is ​​decomposed into eigenvector matrix and eigenvalue matrix, and the DMD mode matrix of the system is constructed based on the eigenvector matrix. Based on the system's DMD mode matrix, and by performing equivalent evolution based on the DMD mode matrix and eigenvalue matrix, the predicted state of the system is obtained.

8. The method according to claim 5, characterized in that, The step of calculating the prediction error based on the system's predicted state and actual state, and evaluating the accuracy of the initial alignment model of SINS based on the prediction deviation, includes: The prediction error is obtained by comparing the predicted state of the system at each time step with the actual state at the corresponding time step. The root mean square error and maximum deviation are calculated based on the prediction error. The degree of deviation between the predicted state and the actual state of the system is determined based on the root mean square error and maximum deviation. The accuracy of the initial alignment model of SINS is evaluated based on the degree of deviation.

9. A system for evaluating the accuracy of SINS initial alignment models based on Koopman operator theory, characterized in that, The system is implemented based on the method according to any one of claims 1-8, and includes: The acquisition module is used to acquire the initial alignment data of the inertial navigation system; The construction module is used to construct the Davenport matrix of the initial alignment model of SINS at each discrete time based on the initial alignment data, and to obtain the system state vector based on the Davenport matrix. The prediction module is used to predict the system state vector based on the Koopman operator to obtain the predicted system state. The evaluation module is used to calculate the prediction error based on the system's predicted and actual states, and to evaluate the accuracy of the initial alignment model of SINS based on the prediction deviation.

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