Constellation operation state consistency evaluation method based on multidimensional data covariance analysis

Abstract

The invention discloses a constellation operation state consistency evaluation method based on multidimensional data covariance analysis, and relates to a constellation operation state consistency evaluation method. The method aims at solving the problems that weight determination based on the data fusion technology often depends on experience or some subjective judgment, objective bases are lacked, and different weight distribution may cause large difference between a fusion result and a consistency evaluation result. The method comprises the following steps: step 1, preprocessing satellite constellation multi-dimensional telemetry data; 2, calculating a covariance matrix of the multi-dimensional telemetry data of the satellite constellation; and step 3, evaluating the consistency of the telemetry data based on the covariance matrix. The invention belongs to the technical field of satellite data analysis.

Description

Technical Field

[0001] The present invention relates to a method for evaluating the consistency of a constellation's operating status, and belongs to the technical field of satellite data analysis. Background Art

[0002] With the continuous advancement of satellite data analysis technology, performance evaluation of various satellite electrical parameters has become an important means of improving space system stability. Consistency assessment primarily measures the degree of match between satellite telemetry data and other observational data (such as ground-based observations and other satellite data). Ensuring data consistency across different sources is crucial for enhancing data credibility. Consistency assessment allows for comparison of data from different sensors, identifying potential sources of error and correcting them accordingly. Quality control of satellite telemetry data is fundamental to ensuring its effective application in scientific research, environmental monitoring, and disaster warning. Statistical analysis plays a crucial role in this process. By establishing appropriate data quality assessment models, it can effectively identify and correct data biases. For example, temporal and spatial consistency assessment of satellite data are common methods for assessing data quality. In summary, statistical analysis and consistency assessment are increasingly widely used in satellite telemetry. Research has demonstrated that these techniques play a significant role in improving the accuracy and reliability of telemetry data. In the future, with the advancement of satellite technology, statistical analysis and consistency assessment methods will be further optimized, providing stronger support for the application of remote sensing data.

[0003] Existing techniques primarily include mean and standard deviation analysis, hypothesis testing, data fusion techniques, and model-based methods. 1) Mean and standard deviation analysis primarily describes trends and dispersion in a dataset, reflecting only the overall level and fluctuations of the data itself and failing to directly reflect the interrelationships and consistency between data of different dimensions. The covariance matrix, on the other hand, effectively reveals the degree of linear correlation between variables. Furthermore, the mean and standard deviation are significantly affected by extreme values ​​and distributional patterns. If the data exhibit skewed distributions or outliers, the mean and standard deviation may not accurately reflect the true characteristics of the data, thereby affecting the assessment of data consistency. The covariance matrix is ​​also affected to some extent by extreme values, but is relatively more stable for analyzing variable relationships. 2) Hypothesis testing typically requires assumptions about conditions such as the data distribution. For example, the t-test typically requires that the data follow a normal distribution. If the actual data do not meet these assumptions, the test results may be inaccurate. The calculation of the covariance matrix, on the other hand, requires fewer assumptions about the data distribution and is therefore more versatile. Furthermore, hypothesis testing can only determine whether there are significant differences between data; it cannot quantitatively describe the degree of correlation and consistency between data, as the covariance matrix can. 3) In the field of ocean color satellite remote sensing, the State Key Laboratory of Marine Environmental Sciences at Xiamen University and the National Satellite Ocean Application Center jointly proposed and released the Cross-Satellite Atmospheric Correction (CSAC) system. This system uses artificial intelligence to fuse data from different satellites, significantly improving the accuracy and consistency of ocean remote sensing reflectance data between ocean color satellites. This system utilizes data fusion technology. However, the determination of weights in data fusion often relies on experience or subjective judgment, lacking objective evidence. Different weight assignments can lead to significant discrepancies between the fusion results and the consistency assessment results. The covariance matrix, on the other hand, is calculated based on the statistical characteristics of the data itself and is relatively more objective. Furthermore, weighted average fusion primarily aims to produce a comprehensive result and has limited ability to analyze complex linear and nonlinear relationships between data, unlike the covariance matrix, which directly displays linear correlations between variables. 4) Model-based consistency assessment: For complex satellite systems, model establishment can be extremely difficult, and the determination of model parameters requires extensive experiments and data support. However, the calculation of the covariance matrix is ​​relatively simple and straightforward. In addition, the satellite system may undergo various changes during operation, and the physical model needs to be continuously updated and maintained to ensure its accuracy, which requires a lot of time and resources. In contrast, the covariance matrix can be calculated and updated at any time based on real-time data. Summary of the Invention

[0004] To address the problem that the determination of weights based on data fusion technology often relies on experience or some subjective judgments and lacks objective basis, and different weight distributions may lead to large differences between fusion results and consistency assessment results, the present invention proposes a constellation operation status consistency assessment method based on multidimensional data covariance analysis.

[0005] The technical solution adopted by the present invention to solve the above problems is: the steps of the present invention include: Step 1: Preprocessing the multi-dimensional telemetry data of the satellite constellation; Step 2: Calculate the covariance matrix of multi-dimensional telemetry data of satellite constellation; Step 3: Evaluate the consistency of telemetry data based on the covariance matrix.

[0006] Furthermore, the process of preprocessing the multi-dimensional telemetry data of the satellite constellation in step 1 is as follows: Step 101: truncate each dimension of the multidimensional telemetry data to the length of the shortest dimension; Step 102: Standardize the multidimensional telemetry data to have a mean of 0 and a variance of 1 to eliminate the dimensionality effect.

[0007] Furthermore, step 101 specifically includes: Assume that the satellite has n different types of telemetry data sources, and the length of each dimension data is , then the satellite multidimensional telemetry data can be expressed as matrix X: , in, Indicates the The dimension in The measured values ​​at each observation location, , The value range depends on the dimension Data length Determined, that is ; When actually processing data, it is necessary to unify the length of each dimension. The truncation operation is performed on each dimension as a benchmark. After truncation, the satellite multidimensional telemetry data can be expressed as a matrix X:

[0008] The specific operation of step II is as follows: , in, represents the mean, Represents standard deviation.

[0009] Furthermore, the algorithm for calculating the covariance matrix of the multidimensional telemetry data of the satellite constellation in step 2 is: For the inclusion samples, The multidimensional telemetry data matrix X of dimensions is obtained by averaging the observation values ​​of each dimension to obtain the sample mean vector Based on the mean vector, the covariance between any two dimensions is calculated to construct the covariance matrix. The covariance matrix can reflect the linear correlation and coordinated change trend between data of different dimensions, which helps to deeply analyze the intrinsic structure and characteristics of multidimensional telemetry data. The specific operations are expressed as: Mean vector is a dimensional column vector, whose Elements For the The mean of all sample observations in dimensions: , Mean vector Obtained by: , in, yes dimensional all-one column vector; Covariance matrix is a A symmetric matrix is ​​used to measure the linear correlation between different dimensions. element Defined as: , Covariance matrix Expressed as: , in, is a A matrix whose columns are the mean vectors , by removing the original matrix Subtract the matrix from the original data to achieve decentralized data processing.

[0010] Furthermore, the process of evaluating the consistency of telemetry data based on the covariance matrix in step 3 is: Step 301: perform eigenvalue decomposition on the covariance matrix to extract eigenvalues; Step 302: Calculate the consistency index, which is defined as the ratio of the non-zero eigenvalue to the maximum value.

[0011] Furthermore, step 301 specifically includes: When the eigenvalue is greater than 0.1, it is defined as a non-zero eigenvalue; The eigenvalue reflects the variance distribution of the data in the direction of each principal component, which is expressed as: , in, represents the eigenvector matrix, represents the diagonal matrix of eigenvalues.

[0012] Furthermore, step 302 specifically includes: Let the eigenvalues ​​of the covariance matrix be ,in is the number of dimensions, assuming that the eigenvalues ​​are sorted from large to small, that is, , the mean of non-zero eigenvalues ​​is expressed as: , The maximum eigenvalue is expressed as: , The ratio of the mean of non-zero eigenvalues ​​to the maximum eigenvalue, that is, the consistency index, is expressed as: .

[0013] The beneficial effects of the present invention are: 1. This invention eliminates the need to directly measure traditional performance degradation characteristics (such as capacity and internal resistance) on orbit, thereby improving the ability to predict satellite system performance degradation without adding additional hardware burden. 2. With its precise quantification capability, the covariance matrix of the present invention can accurately capture and measure the coordinated variation characteristics between variables, and intuitively display the degree of consistency between data with specific numerical values; 3. The present invention has no strict restrictions on the distribution and type of data, is applicable to various types of multi-dimensional telemetry data, and has strong versatility and adaptability. DETAILED DESCRIPTION

[0014] Specific implementation method 1: A method for evaluating the consistency of constellation operation status based on multidimensional data covariance analysis, including the following steps: Step 1: Preprocess the multi-dimensional telemetry data of the satellite constellation; the specific process is as follows: Step 101: truncate each dimension of the multi-dimensional telemetry data to the length of the shortest dimension; specifically, the steps include: Assume that the satellite has Different types of telemetry data sources, the length of each dimension data is , then the satellite multidimensional telemetry data can be expressed as matrix X: , in, Indicates the The dimension in The measured values ​​at each observation location, , The value range depends on the dimension Data length Determined, that is ; When actually processing data, it is necessary to unify the length of each dimension. The truncation operation is performed on each dimension as a benchmark. After truncation, the satellite multidimensional telemetry data can be expressed as a matrix X:

[0015] The specific operation of step II is as follows: , in, represents the mean, represents the standard deviation; Step 102: standardize the multidimensional telemetry data to have a mean of 0 and a variance of 1 to eliminate the dimensionality effect; Step 2: Calculate the covariance matrix of multi-dimensional telemetry data of satellite constellation; For the inclusion samples, The multidimensional telemetry data matrix X of dimensions is obtained by averaging the observation values ​​of each dimension to obtain the sample mean vector Based on the mean vector, the covariance between any two dimensions is calculated to construct the covariance matrix. The covariance matrix can reflect the linear correlation and coordinated change trend between data of different dimensions, which helps to deeply analyze the intrinsic structure and characteristics of multidimensional telemetry data. The specific operations are expressed as: Mean vector is a dimensional column vector, whose Elements For the The mean of all sample observations in dimensions: , Mean vector Obtained by: , in, yes dimensional all-one column vector; Covariance matrix is a A symmetric matrix is ​​used to measure the linear correlation between different dimensions. element Defined as: , Covariance matrix Expressed as:

[0016] in, is a A matrix whose columns are the mean vectors , by removing the original matrix Subtract the matrix from the original data to achieve decentralized data processing; Step 3: Evaluate the consistency of telemetry data based on the covariance matrix. The specific process is as follows: Step 301: perform eigenvalue decomposition on the covariance matrix to extract eigenvalues; When the eigenvalue is greater than 0.1, it is defined as a non-zero eigenvalue; The eigenvalue reflects the variance distribution of the data in the direction of each principal component, which is expressed as: , in, represents the eigenvector matrix, represents the eigenvalue diagonal matrix; Step 302: Calculate the consistency index, which is defined as the ratio of the non-zero eigenvalue to the maximum value; Let the eigenvalues ​​of the covariance matrix be ,in is the number of dimensions, assuming that the eigenvalues ​​are sorted from large to small, that is, , the mean of non-zero eigenvalues ​​is expressed as: , The maximum eigenvalue is expressed as: , The ratio of the mean of non-zero eigenvalues ​​to the maximum eigenvalue, that is, the consistency index, is expressed as: .

[0017] Example Example 1 This embodiment includes two features to evaluate the consistency of multi-dimensional telemetry data. The first is a covariance matrix heat map. The diagonal elements of the matrix represent the variance of data of different dimensions, describing the degree of discreteness of data of different dimensions. The non-diagonal elements are the covariance between two different dimensions, describing the linear relationship between the two dimensions. Positive value: the two dimensions have the same trend, negative value: the two dimensions have opposite trends, zero value: there is no linear relationship between the two dimensions. The second is a consistency evaluation index: the ratio of the mean of non-zero eigenvalues ​​to the maximum eigenvalue. If the ratio is close to 1, it means that the eigenvalue distribution is relatively uniform, and the consistency of the data in each dimension is high. If the ratio is small, it means that the eigenvalue distribution is uneven, and there may be a situation where a few dimensions dominate the data variance.

[0018] Example 2 The method of use of Example 1 comprises the following steps: Step 1: Preprocessing of multi-dimensional telemetry data of satellite constellation; Step 2: Calculate the covariance matrix of multi-dimensional telemetry data of satellite constellation; Step 3: Evaluate the consistency of telemetry data based on the covariance matrix; 1) The data in the first and third dimensions show opposite trends, with a covariance of approximately -1, while the data in the second and fourth dimensions show the same trend, with a covariance of approximately 1.

[0019] 2) The data in the first dimension are almost inconsistent with the data in other dimensions. The heat map shows a light color. Except for the data in the first dimension, the data in other dimensions show the same trend, and the covariance is about 1.

[0020] It can be seen that the method proposed in the present invention can analyze the consistency between two dimensions through the covariance matrix and ensure a high accuracy, providing stronger support for the application of remote sensing data.

[0021] The above description is merely a preferred embodiment of the present invention and does not constitute any form of limitation to the present invention. Although the present invention has been disclosed as a preferred embodiment as above, it is not intended to limit the present invention. Any technician familiar with the present profession can make some changes or modifications to equivalent embodiments of equivalent changes using the technical content disclosed above without departing from the scope of the technical solution of the present invention. However, any simple modification, equivalent replacement and improvement of the above embodiments made according to the technical essence of the present invention, within the spirit and principles of the present invention, without departing from the content of the technical solution of the present invention, shall still fall within the scope of protection of the technical solution of the present invention.

Claims

1. A method for evaluating the consistency of constellation operation status based on multidimensional data covariance analysis, characterized in that: The specific steps include: Step 1: Preprocessing the multi-dimensional telemetry data of the satellite constellation; Step 2: Calculate the covariance matrix of multi-dimensional telemetry data of satellite constellation; Step 3: Evaluate the consistency of telemetry data based on the covariance matrix.

2. The method for evaluating the consistency of constellation operation status based on multidimensional data covariance analysis according to claim 1, characterized in that: The process of preprocessing the multi-dimensional telemetry data of the satellite constellation in step 1 is as follows: Step 101: truncate each dimension of the multidimensional telemetry data to the length of the shortest dimension; Step 102: Standardize the multidimensional telemetry data to have a mean of 0 and a variance of 1 to eliminate the dimensionality effect.

3. The method for constellation operation status consistency assessment based on multidimensional data covariance analysis according to claim 2, characterized in that: Step 101 specifically includes: Assume that the satellite has Different types of telemetry data sources, the length of each dimension data is , then the satellite multidimensional telemetry data can be expressed as matrix X: ， in, Indicates the The dimension in The measured values ​​at each observation location, , The value range depends on the dimension Data length Determined, that is ; When actually processing data, it is necessary to unify the length of each dimension. The truncation operation is performed on each dimension as a benchmark. After truncation, the satellite multidimensional telemetry data can be expressed as a matrix X: The specific operation of step II is as follows: ， in, represents the mean, Represents standard deviation.

4. The method for evaluating the consistency of constellation operation status based on multidimensional data covariance analysis according to claim 1, characterized in that: The algorithm for calculating the covariance matrix of the satellite constellation multidimensional telemetry data in step 2 is: For the inclusion samples, The multidimensional telemetry data matrix X of dimensions is obtained by averaging the observations of each dimension to obtain the sample mean vector Based on the mean vector, the covariance between any two dimensions is calculated to construct the covariance matrix. The covariance matrix can reflect the linear correlation and coordinated change trend between data of different dimensions, which helps to deeply analyze the intrinsic structure and characteristics of multidimensional telemetry data. The specific operations are expressed as: Mean vector is a dimensional column vector, whose Elements For the The mean of all sample observations in dimensions: ， Mean vector Obtained by: ， in, yes dimensional all-one column vector; Covariance matrix is a A symmetric matrix is ​​used to measure the linear correlation between different dimensions. element Defined as: ， Covariance matrix Expressed as: in, is a A matrix whose columns are the mean vectors , by removing the original matrix Subtract the matrix from the original data to achieve decentralized data processing.

5. The method for constellation operation status consistency assessment based on multidimensional data covariance analysis according to claim 1, characterized in that: The process of evaluating the consistency of telemetry data based on the covariance matrix in step 3 is: Step 301: perform eigenvalue decomposition on the covariance matrix to extract eigenvalues; Step 302: Calculate the consistency index, which is defined as the ratio of the non-zero eigenvalue to the maximum value.

6. The method for constellation operation status consistency assessment based on multidimensional data covariance analysis according to claim 5, characterized in that: Step 301 specifically includes: When the eigenvalue is greater than 0.1, it is defined as a non-zero eigenvalue; The eigenvalue reflects the variance distribution of the data in the direction of each principal component, which is expressed as: ， in, represents the eigenvector matrix, represents the diagonal matrix of eigenvalues.

7. The method for evaluating the consistency of constellation operation status based on multidimensional data covariance analysis according to claim 5, characterized in that: Step 302 specifically includes: Let the eigenvalues ​​of the covariance matrix be ,in is the number of dimensions, assuming that the eigenvalues ​​are sorted from large to small, that is, , the mean of non-zero eigenvalues ​​is expressed as: ， The maximum eigenvalue is expressed as: ， The ratio of the mean of non-zero eigenvalues ​​to the maximum eigenvalue, that is, the consistency index, is expressed as: 。

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