Space object meets precise orbit determination DIA algebraic simplification evaluation method, system, storage medium and equipment

Abstract

The application relates to the technical field of space situation awareness, and discloses a DIA algebraic simplification evaluation method, a system, a storage medium and equipment for a space target satisfying precise orbit determination, the method comprising the following steps: acquiring observation data of a space target, and constructing a null hypothesis and a set of alternative hypotheses; constructing a global test statistic for detecting model errors and a local test statistic for identifying error sources based on the set, and determining a null hypothesis acceptance region and a discriminant region of each alternative hypothesis according to a preset false alarm probability; performing analytical calculation by using a simplified algebraic estimation to obtain a test decision probability; constructing an approximate probability density function of a DIA estimator based on the test decision probability, and calculating parameter estimation bias and dispersion under the influence of considering test decision uncertainty, the above method realizes efficient evaluation of the propagation process of detection and identification uncertainty to parameter estimation errors, and can significantly reduce the calculation complexity while ensuring the evaluation precision.

Description

Technical Field

[0001] This invention relates to the field of space situational awareness technology, and in particular to a DIA algebraic simplification evaluation method, system, storage medium, and device for space targets to meet precise orbit determination. Background Technology

[0002] In space target surveillance and measurement missions (such as precise orbit determination of low-Earth orbit satellites, space debris cataloging, and relative positioning of spacecraft formations), observational data of space targets are typically acquired using radar, optical telescopes, or spaceborne GNSS receivers. The target's position, velocity, and other state parameters are then calculated using the least squares adjustment method based on a Gaussian-Markov model. However, least squares estimation can only guarantee unbiasedness and minimum variance characteristics if the observation model is correct and the observation errors satisfy the zero-mean Gaussian distribution assumption.

[0003] In actual space target observation, modeling errors inevitably appear in the observation data due to interference from the space electromagnetic environment, sensor performance degradation, measurement link anomalies, and the influence of complex space environmental factors. These modeling errors may manifest as sudden gross errors or as systematic deviations that are not properly modeled, such as incomplete orbital dynamics modeling or propagation delay errors. When these errors are not effectively detected and identified, directly using least squares estimation will lead to significant deviations in the parameter estimation results, and in severe cases, may even cause instability or divergence in the positioning solution.

[0004] To address modeling errors, the DIA (Detection, Identification, and Adaptation) method has gradually become an important technique in the fields of space surveying and geodesy. The DIA method detects and locates model errors through statistical testing and adaptively adjusts the observation model based on the identification results, thereby reducing the impact of modeling errors on parameter estimation results. Theoretically, this method provides a unified statistical framework for simultaneously handling gross errors and systematic biases, and has been widely applied in GNSS positioning and space surveying.

[0005] However, existing DIA methods still have significant shortcomings in engineering applications: On the one hand, the DIA method is essentially a process of "combining statistical testing and parameter estimation," and its final estimation result is significantly affected by the uncertainty of detection and identification decisions. Traditional reliability analysis focuses on indicators such as minimum detectable deviation, failing to systematically characterize the propagation effect of the uncertainty of testing decisions on the parameter estimation results. On the other hand, when evaluating the performance of DIA methods, existing technologies generally rely on Monte Carlo simulation to statistically evaluate the probability of missed detection, the probability of false identification, and the parameter estimation bias and variance. This method is computationally intensive and inefficient, making it difficult to meet the requirements of real-time performance and engineering feasibility in space target positioning tasks.

[0006] Therefore, there is an urgent need for a method that can efficiently evaluate the probability of detection and identification decisions, as well as the resulting parameter estimation bias and dispersion, within a unified DIA framework, to replace traditional Monte Carlo simulation and achieve a comprehensive quantitative evaluation of the quality of spatial target localization data. Summary of the Invention

[0007] The purpose of this invention is to overcome the shortcomings of the existing technology and provide a simplified algebraic evaluation method for precise orbit determination of space targets using the DIA algorithm. By constructing a Gauss-Markov model system that includes null and multiple alternative hypotheses, the method characterizes the impact of modeling errors on detection and identification decisions. It also uses a simplified algebraic estimation method to analyze and calculate the probabilities of missed detections and false identifications and their propagation effects on parameter estimation bias and dispersion. This significantly improves computational efficiency while ensuring evaluation accuracy, and achieves a unified quantitative evaluation of the reliability and accuracy of space target positioning results.

[0008] On the one hand, the present invention provides a simplified DIA algebraic evaluation method for space targets to satisfy precise orbit determination, comprising the following steps: S1: Acquire observational data of space targets and construct a set of null and alternative hypotheses based on the Gauss-Markov model; S2: Based on the set, construct a global test statistic for detecting model errors and a local test statistic for identifying error sources, and determine the null hypothesis acceptance region and the discriminant region of each alternative hypothesis according to the preset false alarm probability. S3: Given the alternative hypothesis and its error magnitude parameter, simplified algebraic estimation is used to perform analytical calculations to obtain the probability of the test decision; S4: Construct an approximate probability density function for the DIA estimator based on the test decision probability, and calculate the parameter estimation bias and dispersion considering the influence of test decision uncertainty; Among them, analytical calculations using simplified algebraic estimation include: Determine the non-centralized chi-square distribution and its decentralization parameter that the global test statistic follows under the alternative hypothesis, and analyze the false negative probability and the correct detection probability based on the non-centralized chi-square distribution and the critical value. A difference statistic that approximately follows a normal distribution is constructed, and the correct identification probability and incorrect identification probability between alternative hypotheses are analytically calculated based on the difference statistic to replace the Monte Carlo simulation sampling process.

[0009] Furthermore, in step S3, the analytical calculation using simplified algebraic estimation specifically includes: Given alternative hypotheses Its true value and the error magnitude parameter are Under the given conditions, determine the global test statistic. The non-centralized chi-square distribution and its decentralization parameters that it follows under these conditions; Based on the non-central chi-square distribution and the critical value determined by the false alarm probability, the result is obtained analytically. Probability of missed detection when true and according to Calculate the probability of correct detection .

[0010] Preferably, the analytical calculation using simplified algebraic estimation further includes: In the observation-by-observation screening scenario, a local test statistic is constructed based on the error parameter estimate under the alternative hypothesis, and Bararda's method is used. The test forms equivalent expressions, among which The standardized form of the error parameter estimator and with Monotonic correspondence; The probability of correct identification is expressed as in the alternative hypothesis. The probability of the local statistic being dominant over the local statistics of other alternative hypotheses under the given condition is: ; By constructing a difference statistic that approximately follows a normal distribution, we can achieve... The analytical approximation is used to calculate the correct recognition probability. According to the formula The total false recognition probability was calculated. Furthermore, the individual error identification probabilities constituting the total error identification probability are processed through iterative correction or scaling methods to ensure that the sum of probabilities is one.

[0011] More preferably, in step S3, the inspection decision probability includes the probability of missed detection, the probability of correct detection, the probability of correct identification, and the probability of incorrect identification.

[0012] Further, in step S1, the construction of the null hypothesis and alternative hypothesis sets includes: Establish a null hypothesis observation model Its mathematical expectation satisfies ,in For the observation vector, To design the matrix, The vector of position parameters to be estimated; Establish an alternative hypothesis observation model A mean offset term is introduced to characterize the modeling error based on the null hypothesis observation model, and its mathematical expectation satisfies ,in, For mean-biased models, This is the coefficient matrix used to describe the error impact patterns. This refers to the corresponding error amplitude parameter; By configuring multiple different sets of the coefficient matrices This forms a set of multiple parallel alternative hypotheses to cover different observation locations or different numbers of modeling error scenarios.

[0013] Further, in step S2, the construction of the global test statistic and the local test statistic, and the confirmation of the discriminant domain, include: Based on the null hypothesis observation model Using the residual vectors below, construct a global test statistic. The global test statistic It is a quadratic form of the residual; Based on the preset false alarm probability Determine the critical value for the global test and form the acceptance region of the null hypothesis. ;when When the threshold value is exceeded, the null hypothesis is rejected. ; After the null hypothesis is rejected, for each alternative hypothesis... Based on its error parameters Constructing local test statistics from least squares estimators ; The discriminant region for each alternative hypothesis is determined using the maximum local statistic criterion, which is to say, the region that makes the hypothesis so that the hypothesis is ... The alternative hypothesis with the largest value As the identified error model.

[0014] Further, in step S4, the approximate probability density function for constructing the DIA estimator includes: DIA estimator It is expressed as a weighted combination of parameter estimation results under each assumed model, and its expression is: ,in In the first An assumption The parameter estimation results are as follows: To be consistent with the test statistic Related, used to indicate the selection of the first A decision function with one hypothesis; When it is impossible to perform an exact integral solution over the discrimination domain, the DIA estimator will be used. Given the true assumptions, the probability density function approximates a Gaussian mixture model, and its mixture weights are the test decision probabilities calculated by the simplified algebraic estimation method. The determination is to characterize the propagation effect of detection and identification uncertainty on parameter estimation results, whereby... The true assumption is Time Selection The probability of; Based on the Gaussian mixture model, the conditional expectation and conditional covariance of the parameter estimates are calculated by weighted averaging, thereby obtaining the quantified parameter estimation bias and dispersion index.

[0015] Preferably, the analytical calculation using simplified algebraic estimation is performed under the condition that the alternative hypothesis is true and the error magnitude parameter is a definite value; The error amplitude parameter Used to quantify alternative hypotheses Mean offset term The degree of influence on the observation vector, among which To describe the coefficient matrix of the error influence mode, different error magnitude parameters are set. The values ​​are selected, and the test decision probabilities under different error magnitudes are obtained through analytical calculation, thereby realizing the algebraic evaluation of the DIA estimator performance under the influence of modeling errors of different intensities.

[0016] On the other hand, the present invention provides a DIA algebraic simplification evaluation system for space targets to satisfy precise orbit determination, comprising: The data acquisition and modeling module is used to acquire observation data of space targets and construct a set of null and alternative hypotheses based on the Gauss-Markov model. The hypothesis generation and statistical calculation module is used to construct a global test statistic for detecting model errors and a local test statistic for identifying error sources based on the set, and to determine the null hypothesis acceptance region and the discriminant region of each alternative hypothesis according to the preset false alarm probability. The SAE decision evaluation module is used to perform analytical calculations using simplified algebraic estimation to obtain the probability of the test decision, given the alternative hypothesis and its error magnitude parameters. The parameter evaluation and quality output module is used to construct an approximate probability density function of the DIA estimator based on the test decision probability, and to calculate the parameter estimation bias and dispersion considering the influence of test decision uncertainty. Among them, analytical calculations using simplified algebraic estimation include: Determine the non-centralized chi-square distribution and its decentralization parameter that the global test statistic follows under the alternative hypothesis, and analyze the false negative probability and the correct detection probability based on the non-centralized chi-square distribution and the critical value. A difference statistic that approximately follows a normal distribution is constructed, and the correct identification probability and incorrect identification probability between alternative hypotheses are analytically calculated based on the difference statistic to replace the Monte Carlo simulation sampling process.

[0017] In addition, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a processor, implements the DIA algebraic simplification evaluation method for precise orbit determination of space targets as described in any of the preceding claims.

[0018] Meanwhile, an electronic device is provided, comprising: one or more processors; and a storage device for storing one or more programs, which, when executed by the one or more processors, cause the one or more processors to implement the DIA algebraic simplification evaluation method for precise orbit determination of space targets as described in any of the preceding claims.

[0019] Compared with the prior art, the beneficial effects of the present invention are: (1) By constructing a set of null and alternative hypotheses under the unified DIA framework, this invention incorporates the uncertainty of detection and identification decisions into the quality assessment process, and can systematically characterize the impact of modeling errors on the estimation bias and dispersion of spatial target positioning parameters; (2) The present invention adopts a simplified algebraic estimation method to replace the traditional Monte Carlo simulation with analytical calculation, which significantly reduces the computational complexity while ensuring the evaluation accuracy and meets the real-time requirements of space target positioning tasks; (3) By constructing the Gaussian mixture approximation probability density function of the DIA estimator, this invention realizes the quantitative evaluation of the propagation process of the uncertainty of the test decision to the parameter estimation error, and provides a unified quantitative evaluation standard for the reliability and accuracy of the spatial target positioning results, which has important engineering application value. Attached Figure Description

[0020] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1The flowchart below shows a simplified DIA algebraic evaluation method for precise orbit determination of a space target according to the present invention. Figure 2 This is a schematic diagram comparing the evaluation results of the correct identification probability, the missed detection probability, and the false identification probability under the scenario in which the substitution assumption holds. Figure 3 The present invention provides a method for... Figure 2 A comparative diagram showing the evaluation results of estimation bias and dispersion of unknown parameters under the same alternative assumptions. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0022] The specific embodiments of the present invention will be described below with reference to the accompanying drawings and examples.

[0023] Example 1 Please see Figure 1 The technical solution for a simplified DIA algebraic evaluation method for precise orbit determination of space targets provided in this embodiment includes the following steps: S1: Acquire observational data of space targets and construct a set of null and alternative hypotheses based on the Gauss-Markov model; S2: Based on the set, construct a global test statistic for detecting model errors and a local test statistic for identifying error sources, and determine the null hypothesis acceptance region and the discriminant region of each alternative hypothesis according to the preset false alarm probability. S3: Given the alternative hypothesis and its error magnitude parameter, simplified algebraic estimation is used to perform analytical calculations to obtain the probability of the test decision; S4: Construct an approximate probability density function for the DIA estimator based on the test decision probability, and calculate the parameter estimation bias and dispersion considering the influence of test decision uncertainty; Among them, analytical calculations using simplified algebraic estimation include: Determine the non-centralized chi-square distribution and its decentralization parameter that the global test statistic follows under the alternative hypothesis, and analyze the false negative probability and the correct detection probability based on the non-centralized chi-square distribution and the critical value. A difference statistic that approximately follows a normal distribution is constructed, and the correct identification probability and incorrect identification probability between alternative hypotheses are analytically calculated based on the difference statistic to replace the Monte Carlo simulation sampling process.

[0024] First, in step S1, the construction of the null hypothesis and alternative hypothesis sets includes: Establish a null hypothesis observation model Its mathematical expectation satisfies ,in For the observation vector, To design the matrix, The vector of position parameters to be estimated; Establish an alternative hypothesis observation model A mean offset term is introduced to characterize the modeling error based on the null hypothesis observation model, and its mathematical expectation satisfies ,in, For mean-biased models, This is the coefficient matrix used to describe the error impact patterns. This refers to the corresponding error amplitude parameter; By configuring multiple different sets of the coefficient matrices This forms a set of multiple parallel alternative hypotheses to cover different observation locations or different numbers of modeling error scenarios.

[0025] In this embodiment, step S1 involves constructing the observation model and defining assumptions. GNSS, ground-based tracking radar, or optical measurement observation data of space targets (such as low-Earth orbit satellites, space debris, or spacecraft formations) are acquired to construct a basic Gauss-Markov observation model. ,in, For the observation vector of the space target, To design the matrix, Locate the parameter vector for the spatial target to be estimated. Let be a random noise vector following a zero-mean Gaussian distribution. Considering the potential for unmodeled systematic biases or sudden anomalies during actual space target observations, a mean offset term is introduced to construct an alternative hypothesis observation model incorporating modeling errors. .in, The mean shift term, used to describe the impact of modeling errors on the observed mean, is defined by setting different... A set of alternative hypothesis models is formed, which together with the null hypothesis observation model without modeling error constitute a multiple hypothesis system.

[0026] Next, step S2 is performed, involving the generation of multiple hypotheses, construction of test statistics, and determination of the acceptance region. Specifically, in step S2, the construction of the global and local test statistics and the confirmation of the discriminant region include: Based on the null hypothesis observation model Using the residual vectors below, construct a global test statistic. The global test statistic It is a quadratic form of the residual; Based on the preset false alarm probability Determine the critical value for the global test and form the acceptance region of the null hypothesis. ;when When the threshold value is exceeded, the null hypothesis is rejected. ; After the null hypothesis is rejected, for each alternative hypothesis... Based on its error parameters Constructing local test statistics from least squares estimators ; The discriminant region for each alternative hypothesis is determined using the maximum local statistic criterion, which is to say, the region that makes the hypothesis so that the hypothesis is ... The alternative hypothesis with the largest value As the identified error model.

[0027] In this embodiment, based on the index set of observation data that may contain modeling errors, a set of parallel hypothesis models are constructed to address the possibility of anomalies in different observation components. The null hypothesis corresponds to the case where there are no modeling errors, while each alternative hypothesis corresponds to the case where a certain observation component or several observation components have modeling errors. This covers a range of possible scenarios from "no error" to "existence of a specific error pattern," providing a hypothetical basis for subsequent DIA detection and identification.

[0028] Meanwhile, under the aforementioned multiple hypothesis system, a global test statistic for detecting model mismatch is constructed based on the null hypothesis observation model. The statistic is composed of a residual vector or an equivalent closed difference vector, and follows a central chi-square distribution when the null hypothesis is true. Simultaneously, local test statistics are constructed for each alternative hypothesis model. This is used to identify the most likely alternative hypothesis after the null hypothesis has been rejected. It is based on a pre-set false alarm probability. Calculate the corresponding critical values ​​and determine the acceptance regions of the null hypothesis and each alternative hypothesis accordingly, providing a basis for subsequent testing decisions.

[0029] Next, step S3, the calculation of the test decision probability based on SAE, is performed. Given the alternative hypothesis model and its modeling error magnitude, the Simplified Algebraic Estimation (SAE) method is used to analytically calculate the test decision probability. Specifically, this includes: analytically calculating the false negative probability and the true positive probability based on the non-central chi-square distribution of the global test statistic under the condition that the alternative hypothesis is true; and constructing a difference statistic that approximately follows a normal distribution based on the correlation structure between local test statistics, and analytically calculating the true positive probability and the false negative probability accordingly, thus avoiding the use of Monte Carlo methods with extensive random simulations.

[0030] First, the inspection decision probability includes the probability of missed detection, the probability of correct detection, the probability of correct identification, and the probability of incorrect identification.

[0031] Specifically, in step S3, the analytical calculation using simplified algebraic estimation includes: Given alternative hypotheses Its true value and the error magnitude parameter are Under the given conditions, determine the global test statistic. The non-centralized chi-square distribution and its decentralization parameters that it follows under these conditions; Based on the non-central chi-square distribution and the critical value determined by the false alarm probability, the result is obtained analytically. Probability of missed detection when true and according to Calculate the probability of correct detection .

[0032] Furthermore, the analytical computation using simplified algebraic estimation also includes: In the observation-by-observation screening scenario, a local test statistic is constructed based on the error parameter estimate under the alternative hypothesis, and Bararda's method is used. The test forms equivalent expressions, among which The standardized form of the error parameter estimator and with Monotonic correspondence; The probability of correct identification is expressed as in the alternative hypothesis. The probability of the local statistic being dominant over the local statistics of other alternative hypotheses under the given condition is: ; By constructing a difference statistic that approximately follows a normal distribution, we can achieve... The analytical approximation is used to calculate the correct recognition probability. According to the formula The total false recognition probability was calculated. Furthermore, the individual error identification probabilities constituting the total error identification probability are processed through iterative correction or scaling methods to ensure that the sum of probabilities is one.

[0033] The analytical calculation using simplified algebraic estimation is performed under the condition that the alternative hypothesis is true and the error magnitude parameter is a definite value. The error amplitude parameter Used to quantify alternative hypotheses Mean offset term The degree of influence on the observation vector, among which To describe the coefficient matrix of the error influence mode, different error magnitude parameters are set. The values ​​are selected, and the test decision probabilities under different error magnitudes are obtained through analytical calculation, thereby realizing the algebraic evaluation of the DIA estimator performance under the influence of modeling errors of different intensities.

[0034] Finally, in step S4, probability modeling of the DIA estimator and calculation of parameter estimation bias and dispersion are performed.

[0035] Specifically, the approximate probability density function for constructing the DIA estimator includes: DIA estimator It is expressed as a weighted combination of parameter estimation results under each assumed model, and its expression is: ,in In the first An assumption The parameter estimation results are as follows: To be consistent with the test statistic Related, used to indicate the selection of the first A decision function with one hypothesis; When it is impossible to perform an exact integral solution over the discrimination domain, the DIA estimator will be used. Given the true assumptions, the probability density function approximates a Gaussian mixture model, and its mixture weights are the test decision probabilities calculated by the simplified algebraic estimation method. The determination is to characterize the propagation effect of detection and identification uncertainty on parameter estimation results, whereby... The true assumption is Time Selection The probability of; Based on the Gaussian mixture model, the conditional expectation and conditional covariance of the parameter estimates are calculated by weighted averaging, thereby obtaining the quantified parameter estimation bias and dispersion index.

[0036] Next, under the condition that a certain alternative hypothesis model is true, the parameter estimation results under different hypothesis models are weighted and calculated according to the probabilities of various test decisions to obtain the expected bias and dispersion of the DIA estimator. Among them, the parameter estimation bias is used to characterize the systematic impact of modeling error and test uncertainty on the spatial target positioning results, and the parameter estimation dispersion is used to characterize the random uncertainty of the estimation results, thereby realizing the quantitative evaluation of the quality of spatial target positioning data and outputting the corresponding DIA algebraically simplified quality evaluation index.

[0037] To verify the beneficial effects of the proposed method for evaluating space targets that satisfy precise orbit determination using the algebraic simplification of DIA, experimental results comparing the detection, identification performance, and parameter estimation quality of the DIA estimator under the condition of modeling error are provided, demonstrating the evaluation consistency and reliability of the method under complex observation environments.

[0038] like Figure 2 As shown, this is in the case of the alternative hypothesis. The figure compares the evaluation results of the correct identification probability, the false negative probability, and the false positive probability under the established scenario. It also presents the results based on the Monte Carlo simulation method. Compared with the simplified algebraic estimation method proposed in this invention The calculated probability curve also provides the difference curve between the two. ,in , and Let represent the correct identification probability, the missed detection probability, and the false identification probability, respectively. Experimental results show that, for most time periods, the calculated results for the correct identification probability and the missed detection probability are highly consistent, with differences approaching zero. This indicates that the simplified algebraic estimation method proposed in this invention can accurately evaluate the detection and identification performance of the DIA estimator without relying on a large number of random simulations. When the observed geometry weakens, the correct identification probability decreases significantly, while the missed detection probability and the false identification probability increase simultaneously, indicating that the detection and identification ability of the DIA estimator decreases significantly under weak geometry conditions. The method of this invention can accurately reflect this performance degradation process. When the false identification probability is high, there is a certain difference between the simplified algebraic estimation results and the Monte Carlo simulation results, but this difference remains within an acceptable range and does not affect the evaluation conclusion of the overall system performance.

[0039] like Figure 3 As shown, this is under the same alternative assumptions Under these conditions, the evaluation results of estimation bias and dispersion of unknown parameters are compared. The figure shows the changes in bias and dispersion of multiple positioning parameters over different time periods, and compares the calculation results curves of the Monte Carlo simulation method. The curve of the calculation results of the simplified algebraic estimation method proposed in this invention and the difference curve between the two. In the picture, , and These represent the estimation biases of the three sample parameters. , and The standard deviations of the parameter estimation results for the three samples are shown. Experimental results show that, for most time periods, the two methods exhibit high consistency in their evaluation results regarding parameter bias and dispersion, indicating that the simplified algebraic estimation method proposed in this invention can accurately evaluate the parameter estimation quality of the DIA estimator. During periods with poor observation geometry, the bias and dispersion of some parameters increase significantly, indicating that the reliability of the parameter estimation results decreases simultaneously with the decline in detection and recognition performance. The method of this invention can effectively quantify this phenomenon, and the significant differences in the magnitude of changes in bias and dispersion among different parameters reflect the varying sensitivity of different positioning parameters to modeling errors and observation geometry.

[0040] The experimental results above demonstrate that the proposed algebraic simplified evaluation method for precise orbit determination of space targets using the DIA (Digital Interference Aspect) can uniformly evaluate the detection and recognition performance of the DIA estimator, as well as the parameter estimation bias and dispersion, under conditions of complex observation environments and modeling errors. Compared to traditional methods that rely on Monte Carlo simulation, this invention significantly reduces computational complexity while ensuring evaluation accuracy, thus verifying its engineering applicability and practical value in space target positioning tasks.

[0041] Based on this, the present invention provides a DIA algebraic simplification evaluation system for space targets to satisfy precise orbit determination, comprising: The data acquisition and modeling module is used to acquire observation data of space targets and construct a set of null and alternative hypotheses based on the Gauss-Markov model. The hypothesis generation and statistical calculation module is used to construct a global test statistic for detecting model errors and a local test statistic for identifying error sources based on the set, and to determine the null hypothesis acceptance region and the discriminant region of each alternative hypothesis according to the preset false alarm probability. The SAE decision evaluation module is used to perform analytical calculations using simplified algebraic estimation, given alternative hypotheses and their error magnitude parameters, to obtain the test decision probabilities, including the probability of missed detection, the probability of correct detection, the probability of correct identification, and the probability of incorrect identification. The parameter evaluation and quality output module is used to construct an approximate probability density function of the DIA estimator based on the test decision probability, and to calculate the parameter estimation bias and dispersion considering the influence of test decision uncertainty.

[0042] It should be noted that the steps in the DIA algebraic simplification evaluation method for precise orbit determination provided in this embodiment can be implemented based on the corresponding modules in the DIA algebraic simplification evaluation system for precise orbit determination. Those skilled in the art can refer to the technical solution of the system to implement the steps of the method. That is, the embodiments in the system can be understood as preferred examples of implementing the method, and will not be elaborated here.

[0043] In addition to the methods and systems described above, this embodiment also provides a computer device applicable to the case of improving the DIA algebraic simplification evaluation method for precise orbit determination of space targets, including: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the DIA algebraic simplification evaluation method for improving the precise orbit determination of space targets as proposed in the above embodiment.

[0044] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0045] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the DIA algebraic simplification evaluation method for achieving precise orbit determination of space targets as proposed in the above embodiments. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Red-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0046] Besides implementing the system and its various devices provided by this invention in purely computer-readable program code, the same functions can be achieved by logically programming the method steps, making the system and its various devices of this invention appear as logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers. Therefore, the system and its various devices provided by this invention can be considered as a hardware component, and the devices included therein for implementing various functions can also be considered as structures within the hardware component; alternatively, the devices for implementing various functions can be considered as both software modules implementing the method and structures within the hardware component.

[0047] Finally, it should be noted that the above description is only a preferred embodiment of the present invention, and the scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be pointed out that for those skilled in the art, any improvements and modifications made without departing from the principle of the present invention should also be considered within the scope of protection of the present invention.

[0048] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

Claims

1. A simplified algebraic evaluation method for space targets to satisfy precise orbit determination using the DIA algorithm, characterized in that, Includes the following steps: S1: Acquire observational data of space targets and construct a set of null and alternative hypotheses based on the Gauss-Markov model; S2: Based on the set, construct a global test statistic for detecting model errors and a local test statistic for identifying error sources, and determine the null hypothesis acceptance region and the discriminant region of each alternative hypothesis according to the preset false alarm probability. S3: Given the alternative hypothesis and its error magnitude parameter, simplified algebraic estimation is used to perform analytical calculations to obtain the probability of the test decision; S4: Construct an approximate probability density function for the DIA estimator based on the test decision probability, and calculate the parameter estimation bias and dispersion considering the influence of test decision uncertainty; Among them, analytical calculations using simplified algebraic estimation include: Determine the non-centralized chi-square distribution and its decentralization parameter that the global test statistic follows under the alternative hypothesis, and analyze the false negative probability and the correct detection probability based on the non-centralized chi-square distribution and the critical value. A difference statistic that approximately follows a normal distribution is constructed, and the correct identification probability and incorrect identification probability between alternative hypotheses are analytically calculated based on the difference statistic to replace the Monte Carlo simulation sampling process.

2. The DIA algebraic simplification evaluation method for precise orbit determination of space targets according to claim 1, characterized in that, In step S3, the analytical calculation using simplified algebraic estimation specifically includes: Given alternative hypotheses Its true value and the error magnitude parameter are Under the given conditions, determine the global test statistic. The non-centralized chi-square distribution and its decentralization parameters that it follows under these conditions; Based on the non-central chi-square distribution and the critical value determined by the false alarm probability, the result is obtained through analytical calculation. Probability of missed detection when true and according to Calculate the probability of correct detection .

3. The DIA algebraic simplification evaluation method for precise orbit determination of space targets according to claim 2, characterized in that, The analytical calculation using simplified algebraic estimation further includes: In the observation-by-observation screening scenario, a local test statistic is constructed based on the error parameter estimate under the alternative hypothesis, and Bararda's method is used. The test forms equivalent expressions, among which The standardized form of the error parameter estimator and with Monotonic correspondence; The probability of correct identification is expressed as in the alternative hypothesis. The probability of the local statistic being dominant over the local statistics of other alternative hypotheses under the given condition is: ; By constructing a difference statistic that approximately follows a normal distribution, we can achieve... The analytical approximation is used to calculate the correct recognition probability. According to the formula The total false recognition probability was calculated. Furthermore, the individual error identification probabilities constituting the total error identification probability are processed through iterative correction or scaling methods to ensure that the sum of probabilities is one.

4. The DIA algebraic simplification evaluation method for precise orbit determination of space targets according to claim 3, characterized in that, In step S3, the inspection decision probability includes the probability of missed detection, the probability of correct detection, the probability of correct identification, and the probability of incorrect identification.

5. The DIA algebraic simplification evaluation method for precise orbit determination of space targets according to claim 3, characterized in that, In step S1, the construction of the null hypothesis and alternative hypothesis sets includes: Establish a null hypothesis observation model Its mathematical expectation satisfies ,in For the observation vector, To design the matrix, The vector of position parameters to be estimated; Establish an alternative hypothesis observation model A mean offset term is introduced to characterize the modeling error based on the null hypothesis observation model, and its mathematical expectation satisfies ,in, For mean-biased models, This is the coefficient matrix used to describe the error impact patterns. This refers to the corresponding error amplitude parameter; By configuring multiple different sets of the coefficient matrices This forms a set of multiple parallel alternative hypotheses to cover different observation locations or different numbers of modeling error scenarios.

6. The DIA algebraic simplification evaluation method for precise orbit determination of space targets according to claim 5, characterized in that, In step S2, the construction of the global test statistic and the local test statistic, and the confirmation of the discriminant domain, include: Based on the null hypothesis observation model Using the residual vectors below, construct a global test statistic. The global test statistic It is a quadratic form of the residual; Based on the preset false alarm probability Determine the critical value for the global test and form the acceptance region of the null hypothesis. ;when When the threshold value is exceeded, the null hypothesis is rejected. ; After the null hypothesis is rejected, for each alternative hypothesis... Based on its error parameters Constructing local test statistics from least squares estimators ; The discriminant region for each alternative hypothesis is determined using the maximum local statistic criterion, which is to say, the region that makes the hypothesis so that the hypothesis is ... The alternative hypothesis with the largest value As the identified error model.

7. The DIA algebraic simplification evaluation method for precise orbit determination of space targets according to claim 6, characterized in that, In step S4, the approximate probability density function for constructing the DIA estimator includes: DIA estimator It is expressed as a weighted combination of parameter estimation results under each assumed model, and its expression is: ,in In the first One hypothesis The parameter estimation results are as follows: To compare with the test statistic Related, used to indicate the selection of the first A decision function based on a hypothesis; When it is impossible to perform an exact integral solution over the discrimination domain, the DIA estimator will be used. Given the true assumptions, the probability density function approximates a Gaussian mixture model, and its mixture weights are the test decision probabilities calculated by the simplified algebraic estimation method. The determination is to characterize the propagation effect of detection and identification uncertainty on parameter estimation results, whereby... The true assumption is Time selection The probability of; Based on the Gaussian mixture model, the conditional expectation and conditional covariance of the parameter estimates are calculated by weighted averaging, thereby obtaining the quantified parameter estimation bias and dispersion index.

8. The DIA algebraic simplification evaluation method for precise orbit determination of space targets according to claim 3, characterized in that, The analytical calculation using simplified algebraic estimation is performed under the condition that the alternative hypothesis is true and the error magnitude parameter is a definite value; The error amplitude parameter Used to quantify alternative hypotheses Mean offset term The degree of influence on the observation vector, among which To describe the coefficient matrix of the error influence mode, different error magnitude parameters are set. The values ​​are selected, and the test decision probabilities under different error magnitudes are obtained through analytical calculation, thereby realizing the algebraic evaluation of the DIA estimator performance under the influence of modeling errors of different intensities.

9. A DIA algebraic simplification evaluation system for precise orbit determination of space targets, characterized in that, include: The data acquisition and modeling module is used to acquire observational data of space targets and construct a set of null and alternative hypotheses based on the Gauss-Markov model. The hypothesis generation and statistical calculation module is used to construct a global test statistic for detecting model errors and a local test statistic for identifying error sources based on the set, and to determine the null hypothesis acceptance region and the discriminant region of each alternative hypothesis according to the preset false alarm probability. The SAE decision evaluation module is used to perform analytical calculations using simplified algebraic estimation to obtain the probability of the test decision, given the alternative hypothesis and its error magnitude parameters. The parameter evaluation and quality output module is used to construct an approximate probability density function of the DIA estimator based on the test decision probability, and to calculate the parameter estimation bias and dispersion considering the influence of test decision uncertainty. Among them, analytical calculations using simplified algebraic estimation include: Determine the non-centralized chi-square distribution and its decentralization parameter that the global test statistic follows under the alternative hypothesis, and analyze the false negative probability and the correct detection probability based on the non-centralized chi-square distribution and the critical value. A difference statistic that approximately follows a normal distribution is constructed, and the correct identification probability and incorrect identification probability between alternative hypotheses are analytically calculated based on the difference statistic to replace the Monte Carlo simulation sampling process.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the program is executed by the processor, it implements the DIA algebraic simplification evaluation method for precise orbit determination of space targets as described in any one of claims 1-8.

11. An electronic device, characterized in that, include: One or more processors; A storage device for storing one or more programs, which, when executed by one or more processors, cause the one or more processors to implement the DIA algebraic simplification evaluation method for precise orbit determination of space targets as described in any one of claims 1-8.

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