Method for estimating translation and rotation errors of dynamic model constraint space reference

Abstract

The invention discloses a method for estimating translation and rotation errors of a kinetic model constraint space reference, and the method comprises the steps: building an observation equation through employing inter-satellite distance measurement observed quantity obtained by satellite-borne inter-satellite link equipment, and building a satellite kinetic equation through employing the modeling of orbit perturbative force; performing space reference translation and rotation transformation on a satellite kinetic equation, and solving partial derivatives of related parameters to obtain a variational equation containing satellite position relative space reference translation and rotation parameters and satellite state parameter partial derivatives; solving the variational equation and the kinetic equation by adopting a numerical integration method to obtain a state transition matrix containing space reference translation and rotation parameters and satellite orbit state parameters, and a satellite reference orbit; a plurality of epoch inter-satellite distance measurement observation equations are linearized by using a satellite reference orbit to obtain a parameter estimation equation, and the equation is solved by using a parameter reduction method to obtain space reference translation and rotation parameter estimation values and estimation precision.

Description

Technical Field

[0001] The present invention relates to the technical field of satellite autonomous orbit determination applications, and in particular to a method for estimating translation and rotation errors of a dynamic model constrained space reference. Background Art

[0002] The rapid development of satellite technology is driving increasingly stringent requirements for satellite orbit determination accuracy and real-time performance. Traditional orbit determination methods relying on ground stations are unable to meet these requirements. Navigation satellites, such as GPS Block-IIR, have pioneered the development of autonomous orbit determination technology using inter-satellite links. GPS autonomous orbit determination utilizes UHF inter-satellite measurement links and a distributed dynamics orbit determination method, currently achieving an on-orbit accuracy (URE) better than 3 meters. The BeiDou-3 satellite navigation system is a successful example of autonomous orbit determination engineering. BeiDou satellites utilize Ka inter-satellite links, achieving an in-orbit URE better than 3 meters. The development of low-Earth orbiting giant satellites and lunar orbit satellites has significantly promoted the application of autonomous orbit determination technology. Autonomous orbit determination reduces satellite dependence on ground-based measurement and control systems, improving the accuracy and real-time performance of satellite orbit determination. For formation satellites, such as lunar satellites, located far from ground support, autonomous orbit determination based on inter-satellite ranging is virtually the only technology capable of meeting the requirements for real-time, precise orbit determination.

[0003] Autonomous orbit determination is a technology that uses inter-satellite measurements and on-board data processing to determine the precise orbit of a satellite in orbit. It usually adopts the dynamic orbit determination method. Application scenarios include autonomous orbit determination with a reference satellite (such as a GNSS with a precisely known orbit) and autonomous orbit determination without a reference satellite. The inter-satellite measurement technologies it relies on include inter-satellite ranging and inter-satellite angle measurement. Since the satellite orbit determination accuracy is relatively insufficient when using inter-satellite angle measurement technology, autonomous orbit determination in the usual sense refers to dynamic autonomous orbit determination without a reference satellite based on inter-satellite ranging.

[0004] When using intersatellite ranging for dynamic autonomous orbit determination, the satellite position space reference determined by autonomous orbit determination (ADD) experiences global drift relative to the inertial or Earth-fixed space reference, as intersatellite ranging is a relative measurement. Controlling this global rotational drift of the constellation has become a major technical challenge hindering the development of autonomous orbit determination. ANANDA first identified this global drift problem in dynamic autonomous orbit determination for GPS navigation satellites and analyzed that the uncertainty in the longitude of the satellite's ascending node, caused by the J2 perturbation in the Earth's gravity field model, is the cause of the rank deficiency in autonomous orbit determination. However, ANANDA did not delve into the mechanism of global rotation in autonomous orbit determination. Menn explicitly pointed out the uncertainty in the three orientation parameters of the satellite orbit plane in dynamic autonomous orbit determination using intersatellite measurements and proposed a solution to constrain the global rotation of the constellation using predicted orbital orientation parameters. However, the mechanism of global rotation was also not explained. Liu Lin et al. rigorously demonstrated the theoretical nature of the rank deficiency problem in autonomous orbit determination using intersatellite ranging based on the two-body problem, identifying the uncertainty in the longitude of the satellite's orbital ascending node as its specific manifestation. Hill systematically analyzed the impact of satellite dynamics on satellite orbit determination, pointing out that the symmetry of satellite dynamics models leads to non-unique satellite orbits. He also provided a geometric explanation for how satellite dynamics models maintain the spatial datum for autonomous orbit determination. However, Hill's method simply uses the relative ratios between different satellite perturbations to qualitatively analyze the impact of spatial datum uncertainty. Because satellite perturbations vary over time, Hill's method cannot accurately quantify the impact of the dynamics model. Song Xiaoyong et al. proposed using the transformation invariance of the satellite dynamics orbit determination observation equation to explain the impact of the dynamics model on maintaining the spatial datum. They provided a general proof of the uncertainty of the spatial orientation datum for dynamic autonomous orbit determination based on intersatellite measurements, but did not provide a specific method for quantitatively estimating the impact of dynamics model errors.

[0005] Although domestic and foreign scholars have recognized that the satellite dynamics model has a certain constraining effect on the overall drift of the satellite dynamics autonomous orbit determination space reference supported only by inter-satellite ranging, it is limited to qualitative analysis. So far, there is no theoretical method to accurately evaluate the accuracy of the dynamics model in maintaining the space reference. As a result, the problem of maintaining the autonomous space reference has become a bottleneck restricting the development of autonomous orbit determination technology, and there has been no substantial breakthrough in autonomous orbit determination application technology for many years. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for estimating the translation and rotation errors of the space reference constrained by the dynamic model, using the variational equation of the satellite dynamic equation to calculate the design matrix, and adopting the reduced least squares parameter estimation method to calculate the new method of estimating the error of the space reference translation and rotation parameters.

[0007] To solve the above technical problems, the present invention provides a method for estimating translation and rotation errors of a dynamic model constraint space reference, comprising the following steps:

[0008] Obtain inter-satellite ranging observations between satellites and construct inter-satellite ranging observation equations;

[0009] Model the perturbation forces that affect satellite orbital motion and construct satellite orbital dynamics equations;

[0010] According to the satellite orbit dynamics equation, the partial derivative of the satellite state parameters is obtained to obtain the satellite orbit state parameter variation equation;

[0011] Perform space-referenced translation and rotation transformations on the satellite orbit dynamics equations, and obtain partial derivatives of the space-referenced translation and rotation parameters to obtain the space-referenced translation and rotation parameter variational equations.

[0012] Based on the initial values ​​of satellite state parameters, the satellite dynamics equation and the variational equation of the parameters to be estimated are solved by numerical integration method to obtain the fixed-interval satellite reference orbit, the partial derivative matrix of satellite state parameters and the partial derivative matrix of space reference translation and rotation parameters;

[0013] An interpolation method is used to interpolate the fixed-interval satellite reference orbit position velocity information, satellite state parameter partial derivative matrix, and space reference translation and rotation parameter matrix to the intersatellite measurement time. The intersatellite ranging observation equation is linearized using the satellite reference orbit position at the measurement time. The interpolated satellite orbit state transfer matrix and space reference translation and rotation parameter partial derivative matrix at the measurement time are combined to obtain the autonomous orbit determination parameter estimation equation containing the satellite orbit state parameters, space reference translation and rotation parameters.

[0014] The satellite orbit state parameters are eliminated from the autonomous orbit determination parameter estimation equation using the reduced parameter least squares estimation method, resulting in a parameter estimation equation containing only the space reference translation and rotation parameters. The equation is then solved to obtain the estimated values ​​of the space reference translation and rotation parameters.

[0015] The parameter estimation equation that only contains the spatial reference translation and rotation parameters is inverted by the corresponding normal equation to obtain the reference translation and rotation parameter covariance matrix. The diagonal elements of the parameter covariance matrix are counted respectively to obtain the precision factor of the spatial reference translation and rotation parameters affected by the dynamic model. The precision factor can be used to quantitatively analyze and evaluate the estimation accuracy of the two types of parameters.

[0016] Preferably, obtaining inter-satellite ranging observations between satellites and constructing inter-satellite ranging observation equations specifically includes the following steps:

[0017] Each satellite in the constellation carries an inter-satellite link payload that can achieve inter-satellite ranging and inter-satellite communication, and establishes an inter-satellite measurement and communication link with satellites in the same or different orbital planes to obtain ranging observations between satellites;

[0018] After eliminating the equipment transmission and reception delay, signal propagation path delay, tropospheric and ionospheric propagation medium delay, clock error and the influence of relativity, the inter-satellite ranging observation is obtained through data pre-processing of the measured transmission and reception time, and the instantaneous inter-satellite ranging observation is used to construct the inter-satellite ranging observation equation.

[0019]

[0020] Where: ij is the instantaneous inter-satellite distance between satellite i and satellite j after preprocessing, are the three-dimensional position vectors of satellite i and satellite j respectively.

[0021] Preferably, modeling the perturbation force affecting the satellite orbital motion and constructing the satellite orbital dynamics equation specifically includes the following steps:

[0022] Based on the orbital altitude and geometric physical parameters of each satellite, a satellite dynamics model is constructed that takes into account the Earth's gravity, solid tides, the gravity of the Sun and Moon, solar pressure, atmospheric drag, and relativity. The standard gravity field model, JPL planetary ephemeris, and an atmospheric drag model similar to the DTM are used to construct the differential equations of satellite orbital motion dynamics in the inertial coordinate system.

[0023]

[0024] in: are the satellite position, velocity and acceleration vectors at any moment, p is the satellite dynamics model parameter, and t is the time;

[0025] The solution to the differential equation can be written as:

[0026]

[0027] in: are the initial values ​​of satellite position and velocity parameters respectively.

[0028] Preferably, according to the satellite orbit dynamics equation, partial derivatives of the satellite state parameters are taken to obtain the satellite orbit state parameter variational equation, which specifically includes the following steps:

[0029] Taking the satellite position parameters, satellite velocity parameters and satellite dynamics model parameters as the satellite state parameters to be estimated, the satellite dynamics differential equation is varied to obtain the satellite motion variation equation with the partial derivatives of the satellite position relative to the satellite state parameters as variables;

[0030]

[0031]

[0032]

[0033] in: are the position and velocity of any satellite respectively, and p is the satellite dynamic model parameter; are the initial values ​​of satellite position and velocity parameters respectively.

[0034] Preferably, performing space reference translation and rotation transformation on the satellite orbit dynamics equation, and respectively taking partial derivatives of the space reference translation and rotation parameters to obtain space reference translation and rotation parameter variational equations, specifically includes the following steps:

[0035] The satellite dynamics equation is transformed into a space-referenced translation and rotation using the space-referenced translation and rotation transformation matrix to obtain the satellite orbit dynamics equation containing three space-referenced translation parameters and three space-referenced rotation parameters. The space-referenced translation and rotation parameters are used as the parameters to be estimated, and the partial derivatives of the satellite dynamics equation after the space-referenced transformation are obtained to obtain the dynamic variational equation corresponding to the reference translation and rotation parameters.

[0036] Assume that the space reference translation transformation vector is The coordinate rotation vector is ε x , ε y , ε z for Three components, the corresponding coordinate rotation matrix M is:

[0037]

[0038] The satellite dynamics equation after the benchmark transformation is:

[0039]

[0040] The spatial reference translation and rotation parameter variation equations corresponding to the dynamic equations are in the form of:

[0041]

[0042] Preferably, based on the initial values ​​of the satellite state parameters, a numerical integration method is used to solve the satellite dynamics equation and the variational equation of the parameters to be estimated, and the fixed-interval satellite reference orbit, the partial derivatives of the satellite state parameters, and the partial derivative matrices of the space reference translation and rotation parameters are obtained, which specifically includes the following steps:

[0043] Taking the prior values ​​of satellite position, satellite velocity and satellite dynamics model parameters at the initial time as initial values, the satellite orbit dynamics equation, satellite state parameter variation equation and space reference translation and rotation parameter variation equation are solved simultaneously by single-step method or multi-step method to obtain the fixed-interval satellite reference orbit, satellite state parameter partial derivatives and space reference translation and rotation parameter partial derivative matrices within the integration period.

[0044] Preferably, the fixed-interval satellite reference orbit position velocity information is interpolated to the inter-satellite measurement time, and the inter-satellite ranging observation equation is linearized using the satellite reference orbit position at the measurement time. By combining the satellite orbit state transfer matrix and the space reference translation and rotation parameter partial derivative matrix, an autonomous orbit determination parameter estimation equation containing satellite orbit state parameters and space reference translation and rotation parameters can be obtained, which specifically includes the following steps:

[0045] The satellite reference orbit position at the time of intersatellite link measurement is calculated by interpolation method using the fixed-interval satellite reference orbit position velocity information, as well as the satellite orbit state parameters and the partial derivative matrix of the space reference translation and rotation parameters at the measurement time;

[0046] The inter-satellite ranging observation equation is linearized using the satellite reference orbit position at the measurement time. Combining the two satellite partial derivative matrices obtained by interpolation, the linearized autonomous orbit determination observation equation is obtained, with the satellite orbit state parameters, space reference translation and rotation parameters as the parameters to be estimated.

[0047]

[0048] Where: Δρ ij H is the difference between the intersatellite link observation value and the intersatellite link theoretical value calculated by the reference orbit, i and H j are the intersatellite baseline unit vectors between satellite i and satellite j, are the satellite orbit state transfer matrices of satellite i and satellite j at the observation time, are the satellite orbit state parameter corrections, are the state transfer matrices of the spatial reference translation and rotation parameters at the observation time of satellite i and satellite j respectively, and ΔS is the correction of the spatial reference translation and rotation parameters, that is, Δδ ij Measuring noise for intersatellite links;

[0049] H i and H j The calculation formula is:

[0050]

[0051] Where: ij is the instantaneous inter-satellite distance between satellite i and satellite j after preprocessing, are the three-dimensional position vectors of satellite i and satellite j respectively.

[0052] Preferably, the reduced parameter least squares estimation method is used to eliminate the satellite orbit state parameters in the autonomous orbit determination parameter estimation equation to obtain a parameter estimation equation containing space reference translation and rotation parameters, and the equation is solved to obtain space reference translation and rotation parameter state estimation values, which specifically includes the following steps:

[0053] Combining multiple measurement epoch autonomous orbit determination observation equations to obtain satellite autonomous orbit determination equations with satellite orbit state parameters and space reference translation and rotation parameters as parameters to be estimated;

[0054] Taking the satellite orbit state parameters as local parameters and the space reference translation and rotation parameters as global parameters, a parameter reduction method based on least squares estimation is adopted to eliminate the satellite orbit state parameters and obtain a parameter estimation equation containing only the space reference translation and rotation parameters. By solving this equation, the estimated values ​​of the space reference translation and rotation parameters can be obtained.

[0055] Taking the satellite orbit state parameters as a category, the multi-epoch autonomous orbit determination equation can be simply written as:

[0056]

[0057] Where: A is the design matrix corresponding to the satellite position, velocity, and dynamic model parameters to be estimated. is the correction value of satellite position, velocity and dynamic model parameters, B is the design matrix corresponding to the spatial reference translation and rotation parameters, is the correction value of the spatial reference translation and rotation parameters, is the intersatellite measurement residual;

[0058] After parameter reduction and elimination of satellite state parameters, the observation equation containing only the spatial reference translation and rotation parameters of the combined multiple epoch autonomous orbit determination equations is:

[0059]

[0060] The corresponding least squares parameter estimates are:

[0061]

[0062] Where: I is the identity matrix with 1 on the main diagonal.

[0063] Preferably, the parameter estimation equation containing only the spatial reference translation and rotation parameters is inverted corresponding to the normal equation to obtain the reference translation and rotation parameter covariance matrix, and the diagonal elements of the parameter covariance matrix are counted respectively to obtain the precision factor of the spatial reference translation and rotation parameters affected by the dynamic model. The precision factor can be used to quantitatively analyze and evaluate the estimation accuracy of the two types of parameters, which specifically includes the following steps:

[0064] The parameter estimation method equation is calculated using the reduced observation equation containing only the spatial reference translation and rotation parameters. The parameter estimation method equation is inverted to obtain the unit weight covariance matrix of the spatial reference translation and rotation parameter estimation.

[0065] According to the order of the space reference translation and rotation parameters in the parameter estimation equation, the main diagonal elements of the covariance matrix corresponding to the two types of parameters are selected respectively. The three main diagonal elements of the covariance matrix of the two types of parameters are summed and squared to obtain the parameter estimation precision factors, which are defined as the precision factors of the reference translation parameters and the precision factors of the reference rotation parameters, respectively. These are used as the quantitative estimates of the space reference translation and rotation parameters constrained by the satellite dynamics model.

[0066] The covariance matrix is ​​in the form:

[0067]

[0068] Assuming that the spatial reference translation parameters are arranged before the reference rotation factors, the two types of precision factors are in the form of:

[0069] MDOP=(c 11 +c 22 +c 33 ) 1 / 2

[0070] SDOP=(c 44 +c 55 +c 66 ) 1 / 2

[0071] Where: Σ ΔS is the covariance matrix of the spatial reference translation and rotation parameters, c ij is the covariance matrix element, MDOP is the spatial reference translation dilution of precision, and SDOP is the spatial reference rotation dilution of precision.

[0072] Compared with the prior art, the present invention has the following beneficial effects:

[0073] (1) Based on the intersatellite ranging observation equation and combined with the satellite dynamics equation, a method for simultaneously estimating the satellite orbital state parameters and the space reference translation and rotation parameters is proposed. This solves the problem of accurately calculating the error of maintaining the autonomous orbit determination space reference when only the intersatellite ranging observation is constrained by the dynamics model. This method can be easily extended to the Earth-Moon space and solve the problem of maintaining the autonomous space-time reference in the Earth-Moon space supported by intersatellite measurements.

[0074] (2) The satellite dynamics variational equations containing space reference translation and rotation information are used to calculate the design matrix of the satellite position change affected by the space reference translation and rotation parameters using numerical integration methods. This can effectively utilize the existing satellite orbit numerical integration module resources in autonomous orbit determination data processing, reduce the amount of data processing operations, and improve processing efficiency.

[0075] (3) For the first time, two new precision factors are defined to evaluate the impact of the dynamic model on the accuracy of space reference translation and rotation parameter estimation. The use of these precision factors is conducive to separating the influence of satellite dynamic model factors and inter-satellite ranging factors on the accuracy of space reference maintenance, and the evaluation results are more accurate. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] The specific embodiments of the present invention are further described in detail below with reference to the accompanying drawings.

[0077] Figure 1 This is a schematic diagram of the quantitative estimation principle of the translation and rotation parameters of the constrained space reference of the dynamic model;

[0078] In the figure: the middle ellipse is a satellite constellation with inter-satellite ranging connections. The two ellipses above and the one below represent the main perturbations on each satellite in the constellation. The rectangular box represents the dynamic model constraint space reference translation and rotation parameter quantization estimation processing unit. The solid line shows the physical entity data flow, and the dotted line shows the satellite perturbation.

[0079] Figure 2 This is a flow chart of data processing for quantitative estimation of translation and rotation parameters of constrained space references in dynamic models. DETAILED DESCRIPTION

[0080] The following description sets forth numerous specific details to facilitate a thorough understanding of the present invention. However, the present invention can be implemented in many other ways than those described herein, and those skilled in the art can make similar generalizations without departing from the scope of the present invention. Therefore, the present invention is not limited to the specific implementations disclosed below.

[0081] The terms used in one or more embodiments of this specification are for the purpose of describing specific embodiments only and are not intended to limit one or more embodiments of this specification. The singular forms "a," "the," and "the" used in one or more embodiments of this specification and the appended claims are also intended to include plural forms unless the context clearly indicates otherwise. It should also be understood that the term "and / or" used in one or more embodiments of this specification refers to and includes any or all possible combinations of one or more associated listed items.

[0082] It should be understood that although the terms first, second, etc. may be used to describe various information in one or more embodiments of this specification, such information should not be limited to these terms. These terms are only used to distinguish the same type of information from each other. For example, without departing from the scope of one or more embodiments of this specification, the first may also be referred to as the second, and similarly, the second may also be referred to as the first. Depending on the context, the word "if" as used herein may be interpreted as "at the time of" or "when" or "in response to determining".

[0083] The present invention will be described in further detail below with reference to the accompanying drawings:

[0084] The present invention provides a method for estimating translation and rotation errors of a dynamic model constraint space reference, comprising the following steps:

[0085] Obtain inter-satellite ranging observations between satellites and construct inter-satellite ranging observation equations;

[0086] Model the perturbation forces that affect satellite orbital motion and construct satellite orbital dynamics equations;

[0087] According to the satellite orbit dynamics equation, the partial derivative of the satellite state parameters is obtained to obtain the satellite orbit state parameter variation equation;

[0088] Perform space-referenced translation and rotation transformations on the satellite orbit dynamics equations, and obtain partial derivatives of the space-referenced translation and rotation parameters to obtain the space-referenced translation and rotation parameter variational equations.

[0089] Based on the initial values ​​of satellite state parameters, the satellite dynamics equation and the variational equation of the parameters to be estimated are solved by numerical integration method to obtain the fixed-interval satellite reference orbit, the partial derivative matrix of satellite state parameters and the partial derivative matrix of space reference translation and rotation parameters;

[0090] An interpolation method is used to interpolate the fixed-interval satellite reference orbit position velocity information, satellite state parameter partial derivative matrix, and space reference translation and rotation parameter matrix to the intersatellite measurement time. The intersatellite ranging observation equation is linearized using the satellite reference orbit position at the measurement time. The interpolated satellite orbit state transfer matrix and space reference translation and rotation parameter partial derivative matrix at the measurement time are combined to obtain the autonomous orbit determination parameter estimation equation containing the satellite orbit state parameters, space reference translation and rotation parameters.

[0091] The satellite orbit state parameters are eliminated from the autonomous orbit determination parameter estimation equation using the reduced parameter least squares estimation method, resulting in a parameter estimation equation containing only the space reference translation and rotation parameters. The equation is then solved to obtain the estimated values ​​of the space reference translation and rotation parameters.

[0092] The parameter estimation equation that only contains the spatial reference translation and rotation parameters is inverted by the corresponding normal equation to obtain the reference translation and rotation parameter covariance matrix. The diagonal elements of the parameter covariance matrix are counted respectively to obtain the precision factor of the spatial reference translation and rotation parameters affected by the dynamic model. The precision factor can be used to quantitatively analyze and evaluate the estimation accuracy of the two types of parameters.

[0093] Preferably, obtaining inter-satellite ranging observations between satellites and constructing inter-satellite ranging observation equations specifically includes the following steps:

[0094] Each satellite in the constellation carries an inter-satellite link payload that can achieve inter-satellite ranging and inter-satellite communication, and establishes an inter-satellite measurement and communication link with satellites in the same or different orbital planes to obtain ranging observations between satellites;

[0095] After eliminating the equipment transmission and reception delay, signal propagation path delay, tropospheric and ionospheric propagation medium delay, clock error and the influence of relativity, the inter-satellite ranging observation is obtained through data pre-processing of the measured transmission and reception time, and the instantaneous inter-satellite ranging observation is used to construct the inter-satellite ranging observation equation.

[0096]

[0097] Where: ij is the instantaneous inter-satellite distance between satellite i and satellite j after preprocessing, are the three-dimensional position vectors of satellite i and satellite j respectively.

[0098] Preferably, modeling the perturbation force affecting the satellite orbital motion and constructing the satellite orbital dynamics equation specifically includes the following steps:

[0099] Based on the orbital altitude and geometric physical parameters of each satellite, a satellite dynamics model is constructed that takes into account the Earth's gravity, solid tides, the gravity of the Sun and Moon, solar pressure, atmospheric drag, and relativity. The standard gravity field model, JPL planetary ephemeris, and an atmospheric drag model similar to the DTM are used to construct the differential equations of satellite orbital motion dynamics in the inertial coordinate system.

[0100]

[0101] in: are the satellite position, velocity and acceleration vectors at any moment, p is the satellite dynamics model parameter, and t is the time;

[0102] The solution to the differential equation can be written as:

[0103]

[0104] in: are the initial values ​​of satellite position and velocity parameters respectively.

[0105] Preferably, according to the satellite orbit dynamics equation, partial derivatives of the satellite state parameters are taken to obtain the satellite orbit state parameter variational equation, which specifically includes the following steps:

[0106] Taking the satellite position parameters, satellite velocity parameters and satellite dynamics model parameters as the satellite state parameters to be estimated, the satellite dynamics differential equation is varied to obtain the satellite motion variation equation with the partial derivatives of the satellite position relative to the satellite state parameters as variables;

[0107]

[0108]

[0109]

[0110] in: are the position and velocity of any satellite respectively, and p is the satellite dynamic model parameter; are the initial values ​​of satellite position and velocity parameters respectively.

[0111] Preferably, performing space reference translation and rotation transformation on the satellite orbit dynamics equation, and respectively taking partial derivatives of the space reference translation and rotation parameters to obtain space reference translation and rotation parameter variational equations, specifically includes the following steps:

[0112] The satellite dynamics equation is transformed into a space-referenced translation and rotation using the space-referenced translation and rotation transformation matrix to obtain the satellite orbit dynamics equation containing three space-referenced translation parameters and three space-referenced rotation parameters. The space-referenced translation and rotation parameters are used as the parameters to be estimated, and the partial derivatives of the satellite dynamics equation after the space-referenced transformation are obtained to obtain the dynamic variational equation corresponding to the reference translation and rotation parameters.

[0113] Assume that the space reference translation transformation vector is The coordinate rotation vector is ε x , ε y , ε z for Three components, the corresponding coordinate rotation matrix M is:

[0114]

[0115] The satellite dynamics equation after the benchmark transformation is:

[0116]

[0117] The spatial reference translation and rotation parameter variation equations corresponding to the dynamic equations are in the form of:

[0118]

[0119] Preferably, based on the initial values ​​of the satellite state parameters, a numerical integration method is used to solve the satellite dynamics equation and the variational equation of the parameters to be estimated, and the fixed-interval satellite reference orbit, the partial derivatives of the satellite state parameters, and the partial derivative matrices of the space reference translation and rotation parameters are obtained, which specifically includes the following steps:

[0120] Taking the prior values ​​of satellite position, satellite velocity and satellite dynamics model parameters at the initial time as initial values, the satellite orbit dynamics equation, satellite state parameter variation equation and space reference translation and rotation parameter variation equation are solved simultaneously by single-step method or multi-step method to obtain the fixed-interval satellite reference orbit, satellite state parameter partial derivatives and space reference translation and rotation parameter partial derivative matrices within the integration period.

[0121] Preferably, the fixed-interval satellite reference orbit position velocity information is interpolated to the inter-satellite measurement time, and the inter-satellite ranging observation equation is linearized using the satellite reference orbit position at the measurement time. By combining the satellite orbit state transfer matrix and the space reference translation and rotation parameter partial derivative matrix, an autonomous orbit determination parameter estimation equation containing satellite orbit state parameters and space reference translation and rotation parameters can be obtained, which specifically includes the following steps:

[0122] The satellite reference orbit position at the time of intersatellite link measurement is calculated by interpolation method using the fixed-interval satellite reference orbit position velocity information, as well as the satellite orbit state parameters and the partial derivative matrix of the space reference translation and rotation parameters at the measurement time;

[0123] The inter-satellite ranging observation equation is linearized using the satellite reference orbit position at the measurement time. Combining the two satellite partial derivative matrices obtained by interpolation, the linearized autonomous orbit determination observation equation is obtained, with the satellite orbit state parameters, space reference translation and rotation parameters as the parameters to be estimated.

[0124]

[0125] Where: Δρ ij H is the difference between the intersatellite link observation value and the intersatellite link theoretical value calculated by the reference orbit, i and H j are the intersatellite baseline unit vectors between satellite i and satellite j, are the satellite orbit state transfer matrices of satellite i and satellite j at the observation time, are the satellite orbit state parameter corrections, are the state transfer matrices of the spatial reference translation and rotation parameters at the observation time of satellite i and satellite j respectively, and ΔS is the correction of the spatial reference translation and rotation parameters, that is, Δδ ij Measuring noise for intersatellite links;

[0126] H i and H j The calculation formula is:

[0127]

[0128] Where: ij is the instantaneous inter-satellite distance between satellite i and satellite j after preprocessing, are the three-dimensional position vectors of satellite i and satellite j respectively.

[0129] Preferably, the reduced parameter least squares estimation method is used to eliminate the satellite orbit state parameters in the autonomous orbit determination parameter estimation equation to obtain a parameter estimation equation containing space reference translation and rotation parameters, and the equation is solved to obtain space reference translation and rotation parameter state estimation values, which specifically includes the following steps:

[0130] Combining multiple measurement epoch autonomous orbit determination observation equations to obtain satellite autonomous orbit determination equations with satellite orbit state parameters and space reference translation and rotation parameters as parameters to be estimated;

[0131] Taking the satellite orbit state parameters as local parameters and the space reference translation and rotation parameters as global parameters, a parameter reduction method based on least squares estimation is adopted to eliminate the satellite orbit state parameters and obtain a parameter estimation equation containing only the space reference translation and rotation parameters. By solving this equation, the estimated values ​​of the space reference translation and rotation parameters can be obtained.

[0132] Taking the satellite orbit state parameters as a category, the multi-epoch autonomous orbit determination equation can be simply written as:

[0133]

[0134] Where: A is the design matrix corresponding to the satellite position, velocity, and dynamic model parameters to be estimated. is the correction value of satellite position, velocity and dynamic model parameters, B is the design matrix corresponding to the spatial reference translation and rotation parameters, is the correction value of the spatial reference translation and rotation parameters, is the intersatellite measurement residual;

[0135] After parameter reduction and elimination of satellite state parameters, the observation equation containing only the spatial reference translation and rotation parameters of the combined multiple epoch autonomous orbit determination equations is:

[0136]

[0137] The corresponding least squares parameter estimates are:

[0138]

[0139] Where: I is the identity matrix with 1 on the main diagonal.

[0140] Preferably, the parameter estimation equation containing only the spatial reference translation and rotation parameters is inverted corresponding to the normal equation to obtain the reference translation and rotation parameter covariance matrix, and the diagonal elements of the parameter covariance matrix are counted respectively to obtain the precision factor of the spatial reference translation and rotation parameters affected by the dynamic model. The precision factor can be used to quantitatively analyze and evaluate the estimation accuracy of the two types of parameters, which specifically includes the following steps:

[0141] The parameter estimation method equation is calculated using the reduced observation equation containing only the spatial reference translation and rotation parameters. The parameter estimation method equation is inverted to obtain the unit weight covariance matrix of the spatial reference translation and rotation parameter estimation.

[0142] According to the order of the spatial reference translation and rotation parameters in the parameter estimation equation, the main diagonal elements of the covariance matrix corresponding to the two types of parameters are selected respectively. The three main diagonal elements of the covariance matrix of the two types of parameters are summed and squared to obtain the parameter estimation precision factors, which are defined as the precision factors of the reference translation parameters and the precision factors of the reference rotation parameters, respectively. These are used as the quantitative estimates of the spatial reference translation and rotation parameters constrained by the satellite dynamics model.

[0143] The covariance matrix is ​​in the form:

[0144]

[0145] Assuming that the spatial reference translation parameters are arranged before the reference rotation factors, the two types of precision factors are in the form of:

[0146] MDOP=(c 11 +c 22 +c 33 ) 1 / 2

[0147] SDOP=(c 44 +c 55 +c 66 ) 1 / 2

[0148] Where: Σ ΔS is the covariance matrix of the spatial reference translation and rotation parameters, c ij is the covariance matrix element, MDOP is the spatial reference translation dilution of precision, and SDOP is the spatial reference rotation dilution of precision.

[0149] This method facilitates analysis of the impact of different orbital perturbations on the accuracy of maintaining the space reference conversion parameters for autonomous orbit determination, and can be applied to various intersatellite link autonomous orbit determination projects in complex dynamic environments. The method can be applied to autonomous navigation satellites, resolving the problem of estimating the overall rotation error of the space reference in autonomous intersatellite link orbit determination. It can also be applied to autonomous orbit determination in Earth-Moon space, where only intersatellite ranging is supported, providing a theoretical basis for designing autonomous constellations and determining precise orbit determination schemes. Furthermore, the method can be applied to autonomous orbit determination of Giant Star satellites, providing a technical basis for designing onboard data processing algorithms.

[0150] In order to better illustrate the technical effects of the present invention, the present invention provides the following specific examples to illustrate the above technical process:

[0151] Embodiment 1: A method for quantitatively estimating translation and rotation errors of a dynamic model constraint space reference in dynamic autonomous orbit determination with only intersatellite measurement support, comprising the following steps:

[0152] (1) Using the intersatellite measurement payload carried by the satellite, the intersatellite ranging observation quantity between satellites can be obtained. By using the intersatellite ranging observation quantity, the measurement system error can be eliminated and the intersatellite ranging observation equation can be constructed;

[0153] (2) By modeling the perturbations that affect satellite orbital motion, such as the Earth's gravity, the Sun's and Moon's gravity, solid tides, solar pressure, atmospheric drag, and relativity, the satellite orbital dynamics equation can be constructed.

[0154] (3) Using the satellite orbit dynamics equation, the partial derivatives of the satellite state parameters including the satellite initial position, initial velocity and dynamics model parameters are obtained to obtain the satellite orbit state parameter variation equation;

[0155] (4) Performing space-reference translation and rotation transformations on the satellite orbit dynamics equations and taking partial derivatives of the space-reference translation and rotation parameters respectively can obtain the space-reference translation and rotation parameter variational equations;

[0156] (5) The satellite orbit dynamics equation, the satellite orbit state parameter variation equation and the space reference translation and rotation parameter variation equation are integrated by numerical integration method to obtain the reference orbit composed of the satellite reference orbit position and velocity, and the satellite state transfer matrix composed of the partial derivatives of the satellite position relative to the satellite orbit state parameters and the space reference translation and rotation parameters;

[0157] (6) After interpolating the numerical integration results to the intersatellite measurement time, the intersatellite ranging observation equation can be linearized using the satellite reference orbit position at the measurement time. Combined with the satellite orbit state transfer matrix at the measurement time, the autonomous orbit determination parameter estimation equation containing satellite orbit state parameters, space reference translation and rotation parameters can be obtained;

[0158] (7) Using the reduced parameter least squares estimation method, after eliminating the satellite orbit state parameters, a parameter estimation equation containing only the space reference translation and rotation parameters can be obtained. By solving this equation, the state estimation values ​​of the space reference translation and rotation parameters can be obtained;

[0159] (8) The parameter estimation equation containing only the spatial reference translation and rotation parameters is inverted to obtain the reference translation and rotation parameter covariance matrix. The diagonal elements of the parameter covariance matrix are counted respectively to obtain the precision factor of the spatial reference translation and rotation parameters affected by the dynamic model. This precision factor can be used to achieve quantitative analysis and evaluation of the estimation accuracy of the two types of parameters.

[0160] The present invention utilizes intersatellite ranging observations obtained by onboard intersatellite link equipment to construct intersatellite ranging observation equations. By modeling the perturbation force on the satellite, the satellite dynamic equations can be constructed. The satellite dynamics equations are transformed into space-referenced translations and rotations, and the partial derivatives of the satellite state parameters (satellite position, velocity, and dynamics module parameters) and the space-referenced translation and rotation parameters are obtained using the variational method. This results in a variational equation with the partial derivatives of the satellite position relative to the satellite state parameters and the space-referenced translation and rotation parameters as variables. The variational equations and the satellite dynamics equations are solved using the numerical integration method to obtain the state transfer matrix containing the space-referenced translation and rotation parameters and the satellite orbit state parameters, as well as the satellite reference orbit. The satellite reference orbit is used to linearize the inter-satellite ranging observation equations for multiple epochs. Combining the satellite state transfer matrix and the space-referenced translation and rotation parameter matrix at the measurement time, an estimation equation containing the space-referenced translation and rotation parameters and the satellite state parameters is obtained. The reduced least squares parameter estimation method is used to eliminate the satellite orbit state parameters, resulting in an equation containing only the space-referenced translation and rotation parameters. Solving this equation yields the estimated values ​​and estimation accuracy of the space-referenced translation and rotation parameters.

[0161] This paper proposes a method for calculating space-referenced translation and rotation errors using intersatellite ranging observation equations and satellite dynamics variational equations using a dynamics parameter estimation method. Based on the satellite dynamics equations, variational equations for the space-referenced translation and rotation parameters are constructed. The integral variational equations are used to obtain a design matrix showing how the space-referenced translation and rotation parameters affect satellite position changes at any moment. Combined with the intersatellite measurement equations, autonomous orbit determination parameter estimation equations are constructed that include both satellite orbital state parameters (satellite position, velocity, dynamics parameters, etc.) and space-referenced translation and rotation parameters. Using a reduced least squares parameter estimation method, after eliminating the satellite orbital state parameters, an equation containing only the space-referenced translation and rotation parameters is obtained. Solving this equation yields estimated values ​​and estimation errors for the space-referenced translation and rotation parameters.

[0162] The specific implementation process is as follows:

[0163] (1) Each satellite in the constellation carries an intersatellite link payload capable of intersatellite ranging and intersatellite communication. It can establish an intersatellite measurement and communication link with satellites in the same or different orbits to obtain intersatellite ranging observations. After eliminating measurement system errors such as equipment transmission and reception delay, signal propagation path delay, troposphere-ionosphere propagation medium delay, clock error, and relativistic effects, the intersatellite ranging observations are pre-processed to obtain instantaneous intersatellite ranging observations. The instantaneous intersatellite ranging observations can be used to construct the intersatellite ranging observation equation.

[0164]

[0165] where ρ ijis the instantaneous inter-satellite distance between satellite i and satellite j after preprocessing, are the three-dimensional position vectors of satellite i and satellite j respectively.

[0166] (2) Based on the orbital altitude and geometric physical parameters of each satellite, a satellite dynamics model can be constructed that takes into account the perturbations such as the Earth's gravity, solid tides, the gravity of the Sun and the Moon, solar pressure, atmospheric drag, and relativity. Using the standard gravity field model, JPL planetary ephemeris, and an atmospheric drag model similar to DTM, the differential equations of the satellite orbital motion dynamics in the inertial coordinate system can be constructed.

[0167]

[0168] in are the satellite position, velocity and acceleration vector at any moment, p is the satellite dynamic model parameter, and t is the time.

[0169] The solution to the above differential equation can be written as:

[0170]

[0171] in are the initial values ​​of satellite position and velocity parameters respectively.

[0172] (3) Taking the satellite state parameters such as satellite position and velocity parameters, satellite dynamics model parameters as the satellite state parameters to be estimated, the satellite dynamics differential equation is varied to obtain the satellite motion variational equation with the partial derivatives of the satellite position relative to the satellite state parameters as variables.

[0173]

[0174]

[0175]

[0176] in are the position and velocity of any satellite respectively, p is the satellite dynamics model parameter, are the initial values ​​of satellite position and velocity parameters respectively.

[0177] (4) The satellite motion variational equation is transformed into space reference translation and rotation using the space reference translation and rotation transformation matrix, and the satellite orbit dynamics equation containing three space reference translation parameters and three space reference rotation parameters can be obtained. The space reference translation and rotation parameters are used as the parameters to be estimated, and the partial derivative of the satellite dynamics equation after the space reference transformation is obtained to obtain the dynamic variational equation corresponding to the reference translation and rotation parameters.

[0178] Assume that the space reference translation transformation vector is The coordinate rotation vector is ε x , ε y , ε z for Three components, the corresponding coordinate rotation matrix M is:

[0179]

[0180] The satellite dynamics equation after the benchmark transformation is:

[0181]

[0182] The spatial reference translation and rotation parameter variation equations corresponding to the dynamic equations are in the form of:

[0183]

[0184] (5) Taking the a priori values ​​of the satellite orbit state parameters at the initial moment as the initial values, the satellite orbit dynamics equation, the satellite state parameter variation equation (satellite motion variation equation) and the space reference translation and rotation parameter variation equation are integrated by using a single-step or multi-step numerical integration method with estimated correction. The satellite reference orbit position, velocity, partial derivative matrix of satellite position with respect to satellite initial state parameters, partial derivative matrix of satellite position with respect to space reference translation and rotation parameters, etc. at fixed intervals can be obtained.

[0185] (6) Using the fixed-interval satellite reference orbit position velocity, the partial derivative matrix of the satellite initial state parameters, and the partial derivative matrix of the space-based translation and rotation parameters calculated using the numerical integration method, the satellite reference orbit position at the time of intersatellite link measurement, as well as the partial derivative matrix of the satellite orbit state parameters and the space-based translation and rotation parameters at the time of measurement, can be calculated using polynomial interpolation methods. The intersatellite ranging observation equation is linearized using the satellite reference orbit position at the time of measurement. Combined with the two satellite partial derivative matrices obtained by interpolation, the linearized autonomous orbit determination observation equation with the satellite orbit state parameters and the space-based translation and rotation parameters as the parameters to be estimated can be obtained.

[0186]

[0187] where Δρ ij H is the difference between the intersatellite link observation value and the intersatellite link theoretical value calculated by the reference orbit, i and H j are the intersatellite baseline unit vectors between satellite i and satellite j, are the satellite orbit state transfer matrices of satellite i and satellite j at the observation time, are the satellite orbit state parameter corrections, are the state transfer matrices of the spatial reference translation and rotation parameters at the observation time of satellite i and satellite j respectively, and ΔS is the correction of the spatial reference translation and rotation parameters, that is, Δδ ij Measure noise for intersatellite links. i and H j The calculation formula is:

[0188]

[0189] where ρ ij is the instantaneous inter-satellite distance between satellite i and satellite j after preprocessing, are the three-dimensional position vectors of satellite i and satellite j respectively.

[0190] (7) By combining the autonomous orbit determination observation equations of multiple measurement epochs, the satellite autonomous orbit determination equation with the satellite orbit state parameters and the space reference translation and rotation parameters as the parameters to be estimated can be obtained. With the satellite orbit state parameters as local parameters and the space reference translation and rotation parameters as global parameters, a parameter reduction method based on least squares estimation is used to eliminate the satellite orbit state parameters. A parameter estimation equation containing only the space reference translation and rotation parameters can be obtained. Solving this equation can obtain the estimated values ​​of the space reference translation and rotation parameters.

[0191] Taking the satellite orbit state parameters as a category, the multi-epoch autonomous orbit determination equation can be simply written as:

[0192]

[0193] Where A is the design matrix corresponding to the satellite position, velocity, and dynamic model parameters to be estimated. is the correction value of satellite position, velocity and dynamic model parameters, B is the design matrix corresponding to the spatial reference translation and rotation parameters, is the correction value of the spatial reference translation and rotation parameters, is the intersatellite measurement residual.

[0194] After the above equations are parameterized and the satellite state parameters are eliminated, the observation equation containing only the spatial reference translation and rotation parameters is:

[0195]

[0196] The corresponding least squares parameter estimates are:

[0197]

[0198] Where: I is the identity matrix with 1 on the main diagonal.

[0199] (8) Using the reduced observation equation containing only the space reference translation and rotation parameters, the parameter estimation method equation can be calculated. By inverting the method equation, the unit weight covariance matrix of the space reference translation and rotation parameter estimation can be obtained. According to the order of the space reference translation and rotation parameters in the parameter estimation equation, the main diagonal elements of the covariance matrix corresponding to the two types of parameters are selected respectively. The three main diagonal elements of the covariance matrix of the two types of parameters are summed and squared respectively to obtain the parameter estimation precision factor, which is defined as the precision factor of the reference translation parameter and the precision factor of the reference rotation parameter. These two types of precision factors can be used as the quantitative estimation values ​​of the space reference translation and rotation parameters constrained by the satellite dynamics model. The covariance matrix is ​​in the form of:

[0200]

[0201] Assuming that the spatial reference translation parameters are arranged before the reference rotation factors, the two types of precision factors are in the form of:

[0202] MDOP=(c 11 +c 22 +c 33 ) 1 / 2

[0203] SDOP=(c 44 +c 55 +c 66 ) 1 / 2

[0204] where Σ ΔS is the covariance matrix of the spatial reference translation and rotation parameters, c ij is the covariance matrix element, MDOP is the spatial reference translation dilution of precision, and SDOP is the spatial reference rotation dilution of precision.

[0205] (9) When using multi-epoch intersatellite ranging observations to estimate the accuracy of the dynamic model's effect on the space reference translation and rotation parameters, the length of the data processing arc affects the number of intersatellite ranging observations involved in parameter estimation, which in turn affects the evaluation results. To this end, different data processing arc lengths can be selected for different satellite constellation configurations and satellite dynamic environments. By comparing the results of multiple processing arcs, the impact of different arc lengths on the accuracy of space reference translation and rotation parameter estimation can be quantitatively analyzed.

[0206] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions within the technical scope disclosed by the present invention shall be covered by the scope of protection of the present invention. Therefore, the scope of protection of the present invention shall be subject to the scope of protection of the claims.

Claims

1. A method for estimating translation and rotation errors of a constrained space reference of a dynamic model, characterized in that: The following steps are involved: Obtain inter-satellite ranging observations between satellites and construct inter-satellite ranging observation equations; Model the perturbation forces that affect satellite orbital motion and construct satellite orbital dynamics equations; According to the satellite orbit dynamics equation, the partial derivative of the satellite state parameters is obtained to obtain the satellite orbit state parameter variation equation; Perform space-referenced translation and rotation transformations on the satellite orbit dynamics equations, and obtain partial derivatives of the space-referenced translation and rotation parameters to obtain the space-referenced translation and rotation parameter variational equations. Based on the initial values ​​of satellite state parameters, the satellite dynamics equation and the variational equation of the parameters to be estimated are solved by numerical integration method to obtain the fixed-interval satellite reference orbit, the partial derivative matrix of satellite state parameters and the partial derivative matrix of space reference translation and rotation parameters; An interpolation method is used to interpolate the fixed-interval satellite reference orbit position velocity information, satellite state parameter partial derivative matrix, and space reference translation and rotation parameter matrix to the intersatellite measurement time. The intersatellite ranging observation equation is linearized using the satellite reference orbit position at the measurement time. The interpolated satellite orbit state transfer matrix and space reference translation and rotation parameter partial derivative matrix at the measurement time are combined to obtain the autonomous orbit determination parameter estimation equation containing the satellite orbit state parameters, space reference translation and rotation parameters. The satellite orbit state parameters are eliminated from the autonomous orbit determination parameter estimation equation using the reduced parameter least squares estimation method, resulting in a parameter estimation equation containing only the space reference translation and rotation parameters. The equation is then solved to obtain the estimated values ​​of the space reference translation and rotation parameters. The parameter estimation equation that only contains the spatial reference translation and rotation parameters is inverted by the corresponding normal equation to obtain the reference translation and rotation parameter covariance matrix. The diagonal elements of the parameter covariance matrix are counted respectively to obtain the precision factor of the spatial reference translation and rotation parameters affected by the dynamic model. The precision factor can be used to quantitatively analyze and evaluate the estimation accuracy of the two types of parameters.

2. The method for estimating translation and rotation errors of a dynamic model constraint space reference according to claim 1, characterized in that: Obtaining intersatellite ranging observations between satellites and constructing intersatellite ranging observation equations specifically includes the following steps: Each satellite in the constellation carries an inter-satellite link payload that can achieve inter-satellite ranging and inter-satellite communication, and establishes an inter-satellite measurement and communication link with satellites in the same or different orbital planes to obtain ranging observations between satellites; After eliminating the equipment transmission and reception delay, signal propagation path delay, tropospheric and ionospheric propagation medium delay, clock error and the influence of relativity, the inter-satellite ranging observation is obtained through data pre-processing of the measured transmission and reception time, and the instantaneous inter-satellite ranging observation is used to construct the inter-satellite ranging observation equation. Where: ij is the instantaneous inter-satellite distance between satellite i and satellite j after preprocessing, are the three-dimensional position vectors of satellite i and satellite j respectively.

3. The method for estimating translation and rotation errors of a dynamic model constraint space reference according to claim 2, characterized in that: Modeling the perturbation force that affects satellite orbital motion and constructing the satellite orbital dynamics equation includes the following steps: Based on the orbital altitude and geometric physical parameters of each satellite, a satellite dynamics model is constructed that takes into account the Earth's gravity, solid tides, the gravity of the Sun and Moon, solar pressure, atmospheric drag, and relativity. The standard gravity field model, JPL planetary ephemeris, and an atmospheric drag model similar to the DTM are used to construct the differential equations of satellite orbital motion dynamics in the inertial coordinate system. in: are the satellite position, velocity and acceleration vectors at any moment, p is the satellite dynamics model parameter, and t is the time; The solution to the differential equation can be written as: in: are the initial values ​​of satellite position and velocity parameters respectively.

4. The method for estimating translation and rotation errors of a dynamic model constraint space reference according to claim 3, characterized in that: According to the satellite orbit dynamics equation, the partial derivative of the satellite state parameters is obtained to obtain the satellite orbit state parameter variation equation, which specifically includes the following steps: Taking the satellite position parameters, satellite velocity parameters and satellite dynamics model parameters as the satellite state parameters to be estimated, the satellite dynamics differential equation is varied to obtain the satellite motion variation equation with the partial derivatives of the satellite position relative to the satellite state parameters as variables; in: are the position and velocity of any satellite respectively, and p is the satellite dynamic model parameter; are the initial values ​​of satellite position and velocity parameters respectively.

5. The method for estimating translation and rotation errors of a dynamic model constraint space reference according to claim 4, characterized in that: Perform space-referenced translation and rotation transformations on the satellite orbit dynamics equations, and obtain partial derivatives of the space-referenced translation and rotation parameters to obtain the space-referenced translation and rotation parameter variational equations. The specific steps include: The satellite dynamics equation is transformed into a space-referenced translation and rotation using the space-referenced translation and rotation transformation matrix to obtain the satellite orbit dynamics equation containing three space-referenced translation parameters and three space-referenced rotation parameters. The space-referenced translation and rotation parameters are used as the parameters to be estimated, and the partial derivatives of the satellite dynamics equation after the space-referenced transformation are obtained to obtain the dynamic variational equation corresponding to the reference translation and rotation parameters. Assume that the space reference translation transformation vector is The coordinate rotation vector is ε x , ε y , ε z for Three components, the corresponding coordinate rotation matrix M is: The satellite dynamics equation after the benchmark transformation is: The spatial reference translation and rotation parameter variation equations corresponding to the dynamic equations are in the form of:

6. The method for estimating translation and rotation errors of a dynamic model constraint space reference according to claim 5, characterized in that: Based on the initial values ​​of the satellite state parameters, the numerical integration method is used to solve the satellite dynamics equation and the variational equation of the parameters to be estimated, and the fixed-interval satellite reference orbit, the satellite state parameter partial derivative matrix, and the space reference translation and rotation parameter partial derivative matrix are obtained. The specific steps include: Taking the prior values ​​of satellite position, satellite velocity and satellite dynamics model parameters at the initial time as initial values, the satellite orbit dynamics equation, satellite state parameter variation equation and space reference translation and rotation parameter variation equation are solved simultaneously by single-step method or multi-step method to obtain the fixed-interval satellite reference orbit, satellite state parameter partial derivatives and space reference translation and rotation parameter partial derivative matrices within the integration period.

7. The method for estimating translation and rotation errors of a dynamic model constraint space reference according to claim 6, characterized in that: An interpolation method is used to interpolate the fixed-interval satellite reference orbit position velocity information, satellite state parameter partial derivative matrix, and space reference translation and rotation parameter matrix to the intersatellite measurement time. The intersatellite ranging observation equation is linearized using the satellite reference orbit position at the measurement time. The interpolated satellite orbit state transfer matrix and space reference translation and rotation parameter partial derivative matrix at the measurement time are combined to obtain the autonomous orbit determination parameter estimation equation containing the satellite orbit state parameters, space reference translation and rotation parameters. The specific steps include: The satellite reference orbit position at the time of intersatellite link measurement is calculated by interpolation method using the fixed-interval satellite reference orbit position velocity information, as well as the satellite orbit state parameters and the partial derivative matrix of the space reference translation and rotation parameters at the measurement time; The inter-satellite ranging observation equation is linearized using the satellite reference orbit position at the measurement time. Combining the two satellite partial derivative matrices obtained by interpolation, the linearized autonomous orbit determination observation equation is obtained, with the satellite orbit state parameters, space reference translation and rotation parameters as the parameters to be estimated. Where: Δρ ij H is the difference between the intersatellite link observation value and the intersatellite link theoretical value calculated by the reference orbit, i and H j are the intersatellite baseline unit vectors between satellite i and satellite j, are the satellite orbit state transfer matrices of satellite i and satellite j at the observation time, are the satellite orbit state parameter corrections, are the state transfer matrices of the spatial reference translation and rotation parameters at the observation time of satellite i and satellite j respectively, and ΔS is the correction of the spatial reference translation and rotation parameters, that is, Δδ ij Measuring noise for intersatellite links; H i and H j The calculation formula is: Where: ij is the instantaneous inter-satellite distance between satellite i and satellite j after preprocessing, are the three-dimensional position vectors of satellite i and satellite j respectively.

8. The method for estimating translation and rotation errors of a dynamic model constraint space reference according to claim 7, characterized in that: The satellite orbit state parameters in the autonomous orbit determination parameter estimation equation are eliminated by using the reduced parameter least squares estimation method, and a parameter estimation equation containing only the space reference translation and rotation parameters is obtained. The equation is solved to obtain the estimated values ​​of the space reference translation and rotation parameters. Specifically, the following steps are included: Combining multiple measurement epoch autonomous orbit determination observation equations to obtain satellite autonomous orbit determination equations with satellite orbit state parameters and space reference translation and rotation parameters as parameters to be estimated; Taking the satellite orbit state parameters as local parameters and the space reference translation and rotation parameters as global parameters, a parameter reduction method based on least squares estimation is adopted to eliminate the satellite orbit state parameters and obtain a parameter estimation equation containing only the space reference translation and rotation parameters. By solving this equation, the estimated values ​​of the space reference translation and rotation parameters can be obtained. Taking the satellite orbit state parameters as a category, the multi-epoch autonomous orbit determination equation can be simply written as: Where: A is the design matrix corresponding to the satellite position, velocity, and dynamic model parameters, is the correction value of satellite position, velocity and dynamic model parameters, B is the design matrix corresponding to the spatial reference translation and rotation parameters, is the correction value of the spatial reference translation and rotation parameters, is the intersatellite measurement residual; After parameter reduction and elimination of satellite state parameters, the observation equation containing only the spatial reference translation and rotation parameters of the combined multiple epoch autonomous orbit determination equations is: The corresponding least squares parameter estimates are: Where: I is the identity matrix with 1 on the main diagonal.

9. The method for estimating translation and rotation errors of a dynamic model constraint space reference according to claim 8, characterized in that: The parameter estimation equation containing only the spatial reference translation and rotation parameters is inverted to obtain the covariance matrix of the reference translation and rotation parameters. The diagonal elements of the parameter covariance matrix are counted to obtain the precision factor of the spatial reference translation and rotation parameters affected by the dynamic model. The precision factor can be used to quantitatively analyze and evaluate the estimation accuracy of the two types of parameters. The specific steps include: The parameter estimation method equation is calculated using the reduced observation equation containing only the spatial reference translation and rotation parameters. The parameter estimation method equation is inverted to obtain the unit weight covariance matrix of the spatial reference translation and rotation parameter estimation. According to the order of the spatial reference translation and rotation parameters in the parameter estimation equation, the main diagonal elements of the covariance matrix corresponding to the two types of parameters are selected respectively. The three main diagonal elements of the covariance matrix of the two types of parameters are summed and squared to obtain the parameter estimation precision factors, which are defined as the precision factors of the reference translation parameters and the precision factors of the reference rotation parameters, respectively. These are used as the quantitative estimates of the spatial reference translation and rotation parameters constrained by the satellite dynamics model. The covariance matrix is ​​in the form: Assuming that the spatial reference translation parameters are arranged before the reference rotation factors, the two types of precision factors are in the form of: MDOP=(c 11 +c 22 +c 33 ) 1 / 2 SDOP=(c 44 +c 55 +c 66 ) 1 / 2 Where: Σ ΔS is the covariance matrix of the spatial reference translation and rotation parameters, c ij is the covariance matrix element, MDOP is the spatial reference translation dilution of precision, and SDOP is the spatial reference rotation dilution of precision.

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