CN109752744B - Multi-satellite combined orbit determination method based on model error compensation - Google Patents
Multi-satellite combined orbit determination method based on model error compensation Download PDFInfo
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Abstract
The invention relates to the field of satellite orbit determination, in particular to a multi-satellite combined orbit determination method based on model error compensation, which comprises the following steps: establishing a primary multi-satellite combined orbit determination equation of the target satellite according to a dynamic model of a satellite group and the target satellite of the space-based measurement and control network and observation models of the foundation measurement and control network and the space-based measurement and control network; acquiring an orbit calculation value of a target satellite according to a primary multi-satellite combined orbit determination equation, and acquiring an OC residual error by combining an orbit observation value of the target satellite; respectively establishing an error compensation item of a dynamic model and an error compensation item of an observation model by determining an error source corresponding to the OC residual error; and establishing an earth-ground multi-satellite combined orbit determination equation of the target satellite according to the primary multi-satellite combined orbit determination equation and the error compensation terms of the dynamic model and the observation model. The invention utilizes the space and foundation combined orbit determination strategy and compensates errors of two types of models, namely a dynamic model, an observation model and the like, thereby improving the orbit determination precision of the target satellite.
Description
Technical Field
The invention relates to the field of satellite orbit determination, in particular to a multi-satellite combined orbit determination method based on model error compensation.
Background
The space-ground-based joint orbit determination is a process of comprehensively determining the orbit of a space-based satellite and a ground-based satellite by comprehensively utilizing the information of a space-based measurement and control network and a ground-based measurement and control network, and the constraint on the space-based satellite is not only local ground observation but also data of the space-based observation, so that on one hand, the coverage rate of the orbit is improved by utilizing the space-based measurement and control data, and the target orbit is more effectively constrained, on the other hand, the estimated orbit of the space-based satellite and the estimated orbit of the target satellite can reach the optimal balance in the space-ground-based measurement and control information, and the space-based satellite orbit and the space-based target.
In principle, orbit determination is a process of reconstructing a satellite orbit from orbit measurement data containing satellite orbit information according to constraint conditions of a satellite dynamic model.
In the orbit determination, the kinematic orbit determined by the observation model ensures the uniqueness of the orbit state in the airspace, and the dynamic orbit determined by the dynamic model ensures the continuity and smoothness of the orbit state in the time domain. When there is no systematic deviation, the kinematics orbit and the dynamics orbit are coincident at the observation epoch moment, the estimation orbit is unique and optimal, but when there is a model error in the dynamics model or the observation model, the generated kinematics orbit and dynamics orbit will not coincide any more, the estimation orbit can only be determined under a certain criterion, and a reasonable approximation is performed in the observation model and the dynamics model.
Model errors become one of the key factors for restricting the improvement of satellite orbit determination precision, and many scholars carry out intensive research from both hardware and software aspects. Certain gap exists between the hardware model compensation of China and foreign developed countries, and the main mode for improving the orbit determination precision is to adopt a mathematical processing means to make up the deficiency of hardware measurement at the present stage.
The orbit determination precision can be better improved by compensating the dynamic model error by a mathematical processing method, which is an important way for making up for the insufficient process level of hardware. But currently, the research work in the aspect is mainly directed to the situation that the dynamic model error and the error distribution mode are fixed. While relatively few studies are made regarding observation model errors, less common is the study of simultaneous model error compensation for both the kinetic and observation models. Because the action effects of the dynamic model error and the observation model error are different in the track determination, how to classify and research the corresponding compensation mode is the key for fundamentally solving the problem of model error compensation.
Disclosure of Invention
The embodiment of the invention provides a multi-satellite combined orbit determination method and device based on model error compensation, which are used for realizing combined measurement and control orbit determination of a space and a foundation, constructing a corresponding compensation method by combining two levels of a dynamic model and an observation model in a classified manner and compensating uncertainty model errors in a target satellite orbit equation.
In order to achieve the above object, an embodiment of the present invention provides a multi-satellite joint orbit determination method based on model error compensation, where the method includes:
establishing a primary multi-satellite combined orbit determination equation of the target satellite according to a dynamic model of a satellite group and the target satellite of the space-based measurement and control network and observation models of the foundation measurement and control network and the space-based measurement and control network;
acquiring an orbit calculation value of a target satellite according to a primary multi-satellite combined orbit determination equation, and acquiring a difference value between the orbit observation value and the orbit calculation value, namely OC residual error, by combining the orbit observation value of the target satellite;
determining an error source corresponding to the OC residual error through the OC residual error and the frequency spectrum corresponding relation between the OC residual error and the error source of the dynamic model and the error source of the observation model, and respectively establishing an error compensation item of the dynamic model and an error compensation item of the observation model according to the error source corresponding relation;
establishing an earth-ground multi-satellite combined orbit determination equation of the target satellite according to the primary multi-satellite combined orbit determination equation and error compensation items of the dynamic model and the observation model;
and determining the optimal orbit parameter of the space-ground multi-satellite combined orbit determination equation of the target satellite by using a nonlinear multi-model optimal weighted estimation method.
Compared with the prior art, the technical scheme has the following beneficial effects:
the invention jointly fixes the orbit and expands to the moving survey station of the heaven and earth base, have improved the robustness and reliability of the whole orbit determination system. The method is characterized in that the defects of ground measurement and control are made up by using the data of the space-ground measurement and control, the influence of ephemeris error of the space-ground satellite on the target satellite orbit determination precision is restrained by using the combined orbit determination, the defects of a dynamic model and an observation model are made up by using model compensation, the model is divided into the dynamic model and the observation model according to the model structure, and a classification model error compensation strategy is carried out according to the two aspects of the dynamic model and the observation model, so that compensation can be carried out according to the dynamic orbit and the geometric orbit decomposition aiming at different model effects, and favorable technical support is provided for improving the orbit determination precision.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of a multi-satellite joint orbit determination method according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1, the multi-satellite joint orbit determination method based on model error compensation provided by the present invention includes:
101. establishing a primary multi-satellite combined orbit determination equation of the target satellite according to a dynamic model of a satellite group and the target satellite of the space-based measurement and control network and observation models of the foundation measurement and control network and the space-based measurement and control network;
102. acquiring an orbit calculation value of a target satellite according to a primary multi-satellite combined orbit determination equation, and acquiring a difference value between the orbit observation value and the orbit calculation value, namely OC residual error, by combining the orbit observation value of the target satellite;
103. determining an error source corresponding to the OC residual error through the OC residual error and the frequency spectrum corresponding relation between the OC residual error and the error source of the dynamic model and the error source of the observation model, and respectively establishing an error compensation item of the dynamic model and an error compensation item of the observation model according to the error source corresponding relation;
104. establishing an earth-ground multi-satellite combined orbit determination equation of the target satellite according to the primary multi-satellite combined orbit determination equation and model error compensation items of the dynamic model and the observation model;
105. and determining the optimal orbit parameter of the space-ground multi-satellite combined orbit determination equation of the target satellite by using a nonlinear multi-model optimal weighted estimation method.
Specifically, a space-based measurement and control network satellite group and a target satellite group are taken as orbit determination targets, observation data of the ground-based measurement and control network and the space-based measurement and control network are comprehensively applied, a unified multi-satellite combined orbit determination frame, namely a primary multi-satellite combined orbit determination equation, is constructed by the aid of ideas of physical analysis and mathematical modeling, a corresponding compensation method is constructed in a classified mode from a dynamic model and an observation model by the aid of orbit OC residual errors of the target satellites, and model errors are compensated; on the basis, a primary multi-satellite combined orbit determination equation and model error compensation items of a dynamic model and an observation model are combined to construct an all-terrain multi-satellite combined orbit determination equation of a target satellite, and a final optimal parameter estimation result of the multi-satellite orbit determination equation is obtained through a nonlinear multi-model optimal weighting estimation method, so that powerful technical support is provided for establishing an autonomous all-terrain multi-satellite combined orbit determination system in China.
Further, determining an error source corresponding to the OC residual according to the OC residual and the spectrum correspondence between the OC residual and the dynamic model error source and the observation model error source includes:
according to the characteristics of the OC residual error in the continuous arc segment, establishing a basis function of an OC residual error signal on a time domain;
decomposing the OC residual error signal into a high-frequency component and a low-frequency component layer by utilizing the multi-scale effect of wavelet transformation according to the basis functions to obtain different characteristic layer information;
decomposing the trends of the different characteristic layer information to obtain frequency spectrums of the different characteristic layer information;
and determining error sources corresponding to different feature layer information of the OC residual error according to the corresponding relation between the frequency spectrums of the different feature layer information and the frequency spectrums.
The OC residual error is the residual error between the orbit observed value and the orbit calculated value, the orbit calculated value is the orbit parameter estimated by the satellite orbit determination principle, and then the calculated value is obtained by back calculation on the measured element; the track observation value is output data obtained through a track observation sensor; the OC residual thus contains track information and observation data information. The kinetic model error and the observation model error will also be directly or indirectly embodied in the OC residual. Therefore, through the analysis of the OC residual, the orbit dynamics model error characteristic and the observation error characteristic can be obtained. And because the OC residual error is a discrete time sequence and is limited by an observation arc section, the OC residual error is difficult to be composed of continuous full arc sections and often composed of a plurality of discrete short arc sections, and in addition, the analysis difficulty of the OC residual error is increased due to the difference of measured elements and sampling intervals. Therefore, the characteristics of the OC residual under continuous arc segments are firstly analyzed, and the signal represented by the basis function is constructed on the time domain.
The OC residual signal is decomposed into a high-frequency component and a low-frequency component layer by utilizing the multi-scale effect of wavelet transformation, and the properties of the signal can be described by using wavelet coefficients so as to obtain different characteristic layer information of the signal. According to application requirements, the wavelet coefficients are constrained to obtain reconstructed signals with noise removed, the trend of the signals is decomposed, and OC residual error representation information of the corresponding error sources is obtained by contrasting the spectral characteristics of the error sources.
Still further, the determining the error sources corresponding to different feature layers of the OC residual according to the correspondence between the frequency spectrums of the different feature layer information and the frequency spectrums includes:
obtaining a corresponding relation of a dynamic model error source, an observation model error source and a frequency spectrum function of OC residual errors by adopting a mathematical derivation and simulation test method;
and determining error sources corresponding to different feature layers of the OC residual error according to the frequency spectrums of the different feature layer information of the OC residual error and the corresponding relation of the frequency spectrum functions.
Several types of feature layers with the largest influence on the tracking result can be obtained through analysis of the OC residual error, but an error source corresponding to the feature layers needs to be researched. The function corresponding relation between residual error frequency spectrums corresponding to the error sources can be directly obtained by mathematical derivation, for the frequency spectrums which cannot directly obtain the function relation, the numerical value corresponding relation can be obtained by adopting a simulation test mode, and then the function expression is constructed by a fitting method.
Still further, the determining an error source corresponding to the OC residual error, and accordingly respectively establishing an error compensation term of the dynamic model and an error compensation term of the observation model, includes:
when an error source corresponding to the main feature layer information of the OC residual error is a dynamic model error source, establishing an error compensation item of the dynamic model;
when an error source corresponding to the main feature layer information of the OC residual error is an observation model error source, establishing an error compensation item of the observation model;
when the main error source cannot be determined through the OC residual error, decomposing the OC residual error through a mixed mode decomposition method, and correcting the OC residual error through controlling the upper limit of the total error.
Theoretically, residual representation forms of the dynamic model and the observation model are different in a frequency domain, and when the spectral characteristics of certain model errors or other similar prior information are known, the extraction of detail items can be carried out by a wavelet method or a modal decomposition method. Therefore, converting the model spectral characteristics into residual spectral characteristics and separating such information by using an appropriate analysis method are key of the compensation technique when model errors are coupled.
Still further, the error compensation term for establishing the dynamic model includes:
according to the characteristics of the track, a method of combining a physical model and a mathematical model is used, for the perturbation force which cannot be used for modeling of a dynamic model, a basis function is used for fitting the perturbation force to establish the mathematical model, and a perturbation force error compensation item represented by the mathematical model is constructed according to the basis function;
according to the requirement of orbit determination precision and the parameter accuracy of the dynamic model, a mathematical model represented by sparse parameters is constructed by a greedy algorithm or an interior point algorithm and is used as a model error compensation item of the dynamic model;
and establishing an error compensation item of the dynamic model according to the perturbation force error compensation item and the model error compensation item of the dynamic model so as to correct OC residual errors corresponding to the error source of the dynamic model.
Uncertainty dynamics model error refers to the portion of perturbation force error that is not yet recognized or modeled and that arises from inaccuracies in the model parameters. Since both satellite orbit determination and prediction rely on a dynamical model, the dynamical model is first subjected to a modeling compensation process. Starting from the extraction of orbit characteristics by optimizing and reconstructing a satellite orbit dynamic model, and fitting parts which cannot be accurately modeled in the satellite dynamic model by a basis function to form a mathematical model by adopting a method of combining a physical model and the mathematical model; according to the requirement of orbit determination precision and the characteristics of the shooting model, searching out the optimal sparse parameter representation by a greedy algorithm or an interior point algorithm, and establishing a mathematical representation model of the satellite dynamic model error; and respectively establishing hybrid kinetic models of the satellite orbits with different orbit heights and types based on the accurate kinetic model of the satellite, the kinetic perturbation model containing the parameters to be estimated and the mathematical model expressed based on the basis function to obtain the high-precision expression of the satellite kinetic model. Because the representation forms of the dynamic model and the observation model are reflected by residual errors in the orbit equation, the representation forms of the two models are coupled together, and therefore, the research content of the part is suitable for the situation that the error of the dynamic model is far larger than that of the observation model.
Still further, the establishing of the error compensation term of the observation model includes:
estimating the uncertain observation system error by adopting a nonparametric statistical method to obtain a nonparametric represented uncertain model error compensation function;
and establishing an error compensation item of the observation model according to the uncertainty model error compensation function and the certainty system error compensation model of the observation model so as to correct OC residual errors corresponding to the error source of the observation model.
The uncertain observation errors mainly refer to the unknown observation system errors and the cognitive system error correction residuals. Due to different model efficiencies, the method for compensating the uncertainty observation model error is different from the method for compensating the dynamics model error. In addition, because it is difficult to obtain the real track of the measurement and control data, the form mode of the uncertain system error cannot be obtained. Therefore, an uncertain model error represented by a non-parameter is constructed in a non-parameter modeling mode, and a partial linear model is unified by combining a parameterized observation model and a deterministic system error model. And the uncertainty observation error is estimated by researching the partial linear model estimation method. Also, due to coupling reasons, the present section is adapted to situations where the observation model error is much larger than the dynamical model error.
Still further, decomposing the OC residual error by a mixed mode decomposition method, and correcting the OC residual error by controlling an upper limit of a total error includes:
the OC residual error is converted on a frequency domain, the part corresponding to an error source in the OC residual error is decomposed through an empirical mode decomposition technology according to prior information, and the OC residual error is corrected through an error compensation item corresponding to the error source;
and correcting the OC residual error by adjusting the empirical force and controlling the upper limit of the total error for the part of the OC residual error, which cannot determine the corresponding error source.
The part mainly aims at the situation that the errors of a dynamic model and an observation model are similar and coupled. Although the two types of errors are coupled, the mixed signal is converted on a frequency domain, and a certain priori information is utilized, and an empirical mode decomposition technology is utilized, so that partial coupling type error sources are hopefully separated. The key of this part is to process the residual by modal decomposition techniques. When the formal characteristics or the spectral distribution of a certain type of model errors are known, the OC residual error can be eliminated at the characteristic level through decomposition of the OC residual error, and then compensation technology is carried out.
Since each error source has specific spectral characteristics and distribution rules, although coupled together in the time domain, it can still be decomposed in the frequency domain. Decomposing the OC residual signal by an empirical mode decomposition method on the basis of OC residual characteristic analysis. For example, the spectrum characteristics can be effectively decomposed by the empirical force in the dynamic model. The specific technical scheme can adopt the idea of combining theoretical derivation and simulation test, and the real characteristic of the dynamic model error can be subjected to auxiliary analysis by using data of the CHAMP satellite accelerometer.
Without any prior information, the dynamical model error and the observation model error are coupled together in an OC form and are difficult to separate effectively, i.e., the degree of bias of the estimated trajectory between the dynamical trajectory and the geometric trajectory cannot be determined. However, when some kind of error source characteristics are known, such as the systematic error form of the observation model, simultaneous compensation of both models can be performed by adjusting the magnitude of the empirical force. However, when a model spectrum is known, the OC residual is obtained by a conventional method, the characteristic is removed by a mixed mode decomposition method, and then compensation methods of two models are performed.
Further, the determining the optimal orbit parameter of the space-ground multiple-satellite combined orbit determination equation of the target satellite by using the nonlinear multiple-model optimal weighted estimation method includes:
the curvature of the space-ground multi-satellite combined orbit determination equation is used as a quantitative standard to measure the nonlinearity degree and the complexity degree of each model of the space-ground multi-satellite combined orbit determination equation, and the space-ground multi-satellite combined orbit determination equation is subjected to weighting processing according to the curvature of the space-ground multi-satellite combined orbit determination equation;
carrying out interval constraint on the parameters to be estimated in the space-ground multi-satellite combined orbit determination equation by a parameter constraint method;
optimally estimating parameters in the space-ground multi-satellite combined orbit determination equation by adopting a biased estimation method;
and further optimizing and correcting parameters in the multi-satellite combined orbit determination equation of the space foundation by an iterative method.
Specifically, on the basis of a space-ground-based observation model, a dynamics model is expanded, and a space-ground-based satellite orbit and a target satellite orbit are both used as orbits to be estimated to form a space-ground-based satellite combined orbit determination equation. And constructing a corresponding model compensation item according to the proportion of the dynamic model error and the observation model error, and adding the model compensation item into the joint orbit determination equation. In order to prevent the error function of the curve fitting dynamic model from excessively absorbing the model error and enable the track to lose the characteristics of the dynamic equation, the geometric track determined by the track deviation observation data is estimated, the parameter to be estimated in the model is subjected to interval constraint by adopting a parameter constraint method, particularly the self size of the empirical force is monitored, and an inhibition factor capable of representing the interpretation capability of two types of models (a physical model and a mathematical model) is added in the orbit determination equation so as to control the model error term (a mathematical model). Because the non-linearity degree of each model in the orbit determination equation is different, the interpretation capability of the model is reduced when the model is directly solved, so that the model curvature is firstly solved, curvature weighting is carried out on various models so as to achieve the optimal model interpretation, and the orbit determination precision is improved. And on the basis of carrying out interval constraint on the parameters to be estimated in the space-ground multi-satellite combined orbit determination equation, carrying out optimal estimation on the parameters in the space-ground multi-satellite combined orbit determination equation by a biased estimation method. In addition, in order to prevent orbit determination deviation caused by biased estimation, iteration processing is carried out, and an optimal iteration strategy is researched. And finally, quantitatively describing the combined orbit determination precision based on a model structure analysis method and a parameter estimation theory.
Although the model compensation method is deeply studied at home and abroad, the method is mainly limited to a dynamic model or two models are mixed together, and meanwhile, the compensation of the dynamic model mainly adopts an inherent mode. The method is divided into a dynamic model and an observation model compensation strategy according to the model structure, can perform compensation according to dynamic track and geometric track decomposition aiming at different model functions, simultaneously provides a transition prevention compensation strategy, and also provides a compensation strategy when two models are coupled in error, which is the first time at home and abroad and is one of the characteristics and innovation of the method.
The initial purpose of the combined orbit determination is to restrain the influence of ephemeris error of a space-based satellite, and the combined orbit determination is expanded into a space-based mobile station, so that the robustness and the reliability of the whole system are improved. The method is characterized in that the defects of ground measurement and control are made up by using the data of the space-ground measurement and control, the influence of ephemeris errors of the space-ground satellite on the orbit determination precision of a target satellite is restrained by using the combined orbit determination, and the defects of a dynamic model and an observation model are made up by using model compensation. The invention provides a multi-satellite combined orbit determination model and nonlinear multi-model optimal weighting estimation method based on model compensation, aiming at the structural complexity of a model, a model curvature weighting strategy is adopted in the parameter estimation process, and the orbit determination precision is further improved.
It should be understood that the specific order or hierarchy of steps in the processes disclosed is an example of exemplary approaches. Based upon design preferences, it is understood that the specific order or hierarchy of steps in the processes may be rearranged without departing from the scope of the present disclosure. The accompanying method claims present elements of the various steps in a sample order, and are not intended to be limited to the specific order or hierarchy presented.
In the foregoing detailed description, various features are grouped together in a single embodiment for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments of the subject matter require more features than are expressly recited in each claim. Rather, as the following claims reflect, invention lies in less than all features of a single disclosed embodiment. Thus, the following claims are hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. To those skilled in the art; various modifications to these embodiments will be readily apparent, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the disclosure. Thus, the present disclosure is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
What has been described above includes examples of one or more embodiments. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the aforementioned embodiments, but one of ordinary skill in the art may recognize that many further combinations and permutations of various embodiments are possible. Accordingly, the embodiments described herein are intended to embrace all such alterations, modifications and variations that fall within the scope of the appended claims. Furthermore, to the extent that the term "includes" is used in either the detailed description or the claims, such term is intended to be inclusive in a manner similar to the term "comprising" as "comprising" is interpreted when employed as a transitional word in a claim. Furthermore, any use of the term "or" in the specification of the claims is intended to mean a "non-exclusive or".
Those of skill in the art will further appreciate that the various illustrative logical blocks, units, and steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both. To clearly illustrate the interchangeability of hardware and software, various illustrative components, elements, and steps have been described above generally in terms of their functionality. Whether such functionality is implemented as hardware or software depends upon the particular application and design requirements of the overall system. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present embodiments.
The various illustrative logical blocks, or elements, described in connection with the embodiments disclosed herein may be implemented or performed with a general purpose processor, a digital signal processor, an Application Specific Integrated Circuit (ASIC), a field programmable gate array or other programmable logic device, discrete gate or transistor logic, discrete hardware components, or any combination thereof designed to perform the functions described herein. A general-purpose processor may be a microprocessor, but in the alternative, the processor may be any conventional processor, controller, microcontroller, or state machine. A processor may also be implemented as a combination of computing devices, e.g., a digital signal processor and a microprocessor, a plurality of microprocessors, one or more microprocessors in conjunction with a digital signal processor core, or any other similar configuration.
The steps of a method or algorithm described in connection with the embodiments disclosed herein may be embodied directly in hardware, in a software module executed by a processor, or in a combination of the two. A software module may be stored in RAM memory, flash memory, ROM memory, EPROM memory, EEPROM memory, registers, hard disk, a removable disk, a CD-ROM, or any other form of storage medium known in the art. For example, a storage medium may be coupled to the processor such the processor can read information from, and write information to, the storage medium. In the alternative, the storage medium may be integral to the processor. The processor and the storage medium may reside in an ASIC, which may be located in a user terminal. In the alternative, the processor and the storage medium may reside in different components in a user terminal.
In one or more exemplary designs, the functions described above in connection with the embodiments of the invention may be implemented in hardware, software, firmware, or any combination of the three. If implemented in software, the functions may be stored on or transmitted over as one or more instructions or code on a computer-readable medium. Computer-readable media includes both computer storage media and communication media that facilitate transfer of a computer program from one place to another. Storage media may be any available media that can be accessed by a general purpose or special purpose computer. For example, such computer-readable media can include, but is not limited to, RAM, ROM, EEPROM, CD-ROM or other optical disk storage, magnetic disk storage or other magnetic storage devices, or any other medium which can be used to carry or store program code in the form of instructions or data structures and which can be read by a general-purpose or special-purpose computer, or a general-purpose or special-purpose processor. Additionally, any connection is properly termed a computer-readable medium, and, thus, is included if the software is transmitted from a website, server, or other remote source via a coaxial cable, fiber optic cable, twisted pair, Digital Subscriber Line (DSL), or wirelessly, e.g., infrared, radio, and microwave. Such discs (disk) and disks (disc) include compact disks, laser disks, optical disks, DVDs, floppy disks and blu-ray disks where disks usually reproduce data magnetically, while disks usually reproduce data optically with lasers. Combinations of the above may also be included in the computer-readable medium.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (7)
1. A multi-satellite combined orbit determination method based on model error compensation is characterized by comprising the following steps:
establishing a primary multi-satellite combined orbit determination equation of the target satellite according to a dynamic model of a satellite group and the target satellite of the space-based measurement and control network and observation models of the foundation measurement and control network and the space-based measurement and control network;
acquiring an orbit calculation value of a target satellite according to a primary multi-satellite combined orbit determination equation, and acquiring a difference value between the orbit observation value and the orbit calculation value, namely OC residual error, by combining the orbit observation value of the target satellite;
determining an error source corresponding to the OC residual error through the OC residual error and the frequency spectrum corresponding relation between the OC residual error and the error source of the dynamic model and the error source of the observation model, and respectively establishing an error compensation item of the dynamic model and an error compensation item of the observation model according to the error source corresponding relation;
establishing an earth-ground multi-satellite combined orbit determination equation of the target satellite according to the primary multi-satellite combined orbit determination equation and error compensation items of the dynamic model and the observation model;
determining the optimal orbit parameter of the space-ground multi-satellite combined orbit determination equation of the target satellite by using a nonlinear multi-model optimal weighted estimation method;
determining an error source corresponding to the OC residual error through the OC residual error and the frequency spectrum corresponding relation between the OC residual error and the dynamic model error source and the observation model error source, wherein the method comprises the following steps:
according to the characteristics of the OC residual error in the continuous arc segment, establishing a basis function of an OC residual error signal on a time domain;
decomposing the OC residual error signal into a high-frequency component and a low-frequency component layer by utilizing the multi-scale effect of wavelet transformation according to the basis functions to obtain different characteristic layer information;
decomposing the trends of the different characteristic layer information to obtain frequency spectrums of the different characteristic layer information;
and determining error sources corresponding to different feature layer information of the OC residual error according to the corresponding relation between the frequency spectrums of the different feature layer information and the frequency spectrums.
2. The method according to claim 1, wherein the determining error sources corresponding to different feature layers of the OC residual according to the correspondence between the spectra of the different feature layer information and the spectra comprises:
obtaining a corresponding relation of a dynamic model error source, an observation model error source and a frequency spectrum function of OC residual errors by adopting a mathematical derivation and simulation test method;
and determining error sources corresponding to different feature layers of the OC residual error according to the frequency spectrums of the different feature layer information of the OC residual error and the corresponding relation of the frequency spectrum functions.
3. The method according to claim 2, wherein the determining an error source corresponding to the OC residual error and establishing an error compensation term of the dynamic model and an error compensation term of the observation model respectively comprises:
when an error source corresponding to the main feature layer information of the OC residual error is a dynamic model error source, establishing an error compensation item of the dynamic model;
when an error source corresponding to the main feature layer information of the OC residual error is an observation model error source, establishing an error compensation item of the observation model;
when the main error source cannot be determined through the OC residual error, decomposing the OC residual error through a mixed mode decomposition method, and correcting the OC residual error through controlling the upper limit of the total error.
4. The method according to claim 3, wherein the establishing of the error compensation term of the dynamical model comprises:
according to the characteristics of the track, a method of combining a physical model and a mathematical model is used, for the perturbation force which cannot be used for modeling of a dynamic model, a basis function is used for fitting the perturbation force to establish the mathematical model, and a perturbation force error compensation item represented by the mathematical model is constructed according to the basis function;
according to the requirement of orbit determination precision and the parameter accuracy of the dynamic model, a mathematical model represented by sparse parameters is constructed by a greedy algorithm or an interior point algorithm and is used as a model error compensation item of the dynamic model;
and establishing an error compensation item of the dynamic model according to the perturbation force error compensation item and the model error compensation item of the dynamic model so as to correct OC residual errors corresponding to the error source of the dynamic model.
5. The method according to claim 3, wherein the establishing of the error compensation term of the observation model comprises:
estimating the uncertain observation system error by adopting a nonparametric statistical method to obtain a nonparametric represented uncertain model error compensation function;
and establishing an error compensation item of the observation model according to the uncertainty model error compensation function and the certainty system error compensation model of the observation model so as to correct OC residual errors corresponding to the error source of the observation model.
6. The multi-satellite combined orbit determination method based on model error compensation according to claim 3, wherein the decomposing of the OC residual error through the mixed mode decomposition method and the modification of the OC residual error through the control of the total error upper limit comprise:
the OC residual error is converted on a frequency domain, the part corresponding to an error source in the OC residual error is decomposed through an empirical mode decomposition technology according to prior information, and the OC residual error is corrected through an error compensation item corresponding to the error source;
and correcting the OC residual error by adjusting the empirical force and controlling the upper limit of the total error for the part of the OC residual error, which cannot determine the corresponding error source.
7. The model error compensation-based multi-satellite combined orbit determination method according to claim 1, wherein the determining the optimal orbit parameters of the space-ground based multi-satellite combined orbit determination equation of the target satellite by using the nonlinear multi-model optimal weighted estimation method comprises:
the curvature of the space-ground multi-satellite combined orbit determination equation is used as a quantitative standard to measure the nonlinearity degree and the complexity degree of each model of the space-ground multi-satellite combined orbit determination equation, and the space-ground multi-satellite combined orbit determination equation is subjected to weighting processing according to the curvature of the space-ground multi-satellite combined orbit determination equation;
carrying out interval constraint on the parameters to be estimated in the space-ground multi-satellite combined orbit determination equation by a parameter constraint method;
optimally estimating parameters in the space-ground multi-satellite combined orbit determination equation by adopting a biased estimation method;
and further optimizing and correcting parameters in the multi-satellite combined orbit determination equation of the space foundation by an iterative method.
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