Ura calculation method and device for low-orbit navigation satellite, computer storage medium and computer program product

Abstract

Provided are a URA calculation method and device for a low-orbit navigation satellite, a computer storage medium and a computer program product. The URA calculation method comprises: in precise orbit determination and clock error calculation for a low-orbit satellite, a covariance submatrix of a predicted orbit and clock error parameter in a predicted arc segment is given by using a transfer matrix, denoted as a first covariance submatrix; a projection matrix from a geocentric geodetic coordinate system to a satellite orbit coordinate system is calculated; the first covariance submatrix is converted into a second covariance submatrix of the satellite orbit coordinate system according to the projection matrix; the satellite orbit prediction accuracy and the clock error prediction accuracy are calculated according to the second covariance submatrix; and the URA is calculated according to the satellite orbit prediction accuracy and the clock error prediction accuracy. The present disclosure proposes a URA calculation method for a low-orbit satellite based on a covariance matrix, which guarantees the real-time performance and reliability of integrity monitoring.

Description

TECHNICAL FIELD

[0001] The present disclosure relates to the field of satellite communication, and in particular to a URA calculation method, device, computer storage medium and computer program product of a low-orbit navigation satellite. BACKGROUND

[0002] With the application range of satellite navigation system being wider and wider, the integrity requirement of navigation user to the satellite navigation system is also higher and higher, and the system needs to provide the precision level of current service, and when the navigation system is abnormal, the alarm information can be quickly provided to the user to ensure the use safety of the navigation user. In recent years, more and more countries and regions have successively proposed low-orbit navigation enhancement constellation plans. The low-orbit constellation can be used as a space-based monitoring station to realize the enhancement of the global satellite navigation system (GNSS), and can also be used as a navigation satellite to broadcast ranging information to users to independently provide positioning, navigation and timing (PNT) services. Therefore, in order to protect the accuracy, continuity and availability of the low-orbit constellation service, and ensure that the user is provided with reliable navigation information in the case of low probability error, the user ranging accuracy (URA) is an important index for measuring the precision of satellite ephemeris and clock error in integrity monitoring.

[0003] In view of the fact that there is still a lack of a clear calculation scheme of the URA of the low-orbit satellite space signal precision under the background that the low-orbit satellite provides PNT services as a navigation satellite, the present disclosure proposes a low-orbit navigation satellite URA calculation method based on artificial intelligence correction. SUMMARY

[0004] It would be advantageous to provide a mechanism that mitigates, alleviates or eliminates at least one of the above problems.

[0005] In a first aspect, a URA calculation method of a low-orbit navigation satellite is provided, comprising: when performing precise orbit determination and clock error solution on the low-orbit satellite, using a transfer matrix to give a covariance submatrix of the predicted orbit and clock error parameters in a predicted arc segment, denoted as a first covariance submatrix; calculating a projection matrix from the Earth-Centered Earth-Fixed coordinate system to the satellite orbit coordinate system; converting the first covariance submatrix into a second covariance submatrix of the satellite orbit coordinate system according to the projection matrix; calculating the satellite orbit prediction accuracy and the clock error prediction accuracy according to the second covariance submatrix, and calculating the URA according to the satellite orbit prediction accuracy and the clock error prediction accuracy.

[0006] In a second aspect, a URA computing device for low-Earth orbit navigation satellites is provided, the URA computing device including one or more processors configured to perform the methods described above.

[0007] In a third aspect, a low-Earth orbit (LEO) navigation satellite is provided. It includes: one or more processors; and one or more memories coupled to the one or more processors and storing instructions thereon, which, when executed individually or jointly by the one or more processors, cause the LEO navigation satellite to perform the methods described above.

[0008] In a fourth aspect, a computer storage medium is provided that stores instructions thereon, which, when executed individually or jointly by at least one processor of a computing device, cause the computing device to perform the method described above.

[0009] In a fifth aspect, a computer program product is provided. The computer program product includes instructions that, when executed individually or jointly by at least one processor of a computing device, cause the computing device to perform the method described above.

[0010] It should be understood that the summary section is not intended to identify key or essential features of the embodiments of this disclosure, nor is it intended to limit the scope of this disclosure. Other features of this disclosure will become readily apparent from the following description. Attached Figure Description

[0011] The above and other objects, features, and advantages of this disclosure will become more apparent from the more detailed description of some embodiments thereof in the accompanying drawings, in which:

[0012] Figure 1 A schematic diagram of a navigation system according to some embodiments of the present disclosure is shown;

[0013] Figure 2 A flowchart is shown showing a method for calculating the URA of a low-Earth orbit satellite according to some embodiments of the present disclosure;

[0014] Figure 3 A flowchart illustrating the calculation of satellite orbit prediction accuracy based on a second covariance submatrix according to some embodiments of the present disclosure is shown;

[0015] Figure 4 A flowchart illustrating the calculation of clock error prediction accuracy based on a second covariance submatrix according to some embodiments of the present disclosure is shown;

[0016] Figure 5 It shows Figure 2 A flowchart of the URA calculation method for low-Earth orbit satellites in the optimized embodiment; and

[0017] Figure 6 is a simplified block diagram of a URA computation device for a low earth orbit navigation satellite suitable for implementing embodiments of the present disclosure. DETAILED DESCRIPTION

[0018] The principles of the present disclosure will now be described with reference to some embodiments. It should be understood that the description of these embodiments is merely made for the purposes of illustration and helping the understanding and implementation of the present disclosure, and does not suggest any limitation on the scope of the present disclosure. The disclosure described herein can be implemented in a manner different from what is described below.

[0019] In the following description and claims, unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this disclosure belongs.

[0020] Reference throughout this disclosure to "one embodiment", "an embodiment", "exemplary embodiment", etc., means that a particular feature, structure, or characteristic described in connection with the embodiment can be included in at least one implementation of the disclosure. The appearances of such phrases in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics can be combined in any suitable manner on an embodiment by embodiment basis.

[0021] It should be understood that although the terms "first" and "second" etc. can be used herein to describe various elements, these elements should not be limited by these terms. These terms are only used to distinguish one element from another. For example, a first element could be termed a second element, and, similarly, a second element could be termed a first element without departing from the scope of the example embodiments. As used herein, the term "and / or" includes any and all combinations of one or more of the associated listed terms.

[0022] The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting of example embodiments. As used herein, the singular forms "a", "an" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. As used herein, the term "and / or" includes any and all combinations of one or more of the associated listed terms. The use of the term "at least one" will be understood to include one or more instances of the elements that it introduces, as such language is used to

[0023] Figure 1A schematic diagram of a navigation system according to some embodiments of the present disclosure is shown. Navigation system 100 includes a Global Navigation Satellite System (GNSS), a Low Earth Orbit (LEO) navigation constellation 2, and ground users 3. The LEO navigation constellation 2 includes multiple LEO satellites 21. Compared to medium / high orbit satellites, LEO satellites have advantages such as rapid changes in geometric observation configuration and high signal strength, making them highly promising for navigation and positioning. Therefore, the concept of establishing a LEO navigation constellation is proposed, utilizing LEO satellites to broadcast navigation signals to enhance GNSS. To achieve the goal of LEO navigation enhancement, LEO satellites need to broadcast LEO satellite ephemeris and clock errors to ground users in real time, providing accurate LEO satellite spatiotemporal information. User Range Accuracy (URA) is a key indicator in satellite navigation systems used to quantify the impact of satellite ephemeris and clock error errors on user ranging. URA values ​​are typically given in the form of standard deviation or confidence intervals.

[0024] Traditional URA calculation methods include the forecast variance transformation method and the prior accuracy forecast method. The forecast variance transformation method works by obtaining the covariance matrix information of the predicted orbit and clock error during orbit and clock error processing. According to error adjustment theory, the covariance matrix can reflect the internal consistency accuracy of the orbit and clock error processing, and the spatial signal accuracy of the broadcast ephemeris is obtained using the covariance matrix information. The accuracy of the forecast data in the forecast variance transformation method directly affects the result, as forecast errors are propagated into the URA calculation. Secondly, the forecast variance transformation method assumes that the error follows a Gaussian distribution, but the actual error may be more complex, affecting the calculation accuracy. The prior accuracy method, on the other hand, uses observational data for precise orbit determination and clock error processing to obtain highly accurate orbit and clock error results. The predicted orbit and clock error results in the broadcast ephemeris are calculated using models and have lower accuracy. The difference between the two methods reflects the orbit prediction error and clock error prediction error in the broadcast ephemeris, and can be used to obtain the spatial signal accuracy of the broadcast ephemeris. However, the prior accuracy prediction method is difficult to handle sudden error changes, such as sudden disturbances in the ionosphere, and the calculation is complex, requiring complex models and a large amount of computing resources, resulting in poor real-time performance.

[0025] Integrity monitoring is a crucial leap for navigation systems from "usable" to "reliable." Its core objective is to detect and alert users to system or signal anomalies in real time, preventing safety risks caused by erroneous navigation information. URA (Uniform Ranging Analytical Range) is an indicator of user ranging accuracy, and integrity monitoring may need to utilize these accuracy indicators to determine the presence of anomalies.

[0026] The embodiments of this disclosure propose a method for calculating the URA of low-Earth orbit satellites based on the covariance matrix, ensuring the real-time performance and reliability of integrity monitoring. Secondly, the URA calculated based on the covariance matrix is ​​adjusted using artificial intelligence prediction to address the defect that the estimated URA value is too small due to the inability of covariance propagation to reflect the systematic errors of orbit and clock bias.

[0027] Figure 2 A flowchart illustrating a method for calculating the URA of a low-Earth orbit satellite according to some embodiments of this disclosure is shown. Figure 2 As shown, the URA calculation method 200 for low-Earth orbit satellites includes:

[0028] Step S1: When performing precise orbit determination and clock error calculation for low-Earth orbit satellites, the covariance submatrix of the predicted orbit and clock error parameters within the predicted arc segment is given by the transfer matrix, denoted as the first covariance submatrix.

[0029] Precise orbit determination refers to accurately determining a satellite's orbital parameters, such as position and velocity. Clock error calculation, on the other hand, handles the time difference between the satellite's clock and the clocks of ground stations or other satellites. The transition matrix is ​​typically used for state transitions in orbit prediction, that is, propagating the current state parameters (such as orbital parameters and clock errors) to a future point in time through a dynamic model. The covariance matrix reflects the uncertainty of the estimated parameters; therefore, during the prediction process, the covariance matrix also needs to be propagated according to the dynamic model to determine the accuracy of the predicted orbit and clock errors.

[0030] The covariance matrix P(t0) is known at the initial time and includes the covariances of the orbital parameters and clock error parameters, as well as the cross covariances between them. During the prediction process, the predicted value of the covariance matrix at time t is P(t) = Φ(t,t0)*P(t0)*Φ(t,t0)^T. Here, the transition matrix Φ is jointly determined by the dynamical model and the clock error model. Then, the corresponding submatrices of the orbital and clock error parameters are extracted from P(t) as their covariance submatrices.

[0031] Optionally, the first covariance submatrix D e,i This can be expressed by the following formula:

[0032]

[0033] Wherein, the first covariance submatrix D e,i The elements are combinations of x, y, z direction errors and star clock errors, respectively. For example, σ 2 x,i Let σ be the variance of the error in the x-direction. 2 y,i Let σ be the variance of the error in the y-direction. 2 z,iLet σ be the variance of the error in the z-direction. 2 clk,i Let σ be the variance of the star clock error. xy,i Let σ be the covariance of the errors in the x and y directions. xz,i Let σ be the covariance of the error in the xz direction. yz,i Let σ be the covariance of the error in the y-z direction. xclk,i Let σ be the covariance between the x-direction and the star clock error. yclk,i Let σ be the covariance between the y-direction and the star clock error. zclk,i Let be the covariance between the z-direction and the star clock error.

[0034] Step S2: Calculate the projection matrix from the geocentric coordinate system to the satellite orbit coordinate system.

[0035] The Earth-Centered, Earth-Fixed (ECEF) coordinate system has the Earth's center of mass as its origin, with the x-axis pointing to the intersection of the Prime Meridian and the equator, the z-axis pointing to the North Pole, and the y-axis forming a right-handed coordinate system with the x and z axes. The Radial, Transverse, Normal (RTN) coordinate system, on the other hand, is centered on the satellite, with one axis pointing towards the Earth's center (radial), one axis along the direction of orbital motion (tangential), and another axis perpendicular to the orbital plane (normal).

[0036] Calculating the projection matrix from the geocentric Earth-fixed coordinate system to the satellite orbital coordinate system includes:

[0037] (1) Determine the satellite's position r and velocity v in ECEF.

[0038] (2) Calculate the three axes of the orbital coordinate system

[0039] Radial (R): The direction from the Earth's center to the satellite, with a unit vector of:

[0040]

[0041] Normal (N): The direction of the normal to the orbital plane, determined by the cross product of position and velocity, with the unit vector as follows:

[0042]

[0043] Tangential (T): In the orbital plane, perpendicular to the radial direction and forming a right-handed system with the normal, the unit vector is:

[0044] e t =e n ×e r

[0045] (3) Constructing the projection matrix

[0046]

[0047] Step S3: Convert the first covariance submatrix into the second covariance submatrix of the satellite orbit coordinate system based on the projection matrix.

[0048] Alternatively, the second covariance submatrix D' can be calculated using the following formula. e,i :

[0049]

[0050] Among them, R 3×3 It is a projection matrix with dimensions of 3x3.

[0051] The second covariance submatrix D' obtained after calculation e,i for:

[0052]

[0053] Wherein, the second covariance submatrix D' e,i The elements are combinations of radial error, normal error, tangential error, and clock error. For example, σ 2 R,i Let σ be the variance of the radial error. 2 T,i Let σ be the variance of the tangential error. 2 N,i Let σ be the variance of the normal error. 2 clk,i Let σ be the variance of clock bias. RT,i Let σ be the covariance in the RT direction. TN,i Let σ be the covariance in the TN direction. RN,i Let σ be the covariance in the RN direction. Nclk,i Let σ be the covariance between the N direction and the clock bias. Rclk,i Let σ be the covariance between the R direction and the clock bias. Tclk,i Let T be the covariance between the direction of clock and the clock bias.

[0054] Step S4: Calculate the satellite orbit prediction accuracy and clock error prediction accuracy based on the second covariance submatrix, and calculate the URA based on the satellite orbit prediction accuracy and clock error prediction accuracy.

[0055] Figure 3 A flowchart illustrating the calculation of satellite orbit prediction accuracy based on a second covariance submatrix according to some embodiments of this disclosure is shown. Figure 3 As shown, the calculation of satellite orbit prediction accuracy based on the second covariance submatrix includes:

[0056] Step S411: For each epoch, extract the variance of the tangential error, the variance of the normal error, and the covariance of the tangential and normal directions within the satellite orbit tangential plane from its own second covariance submatrix.

[0057] Step S412: Construct an error ellipse based on the variance of the tangential error, the variance of the normal error, and the covariance of the tangential and normal directions. Use the semi-major axis of the error ellipse to represent the satellite orbit prediction accuracy at each epoch.

[0058] Satellite orbit prediction accuracy is represented by a combination of tangential and normal direction errors. Geometrically, the tangential and normal covariance matrices within the tangential plane of a satellite's orbit at a given epoch define a set of error ellipses, corresponding to different error magnitudes. The semi-major axis of these error ellipses represents the satellite orbit prediction accuracy (URA) at that epoch. oe,i .

[0059] Alternatively, the satellite orbit prediction accuracy for each epoch can be calculated using the following formula:

[0060]

[0061] URA oe,i Let be the satellite orbit prediction accuracy for the i-th epoch. The variance of the tangential error. Let σ be the variance of the normal error. TN,i Let be the covariance of the tangential and normal directions.

[0062] Step S413: Use the maximum value among the satellite orbit prediction accuracies of multiple epochs within the prediction arc as the satellite orbit prediction accuracy.

[0063] Alternatively, the accuracy of satellite orbit prediction can be calculated using the following formula:

[0064] URA oe =max(URA oe,i ) i＝1...n

[0065] Where n is the number of epochs within the forecast arc.

[0066] Figure 4 A flowchart illustrating the calculation of clock error prediction accuracy based on a second covariance submatrix according to some embodiments of the present disclosure is shown. For example... Figure 4 As shown, the calculation of clock error prediction accuracy based on the second covariance submatrix includes:

[0067] Step S421: For each epoch, extract the variance of the radial error, the variance of the clock error, and the covariance of the radial and clock errors in the satellite orbit tangent plane from its own second covariance submatrix.

[0068] Step S422: Estimate the epoch clock error prediction accuracy based on the variance of radial error, the variance of clock error, and the covariance of radial and clock errors.

[0069] Clock error prediction accuracy is a combination of satellite orbital radial distance and satellite clock error. The clock error prediction accuracy for each epoch is:

[0070]

[0071] URA oc,i Let be the clock error prediction accuracy for the i-th epoch. The variance of the radial error. Let σ be the variance of clock bias. Rclk,i Let be the covariance between radial and clock bias.

[0072] Step S423: Model the clock error prediction accuracy for all epochs to obtain a prediction model for the clock error prediction accuracy.

[0073] Optionally, the modeling process for the clock deviation prediction accuracy of all epochs includes: fitting the clock deviation prediction accuracy of all epochs with a first-order fitting function to obtain the fitting parameters of the first-order fitting function, including the clock deviation prediction accuracy and the clock deviation rate of change accuracy; the first-order fitting function is the prediction model for the clock deviation prediction accuracy.

[0074] Optionally, the first-order fitting function is:

[0075] URA oc,i =URA ocb +URA oc1 (t i -t o )

[0076] URA oc,i For the clock error prediction accuracy of the i-th epoch, URA ocb To improve the accuracy of clock offset prediction, URA oc1 For the accuracy of the clock deflection rate, t i At each forecast covariance sampling time, t o This is to predict the initial time of age.

[0077] In other embodiments, the fitting parameters also include clock drift accuracy. In other words, refining the clock error prediction accuracy into clock offset prediction accuracy, clock offset rate of change accuracy, and clock drift accuracy results in more accurate clock error prediction.

[0078] In other embodiments, other polynomials may be used to fit the clock error prediction accuracy for all epochs, and this application does not limit the number of terms in the fitting function.

[0079] Step S424: Input the future sampling time into the prediction model to obtain the clock error prediction accuracy.

[0080] After obtaining the satellite orbit prediction accuracy URA oe Clock difference prediction accuracy URAoc URA can then be calculated using the following formula:

[0081]

[0082] In other embodiments, calculating the clock error prediction accuracy for an epoch includes: calculating the clock error prediction accuracy for an epoch based on the satellite nadir angle, radial covariance, clock error covariance, and the covariance between radial and clock errors. Specifically, the clock error prediction accuracy for an epoch is calculated using the following formula:

[0083]

[0084] URA oc,i Let be the clock error prediction accuracy for the i-th epoch, and let ele be the satellite nadir angle. The variance of the radial error. Let σ be the variance of clock bias. Rclk,i Let be the covariance between radial and clock bias.

[0085] For ground stations, the observable nadir angle range of GNSS satellites is 0-14 degrees; for low-orbit satellites, the observable signal range of GNSS satellites is 14-17 degrees. Therefore, ele∈(0,17°).

[0086] The URA calculation method for low-Earth orbit satellites disclosed herein calculates the satellite orbit prediction accuracy and clock error prediction accuracy based on the second covariance submatrix, and calculates the URA based on the satellite orbit prediction accuracy and clock error prediction accuracy, thus ensuring the real-time performance and reliability of integrity monitoring.

[0087] Since covariance propagation cannot reflect the systematic errors of orbit and clock bias, it can lead to an underestimation of the estimated URA value. This disclosure adjusts the URA calculated based on the covariance matrix using an artificial intelligence forecasting method, so that the final predicted URA value is closer to the actual value.

[0088] Figure 5 It shows Figure 2 A flowchart illustrating the URA calculation method for low-Earth orbit satellites in the optimized embodiment. (See attached flowchart.) Figure 5 As shown, the URA calculation method 500 for low-Earth orbit satellites also includes:

[0089] Step S5: Obtain historical URA data and train a URA prediction model using the historical URA data.

[0090] Historical URA data includes, but is not limited to, past broadcast ephemeris and clock bias of the satellite.

[0091] Training a URA prediction model using historical URA data involves dividing the historical URA data into training and testing sets. The training set is input into an artificial intelligence (AI) model, which analyzes the changing characteristics of broadcast ephemeris orbits and clock errors at different ages. The AI ​​model then outputs URA prediction values. AI models include, but are not limited to, Long Short-Term Memory (LSTM) recurrent neural networks and Support Vector Machines (SVMs).

[0092] The test set is input into the trained artificial intelligence model (i.e., the URA prediction model), the URA prediction model outputs the URA prediction value, the loss function of the URA prediction model is calculated based on the URA prediction value and the URA true value of the test set, and the loss function is minimized to optimize the URA prediction model.

[0093] Optionally, the loss function is:

[0094]

[0095] Where J(θ) is the loss function, θ is the weight function of the neural network model, m is the number of samples predicted during training, and y i For URA predicted values, This is the actual URA value.

[0096] Step S6: Calculate the calibration coefficients based on the URA prediction values ​​output by the URA prediction model and the URA values ​​that have already been broadcast prior to the test.

[0097] Alternatively, the calibration coefficient can be calculated using the following formula:

[0098]

[0099] Where, k i URA is the calibration factor. 人工智能 For URA predicted values, URA 播发 This is the URA that was already broadcast before the test.

[0100] Step S7: Multiply the calibration coefficient by the calculated URA to obtain the final predicted URA.

[0101] The URA calculation method for low-Earth orbit satellites disclosed herein adjusts the URA calculated based on the covariance matrix using artificial intelligence prediction, thereby addressing the defect that the estimated URA value is too small due to the inability of covariance propagation to reflect the systematic errors of orbit and clock bias.

[0102] Embodiments of this disclosure also propose a URA computing device for low-Earth orbit navigation satellites.

[0103] Figure 6 This is a simplified block diagram of a URA computing device for low-Earth orbit navigation satellites suitable for implementing embodiments of the present disclosure. The URA computing device 600 includes one or more processors 610, one or more memories 620 coupled to the processors 610, and one or more communication modules 640 coupled to the processors 610.

[0104] Communication module 640 is used for bidirectional communication. Communication module 640 has at least one antenna to facilitate communication. The communication interface can represent any interface necessary for communication with other network elements.

[0105] Processor 610 can be of any type suitable for a local technology network, and as a non-limiting example, can include one or more of the following: general-purpose computer, special-purpose computer, microprocessor, digital signal processor (DSP), and processor based on a multi-core processor architecture. URA computing device 600 can have multiple processors, such as application-specific integrated circuit chips, which are timely driven to a clock that synchronizes with the main processor.

[0106] Memory 620 may include one or more non-volatile memories and one or more volatile memories. Examples of non-volatile memories include, but are not limited to, read-only memory (ROM) 624, electrically programmable read-only memory (EPROM), flash memory, hard disk, optical disc (CD), digital video disc (DVD), and other magnetic and / or optical storage. Examples of volatile memories include, but are not limited to, random access memory (RAM) 622 and other volatile memories that do not persist during power-off periods.

[0107] Computer program 630 includes computer-executable instructions that are executed by a associated processor 610. Program 630 may be stored in ROM 624. Processor 610 may perform any appropriate actions and processes by loading program 630 into RAM 622.

[0108] The embodiments of this disclosure can be implemented via program 630, enabling the URA computing device 600 to execute reference... Figure 2 and Figure 6 Any process disclosed herein. Embodiments of this disclosure may also be implemented in hardware or by a combination of software and hardware.

[0109] In some embodiments, program 630 may be tangibly contained in a computer-readable medium, which may be contained in a URA computing device 600 (e.g., memory 620) or other storage device accessible to the URA computing device 600. The URA computing device 600 may load program 630 from the computer-readable medium into RAM 622 for execution. The computer-readable medium may include any type of tangible non-volatile memory, such as ROM, EPROM, flash memory, hard disk, CD, DVD, etc. Program 630 is stored on the computer-readable medium.

[0110] Generally, the various embodiments of this disclosure can be implemented in hardware or dedicated circuitry, software, logic, or any combination thereof. Some aspects may be implemented in hardware, while others may be implemented in firmware or software, which may be executed by a controller, microprocessor, or other computing device. Although various aspects of the embodiments of this disclosure are shown and described as block diagrams, flowcharts, or other graphical representations, it should be understood that, as non-limiting examples, the blocks, devices, systems, techniques, or methods described herein may be implemented in hardware, software, firmware, dedicated circuitry or logic, general-purpose hardware or controllers or other computing devices, or some combination thereof.

[0111] This disclosure also provides at least one computer program product tangibly stored on a non-transitory computer-readable storage medium. The computer program product includes computer-executable instructions, such as instructions included in a program module, which execute in a device on a target real or virtual processor to perform the aforementioned references. Figure 2 The method described in 200 and / or as referred above Figure 5 The method described in 500. Typically, a program module includes routines, programs, libraries, objects, classes, components, data structures, etc., that perform specific tasks or implement specific abstract data types. In various embodiments, the functionality of a program module can be combined or separated among program modules as needed. The machine-executable instructions for a program module can be executed locally or in a distributed device. In a distributed device, the program module can reside in both local and remote storage media.

[0112] Program code used to perform the methods of this disclosure may be written in any combination of one or more programming languages. This program code may be provided to a processor or controller of a general-purpose computer, a special-purpose computer, or other programmable data processing device, such that when executed by the processor or controller, the functions / operations specified in the flowcharts and / or block diagrams are implemented. The program code may be executed entirely on a machine, partially on a machine, partially on a remote machine, partially on a remote machine, or entirely on a remote machine or server as a standalone software package.

[0113] In the context of this disclosure, computer program code or related data may be carried by any suitable carrier to enable a device, apparatus, or processor to perform the various processes and operations described above. Examples of carriers include signals, computer-readable media, etc.

[0114] Computer-readable media can be computer-readable signal media or computer-readable storage media. Computer-readable media can include, but is not limited to, electronic, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or apparatuses, or any suitable combination thereof. More specific examples of computer-readable storage media include electrical connections having one or more wires, portable computer floppy disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable optical disc read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof.

[0115] Furthermore, although the operations are described in a specific order, this should not be construed as requiring that these operations be performed in the specific order or sequence shown, or that all of the operations shown be performed to obtain the desired result. In some cases, multitasking and parallel processing may be advantageous. Similarly, while several specific implementation details are included in the foregoing discussion, these details should not be construed as limiting the scope of this disclosure, but rather as descriptions of features specific to particular embodiments. Certain features described in the context of individual embodiments may also be implemented in combination in a single embodiment. Conversely, various features described in the context of a single embodiment may also be implemented individually or in any suitable sub-combination in multiple embodiments.

[0116] Although this disclosure has been described in language specific to structural features and / or methodological behavior, it should be understood that this disclosure as defined in the appended claims is not necessarily limited to the specific features or behaviors described above. Rather, the specific features and actions described above are disclosed as exemplary forms for implementing the claims.

[0117] It should be fully understood that the use of personally identifiable information should comply with privacy policies and practices generally considered to meet or exceed industry or governmental requirements for protecting user privacy. In particular, personally identifiable information data should be managed and processed to minimize the risk of unintentional or unauthorized access or use, and the nature of authorized use should be clearly indicated to the user.

Claims

1. A method for calculating the URA of a low-Earth orbit navigation satellite, characterized in that, include: When performing precise orbit determination and clock error calculation for low-Earth orbit satellites, the covariance submatrix of the predicted orbit and clock error parameters within the predicted arc segment is given by the transfer matrix, denoted as the first covariance submatrix; Calculate the projection matrix from the geocentric Earth-fixed coordinate system to the satellite orbital coordinate system; The first covariance submatrix is ​​converted into a second covariance submatrix of the satellite orbit coordinate system based on the projection matrix. Calculate the satellite orbit prediction accuracy and clock error prediction accuracy based on the second covariance submatrix, and calculate the URA based on the satellite orbit prediction accuracy and the clock error prediction accuracy; The calculation of the satellite orbit prediction accuracy based on the second covariance submatrix includes: for each epoch, extracting the variance of the tangential error, the variance of the normal error, and the covariance of the tangential and normal directions within the satellite orbit tangential plane from its own second covariance submatrix; constructing an error ellipse based on the variance of the tangential error, the variance of the normal error, and the covariance of the tangential and normal directions, using the major semi-axis of the error ellipse to represent the satellite orbit prediction accuracy of the epoch; and using the maximum value among the satellite orbit prediction accuracies of multiple epochs within the prediction arc as the satellite orbit prediction accuracy. The calculation of the clock error prediction accuracy based on the second covariance submatrix includes: for each epoch, extracting the variance of the radial error, the variance of the clock error, and the covariance of the radial and clock errors within the satellite orbital tangent plane from its own second covariance submatrix; estimating the clock error prediction accuracy of the epoch based on the variance of the radial error, the variance of the clock error, and the covariance of the radial and clock errors; modeling the clock error prediction accuracy of all epochs to obtain a prediction model for the clock error prediction accuracy; and inputting the future sampling time into the prediction model to obtain the clock error prediction accuracy.

2. The URA calculation method as described in claim 1, characterized in that, The satellite orbit prediction accuracy for the given epoch is calculated using the following formula: in, Let be the satellite orbit prediction accuracy for the i-th epoch. The variance of the tangential error is... The variance of the normal error is... Let be the covariance between the tangential and normal directions.

3. The URA calculation method as described in claim 1, characterized in that, The accuracy of epochal clock error predictions can be estimated using the following formula: in, Let be the clock error prediction accuracy for the i-th epoch. Let V be the variance of the radial error. Let Variance be the clock bias. Let be the covariance between the radial direction and the clock difference.

4. The URA calculation method as described in claim 1, characterized in that, Also includes: The epoch clock error prediction accuracy is calculated based on the satellite nadir angle, the variance of the radial error, the variance of the clock error, and the covariance of the radial and clock errors. The epoch clock error prediction accuracy is calculated using the following formula: in, Let be the clock error prediction accuracy for the i-th epoch, representing . For the satellite nadir angle, Let V be the variance of the radial error. Let Variance be the clock bias. Let be the covariance between the radial direction and the clock difference.

5. The URA calculation method as described in claim 4, characterized in that, The range of the satellite nadir angle is: .

6. The URA calculation method as described in claim 1, characterized in that, Modeling the accuracy of clock error predictions for all epochs includes: The clock deviation prediction accuracy for all epochs is fitted using a first-order fitting function to obtain the fitting parameters of the first-order fitting function, which include the clock deviation prediction accuracy and the clock deviation rate of change accuracy. The first-order fitting function is the prediction model for the clock error prediction accuracy.

7. The URA calculation method as described in claim 6, characterized in that, The first-order fitting function is: in, Let be the clock error prediction accuracy for the i-th epoch. The accuracy of the clock offset prediction is given. The accuracy of the clock deflection rate is given. Sampling times for each forecast covariance This is to predict the initial time of age.

8. The URA calculation method as described in claim 1, characterized in that, Also includes: Retrieve historical URA data; A URA prediction model was trained using the historical URA data. The calibration coefficients are calculated based on the URA prediction values ​​output by the URA prediction model and the URA values ​​that have already been broadcast prior to the test. The final predicted URA is obtained by multiplying the calibration coefficient by the calculated URA.

9. The URA calculation method as described in claim 8, characterized in that, The calibration coefficient is calculated using the following formula: in, The calibration coefficient is... The predicted value of URA, This is the URA that was already broadcast before the test.

10. The URA calculation method as described in claim 8, characterized in that, Also includes: The loss function of the URA prediction model is calculated based on the URA predicted values ​​and historical URA data. Minimize the loss function to optimize the URA prediction model.

11. A URA computing device for low Earth orbit navigation satellites, the URA computing device comprising one or more processors configured to perform the method of any one of claims 1-10.

12. A low-Earth orbit navigation satellite, comprising: One or more processors; as well as One or more memories coupled to and storing instructions thereon, which, when executed individually or jointly by the one or more processors, cause the low-Earth orbit navigation satellite to perform the method according to any one of claims 1-10.

13. A computer storage medium storing instructions thereon, characterized in that, When the instructions are executed individually or jointly by at least one processor of the computing device, the computing device performs the method according to any one of claims 1-10.

14. A computer program product comprising instructions, characterized in that, When the instructions are executed individually or jointly by at least one processor of the computing device, the computing device performs the method according to any one of claims 1-10.

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