Low-orbit satellite orbit error correction method and system based on GNSS positioning information

Abstract

The present invention provides a method and system for correcting low-orbit satellite orbit errors based on GNSS positioning information. The method includes: establishing a motion equation for a low-orbit satellite; obtaining a TLE file for the low-orbit satellite; using a GNSS receiver to capture satellite navigation signals to obtain a local position vector and a local velocity vector; using the low-orbit satellite receiver to measure a Doppler shift measurement between the low-orbit satellite and the low-orbit satellite receiver; establishing a state equation based on the motion equation, using the position vector and velocity vector of the low-orbit satellite as state quantities; establishing a measurement equation based on the TLE file, the local position vector, the local velocity vector, and the Doppler shift measurement; and correcting the orbit error of the low-orbit satellite using a Kalman filter based on the state equation and the measurement equation. The technical solution of the present invention is applied to solve the technical problem in the prior art of low positioning accuracy caused by large errors in low-orbit satellite orbit information calculated using TLE files.

Description

Technical Field

[0001] The present invention relates to the field of opportunity signal navigation technology, and in particular to a low-orbit satellite orbit error correction method and system based on GNSS positioning information. Background Art

[0002] Satellite navigation is currently used in a wide range of fields, affecting every aspect of people's daily lives and production. It is also a crucial component of various precision-guided weapons. Traditional navigation satellites are located in medium and high orbits, and their signals are already very weak by the time they reach the ground. Furthermore, the signal format is public, making them susceptible to interference and spoofing. In comparison, low-orbit satellites, due to their lower orbital altitude, have stronger signals reaching the ground, and the satellites' geometric positions change rapidly. Consequently, countries are currently competing to launch low-orbit satellites.

[0003] Positioning using low-orbit satellites is currently widely used. For example, the Satellite Timing and Positioning System (STL) provided by Iridium Communications is used as a backup to the Global Positioning System (GPS). However, low-orbit satellites are primarily used for communication and do not broadcast navigation messages in real time like the Global Navigation Satellite System (GNSS). Moreover, the content and format of communications with non-cooperative satellites are encrypted. Therefore, obtaining low-orbit satellite orbit information mostly relies on the Two-Line Element File (TLE file) published by the North American Aerospace Command. Although TLE files are updated daily, the satellite orbits calculated based on these files can have very large errors, even at the kilometer level, significantly affecting positioning results. Reducing the orbital errors introduced by TLE files can help improve positioning accuracy for low-orbit satellites. Summary of the Invention

[0004] In order to solve one of the problems existing in the prior art, the present invention provides a low-orbit satellite orbit error correction method and system based on GNSS positioning information.

[0005] According to one aspect of the present invention, a method for correcting low-orbit satellite orbit errors based on GNSS positioning information is provided. The orbit error correction method includes:

[0006] Establish the equations of motion for low-orbit satellites;

[0007] Get TLE files of low-orbit satellites;

[0008] Using a GNSS receiver to capture satellite navigation signals to obtain a local position vector and a local velocity vector;

[0009] A Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver is obtained by measuring with a low-orbit satellite receiver;

[0010] According to the equation of motion, a state equation is established with the position vector and velocity vector of the low-orbit satellite as state quantities;

[0011] Establish measurement equations based on TLE files, local position vectors, local velocity vectors, and Doppler shift measurements;

[0012] The orbit error of low-orbit satellite is corrected through Kalman filtering based on the state equation and measurement equation.

[0013] Furthermore, the measurement equation is established based on the TLE file, the local position vector, the local velocity vector, and the Doppler shift measurement value, including:

[0014] The Doppler shift prediction value between the LEO satellite and the LEO satellite receiver is obtained based on the TLE file, the local position vector and the local velocity vector;

[0015] A measurement equation is established based on the Doppler frequency shift measurement value and the Doppler frequency shift prediction value.

[0016] Furthermore, the Doppler shift prediction value between the LEO satellite and the LEO satellite receiver is obtained based on the TLE file, the local position vector, and the local velocity vector, including:

[0017] The predicted position vector and predicted velocity vector of the low-orbit satellite are obtained according to the TLE file prediction;

[0018] The relative position vector from the low-orbit satellite to the low-orbit satellite receiver is calculated based on the predicted position vector and the local position vector;

[0019] The relative velocity vector from the low-orbit satellite to the low-orbit satellite receiver is calculated based on the predicted velocity vector and the local velocity vector;

[0020] The Doppler shift prediction value is calculated based on the relative position vector and the relative velocity vector.

[0021] Furthermore, establishing a measurement equation based on the Doppler frequency shift measurement value and the Doppler frequency shift prediction value includes:

[0022] Calculating a Doppler frequency shift difference between a predicted Doppler frequency shift value and a measured Doppler frequency shift value;

[0023] A measurement equation is established using the Doppler frequency shift difference as the measurement quantity.

[0024] Furthermore, the Doppler shift prediction value is calculated based on the relative position vector and the relative velocity vector using the following formula:

[0025]

[0026] In the above formula, f r(k) represents the Doppler frequency shift prediction value of the k-th sampling point, f0(k) represents the transmission frequency of the low-orbit satellite at the k-th sampling point, c represents the propagation speed of electromagnetic waves in space, n(k) represents the measurement error of the transmission frequency of the low-orbit satellite at the k-th sampling point, ρ(k) represents the relative position vector from the low-orbit satellite at the k-th sampling point to the low-orbit satellite receiver, represents the relative velocity vector from the LEO satellite to the LEO satellite receiver at the kth sampling point, ρ x (k),ρ y (k) and ρ z (k) represents the components of the relative position vector ρ(k) in three directions, and Relative velocity vector Components in three directions.

[0027] Furthermore, the orbit error of the low-orbit satellite is corrected by Kalman filtering based on the state equation and the measurement equation, including:

[0028] Based on the state equation and measurement equation, the position error and velocity error of the low-orbit satellite are obtained through Kalman filtering;

[0029] Correcting the predicted position vector and the predicted velocity vector according to the position error and the velocity error to obtain a corrected position vector and a corrected velocity vector of the low-orbit satellite;

[0030] The orbital parameters of the low-orbit satellite after the orbit error is corrected are obtained based on the conversion of the corrected position vector and the corrected velocity vector.

[0031] Furthermore, the equation of motion of a low-orbit satellite is:

[0032]

[0033] In the above formula, x, y and z represent the components of the position vector of the low-orbit satellite in the inertial rectangular coordinate system in three directions, and They represent the components of the acceleration of the low-orbit satellite in the inertial rectangular coordinate system in the x, y, and z directions, μ represents the Kepler constant of the Earth, and R e represents the earth's equatorial radius, J2 represents the earth's shape mechanics factor, Indicates the distance to the origin of the low-orbit satellite inertial rectangular coordinate system.

[0034] Furthermore, the state equation is:

[0035]

[0036] In the above formula, X(k+1) represents the state quantity of the k+1th sampling point, X(k) represents the state quantity of the kth sampling point, X(t) represents the state quantity at time t, and t k represents the moment of the kth sampling point, r(k) represents the position vector of the low-orbit satellite at the kth sampling point in the inertial rectangular coordinate system, represents the velocity vector of the low-orbit satellite at the kth sampling point in the inertial rectangular coordinate system, r(k) = [x k y k z k ], x k 、y k and z k They represent the components of the position vector of the low-orbit satellite at the kth sampling point in the inertial rectangular coordinate system in three directions, and They represent the components of the velocity vector in three directions of the low-orbit satellite at the kth sampling point in the inertial rectangular coordinate system, T represents the sampling interval, I represents the identity matrix, F represents the nonlinear transformation matrix of the state quantity X, and ω(k) represents the system noise matrix.

[0037] Furthermore, the measurement equation is:

[0038]

[0039] In the above formula, Z(k) represents the quantity measurement of the kth sampling point, Δf k represents the Doppler shift difference, Indicates the distance from the LEO satellite to the LEO satellite receiver.

[0040] According to another aspect of the present invention, a low-orbit satellite orbit error correction system based on GNSS positioning information is provided, the error correction system comprising:

[0041] A data reading unit is used to read TLE files of low-orbit satellites;

[0042] GNSS receiver, which is used to capture satellite navigation signals to obtain local position vector and local velocity vector;

[0043] A low-orbit satellite receiver, the low-orbit satellite receiver is used to measure a Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver;

[0044] Kalman filter correction unit, the Kalman filter unit is used to perform Kalman filtering based on the established low-orbit satellite motion equation, state equation and measurement equation to correct the orbit error of the low-orbit satellite. The state equation is established based on the motion equation and takes the position vector and velocity vector of the low-orbit satellite as state quantities. The measurement equation is established based on the TLE file, the local position vector, the local velocity vector and the Doppler frequency shift measurement value.

[0045] By applying the technical solution of the present invention, a method and system for correcting the orbital error of a low-orbit satellite based on GNSS positioning information are provided. The method establishes a low-orbit satellite motion equation, obtains the TLE file of the low-orbit satellite, the Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver, and the GNSS positioning information, establishes a state equation and a measurement equation based on the aforementioned established motion equation and the obtained information, and then corrects the orbital error of the low-orbit satellite through Kalman filtering based on the state equation and the measurement equation. This method can significantly reduce the orbital error of the low-orbit satellite, thereby greatly improving the positioning accuracy of the low-orbit satellite and ensuring that the positioning error converges within a certain range. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] The accompanying drawings are included to provide a further understanding of the embodiments of the present invention, constitute a part of the specification, illustrate the embodiments of the present invention, and together with the description, explain the principles of the present invention. Obviously, the drawings described below are only some embodiments of the present invention, and those skilled in the art can derive other drawings based on these drawings without inventive effort.

[0047] Figure 1 A schematic flow chart of a method for correcting low-orbit satellite orbit errors based on GNSS positioning information according to a specific embodiment of the present invention is shown;

[0048] Figure 2 A schematic diagram showing the principle of a low-orbit satellite orbit error correction method based on GNSS positioning information provided according to a specific embodiment of the present invention is shown. DETAILED DESCRIPTION

[0049] It should be noted that, in the absence of conflict, the embodiments in this application and the features in the embodiments can be combined with each other. The technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. The following description of at least one exemplary embodiment is actually only illustrative and is in no way intended to limit the present invention and its application or use. Based on the embodiments in the present invention, all other embodiments obtained by ordinary technicians in this field without making creative work are within the scope of protection of the present invention.

[0050] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or combinations thereof.

[0051] Unless otherwise specifically stated, the relative arrangement of the parts and steps, the numerical expressions and the numerical values set forth in these embodiments do not limit the scope of the present invention. At the same time, it should be understood that, for ease of description, the sizes of the various parts shown in the drawings are not drawn according to the actual proportional relationship. The techniques, methods and equipment known to those of ordinary skill in the relevant art may not be discussed in detail, but where appropriate, the techniques, methods and equipment should be considered as part of the authorization specification. In all examples shown and discussed here, any specific values should be interpreted as being merely exemplary and not as limiting. Therefore, other examples of the exemplary embodiments may have different values. It should be noted that similar numbers and letters represent similar items in the following figures, and therefore, once an item is defined in one figure, it does not need to be further discussed in subsequent figures.

[0052] like Figure 1 As shown, according to a specific embodiment of the present invention, a low-orbit satellite orbit error correction method based on GNSS positioning information is provided, and the orbit error correction method includes:

[0053] S1, establish the equation of motion of low-orbit satellites;

[0054] S2, obtains the TLE file of the low-orbit satellite;

[0055] S3, using a GNSS receiver to capture satellite navigation signals to obtain a local position vector and a local velocity vector;

[0056] S4, using the low-orbit satellite receiver to measure and obtain a Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver;

[0057] S5, establishing a state equation with the position vector and velocity vector of the low-orbit satellite as state quantities according to the motion equation;

[0058] S6, establishing a measurement equation based on the TLE file, the local position vector, the local velocity vector, and the Doppler shift measurement value;

[0059] S7, based on the state equation and measurement equation, the orbit error of the low-orbit satellite is corrected through Kalman filtering.

[0060] Among them, the GNSS receiver captures satellite navigation signals in sequence, parses the original message through the steps of capture, tracking, frame synchronization, bit synchronization, etc., and obtains the positioning result, that is, the local position vector and the local velocity vector, through the least square method. In the embodiment of the present invention, the coordinate system adopts an inertial rectangular coordinate system, such as the WGS84 inertial coordinate system. The Kalman filter method is selected according to the actual situation, for example, Figure 2 As shown, an extended Kalman filter can be used. The initial filter value of the state variable is set to the satellite position vector and velocity vector obtained by solving the TLE file. The state vector, namely the position vector and velocity vector of the low-orbit satellite, is solved in real time according to the established state equation and measurement equation. The Kalman filter is only updated when the low-orbit satellite signal (the instantaneous Doppler shift of the visible satellite) can be received. At the same time, the state variable of the present invention does not include the clock error and drift of the low-orbit satellite receiver. The time is based on GNSS, which can reduce the amount of calculation and facilitate engineering implementation.

[0061] Applying this configuration method, a low-orbit satellite orbit error correction method based on GNSS positioning information is provided. This method establishes a low-orbit satellite motion equation, obtains the low-orbit satellite's TLE file, the Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver, and GNSS positioning information, establishes a state equation and a measurement equation based on the aforementioned established motion equation and the acquired information, and then corrects the low-orbit satellite's orbit error through Kalman filtering based on the state equation and the measurement equation. This can significantly reduce the low-orbit satellite's orbit error, thereby greatly improving the positioning accuracy of the low-orbit satellite and ensuring that the positioning error converges within a certain range. Compared with the prior art, the technical solution of the present invention can solve the technical problem in the prior art that the low-orbit satellite orbit information calculated through the TLE file has a large error, resulting in low positioning accuracy.

[0062] In the embodiment of the present invention, the expression of the state quantity X is:

[0063]

[0064] Where r = [xyz] and They represent the position vector and velocity vector of the low-orbit satellite in the WGS84 inertial coordinate system respectively.

[0065] The state differential equation of a low-orbit satellite is:

[0066]

[0067] Where F represents the nonlinear transformation matrix of the state quantity X.

[0068] According to the law of universal gravitation, the equation of motion of a low-orbit satellite is:

[0069]

[0070] Furthermore, the motion equation of the low-orbit satellite is an equation that takes into account the J2 perturbation term, that is, the motion equation of the low-orbit satellite is:

[0071]

[0072] In the above formula, x, y and z represent the components of the position vector of the low-orbit satellite in the inertial rectangular coordinate system in three directions, and They represent the components of the acceleration of the low-orbit satellite in the inertial rectangular coordinate system in the x, y, and z directions, μ represents the Kepler constant of the Earth, and R e represents the earth's equatorial radius, J2 represents the earth's shape mechanics factor, Indicates the distance to the origin of the low-orbit satellite inertial rectangular coordinate system.

[0073] The state prediction equation is:

[0074]

[0075] in, T represents the sampling interval, t k Indicates the sampling point time.

[0076] After discretization of the state transfer matrix, we can get:

[0077]

[0078] The state equation obtained after linearization and discretization is:

[0079] X(k+1)=Φ(k+1 / k)·X(k)+ω(k),

[0080] That is, in the embodiment of the present invention, the state equation is:

[0081]

[0082] In the above formula, X(k+1) represents the state quantity of the k+1th sampling point, X(k) represents the state quantity of the kth sampling point, X(t) represents the state quantity at time t, and t k represents the moment of the kth sampling point, r(k) represents the position vector of the low-orbit satellite at the kth sampling point in the inertial rectangular coordinate system, represents the velocity vector of the low-orbit satellite at the kth sampling point in the inertial rectangular coordinate system, r(k) = [x k y k z k ], x k 、yk and z k They represent the components of the position vector of the low-orbit satellite at the kth sampling point in the inertial rectangular coordinate system in three directions, and They represent the components of the velocity vector of the low-orbit satellite in the inertial rectangular coordinate system at the kth sampling point in the three directions, T represents the sampling interval, I represents the unit matrix, F represents the nonlinear transformation matrix of the state quantity X, ω(k) represents the system noise matrix, and the corresponding covariance matrix is Q(k)=E[ω(k)ω T (k)].

[0083] Furthermore, in the present invention, since there is relative motion between the GNSS receiver and the LEO satellite, and between the LEO satellite receiver and the LEO satellite, there is a Doppler shift between the GNSS receiver and the LEO satellite, and between the LEO satellite receiver and the LEO satellite. Based on this, in an embodiment of the present invention, establishing a measurement equation based on the TLE file, the local position vector, the local velocity vector, and the Doppler shift measurement value includes:

[0084] The Doppler shift prediction value between the LEO satellite and the LEO satellite receiver is obtained based on the TLE file, the local position vector and the local velocity vector;

[0085] A measurement equation is established based on the Doppler frequency shift measurement value and the Doppler frequency shift prediction value.

[0086] Based on the above embodiment, in an embodiment of the present invention, the predicted value of the Doppler shift between the low-orbit satellite and the low-orbit satellite receiver is obtained according to the TLE file, the local position vector, and the local velocity vector, including:

[0087] The predicted position vector and predicted velocity vector of the low-orbit satellite are obtained according to the TLE file prediction;

[0088] The relative position vector from the low-orbit satellite to the low-orbit satellite receiver is calculated based on the predicted position vector and the local position vector;

[0089] The relative velocity vector from the low-orbit satellite to the low-orbit satellite receiver is calculated based on the predicted velocity vector and the local velocity vector;

[0090] The Doppler shift prediction value is calculated based on the relative position vector and the relative velocity vector.

[0091] Furthermore, as a specific embodiment of the present invention, the Doppler shift prediction value is calculated based on the relative position vector and the relative velocity vector using the following formula:

[0092]

[0093] In the above formula, f r(k) represents the Doppler frequency shift prediction value of the k-th sampling point, f0(k) represents the transmission frequency of the low-orbit satellite at the k-th sampling point, c represents the propagation speed of electromagnetic waves in space, n(k) represents the measurement error of the transmission frequency of the low-orbit satellite at the k-th sampling point, ρ(k) represents the relative position vector from the low-orbit satellite at the k-th sampling point to the low-orbit satellite receiver, represents the relative velocity vector from the LEO satellite to the LEO satellite receiver at the kth sampling point, ρ x (k),ρ y (k) and ρ z (k) represents the components of the relative position vector ρ(k) in three directions, and Relative velocity vector Components in three directions, where n(k) is generally white noise with a mean of zero and a variance of σ 2 , k=0,1,…,N, N represents the number of sampling points, which are also observation points.

[0094] In addition, in an embodiment of the present invention, establishing a measurement equation based on the Doppler frequency shift measurement value and the Doppler frequency shift prediction value includes:

[0095] Calculating a Doppler frequency shift difference between a predicted Doppler frequency shift value and a measured Doppler frequency shift value;

[0096] A measurement equation is established using the Doppler frequency shift difference as the measurement quantity.

[0097] As a specific embodiment of the present invention, the expression of the quantity measurement Z(k) is Z(k)=Δf k =f r (k)-f c (k), where Δf k represents the Doppler shift difference between the predicted Doppler shift value and the measured Doppler shift value, that is, the predicted Doppler shift value minus the measured Doppler shift value, f c (k) represents the Doppler frequency shift measurement value. Based on this embodiment, the measurement Z(k) is expressed as a nonlinear function of the state quantity X:

[0098] Z(k)=H(X(k))+n(k),

[0099] Among them, H(X(k)) represents the nonlinear transformation matrix of the measurement quantity to the state quantity, and the covariance matrix corresponding to n(k) is R(k)=E[n(k)n T (k)]=σ 2 .

[0100] Furthermore, the measurement Jacobian matrix is:

[0101]

[0102] The partial differentials are:

[0103]

[0104]

[0105] in Indicates the distance from the LEO satellite to the LEO satellite receiver.

[0106] The measurement equation obtained after linearization and discretization is:

[0107] Z(k)=H(k+1 / k)·X(k)+n(k),

[0108] That is, in the embodiment of the present invention, the measurement equation is:

[0109]

[0110] In the above formula, Z(k) represents the quantity measurement of the kth sampling point, Δf k represents the Doppler shift difference, Indicates the distance from the LEO satellite to the LEO satellite receiver.

[0111] Furthermore, the discretized and linearized state equation and measurement equation constructed above are brought into the Kalman filter for calculation, thereby correcting the orbit error of the low-orbit satellite. In an embodiment of the present invention, correcting the orbit error of the low-orbit satellite through the Kalman filter based on the state equation and the measurement equation includes:

[0112] Based on the state equation and measurement equation, the position error and velocity error of the low-orbit satellite are obtained through Kalman filtering;

[0113] Correcting the predicted position vector and the predicted velocity vector according to the position error and the velocity error to obtain a corrected position vector and a corrected velocity vector of the low-orbit satellite;

[0114] The orbital parameters of the low-orbit satellite after the orbit error is corrected are obtained based on the conversion of the corrected position vector and the corrected velocity vector.

[0115] The filtering estimation steps are as follows:

[0116] State one-step prediction mean square error matrix:

[0117] P(k+1 / k)=Φ(k+1 / k)·P(k)·Φ T (k+1 / k)+Q,

[0118] The parameters in the Q array are reasonably selected according to actual conditions.

[0119] K(k+1)=P(k+1 / k)·H(k+1 / k)·(H(k+1 / k)·P(k)·H T (k+1 / k)+R(k+1)),

[0120] State Estimation:

[0121]

[0122] State estimation mean square error matrix:

[0123] P(k+1)=(IK(k+1)·H(k+1))·P(k+1 / k),

[0124] The filtering and estimation process is well known to those skilled in the art and will not be described in detail here. The position error and velocity error of the low-orbit satellite can be obtained through filtering and estimation. The predicted position vector and predicted velocity vector are corrected according to the position error and velocity error to obtain the corrected position vector and corrected velocity vector of the low-orbit satellite. The corrected position vector and corrected velocity vector are then converted into orbital parameters to obtain the orbital parameters after orbital error correction. In the embodiment of the present invention, the orbital parameters mainly include six parameters: orbital inclination, right ascension of the ascending node, perigee angular distance, orbital semi-major axis, latitude argument, and true anomaly. The specific process of orbital parameter conversion is as follows:

[0125] Satellite area integral formula Where h is the integral constant vector, which is expressed in the inertial rectangular coordinate system as h = (h x ,h y ,h z ),but Among them, h represents the length of the integral constant vector h, h x 、h y and h z They represent the components of the integral constant vector h in three directions respectively.

[0126] In the orbital coordinate system with h as the z' axis and r as the x' axis, h = (0, 0, h). From the conversion relationship between the inertial rectangular coordinate system and the orbital rectangular coordinate system, we can get:

[0127]

[0128] In the above formula, i represents the orbital inclination, and Ω represents the right ascension of the ascending node. Both can be obtained by the following formula:

[0129]

[0130]

[0131] Further, by We can get:

[0132]

[0133] In the above formula, e represents the orbital eccentricity, and its coordinate in the inertial rectangular coordinate system is e=(e x ,e y ,e z ),but Among them, e x 、e y and e z They represent the projections of the orbital eccentricity vector in the three directions of the coordinate axis.

[0134] Next, the perigee angular distance w can be calculated using the formula:

[0135]

[0136] According to the formula of conic sections, the calculation formula of the semi-major axis a of the orbit is:

[0137]

[0138] The latitude argument u is then calculated as follows:

[0139]

[0140] The calculation formula of true anomaly f is:

[0141] f=uw,

[0142] In addition, the relationship between the eccentric anomaly and the true anomaly is The mean anomaly M can then be calculated from Kepler's equation. The mean anomaly refers to the angle in the orbital plane measured from the perigee when a low-orbit satellite moves at an average angular velocity. Its calculation formula is M = Ee sin E, where E represents the eccentric anomaly.

[0143] According to another aspect of the present invention, a low-orbit satellite orbit error correction system based on GNSS positioning information is provided, the error correction system comprising:

[0144] A data reading unit is used to read TLE files of low-orbit satellites;

[0145] GNSS receiver, which is used to capture satellite navigation signals to obtain local position vector and local velocity vector;

[0146] A low-orbit satellite receiver, the low-orbit satellite receiver is used to measure a Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver;

[0147] Kalman filter correction unit, the Kalman filter unit is used to perform Kalman filtering based on the established low-orbit satellite motion equation, state equation and measurement equation to correct the orbit error of the low-orbit satellite. The state equation is established based on the motion equation and takes the position vector and velocity vector of the low-orbit satellite as state quantities. The measurement equation is established based on the TLE file, the local position vector, the local velocity vector and the Doppler frequency shift measurement value.

[0148] For the relevant exemplary description of the satellite orbit error correction system, please refer to the aforementioned relevant exemplary description of the satellite orbit error correction method, which will not be repeated here. The use of this system can significantly reduce the orbit error of low-orbit satellites, thereby greatly improving the positioning accuracy of low-orbit satellites and ensuring that the positioning error converges within a certain range.

[0149] Furthermore, based on the low-orbit satellite orbit error correction method or system proposed in the present invention, the present invention also provides a combined navigation and positioning method and system. Specifically, after the orbit error is corrected using the low-orbit satellite orbit error correction method or system proposed in the present invention, the corrected orbit parameters and the original orbit parameters calculated according to the TLE file are used as the training set of the neural network, and a prediction model of the low-orbit satellite orbit parameters is obtained through training. The prediction model is used to predict the orbit parameters to obtain predicted orbit parameters, and then an orbit database composed of the predicted orbit parameters of the low-orbit satellite is obtained, so that the predicted orbit parameters in the database can be directly called when low-orbit satellite navigation is required. For details, please refer to Figure 2 In an embodiment, the integrated navigation and positioning system includes a GNSS receiver and a low-orbit satellite receiver. When GNSS positioning information is available, the integrated navigation and positioning system operates in the GNSS positioning mode and uses the orbit error correction method or system proposed in the present invention to correct the orbit error of the low-orbit satellite in real time. At the same time, the neural network algorithm uses the corrected orbit parameters and the original orbit parameters calculated from the TLE file to predict the orbit parameters of the low-orbit satellite in real time to obtain predicted orbit parameters (time series), which are stored in the orbit database. Once the GNSS positioning result is unreliable or the GNSS receiver is blocked or interfered with and the GNSS navigation observation cannot be extracted, the integrated navigation and positioning system switches to the low-orbit satellite positioning mode, extracts the predicted low-orbit satellite orbit parameters at the current moment from the aforementioned orbit database, and obtains the current position vector and velocity vector of the low-orbit satellite by solving the predicted orbit parameters. The positioning is then performed in combination with the Doppler observation of the low-orbit satellite, that is, the Doppler frequency shift measurement, thereby ensuring that the positioning error converges within a certain range. The neural network algorithm is selected according to the actual situation. As a specific embodiment of the present invention, the LSTM prediction algorithm is used for training. This navigation method and the corresponding navigation system can significantly improve the accuracy and reliability of navigation.

[0150] Furthermore, when using the LSTM algorithm to predict LEO satellite orbital parameters (time series), the neural network input is the six orbital parameters, including the original six orbital parameters calculated from the TLE file and the revised six orbital parameters, with the original six orbital parameters serving as prior information. The training process is as follows: first, the network is initialized, the bias value is set, and the output value is obtained through a forward operation. Then, the objective function is determined, the error between the actual value and the estimated value is calculated, and the error function is constructed. Finally, the network weights and bias are updated according to the principle of gradient descent. The process of neural network algorithm training is well known to those skilled in the field of neural networks and will not be elaborated here.

[0151] In summary, the present invention provides a method and system for correcting the orbital error of a low-orbit satellite based on GNSS positioning information. The method establishes a low-orbit satellite motion equation, obtains the TLE file of the low-orbit satellite, the Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver, and the GNSS positioning information, establishes a state equation and a measurement equation based on the aforementioned established motion equation and the acquired information, and then corrects the orbital error of the low-orbit satellite through Kalman filtering based on the state equation and the measurement equation. This can significantly reduce the orbital error of the low-orbit satellite, thereby greatly improving the positioning accuracy of the low-orbit satellite and ensuring that the positioning error converges within a certain range. Compared with the prior art, the technical solution of the present invention can solve the technical problem in the prior art that the low-orbit satellite orbital information calculated through the TLE file has a large error, resulting in low positioning accuracy.

[0152] For ease of description, spatially relative terms such as "above", "above", "on the upper surface of", "above", etc. may be used herein to describe the spatial positional relationship of a device or feature to other devices or features as shown in the figures. It should be understood that spatially relative terms are intended to include different orientations of the device in use or operation in addition to the orientation described in the figures. For example, if the device in the drawings is inverted, the device described as "above other devices or structures" or "above other devices or structures" will be positioned as "below other devices or structures" or "below other devices or structures". Thus, the exemplary term "above" can include both "above" and "below". The device can also be positioned in other different ways (rotated 90 degrees or in other orientations), and the spatially relative descriptions used here are interpreted accordingly.

[0153] In addition, it should be noted that the use of terms such as "first" and "second" to limit components is only for the convenience of distinguishing the corresponding components. Unless otherwise stated, the above terms have no special meaning and therefore cannot be understood as limiting the scope of protection of the present invention.

[0154] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A low-orbit satellite orbit error correction method based on GNSS positioning information, characterized in that: The track error correction method comprises: Establishing the motion equation of the low-orbit satellite; Obtaining the TLE file of the low-orbit satellite; Using a GNSS receiver to capture satellite navigation signals to obtain a local position vector and a local velocity vector; Using a low-orbit satellite receiver, the Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver is obtained; Establishing a state equation with the position vector and velocity vector of the low-orbit satellite as state quantities according to the motion equation; Establishing a measurement equation according to the TLE file, the local position vector, the local velocity vector, and the Doppler shift measurement value, including: predicting a predicted position vector and a predicted velocity vector of the low-orbit satellite according to the TLE file; calculating a relative position vector from the low-orbit satellite to the low-orbit satellite receiver according to the predicted position vector and the local position vector; calculating a relative velocity vector from the low-orbit satellite to the low-orbit satellite receiver according to the predicted velocity vector and the local velocity vector; calculating a Doppler shift prediction value according to the relative position vector and the relative velocity vector; and establishing a measurement equation according to the Doppler shift measurement value and the Doppler shift prediction value; The orbital error of the low-orbit satellite is corrected through Kalman filtering based on the state equation and the measurement equation, including: obtaining the position error and velocity error of the low-orbit satellite through Kalman filtering based on the state equation and the measurement equation; correcting the predicted position vector and the predicted velocity vector according to the position error and the velocity error to obtain the corrected position vector and the corrected velocity vector of the low-orbit satellite; and obtaining the orbital parameters of the low-orbit satellite after the orbital error is corrected according to the corrected position vector and the corrected velocity vector.

2. The track error correction method according to claim 1, characterized in that: Establishing a measurement equation according to the Doppler frequency shift measurement value and the Doppler frequency shift prediction value includes: Calculating a Doppler frequency shift difference between the Doppler frequency shift prediction value and the Doppler frequency shift measurement value; A measurement equation is established using the Doppler frequency shift difference as a measurement.

3. The track error correction method according to claim 2, characterized in that: The Doppler shift prediction value is calculated according to the relative position vector and the relative velocity vector using the following formula: In the above formula, f r (k) represents the Doppler frequency shift prediction value of the k-th sampling point, f0(k) represents the transmission frequency of the low-orbit satellite at the k-th sampling point, c represents the propagation speed of electromagnetic waves in space, n(k) represents the measurement error of the transmission frequency of the low-orbit satellite at the k-th sampling point, ρ(k) represents the relative position vector from the low-orbit satellite at the k-th sampling point to the low-orbit satellite receiver, represents the relative velocity vector from the LEO satellite to the LEO satellite receiver at the kth sampling point, ρ x (k),ρ y (k) and ρ z (k) represents the components of the relative position vector ρ(k) in three directions, and Represents the relative velocity vector Components in three directions.

4. The track error correction method according to claim 3, characterized in that: The equation of motion of the low-orbit satellite is: In the above formula, x, y and z represent the components of the position vector of the low-orbit satellite in the inertial rectangular coordinate system in three directions, and They represent the components of the acceleration of the low-orbit satellite in the inertial rectangular coordinate system in the x, y, and z directions, μ represents the Kepler constant of the Earth, and R e represents the earth's equatorial radius, J2 represents the earth's shape mechanics factor, Indicates the distance to the origin of the low-orbit satellite inertial rectangular coordinate system.

5. The track error correction method according to claim 4, characterized in that: The state equation is: In the above formula, X(k+1) represents the state quantity of the k+1th sampling point, X(k) represents the state quantity of the kth sampling point, X(t) represents the state quantity at time t, and t k represents the moment of the kth sampling point, r(k) represents the position vector of the low-orbit satellite at the kth sampling point in the inertial rectangular coordinate system, represents the velocity vector of the low-orbit satellite at the kth sampling point in the inertial rectangular coordinate system, r(k)=[x k y k z k ], x k 、y k and z k They represent the components of the position vector of the low-orbit satellite at the kth sampling point in the inertial rectangular coordinate system in three directions, and They respectively represent the components of the velocity vector of the low-orbit satellite in the three directions at the k-th sampling point in the inertial rectangular coordinate system, T represents the sampling interval, I represents the unit matrix, F represents the nonlinear transformation matrix of the state quantity X, and ω(k) represents the system noise matrix.

6. The track error correction method according to claim 5, characterized in that: The measurement equation is: In the above formula, Z(k) represents the quantity measurement of the kth sampling point, Δf k represents the Doppler frequency shift difference, represents the distance from the low-orbit satellite to the low-orbit satellite receiver at the k-th sampling point.

7. A low-orbit satellite orbit error correction system based on GNSS positioning information, characterized in that: The error correction system comprises: A data reading unit, configured to read the TLE file of the low-orbit satellite; A GNSS receiver, wherein the GNSS receiver is used to capture satellite navigation signals to obtain a local position vector and a local velocity vector; A low-orbit satellite receiver, wherein the low-orbit satellite receiver is used to measure a Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver; A Kalman filter correction unit, the Kalman filter correction unit is used to perform Kalman filtering based on the established low-orbit satellite motion equation, state equation and measurement equation to correct the orbit error of the low-orbit satellite, the state equation is established based on the motion equation and uses the position vector and velocity vector of the low-orbit satellite as state quantities; the measurement equation is established based on the TLE file, the local position vector, the local velocity vector and the Doppler shift measurement value, including: predicting the predicted position vector and predicted velocity vector of the low-orbit satellite based on the TLE file; calculating the relative position vector from the low-orbit satellite to the low-orbit satellite receiver based on the predicted position vector and the local position vector; calculating the relative velocity vector from the low-orbit satellite to the low-orbit satellite receiver based on the predicted velocity vector and the local velocity vector; calculating the Doppler shift prediction value based on the relative position vector and the relative velocity vector; and establishing a measurement equation based on the Doppler shift measurement value and the Doppler shift prediction value; The Kalman filter correction unit performs Kalman filtering based on the established low-orbit satellite motion equation, state equation and measurement equation to correct the orbit error of the low-orbit satellite, including: obtaining the position error and velocity error of the low-orbit satellite through Kalman filtering based on the state equation and the measurement equation; correcting the predicted position vector and the predicted velocity vector according to the position error and the velocity error to obtain the corrected position vector and corrected velocity vector of the low-orbit satellite; and converting the corrected position vector and the corrected velocity vector to obtain the orbit parameters of the low-orbit satellite after correcting the orbit error.

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