A combined navigation and positioning method based on GNSS and low-orbit satellites

Abstract

The present invention provides a combined navigation and positioning method based on GNSS and low-orbit satellites. The method includes: obtaining a TLE file of a low-orbit satellite and calculating the original orbital parameters of the low-orbit satellite based on the TLE file; using a low-orbit satellite receiver to measure the Doppler frequency shift measurement value between the low-orbit satellite and the low-orbit satellite receiver; when GNSS positioning information is available, using the GNSS positioning information for navigation and positioning, and using the TLE file, the Doppler frequency shift measurement value, and the GNSS positioning information to perform real-time correction of the low-orbit satellite's orbital error through Kalman filtering to obtain corrected orbital parameters, and using a neural network to predict the orbital parameters to obtain predicted orbital parameters; when GNSS positioning information is unavailable, using the predicted orbital parameters and the Doppler frequency shift measurement value for navigation and positioning. The technical solution of the present invention is applied to solve the technical problems in the prior art of poor low-orbit satellite navigation accuracy and unstable GNSS signals that affect navigation and positioning effects.

Description

Technical Field

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

[0002] Satellite navigation is currently used in a wide range of applications, 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-orbit orbits. Their signals are already very weak by the time they reach the ground, and can be easily interrupted by obstructions. Furthermore, the signal formats are publicly available, making them susceptible to interference and spoofing. In comparison, low-orbit satellites (LEOs) offer stronger signals due to their lower orbital altitudes, and their geometric positions change rapidly. Consequently, countries are currently competing to launch LEO satellites. However, LEO satellites are primarily used for communications and do not broadcast navigation messages in real time like the Global Navigation Satellite System (GNSS). Furthermore, the content and format of communications with non-cooperative satellites are encrypted. Therefore, obtaining LEO satellite orbit information often relies on the Two-Line Element files (TLE files) published by the North American Aerospace Command. Although TLE files are updated daily, the satellite orbits calculated based on these files can have significant errors, sometimes even at the kilometer level, significantly impacting positioning results. Summary of the Invention

[0003] In order to solve one of the problems existing in the prior art, the present invention provides a combined navigation and positioning method based on GNSS and low-orbit satellites.

[0004] According to one aspect of the present invention, a combined navigation and positioning method based on GNSS and low-orbit satellites is provided, the combined navigation and positioning method comprising:

[0005] Obtain the TLE file of the low-orbit satellite and calculate the original orbit parameters of the low-orbit satellite based on the TLE file;

[0006] 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;

[0007] When GNSS positioning information is available, use the GNSS positioning information for navigation and positioning, and use the TLE file, Doppler frequency shift measurement values, and GNSS positioning information to perform real-time correction of the low-orbit satellite's orbit error through Kalman filtering to obtain corrected orbit parameters. Use a neural network to predict orbit parameters based on the original orbit parameters and the corrected orbit parameters to obtain predicted orbit parameters.

[0008] When GNSS positioning information is unavailable, navigation positioning is performed using predicted orbit parameters and Doppler frequency shift measurements.

[0009] Furthermore, the GNSS positioning information includes a local position vector and a local velocity vector. The orbit error of the low-orbit satellite is corrected in real time by using the TLE file, the Doppler frequency shift measurement value, and the GNSS positioning information through Kalman filtering to obtain the corrected orbit parameters including:

[0010] Establish the equations of motion for low-orbit satellites;

[0011] 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;

[0012] Establish measurement equations based on the TLE file, local position vector, local velocity vector, and Doppler shift measurement value;

[0013] Based on the state equation and measurement equation, the orbit error of the low-orbit satellite is corrected in real time through Kalman filtering to obtain the corrected orbit parameters.

[0014] Furthermore, establishing a measurement equation based on the TLE file, the local position vector, the local velocity vector, and the Doppler shift measurement value includes:

[0015] 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;

[0016] A measurement equation is established based on the Doppler frequency shift measurement value and the Doppler frequency shift prediction value.

[0017] 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:

[0018] The predicted position vector and predicted velocity vector of the low-orbit satellite are obtained according to the TLE file prediction;

[0019] 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;

[0020] 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;

[0021] The Doppler shift prediction value is calculated based on the relative position vector and the relative velocity vector.

[0022] Furthermore, establishing a measurement equation based on the Doppler frequency shift measurement value and the Doppler frequency shift prediction value includes:

[0023] Calculating a Doppler frequency shift difference between a predicted Doppler frequency shift value and a measured Doppler frequency shift value;

[0024] A measurement equation is established using the Doppler frequency shift difference as the measurement quantity.

[0025] Furthermore, the Doppler shift prediction value is calculated based on the relative position vector and the relative velocity vector using the following formula:

[0026]

[0027] 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.

[0028] Furthermore, the real-time correction of the orbit error of the low-orbit satellite is performed through Kalman filtering based on the state equation and the measurement equation, including:

[0029] Based on the state equation and measurement equation, the position error and velocity error of the low-orbit satellite are obtained through Kalman filtering;

[0030] Correcting the predicted position vector and the predicted velocity vector in real time 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;

[0031] 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.

[0032] Furthermore, the equation of motion of a low-orbit satellite is:

[0033]

[0034] 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.

[0035] Furthermore, the state equation is:

[0036]

[0037] 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.

[0038] Furthermore, the measurement equation is:

[0039]

[0040] 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.

[0041] By applying the technical solution of the present invention, a combined navigation and positioning method based on GNSS and low-orbit satellites is provided. The method uses GNSS positioning information for navigation and positioning when the GNSS positioning information is available, and uses the TLE file of the low-orbit satellite, Doppler frequency shift measurement value and GNSS positioning information to perform real-time correction of the orbit error of the low-orbit satellite through Kalman filtering to obtain the corrected orbit parameters. The orbit parameters are then predicted based on the original orbit parameters and the corrected orbit parameters through a neural network algorithm to obtain the predicted orbit parameters of the low-orbit satellite. When the GNSS positioning information is unavailable, the predicted orbit parameters and Doppler frequency shift measurement value are called for navigation and positioning, that is, switching to low-orbit satellite navigation and positioning. This method can significantly improve the positioning accuracy of the low-orbit satellite, and thus can achieve continuous, reliable and high-precision navigation and positioning through combined navigation. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] 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.

[0043] Figure 1 A schematic diagram of the process of a combined navigation and positioning method based on GNSS and low-orbit satellites according to a specific embodiment of the present invention is shown;

[0044] Figure 2 A schematic diagram showing the principle of a combined navigation and positioning method based on GNSS and low-orbit satellites provided according to a specific embodiment of the present invention is shown. DETAILED DESCRIPTION

[0045] 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.

[0046] 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.

[0047] 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.

[0048] like Figure 1 As shown, according to a specific embodiment of the present invention, a combined navigation and positioning method based on GNSS and low-orbit satellites is provided, and the combined navigation and positioning method includes:

[0049] S1, obtain the TLE file of the low-orbit satellite and calculate the original orbit parameters of the low-orbit satellite based on the TLE file;

[0050] S2, using a 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;

[0051] S3, when GNSS positioning information is available, using the GNSS positioning information for navigation positioning, and using the TLE file, Doppler frequency shift measurement value and GNSS positioning information to correct the orbit error of the low-orbit satellite in real time through Kalman filtering to obtain corrected orbit parameters, and using a neural network to predict the orbit parameters based on the original orbit parameters and the corrected orbit parameters to obtain predicted orbit parameters;

[0052] S4, when GNSS positioning information is unavailable, uses predicted orbit parameters and Doppler frequency shift measurements for navigation positioning.

[0053] In the embodiments of the present invention, the coordinate system uses an inertial rectangular coordinate system, such as the WGS84 inertial coordinate system. GNSS positioning information is acquired through a GNSS receiver. The GNSS receiver sequentially captures satellite navigation signals, parses the original message through capture, tracking, frame synchronization, bit synchronization, and other steps, and obtains the positioning result through least squares. GNSS receivers and low-orbit satellite receivers both belong to integrated navigation and positioning systems.

[0054] Please refer to Figure 2 Figure 1 is a schematic diagram of the principle of integrated navigation positioning. The integrated navigation system includes a GNSS receiver and a low-orbit satellite receiver. When GNSS positioning information is available, the integrated navigation positioning system operates in the GNSS positioning mode. At the same time, the corrected orbit parameters corrected in real time and the original orbit parameters calculated according to the TLE file are used as the training set of the neural network. A prediction model for 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 consisting of the predicted orbit parameters (time series) of the low-orbit satellite is obtained. Once the GNSS positioning result is unreliable or the GNSS receiver is blocked or interfered and the GNSS navigation observations cannot be extracted, the integrated navigation positioning system switches to the low-orbit satellite navigation 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, to ensure that the positioning error converges within a certain range.

[0055] The neural network algorithm is selected based on practical needs. As a specific embodiment of the present invention, an LSTM prediction algorithm is used for training. The neural network input is the six orbital parameters, including the original six orbital parameters calculated from the TLE file and the corrected six orbital parameters, with the original six orbital parameters serving as prior information. The training process is as follows: first, the network is initialized, a bias value is set, and the output value is obtained through forward operations. Then, the objective function is determined, the error between the actual value and the estimated value is calculated, an error function is constructed, and finally, the network weights and biases are updated according to the principle of gradient descent. The process of neural network algorithm training is well known to those skilled in the art of neural networks and will not be elaborated here.

[0056] By applying this configuration, a combined navigation and positioning method based on GNSS and low-orbit satellites is provided. This method uses GNSS positioning information for navigation and positioning when GNSS positioning information is available, and uses the TLE file of the low-orbit satellite, Doppler frequency shift measurement value and GNSS positioning information to correct the orbit error of the low-orbit satellite in real time through Kalman filtering to obtain the corrected orbit parameters. Then, based on the original orbit parameters and the corrected orbit parameters, the orbit parameters are predicted through a neural network algorithm to obtain the predicted orbit parameters of the low-orbit satellite. When the GNSS positioning information is unavailable, the predicted orbit parameters and Doppler frequency shift measurement value are called for navigation and positioning, that is, switching to low-orbit satellite navigation and positioning. This method can significantly improve the positioning accuracy of low-orbit satellites, and then achieve continuous, reliable and high-precision navigation and positioning through combined navigation. Compared with the prior art, the technical solution of the present invention can solve the technical problems in the prior art that the low-orbit satellite navigation accuracy is poor and the unstable GNSS signal affects the navigation and positioning effect.

[0057] Furthermore, in an embodiment of the present invention, the GNSS positioning information includes a local position vector and a local velocity vector. Using the TLE file, the Doppler shift measurement value, and the GNSS positioning information, the orbit error of the low-orbit satellite is corrected in real time through Kalman filtering to obtain the corrected orbit parameters, including:

[0058] Establish the equations of motion for low-orbit satellites;

[0059] 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;

[0060] Establish measurement equations based on the TLE file, local position vector, local velocity vector, and Doppler shift measurement value;

[0061] Based on the state equation and measurement equation, the orbit error of the low-orbit satellite is corrected in real time through Kalman filtering to obtain the corrected orbit parameters.

[0062] In the embodiment of the present invention, the Kalman filter mode 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.

[0063] In the embodiment of the present invention, the expression of the state quantity X is:

[0064]

[0065] Where r = [xyz] and They represent the position vector and velocity vector of the low-orbit satellite in the WGS84 inertial coordinate system respectively.

[0066] The state differential equation of a low-orbit satellite is:

[0067]

[0068] Where F represents the nonlinear transformation matrix of the state quantity X.

[0069] According to the law of universal gravitation, the equation of motion of a low-orbit satellite is:

[0070]

[0071] 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:

[0072]

[0073] 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.

[0074] The state prediction equation is:

[0075]

[0076] in, T represents the sampling interval, t k Indicates the sampling point time.

[0077] After discretization of the state transfer matrix, we can get:

[0078]

[0079] The state equation obtained after linearization and discretization is:

[0080] X(k+1)=Φ(k+1 / k)·X(k)+ω(k),

[0081] That is, in the embodiment of the present invention, the state equation is:

[0082]

[0083] 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 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)].

[0084] 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:

[0085] 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;

[0086] A measurement equation is established based on the Doppler frequency shift measurement value and the Doppler frequency shift prediction value.

[0087] 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:

[0088] The predicted position vector and predicted velocity vector of the low-orbit satellite are obtained according to the TLE file prediction;

[0089] 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;

[0090] 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;

[0091] The Doppler shift prediction value is calculated based on the relative position vector and the relative velocity vector.

[0092] 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:

[0093]

[0094] 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.

[0095] 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:

[0096] Calculating a Doppler frequency shift difference between a predicted Doppler frequency shift value and a measured Doppler frequency shift value;

[0097] A measurement equation is established using the Doppler frequency shift difference as the measurement quantity.

[0098] 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 krepresents 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:

[0099] Z(k)=H(X(k))+n(k),

[0100] 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 .

[0101] Furthermore, the measurement Jacobian matrix is:

[0102]

[0103] The partial differentials are:

[0104]

[0105]

[0106] in Indicates the distance from the LEO satellite to the LEO satellite receiver.

[0107] The measurement equation obtained after linearization and discretization is:

[0108] Z(k)=H(k+1 / k)·X(k)+n(k),

[0109] That is, in the embodiment of the present invention, the measurement equation is:

[0110]

[0111] 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.

[0112] 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, the real-time correction of the orbit error of the low-orbit satellite through the Kalman filter based on the state equation and measurement equation includes:

[0113] Based on the state equation and measurement equation, the position error and velocity error of the low-orbit satellite are obtained through Kalman filtering;

[0114] Correcting the predicted position vector and the predicted velocity vector in real time 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;

[0115] 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.

[0116] The filtering estimation steps are as follows:

[0117] State one-step prediction mean square error matrix:

[0118] P(k+1 / k)=Φ(k+1 / k)·P(k)·Φ T (k+1 / k)+Q,

[0119] The parameters in the Q array are reasonably selected according to actual conditions.

[0120] 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)),

[0121] State Estimation:

[0122]

[0123] State estimation mean square error matrix:

[0124] P(k+1)=(IK(k+1)·H(k+1))·P(k+1 / k),

[0125] 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:

[0126] 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 yand h z They represent the components of the integral constant vector h in three directions respectively.

[0127] 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:

[0128]

[0129] 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:

[0130]

[0131]

[0132] Further, by We can get:

[0133]

[0134] 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 in the three directions of the coordinate axis.

[0135] Next, the perigee angular distance w can be calculated using the formula:

[0136]

[0137] According to the formula of conic sections, the calculation formula of the semi-major axis a of the orbit is:

[0138]

[0139] The latitude argument u is then calculated as follows:

[0140]

[0141] The calculation formula of true anomaly f is:

[0142] f=uw,

[0143] In addition, the relationship between the eccentric anomaly and the true anomaly is The mean anomaly M can then be calculated from the Kepler equation. The mean anomaly refers to the angle in the orbital plane where a low-orbit satellite moves at an average angular velocity starting from the perigee. The calculation formula is M=E-esinE, where E represents the eccentric anomaly.

[0144] In summary, the present invention provides a combined navigation and positioning method based on GNSS and low-orbit satellites. The method uses GNSS positioning information for navigation and positioning when GNSS positioning information is available, and uses the TLE file, Doppler frequency shift measurement value and GNSS positioning information of the low-orbit satellite to correct the orbit error of the low-orbit satellite in real time through Kalman filtering to obtain the corrected orbit parameters. The orbit parameters are then predicted based on the original orbit parameters and the corrected orbit parameters through a neural network algorithm to obtain the predicted orbit parameters of the low-orbit satellite. When the GNSS positioning information is not available, the predicted orbit parameters and Doppler frequency shift measurement value are called for navigation and positioning, that is, switching to low-orbit satellite navigation and positioning. This method can significantly improve the positioning accuracy of low-orbit satellites, and then achieve continuous, reliable and high-precision navigation and positioning through combined navigation. Compared with the prior art, the technical solution of the present invention can solve the technical problems in the prior art that the low-orbit satellite navigation accuracy is poor and the unstable GNSS signal affects the navigation and positioning effect.

[0145] 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.

[0146] 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.

[0147] 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 are intended to be within the scope of protection of the present invention.

Claims

1. A combined navigation and positioning method based on GNSS and low-orbit satellites, characterized in that: The combined navigation positioning method comprises: Obtaining a TLE file of the low-orbit satellite, and calculating original orbital parameters of the low-orbit satellite according to the TLE file; 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; When GNSS positioning information is available, use the GNSS positioning information to perform navigation positioning, and use the TLE file, the Doppler shift measurement value, and the GNSS positioning information to perform real-time correction of the orbit error of the low-orbit satellite through Kalman filtering to obtain corrected orbit parameters, and use a neural network to predict orbit parameters based on the original orbit parameters and the corrected orbit parameters to obtain predicted orbit parameters; When the GNSS positioning information is unavailable, navigation positioning is performed using the predicted orbit parameters and the Doppler frequency shift measurement value.

2. The integrated navigation positioning method according to claim 1, characterized in that: The GNSS positioning information includes a local position vector and a local velocity vector. Using the TLE file, the Doppler frequency shift measurement value, and the GNSS positioning information, performing real-time correction on the orbit error of the low-orbit satellite through Kalman filtering to obtain corrected orbit parameters includes: Establishing the motion equation of the low-orbit satellite; 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 based on the TLE file, the local position vector, the local velocity vector, and the Doppler shift measurement value; Based on the state equation and the measurement equation, the orbit error of the low-orbit satellite is corrected in real time through Kalman filtering to obtain corrected orbit parameters.

3. The integrated navigation and positioning method according to claim 2, characterized in that: Establishing a measurement equation based on the TLE file, the local position vector, the local velocity vector, and the Doppler shift measurement value includes: Predicting a Doppler shift prediction value between the low-orbit satellite and the low-orbit satellite receiver according to the TLE file, the local position vector, and the local velocity vector; A measurement equation is established according to the Doppler frequency shift measurement value and the Doppler frequency shift prediction value.

4. The integrated navigation and positioning method according to claim 3, characterized in that: Predicting a Doppler shift prediction value between the low-orbit satellite and the low-orbit satellite receiver according to the TLE file, the local position vector, and the local velocity vector includes: Predicting the predicted position vector and the 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; The Doppler shift prediction value is calculated based on the relative position vector and the relative velocity vector.

5. The integrated navigation and positioning method according to claim 4, 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.

6. The integrated navigation and positioning method according to claim 5, 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.

7. The integrated navigation and positioning method according to claim 6, characterized in that: Correcting the orbit error of the low-orbit satellite in real time by using Kalman filtering based on the state equation and the measurement equation includes: Obtaining a position error and a 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 in real time 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; The orbital parameters of the low-orbit satellite after the orbit error is corrected are obtained according to the correction position vector and the correction velocity vector.

8. The integrated navigation and positioning method according to claim 7, 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.

9. The integrated navigation and positioning method according to claim 8, 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.

10. The integrated navigation and positioning method according to claim 9, 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 at the kth sampling point to the low-orbit satellite receiver.

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