A low earth orbit satellite orbit prediction method and device based on Doppler dynamic constraint

Abstract

The application discloses a kind of low-orbit satellite orbit prediction method and device based on Doppler dynamic constraint, belong to spaceflight measurement and control and satellite navigation technical field.The method obtains two-way coherent Doppler observation data by inter-satellite laser link, combined with GNSS precise orbit determination information, constructs Doppler dynamic constraint mechanism, realizes high-precision prediction to low-orbit satellite orbit.Core includes: using the energy change of Doppler observation residual in tangential sensitive band, self-adapting adjustment process noise matrix, dynamically revising the modeling error of non-conservative force such as atmospheric resistance and solar radiation pressure;When GNSS signal is weak or lost, still can provide stable and reliable orbit constraint;By filtering update and dynamics extrapolation, the orbit state and uncertainty evaluation of future 30-120 minutes are output.The application significantly improves the precision and robustness of orbit prediction, and is suitable for low-orbit satellite task scheduling and safety control.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of spaceflight measurement and control and satellite navigation technology, and particularly relates to a low-orbit satellite orbit prediction method and device based on Doppler dynamic constraint. BACKGROUND

[0002] Low-orbit satellites (LEO) have important application value in the fields of communication, earth observation and meteorological monitoring, and the orbit prediction accuracy directly affects the mission performance and satellite safety. At present, the orbit determination and short-term prediction of low-orbit satellites mainly rely on the on-board global navigation satellite system (GNSS) observation data, combined with a dynamic model for precise orbit determination and numerical extrapolation. The typical method is to obtain satellite position information through GNSS signals, estimate the initial orbit state by using least squares fitting or a simplified dynamic model, and then realize short-term orbit prediction by using numerical integration (such as Runge-Kutta method).

[0003] However, this kind of method has obvious limitations. First, GNSS signals are easily blocked (such as high-latitude areas or inter-satellite blocking), which leads to the interruption or degradation of the orbit determination data, and the prediction error increases significantly. Second, low-orbit satellites are significantly affected by atmospheric resistance, solar radiation pressure and other non-conservative forces, and the existing dynamic model is simplified for these disturbances, which cannot accurately reflect the dynamic changes, especially when the disturbance is severe, the prediction deviation is aggravated. In addition, the process noise matrix in the traditional method is usually fixedly set, which cannot be adjusted adaptively according to the actual disturbance, resulting in the accumulation and divergence of prediction error with time, and it is difficult to maintain high accuracy in the short-term prediction of 30-120 minutes.

[0004] In recent years, with the development of inter-satellite laser measurement technology, low-orbit satellites can obtain high-precision ranging and two-way coherent Doppler observation values through inter-satellite laser links, providing a new data source for orbit determination and prediction. This kind of data can still provide reliable relative positioning and velocity constraints when GNSS signals are missing, which is expected to make up for the shortcomings of the traditional orbit prediction method which only relies on on-board GNSS observation data. However, how to effectively integrate Doppler observation into the dynamic orbit prediction process and realize adaptive optimization of disturbance modeling is still a key problem to be solved in current technology.

[0005] Therefore, it is necessary to develop an orbit prediction method that can integrate inter-satellite laser Doppler observation and has the ability of dynamic adjustment of process noise, in order to improve the prediction accuracy and robustness of low-orbit satellites in complex space environment. SUMMARY

[0006] To solve the above technical problems, the application provides a low-orbit satellite orbit prediction method and device based on Doppler dynamic constraint, which introduces inter-satellite laser ranging and communication technology, combines bidirectional coherent Doppler measurement, provides high-precision orbit constraint and satellite relative positioning information in the case of loss of satellite-borne GNSS signal, and ensures the stability of orbit prediction. In addition, the dynamic process noise adjustment method based on Doppler observation residual provided by the application can adaptively correct the process noise matrix parameters according to the frequency band energy change of the observation residual in each orbit update period, so as to realize more precise modeling and rapid response to non-conservative disturbances such as atmospheric drag and solar radiation pressure. When the disturbance changes significantly or the modeling is insufficient, the method can automatically adjust the model prediction uncertainty, effectively improving the precision and stability of the short-term orbit extrapolation of the low-orbit satellite.

[0007] To achieve the above object, the technical scheme adopted by the application is as follows:

[0008] A low-orbit satellite orbit prediction method based on Doppler dynamic constraint, the method comprising:

[0009] Step S1, receiving the precise orbit state prior information obtained by satellite-borne GNSS resolution, and the inter-satellite laser ranging and bidirectional coherent Doppler observation value, and performing preprocessing;

[0010] Step S2, defining a state vector containing position, velocity, atmospheric drag coefficient, solar radiation pressure coefficient, ranging hardware delay and Doppler zero offset, and constructing a satellite motion equation;

[0011] Step S3, constructing a round-trip laser ranging observation equation and a bidirectional coherent Doppler observation equation respectively;

[0012] Step S4, calculating the predicted observation value according to the two observation equations of step S3, and comparing it with the actual observation value to obtain the corresponding two observation residuals;

[0013] Step S5, projecting the Doppler observation residual to the star-fixed coordinate system, calculating the weighted frequency band energy of the tangent sensitive frequency band, and dynamically adjusting the process noise corresponding to the atmospheric drag and solar radiation pressure based on the comparison result of the weighted frequency band energy and the reference energy;

[0014] Step S6, performing time update and observation update of state and covariance by using the state transition matrix and the adjusted process noise, to obtain the latest state estimation;

[0015] Step S7, taking the latest state and covariance as initial values, extrapolating to the target time through numerical integration, obtaining the predicted orbit and evaluating its uncertainty.

[0016] On the other hand, the application provides a low-orbit satellite orbit prediction device based on Doppler dynamic constraint, comprising:

[0017] a preprocessing module, configured to receive precise orbit state prior information obtained by a spaceborne GNSS solution and inter-satellite laser ranging and two-way coherent Doppler observation values, and perform preprocessing;

[0018] an initialization module, configured to define a state vector comprising position, velocity, atmospheric drag coefficient, solar radiation pressure coefficient, ranging hardware delay and Doppler zero bias, and construct a satellite motion equation;

[0019] an observation module, configured to construct a round-trip laser ranging observation equation and a two-way coherent Doppler observation equation respectively;

[0020] a calculation module, configured to calculate predicted observation values according to the two observation equations of the observation module, and compare the predicted observation values with actual observation values to obtain corresponding two observation residuals;

[0021] an adjustment module, configured to project the Doppler observation residual to a satellite-fixed coordinate system, calculate weighted band energy of the Doppler observation residual in a tangential sensitive band, and dynamically adjust process noise corresponding to the atmospheric drag and the solar radiation pressure coefficient based on a comparison result of the weighted band energy and reference energy;

[0022] an update module, configured to perform state and covariance time update and observation update by using a state transition matrix and the adjusted process noise, to obtain latest state estimation;

[0023] a prediction module, configured to take the latest state and covariance as initial values, extrapolate to a target time through numerical integration, obtain a predicted orbit and evaluate uncertainty of the predicted orbit.

[0024] In a third aspect, the present application provides an electronic device, comprising: one or more processors; a memory for storing one or more programs; wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the foregoing method for low-orbit satellite orbit prediction based on dynamic Doppler constraint.

[0025] In a fourth aspect, the present application provides a computer-readable storage medium having stored executable instructions, which, when executed by a processor, enable the processor to implement the foregoing method for low-orbit satellite orbit prediction based on dynamic Doppler constraint.

[0026] The present application has the following beneficial effects:

[0027] Firstly, the present application effectively overcomes excessive dependence on GNSS signals. The dynamic constraint is constructed by using inter-satellite two-way coherent Doppler observation, which can still provide high-precision radial velocity measurement when GNSS signals are weakened or completely interrupted, thereby significantly enhancing the independence and robustness of the orbit prediction system.

[0028] Secondly, the adaptive optimization of process noise is realized. By extracting the energy characteristics of Doppler observation residuals in the tangential sensitive band (0.02-0.08 Hz), the process noise level corresponding to the atmospheric drag and the solar radiation pressure coefficient is dynamically adjusted, the defects that the traditional fixed noise matrix is difficult to respond to the sudden change of non-conservative force are overcome, and the divergence trend of the prediction error with time is effectively suppressed.

[0029] Finally, the overall precision and availability of orbit prediction are improved. The present application can realize the precision of centimeter to decimeter in the short-term prediction window of 30-120 minutes, and can output the prediction uncertainty in each direction in the star-fixed coordinate system, so as to provide more reliable data support for satellite collision avoidance, formation control and mission planning. BRIEF DESCRIPTION OF DRAWINGS

[0030] Figure 1 It is a flow chart of a low-orbit satellite orbit prediction method based on Doppler dynamic constraint. DETAILED DESCRIPTION

[0031] The present application will be further described below in combination with the drawings and examples.

[0032] As shown in the figure, it is a flow chart of a low-orbit satellite orbit prediction method based on Doppler dynamic constraint, which specifically comprises: Figure 1

[0033] Step S1: data receiving and preprocessing; receiving the latest centimeter-level precise orbiting state obtained by solving the on-board GNSS and satellite-based navigation enhancement information as prior information: ; wherein: , : the position and velocity vector of the low-orbit satellite to be estimated in the inertial system; : the kth epoch time; receiving the inter-satellite laser ranging and bidirectional coherent Doppler observation values, and performing time synchronization, gross error elimination and effective epoch screening.

[0034] Step S2: dynamics and state modeling; defining the state vector containing position, velocity, atmospheric drag coefficient, solar radiation pressure coefficient, ranging hardware delay and Doppler zero offset, and constructing the satellite motion equation.

[0035] (1) the state vector is defined as follows:

[0036] ,

[0037] (2) the motion equation is constructed as follows:

[0038] ,

[0039] ,

[0040] ​where is the acceleration caused by the gravitational field; is the perturbation acceleration caused by the sun and moon gravity; is the acceleration caused by the atmospheric drag; is the acceleration caused by the solar radiation pressure; is the atmospheric drag coefficient; is the solar radiation pressure coefficient; is the ranging hardware delay calibration; is the Doppler zero bias, the superscript denotes the first derivative, and the superscript T denotes the transpose.

[0041] Step S3: Constructing the round-trip laser ranging observation equation and the bidirectional coherent Doppler observation equation respectively.

[0042] (1) Constructing the round-trip laser ranging observation equation:

[0043] , ,

[0044] wherein, is the position vector of the opposite end satellite in the inertial system; is the laser ranging observation value at the kth epoch; is the geometric distance between the two low-orbit satellites; is the inter-satellite laser ranging observation noise.

[0045] (2) Constructing the bidirectional coherent Doppler observation equation:

[0046] , ,

[0047] wherein, , are the position vector and the velocity vector of the opposite end satellite in the inertial system respectively; is the bidirectional coherent Doppler observation value at the kth epoch; is the velocity component in the line-of-sight direction; is the wavelength of the laser carrier; is the unit vector in the line-of-sight direction; is the bidirectional coherent Doppler observation noise.

[0048] Step S4: Observation residual calculation; the predicted observation value is calculated according to the current predicted state, and the observation residual is obtained by comparing the actual observation value, wherein the Doppler observation residual is the core driving force.

[0049] (1) Predicted observation value calculation; according to the observation model in step S3, the predicted observation value at the kth epoch is calculated under the current predicted state , the laser ranging predicted value is calculated as follows:

[0050] ,

[0051] Bidirectional coherent Doppler prediction The calculation is as follows:

[0052] ,

[0053] (2) Residual calculation, using the difference between the actual measurement value and the prediction value to obtain the observation residual:

[0054] Laser ranging observation residual: ;

[0055] Bidirectional coherent Doppler observation residual: ,

[0056] Wherein, the Doppler observation residual is the core driving quantity of the adaptive adjustment of the subsequent process noise.

[0057] Step S5: Process noise adaptive adjustment driven by "Doppler observation residual": Project the Doppler observation residual into the star-fixed coordinate system, calculate its weighted band energy in the tangential sensitive band, and based on the comparison result of the energy and the reference energy, dynamically adjust the process noise corresponding to the atmospheric drag and the solar radiation pressure coefficient.

[0058] Because the tangential direction is most sensitive to atmospheric drag, the Doppler mainly measures the line-of-sight direction velocity, so more attention is paid to the residual that can stimulate tangential modeling error.

[0059] (1) Projection of line-of-sight Doppler residual in the star-fixed coordinate system:

[0060] , , , ,

[0061] ,

[0062] Tangential geometric weight ,

[0063] Wherein, , , , respectively, represent the unit vectors of the radial, tangential, and normal directions of the star-fixed coordinate system; , , , respectively, represent the projection components of the line-of-sight residual in the three directions of the star-fixed coordinate system, and h represents the projection vector of the Doppler observation residual in the star-fixed coordinate system.

[0064] (2) Sliding window band energy evaluation; the window Doppler observation residual sequence within Power spectral density , calculate the tangential sensitive band energy:

[0065] ,

[0066] and denote the band limits, where = 0.02 Hz, = 0.08 Hz; and average with geometric weighting Strengthen tangential sensitivity:

[0067] ,

[0068] where, denotes the current epoch, denotes the sliding window length, denotes a certain epoch in the sliding window, denotes the sliding window range.

[0069] (3) Adaptive adjustment of process noise; compare the weighted band energy with the reference energy to obtain the energy increment, and adjust the process noise size of atmospheric drag and solar radiation pressure parameters according to the set amplification gain and smoothing factor, so as to automatically relax the prediction uncertainty when there are unmodeled disturbances in the dynamic model.

[0070] Normalize with the reference during the stationary period: ,

[0071] Calculate the atmospheric drag process noise amplification factor after smoothing: ,

[0072] ,

[0073] Calculate the solar radiation pressure amplification factor: ,

[0074] Updated process noise matrix: ,

[0075] In the above formula, is the normalized energy increment, denotes the reference band energy during the stationary period, denotes the amplification factor of the atmospheric drag process noise; , denote the atmospheric drag and solar radiation pressure method gain, respectively; is a first-order exponential smoothing coefficient; denotes the amplitude limiting; the basic process noise (position / velocity, etc.); , , , atmospheric drag coefficient, solar radiation pressure coefficient, ranging hardware delay calibration quantity, and Doppler zero bias, respectively; is an indicator of illumination, taking a value of 1 if the satellite is in the sun / sun- shadow region and 0 if the satellite is in the shadow region, clip denotes a clipping operation, and diag denotes a diagonal operation.

[0076] Step S6: Filter update, time update of state and covariance using the state transition matrix and the adjusted process noise, and observation update by fusing the observation residuals to obtain the latest state estimate.

[0077] The state and covariance of the previous epoch are propagated to the current epoch using the state transition matrix and the updated process noise to obtain the predicted state and predicted covariance.

[0078] The time update process includes: propagating the state vector and state covariance matrix of the previous epoch to the current epoch using the state transition matrix and the adjusted process noise covariance matrix to obtain the predicted state and predicted covariance of the current epoch:

[0079] , ,

[0080] The observation update process includes: based on the predicted state and predicted covariance, combining the observation Jacobian matrix and the observation noise covariance matrix to calculate the Kalman gain; fusing the laser ranging observation residuals and the Doppler observation residuals using the Kalman gain to correct the predicted state and predicted covariance to obtain the optimal state estimate and the updated covariance matrix of the current epoch. Specifically, the observation update (fusion) is: ,

[0081] , ,

[0082] , ,

[0083] wherein, is a state transition matrix, is a state vector; is a state covariance matrix; is a process noise input matrix; is a process noise covariance matrix; is an observation Jacobian matrix, is an observation noise covariance matrix; ​The residual covariance matrix; The Kalman gain matrix; It is an identity matrix, and the subscript k / k-1 represents the current epoch / previous epoch.

[0084] Step S7: Short-term orbit forecast; Using the latest state and covariance as initial values, extrapolate to the target time through numerical integration to obtain the forecast orbit and evaluate its uncertainty.

[0085] After completing state updates and adaptive adjustment of process noise, the latest state estimate and its covariance are used as initial conditions. The predicted trajectory is obtained by extrapolating to the target time under the dynamic model using numerical integration. During the extrapolation process, the state transition matrix... Process noise covariance The uncertainty of the propagation state is used to obtain the predicted trajectory at the target time and its uncertainty assessment.

[0086] State vector extrapolation: ,

[0087] in, For the current epoch prediction Time after (target epoch) The state vector of ) Indicates the time interval The state transition matrix is ​​given below.

[0088] Covariance extrapolation: ,

[0089] in, For the current epoch prediction State covariance after time, This represents the integral variable, i.e., the propagation time from the current moment.

[0090] The orbit prediction uncertainty estimation extrapolates the state covariance matrix of the target time obtained during propagation, and transforms it from the inertial coordinate system to the star-fixed coordinate system using the direction cosine matrix:

[0091] ,

[0092] , , ,

[0093] in, The representation of the predicted covariance in star-fixed coordinates, where subscripts RR, TT, and NN represent radial, tangential, and normal directions, respectively. Let be the direction cosine matrix from the inertial coordinate system to the star-fixed coordinate system. , , respectively represent the 1σ uncertainty of the predicted position in radial, tangential, and normal directions.

[0094] In another aspect, the present application provides a low earth orbit satellite orbit prediction device based on Doppler dynamic constraint, which comprises various modules capable of realizing various steps of the foregoing method, and specifically comprises:

[0095] a preprocessing module, configured to receive precise orbit state prior information obtained by on-board GNSS solution and inter-satellite laser ranging and bidirectional coherent Doppler observation values, and perform preprocessing;

[0096] an initialization module, configured to define a state vector comprising position, velocity, atmospheric drag coefficient, solar radiation pressure coefficient, ranging hardware delay, and Doppler zero offset, and construct a satellite motion equation;

[0097] an observation module, configured to construct a round-trip laser ranging observation equation and a bidirectional coherent Doppler observation equation respectively;

[0098] a calculation module, configured to calculate predicted observation values according to the two observation equations of the observation module, and compare the predicted observation values with actual observation values to obtain corresponding two observation residuals;

[0099] an adjustment module, configured to project the Doppler observation residual into a satellite-fixed coordinate system, calculate weighted band energy of the Doppler observation residual in a tangential sensitive band, and dynamically adjust process noise corresponding to the atmospheric drag and the solar radiation pressure coefficient based on a comparison result of the weighted band energy and a reference energy;

[0100] an update module, configured to perform state and covariance time update and observation update by using a state transition matrix and the adjusted process noise, to obtain the latest state estimation;

[0101] a prediction module, configured to take the latest state and covariance as initial values, extrapolate to a target time by numerical integration, obtain a predicted orbit, and evaluate an uncertainty of the predicted orbit.

[0102] In a third aspect, the present application provides an electronic device, comprising: one or more processors; a memory configured to store one or more programs; wherein when the one or more programs are executed by the one or more processors, the one or more processors implement the foregoing method for low earth orbit satellite orbit prediction based on Doppler dynamic constraint.

[0103] In a fourth aspect, the present application provides a computer readable storage medium having stored executable instructions, which when executed by a processor, enable the processor to implement the foregoing method for low earth orbit satellite orbit prediction based on Doppler dynamic constraint.

[0104] The above-described specific embodiments further illustrate the purpose, technical solutions and beneficial effects of the present application, and it should be understood that the above-described is only a specific embodiment of the present application and is not intended to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application should be included in the protection scope of the present application.

Claims

1. A method for low earth orbit satellite orbit prediction based on Doppler dynamic constraints, characterized in that, The method comprises: Step S1, receiving precise orbit state prior information obtained by spaceborne GNSS resolution and inter-satellite laser ranging and bidirectional coherent Doppler observation values, and performing preprocessing; Step S2, defining a state vector comprising position, velocity, atmospheric drag coefficient, solar radiation pressure coefficient, ranging hardware delay and Doppler zero offset, and constructing a satellite motion equation; Step S3, respectively constructing a round-trip laser ranging observation equation and a bidirectional coherent Doppler observation equation; wherein, when constructing the round-trip laser ranging observation equation, the observation value is represented as the sum of the geometric distance between the two satellites and the ranging hardware delay, and the observation noise is added; when constructing the bidirectional coherent Doppler observation equation, the observation value is represented as the ratio of the relative velocity in the line-of-sight direction to the laser carrier wavelength, and the Doppler zero offset and the observation noise are added; Step S4, calculating predicted observation values according to the two observation equations of step S3, and comparing the predicted observation values with actual observation values to obtain corresponding two observation residuals; Step S5, projecting the Doppler observation residuals into the star-fixed coordinate system, calculating the weighted band energy of the residuals in the tangential sensitive band, and dynamically adjusting the process noise corresponding to the atmospheric drag and the solar radiation pressure coefficient based on the comparison result of the weighted band energy and the reference energy; wherein, the power spectral density estimation is performed on the Doppler observation residual sequence in the sliding window, the energy value in the preset tangential sensitive band is extracted, and the projection component of the Doppler observation residual in the tangential direction of the star-fixed coordinate system is used as the geometric weight for weighting; the energy increment is calculated according to the ratio of the weighted band energy to the stationary period reference energy, the atmospheric drag amplification factor and the solar radiation pressure amplification factor are calculated based on the energy increment, and the process noise size is adjusted through first-order exponential smoothing and amplitude limiting processing; Step S6, performing time update and observation update of the state and the covariance using the state transition matrix and the adjusted process noise to obtain the latest state estimation; Step S7, extrapolating to the target time by numerical integration with the latest state and covariance as initial values to obtain the predicted orbit and evaluate the uncertainty thereof, including: taking the latest state estimation and the updated covariance matrix obtained after the filtering update as initial conditions, extrapolating the satellite orbit state to the target time under the dynamic model by using the numerical integration method to obtain the predicted orbit; converting the state covariance matrix at the target time propagated in the extrapolation process from the inertial coordinate system to the star-fixed coordinate system through the direction cosine matrix; solving the converted covariance matrix in the star-fixed coordinate system to obtain the standard deviations of the predicted position in the radial direction, the tangential direction and the normal direction, respectively, as the evaluation indicators of the orbit prediction uncertainty.

2. The low earth orbit satellite orbit prediction method based on Doppler dynamic constraint according to claim 1, characterized in that, In step S1, the preprocessing includes time synchronization, gross error elimination and effective epoch screening. 3.The low earth orbit satellite orbit prediction method based on Doppler dynamic constraint according to claim 1, wherein, In step S2, the satellite motion equation comprises the earth's gravitational field perturbation acceleration, the third body gravitational perturbation acceleration of the sun and the moon, the atmospheric drag acceleration and the solar radiation pressure acceleration.

4. The low earth orbit satellite orbit prediction method based on Doppler dynamic constraint of claim 1, wherein, The time updating process in the step S6 includes: propagating the state vector and the state covariance matrix of the last epoch to the current epoch by using the state transition matrix and the adjusted process noise covariance matrix, to obtain the predicted state and the predicted covariance of the current epoch; the observation updating process includes: calculating the Kalman gain based on the predicted state and the predicted covariance, combining the observation Jacobian matrix and the observation noise covariance matrix; fusing the laser ranging observation residual and the Doppler observation residual by using the Kalman gain, and correcting the predicted state and the predicted covariance to obtain the latest state estimation and the updated covariance matrix of the current epoch.

5. A device for low earth orbit satellite orbit prediction based on Doppler dynamic constraints for performing the method of any one of claims 1 to 4, characterized in that, The method comprises the following steps: a preprocessing module, configured to receive the precise orbit state prior information obtained by the space-borne GNSS solution and the inter-satellite laser ranging and bidirectional coherent Doppler observation values, and perform preprocessing; an initialization module, configured to define a state vector comprising position, velocity, atmospheric drag coefficient, solar radiation pressure coefficient, ranging hardware delay and Doppler zero bias, and construct a satellite motion equation; an observation module, configured to construct a round-trip laser ranging observation equation and a bidirectional coherent Doppler observation equation respectively; a calculation module, configured to calculate predicted observation values according to the two observation equations of the observation module, and obtain corresponding two observation residuals by comparing the predicted observation values with actual observation values; an adjustment module, configured to project the Doppler observation residual to a satellite-fixed coordinate system, calculate the weighted band energy of the Doppler observation residual in the tangential sensitive band, and dynamically adjust the process noise corresponding to the atmospheric drag and the solar radiation pressure coefficient based on the comparison result of the weighted band energy and a reference energy; an updating module, configured to perform time updating and observation updating of state and covariance by using the state transition matrix and the adjusted process noise, to obtain the latest state estimation; a prediction module, configured to extrapolate to a target time by taking the latest state and covariance as initial values, to obtain a predicted orbit and evaluate the uncertainty thereof.

6. An electronic device, comprising: The method comprises the following steps: one or more processors; a memory, configured to store one or more programs; wherein, when the one or more programs are executed by the one or more processors, the one or more processors implement the low-orbit satellite orbit prediction method based on Doppler dynamic constraint according to any one of claims 1-4.

7. A computer readable storage medium characterized by, A computer readable storage medium having stored thereon executable instructions that, when executed by a processor, enable the processor to implement the low-orbit satellite orbit prediction method based on Doppler dynamic constraint according to any one of claims 1-4.

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