A method for fast re-convergence of orbit-constrained LEO geometric method defined orbit ambiguity

Abstract

The present application relates to a kind of LEO geometric method orbit determination ambiguity fast re-convergence method based on orbit constraint, first, select appropriate length time window, utilize the position of each epoch in window to solve the dynamics model of observed object in this time window, then with the dynamics model obtained, orbit extrapolation is carried out, extrapolated orbit is taken as initial orbit and is given smaller initial variance, then the solution of position parameter is carried out.The present application is designed for the characteristics of multi-frequency GNSS spaceborne receiver low-orbit satellite data;It is suitable for real-time and post low-orbit satellite geometric method orbit determination mode;It is suitable for single-satellite system and the combined application between multi-satellite system;Based on position parameter fitting dynamics model, the extrapolated orbit precision is higher than geometric method orbit;Compared with traditional real-time geometric method orbit determination, it provides orbit constraint condition, weakens the influence of data interruption on orbit determination result, and the orbit quality is better, more suitable for practical application.

Description

Technical Field

[0001] This invention relates to the field of GNSS data processing for satellite positioning and navigation, and in particular to a fast reconvergence method for geometric orbit determination ambiguity of spaceborne GNSS receivers used in applications such as satellite orbit determination. Background Technology

[0002] With the increasing demand for high-precision Earth science research, the use of low-Earth orbit (LEO) satellites for geophysical phenomenon detection has become a mainstream research trend. However, high-precision Earth observation requires not only detection information from onboard LEO satellite sensors but also precise LEO satellite orbits. In the field of Earth's gravity field research, geometric LEO satellite orbits that do not contain mechanical errors have received widespread attention and application.

[0003] Spaceborne GNSS receiver orbit determination, with its advantages of low cost, ease of equipment setup, high precision, global coverage, and continuous observation, has become the primary method for precise orbit determination of low-Earth orbit (LEO) satellites and inter-satellite baseline ranging. The orbit determination accuracy of this method mainly depends on the quality of the observations and the satellite geometry. When the number of satellites is small or the satellite geometry is poor, the orbit determination accuracy is often low. Geometric orbit determination requires GNSS observations. In the event of data interruption, geometric orbit determination cannot be obtained. Furthermore, ambiguity parameters need to be reconverged after data interruption. This leads to a decrease in orbit quality during the initial data recovery phase, making it difficult to achieve centimeter-level orbit determination accuracy, which is detrimental to real-time orbit determination of LEO satellites. Summary of the Invention

[0004] The purpose of this invention is to propose a fast reconvergence method for LEO geometric orbit determination ambiguity based on orbit constraints. This method solves the problem of orbit determination quality degradation after data interruption and can handle the issue of orbit error reconvergence after data interruption in satellite GNSS receiver geometric orbit determination applications. This invention has certain application value for real-time orbit determination and navigation of low-Earth orbit satellites.

[0005] To achieve the above objectives, this invention provides a fast reconvergence method for LEO geometric ambiguity based on orbit constraints, comprising:

[0006] Step S1: Obtain multi-frequency GNSS observation data of the observed object, and construct observation equations based on the GNSS observation data;

[0007] Step S2: Calculate the time difference Δt between the current k and the previous epoch k-1, and determine whether the time difference Δt is less than the threshold T, where T≥60s, k≥2, and k is a positive integer;

[0008] If so, proceed to step S3;

[0009] If not, proceed to step S4;

[0010] Step S3: Obtain the position parameters according to the observation equation described in step S1;

[0011] Step S4: Select a time window of length n, and determine whether the current cumulative observation duration of the observed object is less than n, where 12h≤n≤24h;

[0012] If so, proceed to step S3;

[0013] If not, proceed to step S5;

[0014] Step S5: Obtain the dynamic model based on the position parameters of each epoch in the time window described in step S4, and obtain the motion state of the observed object in the time window;

[0015] Step S6: Based on the dynamic model described in Step S5, obtain the low-Earth orbit satellite orbit extrapolated for 20 minutes and construct the observation equation with orbit constraints;

[0016] Step S7: Obtain the low-Earth orbit satellite's geometric orbit based on the observation equations of the orbital constraints described in Step S6.

[0017] Optionally, in the above-described fast ambiguity reconvergence method, step S1 includes:

[0018] Acquire observation data from the multi-frequency GNSS satellite-borne receiver of the observed object;

[0019] The GNSS observation data is preprocessed.

[0020] Construct a combined ionosphere-free observation equation based on phase and pseudorange.

[0021] Optionally, in the above-described fast ambiguity reconvergence method, the step of preprocessing the GNSS observation data includes:

[0022] Single-point positioning of low-orbit satellites, setting of satellite cutoff elevation angle, atmospheric delay correction, gross error detection and processing, and correction of antenna phase center of satellites and onboard receivers.

[0023] Optionally, in the above-described fast ambiguity reconvergence method, step S3 includes:

[0024] Linearize the GNSS observation equations;

[0025] By combining the phase and pseudorange observation equations, the geometric orbit of the low-Earth orbit satellite can be obtained;

[0026] Optionally, in the above-mentioned fast ambiguity reconvergence method, the low-Earth orbit satellite's geometric orbit is obtained through Kalman filtering.

[0027] Optionally, in the above-described fast ambiguity reconvergence method, step S5 includes:

[0028] The dynamic model is obtained based on the position parameters of the observed object within the time window n epochs, and the motion state of the observed object at any epoch within the time window n epochs is obtained.

[0029] Optionally, in the above-described fast ambiguity reconvergence method, step S6 further includes:

[0030] The dynamic model obtained within the time window is used to extrapolate the low-Earth orbit satellite orbit for 20 minutes. The extrapolated orbit is used as the initial orbit and a smaller initial equation is assigned to it to obtain the observation equation with orbital constraints.

[0031] Optionally, in the above-mentioned fast reconvergence method for ambiguity, the initial variance assigned to the extrapolation trajectory should increase with the extrapolation time.

[0032] In summary, this invention employs a dynamic model fitting extrapolation, effectively utilizing the observation information of each epoch by taking advantage of the position parameters of the observed object, thus ensuring the accuracy of the geometric orbit extrapolation and enhancing the usability of the method.

[0033] Specifically, compared with the prior art, the present invention has the following advantages:

[0034] Existing geometric orbit fitting extrapolation methods are generally based on mathematical orbit fitting. When fitting epoch by epoch, the fitting results are easily affected by various observation errors, resulting in weak fitting accuracy. Furthermore, they are susceptible to the sampling rate; when the sampling rate is too low, the fitting fails to converge. In contrast, physical dynamic model fitting extrapolation methods consider the physical state of low-Earth orbit satellite motion, resulting in higher fitting accuracy.

[0035] Existing fast ambiguity reconvergence methods generally utilize ionospheric parameters and tropospheric wet delay as external constraints. However, since most low-Earth orbit (LEO) satellites orbit around 500 kilometers, the observation signals from onboard receivers are unaffected by tropospheric delay, making tropospheric constraints unsuitable. Furthermore, existing ionospheric models lack information about the ionosphere above LEO satellites, similarly preventing the use of ionospheric delay as a constraint. In contrast, ambiguity reconvergence methods based on orbital constraints effectively utilize fully converged orbital information, providing a more accurate initial orbit and demonstrating applicability to LEO satellites lacking external information such as ionospheric and tropospheric parameters.

[0036] Existing methods for rapid ambiguity reconvergence do not adequately consider the characteristics of low-Earth orbit (LEO) satellite orbits and motions. When orbit sampling rates are low and external information from the ionosphere and troposphere is lacking, existing methods exhibit limitations. This invention takes into account the motion characteristics of LEO satellites, providing a relatively accurate extrapolated orbit when data interruptions occur. Orbital constraints are applied in the early stages of data recovery, thereby accelerating rapid ambiguity reconvergence and ensuring high-precision geometric orbit determination of LEO satellites in real-time. Attached Figure Description

[0037] Figure 1 This is a schematic diagram of the ambiguity fast reconvergence method in a preferred embodiment of the present invention;

[0038] Figure 2 for Figure 1 A detailed flowchart of step S1 is shown below;

[0039] Figure 3 for Figure 1 A detailed flowchart of step S3 is shown below;

[0040] Figure 4 for Figure 1 A schematic diagram of the specific process for step S6. Detailed Implementation

[0041] To ensure high-precision real-time orbit determination for low-Earth orbit (LEO) satellites, this invention proposes a rapid ambiguity reconvergence method. The basic idea is as follows: When data interruption occurs, the dynamic model is fitted using the LEO coordinates before the interruption, and orbit extrapolation is performed. To ensure the extrapolation duration is greater than the interruption duration, the orbit extrapolation duration is set to 20 minutes. During data recovery, the extrapolated orbit is used as the initial coordinate value, and a small variance is assigned to it during filtering. Based on the characteristic that extrapolation accuracy decreases with extrapolation duration, the assigned initial variance should gradually increase with each epoch. By providing relatively accurate initial orbit information and strong orbit constraints, rapid ambiguity reconvergence after data interruption is achieved, thereby providing high-precision real-time orbit determination for LEO satellites.

[0042] The specific embodiments of the present invention will now be described in more detail with reference to the accompanying drawings. The advantages and features of the present invention will become clearer from the following description and claims. It should be noted that the drawings are all in a very simplified form and use non-precise proportions, and are only used to facilitate and clarify the illustration of the embodiments of the present invention.

[0043] refer to Figure 1 In a preferred embodiment of the present invention, a method for fast reconvergence of ambiguity includes:

[0044] Step S1: Obtain multi-frequency GNSS observation data of the observed object, and construct observation equations based on the GNSS observation data;

[0045] For details, please refer to Figure 2 Step S1 includes (step S1 is conventional technology in the art):

[0046] Step S11: Obtain observation data from the multi-frequency GNSS satellite receiver of the observed object.

[0047] Step S12: Perform data preprocessing on the GNSS observation data.

[0048] Data preprocessing includes, but is not limited to, point positioning, satellite cutoff elevation angle setting, atmospheric delay correction, gross error detection and processing, and antenna phase center correction for satellites and receivers. This invention does not impose any limitations on these aspects.

[0049] Preferably, the weighted formula for the elevation angle is:

[0050]

[0051] Where the subscript i represents the i-th satellite, θ represents its elevation angle, σ0 is the prior unit weighted mean square error, and σ is the prior standard deviation of the current observation.

[0052] Step S13: Construct the phase and pseudorange observation equations.

[0053] The observation equation is as follows:

[0054]

[0055]

[0056] Wherein, the subscript j represents the signal frequency; dt is the geometric distance between the satellite and the receiver; c is the speed of light; r and dt s These represent the clock biases at the receiver and satellite ends, respectively. This is the tropospheric delay. It represents the factor of ionospheric delay and is used to calculate the amount of ionospheric delay at other frequencies; This represents the ionospheric delay of the f1 frequency signal along the oblique path. For random noise; λ j φ is the wavelength corresponding to frequency point f1. r,j (t0) represents the receiver end f j Initial phase deviation of the frequency; For satellite end f j Initial phase deviation of the frequency; f j Integer ambiguity of frequency; D j,r and These are the receiver end and the satellite end, respectively. jFrequency code hardware delay; B j,r and These are the receiver end and the satellite end, respectively. j The phase hardware delay of the frequency. Other errors, such as Earth's rotation, antenna phase center deviation (PCO), antenna phase center variation (PCV), phase entanglement, and relativistic effects, are all corrected through the model.

[0057] Step S2: Calculate the time difference Δt between the current k and the previous epoch k-1, and determine whether the time difference Δt is less than the threshold T, where T≥60s, k≥2, and k is a positive integer;

[0058] If so, proceed to step S3;

[0059] If not, proceed to step S4.

[0060] Step S3: Obtain the position parameters according to equations (1) and (2).

[0061] For details, please refer to Figure 3 Step S3 includes:

[0062] Step S31: First, linearize equations (1) and (2), that is, linearize the pseudorange and phase observation equations, to obtain:

[0063]

[0064]

[0065] Among them, l s ,m s ,n s δx, δy, and δz are the cosines of the coordinates from the station to the satellite in the Earth-fixed system; δx, δy, and δz are the coordinate corrections for the low-Earth orbit satellite. This is the floating-point ambiguity parameter.

[0066] Step S32: Simultaneously establish the phase and pseudorange observation equations, and write the linearized observation equations in matrix form:

[0067]

[0068] in, This represents the position parameter and the floating-point ambiguity parameter, and A is the coefficient matrix.

[0069] Step S33: Obtain the position parameters of the observed object.

[0070] Preferably, the present invention uses Kalman filtering for solving the problem. The present invention does not impose any limitations on this method. The time update step is as follows:

[0071]

[0072]

[0073] in, The state prediction value at time K. Let K-1 be the state vector. Let A be the effect of external forces on the system at time K-1, A be the state transition matrix, and B be the input control matrix, transforming the external influences into their effects on the state. Let P be the prior error covariance matrix at time K. k-1 Let Q be the posterior error covariance matrix at time K-1, and let Q be the process noise covariance matrix.

[0074] Furthermore, the Kalman filter state update steps are as follows:

[0075]

[0076]

[0077]

[0078] Where H is the observation matrix, R is the observation noise covariance matrix, and K k Let δ be the Kalman gain matrix at time K. k The observation value at time K, Let P be the state vector at time K. k Let K be the posterior error covariance matrix. Optimal parameter estimation can be achieved through time and state updates.

[0079] Step S4: Select a time window of length n and determine whether the current cumulative observation duration of the observed object is less than n, where 12h≤n≤24h.

[0080] Since the accuracy of dynamic fitting extrapolation is related to the fitting time, to ensure the accuracy of orbit extrapolation, the cumulative observation time before orbit extrapolation should be greater than 12 hours. Considering the impact of the calculation time of fitting extrapolation on real-time orbit determination, the cumulative observation time is set to be less than or equal to 24 hours.

[0081] Step S5: Obtain the dynamic model based on the position parameters of each epoch in the time window, and obtain the motion state of the observed object in the time window.

[0082] Since the motion of low-Earth orbit satellites has certain physical significance, and the position parameters between different epochs are correlated, the principle of satellite orbiting the Earth can be used to derive a dynamic model that describes the motion state of an object within a given time window, based on the position parameters at each epoch. The specific solution method for the dynamic model is described in step S6.

[0083] Step S6: Based on the dynamic model, obtain the low-Earth orbit satellite orbit extrapolated for 20 minutes and construct the observation equation with orbital constraints.

[0084] For details, please refer to Figure 4 In a preferred embodiment of the present invention, step S6 includes:

[0085] Step S61: Obtain the dynamic model based on the position parameters of the observed object within the time window n epochs, and obtain the motion state of the observed object at any epoch within the time window n epochs. Optionally, the dynamic model considers the influence of various perturbation forces. In a preferred embodiment of the present invention, the motion differential equation of the low-orbit satellite is expressed as:

[0086]

[0087] Among them, r, and , respectively, represent the position, velocity, and acceleration of the low-Earth orbit satellite; f is the disturbance acceleration; and q is the sum of the disturbance force parameters and orbital element parameters.

[0088] Step S62: Construct the dynamic observation equation. The dynamic observation equation for any epoch within the n time intervals can be expressed as:

[0089]

[0090] in, This is the linearized state transition matrix. The positional information of each epoch within the time window is substituted into the established dynamic model.

[0091] Step S63: Combine the time windows (t1, t2) n The dynamic observation equations for each epoch within the timeframe are used to establish an n-dimensional observation equation:

[0092]

[0093] Where, r ti For t i The satellite position is obtained through orbital integration at all times; For t i The satellite's geometric orbit corresponding to the given time. Based on equation (13), the position and dynamic parameters (r0, r0, r0) of the low-orbit satellite at the initial time t0 are estimated using least squares estimation. p0), and based on this set of parameters, the predicted value of the low-Earth orbit satellite orbit is obtained through orbit integration, where the prediction duration is set to 20 minutes.

[0094] Step S64: Extrapolate the orbit using the dynamic model and construct the observation equations with orbital constraints. The extrapolated orbit is used as the initial orbit, and a small initial variance is assigned:

[0095] r i =r ep (14)

[0096]

[0097] Where, r i r is the initial orbit corresponding to the i-th epoch during data recovery; ep The extrapolated orbit at the corresponding time; Let dσ be the initial variance of the three positional parameters (X, Y, Z). 2 This is the variance increasing factor.

[0098] Step S7: Obtain the geometric orbit of the low-Earth orbit satellite according to the observation equation with orbital constraints. Substitute the orbital constraints established by equations (14) and (15) into equations (6) to (10) to calculate the geometric orbit of the low-Earth orbit satellite.

[0099] In summary, this invention employs a dynamic model fitting extrapolation, effectively utilizing the observation information of each epoch by taking advantage of the position parameters of the observed object, thus ensuring the accuracy of the geometric orbit extrapolation and enhancing the usability of the method.

[0100] Specifically, compared with the prior art, the present invention has the following advantages:

[0101] Existing geometric orbit fitting extrapolation methods are generally based on mathematical orbit fitting. When fitting epoch by epoch, the fitting results are easily affected by various observation errors, resulting in weak fitting accuracy. Furthermore, they are susceptible to the sampling rate; when the sampling rate is too low, the fitting fails to converge. In contrast, physical dynamic model fitting extrapolation methods consider the physical state of low-Earth orbit satellite motion, resulting in higher fitting accuracy.

[0102] Existing fast ambiguity reconvergence methods generally utilize ionospheric parameters and tropospheric wet delay as external constraints. However, since most low-Earth orbit (LEO) satellites orbit around 500 kilometers, the observation signals from onboard receivers are unaffected by tropospheric delay, making tropospheric constraints unsuitable. Furthermore, existing ionospheric models lack information about the ionosphere above LEO satellites, similarly preventing the use of ionospheric delay as a constraint. In contrast, ambiguity reconvergence methods based on orbital constraints effectively utilize fully converged orbital information, providing a more accurate initial orbit and demonstrating applicability to LEO satellites lacking external information such as ionospheric and tropospheric parameters.

[0103] Existing methods for rapid ambiguity reconvergence do not adequately consider the characteristics of low-Earth orbit (LEO) satellite orbits and motions. When orbit sampling rates are low and external information from the ionosphere and troposphere is lacking, existing methods exhibit limitations. This invention takes into account the motion characteristics of LEO satellites, providing a relatively accurate extrapolated orbit when data interruptions occur. Orbital constraints are applied in the early stages of data recovery, thereby accelerating rapid ambiguity reconvergence and ensuring high-precision geometric orbit determination of LEO satellites in real-time.

[0104] The above are merely preferred embodiments of the present invention and do not constitute any limitation on the present invention. Any equivalent substitutions or modifications made by those skilled in the art to the technical solutions and content disclosed in the present invention without departing from the scope of the present invention shall be deemed to have remained within the protection scope of the present invention.

Claims

1. A method for fast re-convergence of orbit-constrained LEO geometric method-determined ambiguity, characterized in that, include: Step S1: Obtain multi-frequency GNSS observation data of the observed object, and construct observation equations based on the GNSS observation data; Step S2: calculating the current k time difference with the previous epoch k -1 , determining whether the time difference is less than a threshold T , wherein , , k is a positive integer; If so, proceed to step S3; If not, proceed to step S4; Step S3: Obtain the position parameters according to the observation equation described in step S1; Step S4: select a time window with length of n , and determine whether the current accumulated observation time length of the observation object is less than n , wherein ; If so, proceed to step S3; If not, proceed to step S5; Step S5: Obtain the dynamic model based on the position parameters of each epoch in the time window described in step S4, and obtain the motion state of the observed object in the time window; Step S6: Based on the dynamic model described in Step S5, obtain the extrapolated low-Earth orbit satellite orbit for 20 minutes and construct the observation equation with orbital constraints; specifically including: Step S61: obtaining a dynamic model of the position parameter of the observation object in the time window n according to the position parameter of the observation object in the time window n obtaining the motion state of any epoch of the observation object in the time window The equations of motion for the low-orbit satellite are expressed as follows: （11） wherein, , and are the position, velocity and acceleration of the low earth orbit satellite respectively; f（） is the perturbation acceleration; is the sum of the perturbation force parameters and the orbital element parameters; Step S62: Constructing the kinematic observation equation, which is n The kinematic observation equation at any epoch within the time interval is expressed as: （12） wherein, is the linearized state transition matrix; substituting the position information of each epoch within the time window into the established dynamic model; Step S63: Combine the time windows ( The dynamic observation equations for each epoch within the timeframe are established. n 3D observation equation: （13） in, for The satellite position is obtained through orbital integration at all times; for The satellite's geometric orbit corresponding to the time; according to equation (13), the initial time of the low-orbit satellite is estimated using least squares estimation. Location and dynamic parameters ( , , Based on this set of parameters, the predicted value of the low-Earth orbit satellite orbit is obtained through orbit integration; Step S64: Extrapolate the trajectory using the dynamic model and construct the observation equations with trajectory constraints; The extrapolated orbit is used as the initial orbit, and an initial variance is assigned: （14） （15） in, During the data recovery period i The initial orbit corresponding to each epoch; The extrapolated orbit at the corresponding time; for( X , Y , Z The initial variances of the three positional parameters, It is the variance increasing factor; Step S7: Obtain the low-Earth orbit satellite's geometric orbit based on the observation equations of the orbital constraints described in Step S6.

2. The ambiguity fast reconvergence method as described in claim 1, characterized in that, Step S1 includes: Acquire observation data from the multi-frequency GNSS satellite-borne receiver of the observed object; The GNSS observation data is preprocessed. Construct a combined ionosphere-free observation equation based on phase and pseudorange.

3. The ambiguity fast reconvergence method as described in claim 2, characterized in that, The steps for preprocessing the GNSS observation data include: Single-point positioning of low-orbit satellites, setting of satellite cutoff elevation angle, atmospheric delay correction, gross error detection and processing, and correction of antenna phase center of satellites and onboard receivers.

4. The fast ambiguity reconvergence method as described in claim 2, characterized in that, Step S3 includes: Linearize the GNSS observation equations; By combining the phase and pseudorange observation equations, the geometric orbit of the low-Earth orbit satellite can be obtained.

5. The ambiguity fast reconvergence method as described in claim 4, characterized in that, The low-Earth orbit satellite's geometric orbit is obtained using Kalman filtering.

6. The fast ambiguity reconvergence method as described in claim 1, characterized in that, Step S5 includes: Based on the observed object within the time window n The position parameters of the inner epoch are obtained from the dynamic model, which acquires the observed object within the time window. n The motion state of any epoch within the inner epoch.

7. The ambiguity fast reconvergence method as described in claim 1, characterized in that, Step S6 further includes: The dynamic model obtained within the time window is used to extrapolate the low-Earth orbit satellite orbit for 20 minutes. The extrapolated orbit is used as the initial orbit and assigned an initial equation to obtain the observation equation with orbital constraints.

8. The ambiguity fast reconvergence method as described in claim 7, characterized in that, The initial equation assigned to the extrapolated trajectory should increase as the extrapolation time increases.

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