Navigation constellation space-based timekeeping method

Abstract

The present application relates to navigation constellation space-based time keeping method, comprising: S1, satellite in-orbit based on the last time's star clock estimation, time update prediction current epoch state's star clock initial value;S2, based on the input of external prior orbit information, each star calculates the relativistic error of the corresponding time according to the preset integral step and gradually accumulates to obtain the star clock frequency error caused by the current epoch relativistic effect;S3, the relativistic effect obtained by in-orbit integration of the two ends of the inter-satellite link is corrected to the inter-satellite clock difference observation, and data preprocessing is carried out to obtain the inter-satellite relative clock difference measurement;S4, after all the satellites in the constellation perform S1-S3, the star clock state filtering measurement is updated;S5, based on the preset KPW time scale algorithm, the space-based time reference is constructed, and the satellite clock difference is reconstructed.The present application fully considers the difference of the gravity potential and the running speed of the two satellites at the two ends of the inter-satellite link, can play the maximum performance of the satellite-borne atomic clock, and realizes reliable constellation long-term space-based time keeping.

Description

Technical Field

[0001] This invention relates to the field of satellite technology, and more specifically to a space-based timekeeping method for navigation constellations. Background Technology

[0002] Providing high-precision time transmission or synchronization to global users and near-Earth space vehicles is one of the core tasks of GNSS satellite navigation systems. The ephemeris clock information broadcast in real time by the navigation system is generated, updated, and uploaded by the ground system. Establishing a highly stable GNSS time reference based on space-based observations and onboard atomic clocks can significantly reduce the complexity of ground operation and maintenance. Currently, international satellite navigation systems are focusing on promoting the development of constellation-based long-term timekeeping capabilities supported by inter-satellite measurement interactions.

[0003] The long-term, highly reliable space-based timekeeping of a constellation relies not only on factors such as highly stable onboard atomic clocks, accurate setting of clock process noise, high-precision inter-satellite measurements, initial values ​​of clock states, and the construction of a space-based time reference, but also on the degree of perfection of the error model correction. After epoch normalization in traditional inter-satellite two-way measurements, the decoupled clock error relative to the measurement error in observation mainly includes relativistic effects and the difference in transmission and reception delays of the inter-satellite link. Inter-satellite link delays generally have high stability and can be calibrated in advance. For the relativistic effects caused by differences in gravitational potential and orbital velocity at the instantaneous positions of the satellites at both ends of the inter-satellite link, conventional constellation-based timekeeping algorithms, following the IGS protocol, only consider corrections for the constant drift components of general and special relativity and the periodic fluctuations caused by orbital eccentricity.

[0004] The main problem that still needs to be solved in current technologies is that conventional constellation-based timekeeping techniques only address the correction of relativistic effects in terms of the constant drift components of general and special relativity and the periodic fluctuations caused by orbital eccentricity. They neglect higher-order relativistic errors such as the half-orbital period caused by Earth's J2 perturbation and the half-moon phase and semi-annual period caused by solar and lunar effects. Ignoring these higher-order relativistic effects significantly affects the accuracy of inter-satellite clock error measurement, satellite clock prediction performance, and frequency stability, thereby reducing the construction of space-based time references and the long-term timekeeping capability of constellations. Previous research on space-based timekeeping schemes did not consider the impact of higher-order relativistic effects, inhibiting the maximum performance of highly stable onboard atomic clocks and reducing the long-term space-based timekeeping performance of constellations. Summary of the Invention

[0005] To address the problems existing in the prior art, this invention proposes a long-term space-based timekeeping method for navigation constellations that takes into account high-precision relativistic corrections. This method eliminates periodic frequency errors such as star clock half-orbit errors caused by defects in the current IGS protocol relativistic model, thereby improving the long-term timekeeping and timing service performance of the constellation.

[0006] To achieve the above-mentioned objectives of this invention, an embodiment of this invention proposes a space-based timekeeping method for navigation constellations, comprising:

[0007] S1, the satellite's on-orbit clock estimate is based on the previous moment, and the initial value of the clock is updated to predict the current epoch state.

[0008] S2, based on external prior orbital information input, each star calculates the relativistic error at the corresponding moment according to the preset integration step size and gradually accumulates to obtain the star clock frequency error caused by the relativistic effect of the current epoch;

[0009] S3 corrects the relativistic effects obtained by on-orbit integration of satellites at both ends of the inter-satellite link to the inter-satellite clock error observation, and performs data preprocessing to obtain the inter-satellite relative clock error measurement;

[0010] S4, after all satellites in the constellation have performed S1-S3, perform star clock status filtering measurement update;

[0011] S5, based on the preset KPW timescale algorithm, constructs a space-based time reference and reconstructs satellite clock errors.

[0012] In a preferred embodiment of the present invention, the time update of the satellite clock bias parameter in step S1 is expressed as follows:

[0013] X k,k-1 =Φ k,k-1 ·X k-1 +w k-1 ,w k-1 ~N(0,Q) k-1 )

[0014] D k,k-1 =Φ k,k-1 ·D k-1 ·Φ k,k-1 +Q k-1

[0015] Wherein, subscripts k and k-1 represent the current epoch and the previous epoch, respectively; X is the star clock state vector, including time difference a0, time drift a1, and frequency drift a2; w is the dynamic noise vector; Q is the covariance matrix of the dynamic noise w; and D... k-1 and D k,k-1 Let Φ be the error covariance matrix of the previous epoch and the prediction covariance matrix of the current epoch. k,k-1 Let represent the state transition matrix from the previous epoch to the current epoch.

[0016] In a preferred embodiment of the present invention, in step S2, the external prior orbit information includes broadcast ephemeris orbits or space-based space reference maintaining satellite position information;

[0017] In S2, the relativistic error includes higher-order relativistic effects caused by the Earth's non-spherical gravitational potential and the total tidal potential of the Sun and Moon.

[0018] In a preferred embodiment of the present invention, in S2, the change in star clock frequency caused by relativistic effects at the current epoch is expressed as:

[0019]

[0020] Where c represents the speed of light, v is the satellite velocity, R is the Earth's non-spherical gravitational potential, and V s and V M These are the total tidal potentials of the Sun and Moon, G and M, respectively. E These represent the Earth's gravitational constant and Earth's mass, respectively, where h is the preset integration step size, and t is the Earth's gravitational constant and Earth's mass. k t k-1 These represent the current epoch and the previous epoch, respectively.

[0021] In a preferred embodiment of the present invention, in step S3, the inter-satellite clock error observation P is performed to decouple the inter-satellite bidirectional link with satellites A and B at both ends. AB Corrections were made for inter-satellite clock bias observations P. AB Represented as:

[0022] P AB =c·[dt B (t k )-dt A (t k )]+c(δ A ′ A -δ B ′)+c(Δτ A,r -Δτ B,r )+ε AB

[0023] Where, δ′ A and δ′ A ε is half the difference between the transmit and receive delays of the inter-satellite link payload equipment of satellite A and satellite B, respectively. AB To measure noise, Δτ A,r and Δτ B,r Let dt represent the clock bias changes caused by the relativistic effects of the integral accumulation of satellites A and B, respectively. A (tk) and dt B (t k ) represent the current epoch t respectively k The clock difference between satellite A and satellite B can be expressed as:

[0024] dt A (t k ) = a A,0 +a A,1·(t k -t k-1 )+a A,2 ·(t k -t k-1 ) 2

[0025] dt B (t k ) = a B,0 +a B,1 ·(t k -t k-1 )+a B,2 ·(t k -t k-1 ) 2

[0026] Among them, a A,0 a A,1 and a A,2 Let a represent the time difference, time drift, and frequency drift of satellite A, respectively. B,0 a B,1 and a B,2 These represent the time difference, time drift, and frequency drift of satellite B, respectively.

[0027] After error correction, data preprocessing is performed on inter-satellite clock error observations. First, the pre-a priori residuals of inter-satellite clock error are calculated:

[0028]

[0029] in, and Based on equation X, the time difference a0, time drift a1, and frequency drift a2 from the previous epoch are respectively calculated. k,k-1 One-step prediction value;

[0030] A consistency check is performed on the residuals to identify and remove inter-satellite clock error observations, resulting in clean inter-satellite two-way clock error observations. Assume that satellite A at the current epoch t... k There are n inter-satellite clock error observations:

[0031] l 1×n =[res1 res2 ... res i ... res n ]

[0032] Prior residuals of inter-satellite clock errors l 1×n The median (MAD) of a vector is calculated. If the following condition is met, the observation is considered abnormal and is removed or marked:

[0033] |res i -MAD|>λ·m

[0034] Wherein, λ and m are empirical values, and m is related to the noise level of the inter-satellite link clock difference measurement.

[0035] In a preferred embodiment of the present invention, in step S4, the star clock state filtering measurement update is performed by first constructing the observation equation:

[0036] z k =H k ·X k,k-1 +l k ,l k ~N(0,R k )

[0037] Among them, z k H k and l k Design the matrix and prior residual matrix for the inter-satellite relative clock error observations and star clock filtering estimation of the entire constellation, R k Let Variance be the observed values;

[0038] The star clock difference filter estimation form is expressed as:

[0039]

[0040] l k =z k -H k X k,k-1

[0041] X k =X k,k-1 +K k J k

[0042] Where K and J are filter gain matrices, X k For the current epoch t k Time-based star clock filtering estimation.

[0043] In a preferred embodiment of the present invention, in step S5, the space-based KPW timescale algorithm is used to discard the star clock phase estimate and use the frequency estimate to reconstruct the clock error as the clock error prediction value of the weighted average timescale, thereby achieving long-term maintenance of system time in the constellation without ground support mode, as expressed as:

[0044]

[0045] Where, x i (t) represents the clock difference of atomic clock i relative to the ideal time scale. This is an estimate of the clock error of the atomic clock relative to the space-based Kalman timescale, where xe(t) is the clock error of the space-based Kalman timescale relative to the ideal timescale, and w i (t) is a weighting factor reflecting the wandering noise intensity of atomic clock i, and N is the number of satellite atomic clocks.

[0046] The navigation constellation space-based timekeeping method of the present invention utilizes a high-precision relativistic correction model to fully consider the differences in gravitational potential and orbital speed at the instantaneous positions of the two satellites at the two ends of the inter-satellite link, which leads to periodic errors in the satellite clock frequency. This, in turn, enables each onboard atomic clock to perform at its maximum capacity, achieving more reliable long-term space-based timekeeping for the constellation. Attached Figure Description

[0047] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0048] Figure 1 This is a flowchart illustrating the space-based timekeeping method for navigation constellations according to an embodiment of the present invention;

[0049] Figure 2 This is a schematic diagram illustrating the principle of the navigation constellation space-based timekeeping method according to an embodiment of the present invention. Detailed Implementation

[0050] The description of the embodiments in this specification should be taken in conjunction with the accompanying drawings, which should form part of the complete specification. In the drawings, the shape or thickness of the embodiments may be exaggerated and may be indicated in a simplified or convenient manner. Furthermore, parts of the various structures in the drawings will be described separately; it is worth noting that elements not shown in the figures or not described in words are in a form known to those skilled in the art.

[0051] The descriptions of the embodiments herein, including any references to directions and orientations, are for ease of description only and should not be construed as limiting the scope of the invention. The following description of preferred embodiments involves combinations of features, which may exist independently or in combination; the invention is not particularly limited to the preferred embodiments. The scope of the invention is defined by the claims.

[0052] like Figure 1 and Figure 2 As shown, this embodiment of the invention proposes a space-based timekeeping method for navigation constellations, comprising:

[0053] S1, the satellite's on-orbit clock estimate is based on the previous moment, and the initial clock value for the current epoch is predicted by time updates.

[0054] The satellite clock state time update mainly involves extrapolating the estimated state information from the previous epoch to obtain the initial values ​​of the satellite clock parameters for the solution epoch. This provides the necessary input for preprocessing inter-satellite clock error observation data and for filtering measurement correction. The time update of the satellite clock error parameters is expressed as:

[0055] X k,k-1 =Φ k,k-1 ·X k-1 +w k-1 ,w k-1 ~N(0,Q) k-1 )

[0056] D k,k-1 =Φ k,k-1 ·D k-1 ·Φ k,k-1 +Q k-1

[0057] Wherein, subscripts k and k-1 represent the current epoch and the previous epoch, respectively; X is the star clock state vector, including time difference a0, time drift a1, and frequency drift a2; w is the dynamic noise vector; Q is the covariance matrix of the dynamic noise w; and D... k-1 and D k,k-1 Let Φ be the error covariance matrix of the previous epoch and the prediction covariance matrix of the current epoch. k,k-1 Let represent the state transition matrix from the previous epoch to the current epoch.

[0058] S2, based on external prior orbital information input, each star calculates the relativistic error at the corresponding moment according to the preset integration step size and gradually accumulates to obtain the star clock frequency error caused by the relativistic effect of the current epoch.

[0059] This includes external prior orbital information, such as broadcast ephemeris orbits or space-based references maintaining satellite position information. Higher-order relativistic errors include the Earth's non-spherical harmonic gravitational potential and the total solar-lunar tidal potential.

[0060] The change in star clock frequency caused by relativistic effects at the current epoch is expressed as:

[0061]

[0062] Where c represents the speed of light, v is the satellite velocity, R is the Earth's non-spherical gravitational potential, and V s and V M These are the total tidal potentials of the Sun and Moon, G and M, respectively. E These represent the Earth's gravitational constant and Earth's mass, respectively, where h is the preset integration step size, and t is the Earth's gravitational constant and Earth's mass. k t k-1 These represent the current epoch and the previous epoch, respectively.

[0063] S3 corrects the relativistic effects obtained by on-orbit integration of satellites at both ends of the inter-satellite link to the inter-satellite clock error observation, and performs data preprocessing to obtain the inter-satellite relative clock error measurement.

[0064] Inter-satellite clock error observation P for decoupling of inter-satellite bidirectional links with satellites A and B at both ends. AB Corrections were made for inter-satellite clock bias observations P. AB Represented as:

[0065] P AB =c·[dt B (t k )-dt A (t k )]+c(δ′ A -δ′ B )+c(Δτ A,r -Δτ B,r )+ε AB

[0066] Where, δ′ A and δ′ A ε is half the difference between the transmit and receive delays of the inter-satellite link payload equipment of satellite A and satellite B, respectively. AB To measure noise, Δτ A,r and Δτ B,r Let dt represent the clock bias changes caused by the relativistic effects of the integral accumulation of satellites A and B, respectively. A (t k ) and dt B (t k ) represent the current epoch t respectively k The clock difference between satellite A and satellite B can be expressed as:

[0067] dt A (t k ) = a A,0 +a A,1 ·(t k -t k-1 )+a A,2 ·(t k -t k-1 ) 2

[0068] dt B (t k ) = a B,0 +a B,1 ·(t k -t k-1 )+a B,2 ·(t k -t k-1 ) 2

[0069] Among them, a A,0 a A,1 and a A,2 Let a represent the time difference, time drift, and frequency drift of satellite A, respectively. B,0 a B,1 and a B,2 These represent the time difference, time drift, and frequency drift of satellite B, respectively.

[0070] After error correction, data preprocessing is performed on inter-satellite clock error observations. First, the pre-a priori residuals of inter-satellite clock error are calculated:

[0071]

[0072] in, and Based on equation X, the time difference a0, time drift a1, and frequency drift a2 from the previous epoch are respectively calculated. k,k-1 One-step prediction value;

[0073] A consistency check is performed on the residuals to identify and remove inter-satellite clock error observations, resulting in clean inter-satellite two-way clock error observations. Assume that satellite A at the current epoch t... k There are n inter-satellite clock error observations:

[0074] l 1×n =[res1 res2 ... res i ... res n ]

[0075] Prior residuals of inter-satellite clock errors l 1×n The median (MAD) of a vector is calculated. If the following condition is met, the observation is considered abnormal and is removed or marked:

[0076] |res i -MAD|>λ·m

[0077] Wherein, λ and m are empirical values, and m is related to the noise level of the inter-satellite link clock difference measurement.

[0078] S4: After all satellites in the constellation have performed S1-S3, perform a satellite clock status filtering measurement update.

[0079] First, construct the observation equation:

[0080] z k =H k ·X k,k-1 +l k ,l k ~N(0,R k )

[0081] Among them, z k J and l kDesign the matrix and prior residual matrix for the inter-satellite relative clock error observations and star clock filtering estimation of the entire constellation, R k Let Variance be the observed values;

[0082] The star clock difference filter estimation form is expressed as:

[0083]

[0084] l k =z k -H k X k,k-1

[0085] X k =X k,k-1 +K k J k

[0086] Where K and J are filter gain matrices, X k For the current epoch t k Time-based star clock filtering estimation.

[0087] S5, based on the preset KPW timescale algorithm, constructs a space-based time reference and reconstructs satellite clock errors.

[0088] In space-based timekeeping using Kalman filtering of star clocks, the state estimation error can continuously diverge, easily causing numerical calculation results to overflow and rapidly deviate from the ground time reference. Therefore, this paper utilizes a space-based KPW timescale algorithm, discarding star clock phase estimates and using frequency estimates to reconstruct clock errors as the weighted average timescale clock error prediction value. Essentially, this integrates ALGOS and Kalman algorithms to optimize the long-term and short-term stability of the comprehensive timescale, achieving long-term time preservation of the system under constellation-based timekeeping without ground support. The core equations are as follows:

[0089]

[0090] Where, x i (t) represents the clock difference of atomic clock i relative to the ideal time scale. This is an estimate of the clock error of the atomic clock relative to the space-based Kalman timescale, where xe(t) is the clock error of the space-based Kalman timescale relative to the ideal timescale, and w i (t) is a weighting factor reflecting the wandering noise intensity of atomic clock i, and N is the number of satellite atomic clocks.

[0091] The navigation constellation space-based timekeeping method of the present invention utilizes a high-precision relativistic correction model to fully consider the differences in gravitational potential and orbital speed at the instantaneous positions of the two satellites at the two ends of the inter-satellite link, which leads to periodic errors in the satellite clock frequency. This, in turn, enables each onboard atomic clock to perform at its maximum capacity, achieving more reliable long-term space-based timekeeping for the constellation.

[0092] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A space-based timekeeping method for a navigation constellation, characterized in that, include: S1, the satellite's on-orbit clock estimate is based on the previous moment, and the initial value of the clock is updated to predict the current epoch state. S2, based on external prior orbital information input, each star calculates the relativistic error at the corresponding moment according to the preset integration step size and gradually accumulates to obtain the star clock frequency error caused by the relativistic effect of the current epoch; S3 corrects the relativistic effects obtained by on-orbit integration of satellites at both ends of the inter-satellite link to the inter-satellite clock error observation, and performs data preprocessing to obtain the inter-satellite relative clock error measurement; S4, after all satellites in the constellation have performed S1-S3, perform star clock status filtering measurement update; S5, based on the preset KPW timescale algorithm, constructs a space-based time reference and reconstructs satellite clock errors; In S2, the change in star clock frequency caused by relativistic effects at the current epoch is expressed as: in, Represents the speed of light. For satellite speed, For the Earth's non-spherical harmonic gravitational potential, and These are the total tidal potentials of the Sun and the Moon, respectively. and These are the Earth's gravitational constant and the Earth's mass, respectively. To preset the integration step size, t k t k-1 These represent the current epoch and the previous epoch, respectively; In S3, the inter-satellite clock error observation is performed to decouple the two-way inter-satellite link between satellites A and B. Corrections were made, and inter-satellite clock bias observations were performed. Represented as: in, and These are half the difference in transmission and reception delays between the inter-satellite link payload devices of satellite A and satellite B, respectively. To measure noise, and These represent the clock bias variations caused by the relativistic effects of the integral accumulation of satellites A and B, respectively. and Representing the current epoch The clock difference between satellite A and satellite B can be expressed as: in, , and These represent the time difference, time drift, and frequency drift of satellite A, respectively. , and These represent the time difference, time drift, and frequency drift of satellite B, respectively. After error correction, data preprocessing is performed on inter-satellite clock error observations. First, the pre-a priori residuals of inter-satellite clock error are calculated: in, , and The time difference from the previous epoch Time drift Frequency drift According to the formula One-step prediction value; A consistency check is performed on the residuals to identify and remove inter-satellite clock error observations, resulting in clean inter-satellite two-way clock error observations. It is assumed that satellite A is at the current epoch... There are n inter-satellite clock bias observations at any given time: a priori residuals of inter-satellite clock bias The median (MAD) of a vector is calculated. If the following condition is met, the observation is considered abnormal and is removed or marked: in, and Based on experience points. It is related to the noise level of the inter-satellite link clock difference measurement.

2. The space-based timekeeping method for navigation constellations according to claim 1, characterized in that, In S1, the time update of the satellite clock bias parameter is expressed as follows: Among them, subscript and These represent the current epoch and the previous epoch, respectively. The star clock state vector includes time difference. Time drift Frequency drift , For dynamic noise vectors, For dynamic noise covariance matrix and Let be the error covariance matrix of the previous epoch and the prediction covariance matrix of the current epoch. Let represent the state transition matrix from the previous epoch to the current epoch.

3. The space-based timekeeping method for navigation constellations according to claim 1, characterized in that, In S2, the external prior orbit information includes broadcast ephemeris orbits or space-based space reference maintaining satellite position information; In S2, the relativistic error includes higher-order relativistic effects caused by the Earth's non-spherical gravitational potential and the total tidal potential of the Sun and Moon.

4. The space-based timekeeping method for navigation constellations according to claim 2, characterized in that, In step S4, the star clock state filtering measurement update is performed by first constructing the observation equation: in, , and These are, respectively, the inter-star relative clock error observations for the entire constellation, the star clock filtering estimation design matrix, and the prior residual matrix. Let Variance be the observed values; The star clock difference filter estimation form is expressed as: in, , For filtering gain matrix, For the current epoch Time-based star clock filtering estimation.

5. The space-based timekeeping method for navigation constellations according to claim 1, characterized in that, In S5, the space-based KPW timescale algorithm is used, discarding the star clock phase estimate and using the frequency estimate to reconstruct the clock error as the weighted average timescale clock error prediction value, thus achieving long-term maintenance of system time in the constellation without ground support mode, expressed as: in, atomic clock Clock bias relative to an ideal time scale To estimate the clock error of atomic clocks relative to the space-based Kalman timescale. The clock difference for space-based Kalman time relative to an ideal time scale. To reflect the atomic clock Weighting factor for wandering noise intensity This represents the number of atomic clocks on the satellite.

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