A method and system for determining a time-varying gravity field

Abstract

The present invention relates to a method and system for determining a time-varying gravity field. The method includes obtaining observation data before the j-th day in the current month; determining an observation vector, a coefficient matrix, and a weight matrix according to an observation equation; determining initial gravity field model parameters based on the least squares criterion according to the observation vector, the coefficient matrix, and the weight matrix; updating the observation equation, and determining the observation vector, the coefficient matrix, and the weight matrix of the j-th day according to the observation equation of the j-th day; determining updated gravity field model parameters based on the least squares criterion according to the observation vector, the coefficient matrix, and the weight matrix of the j-th day; traversing all days in the current month; traversing all months, determining corresponding gravity field model parameters, and determining the time-varying gravity field according to all the gravity field model parameters. The present invention can improve the determination efficiency of the time-varying gravity field and shorten the running time.

Description

Technical Field

[0001] The present invention relates to the field of satellite gravity measurement, and particularly to a method and system for determining a time-varying gravity field. Background Art

[0002] The successful implementation of gravity satellites has opened up a new way for space exploration of surface mass changes, played an important role in large-scale monitoring of global climate changes such as the atmosphere, ocean, groundwater, and cryosphere, and realized the monitoring of surface mass changes at multiple time scales under a global unified reference framework. The observation data obtained from low-low satellite tracking gravity satellites are solved to determine the time-varying gravity field; the time-varying gravity field is an important means to detect global mass migration changes, such as the ablation of the Antarctic and Greenland ice sheets caused by global climate change, groundwater depletion, ocean mass changes, and co-seismic deformation. High-precision static Earth gravity field models are of great significance in geoid refinement, gravity anomaly and ocean current detection, as well as satellite and missile guidance. However, the data processing process of gravity satellites is complex. Traditional gravity satellite inversion usually adopts the batch processing least squares method, that is, it is necessary to cumulatively collect single-month data before solving the monthly time-varying gravity field coefficients, and there is a problem that it needs to be reprocessed after new observation data is added, bringing unnecessary computational complexity.

[0003] Therefore, in order to improve the determination efficiency of the time-varying gravity field, there is an urgent need to provide a new method or system for determining the time-varying gravity field. Summary of the Invention

[0004] The object of the present invention is to provide a method and system for determining a time-varying gravity field, which can improve the determination efficiency of the time-varying gravity field and shorten the running time.

[0005] To achieve the above object, the present invention provides the following solutions:

[0006] A method for determining a time-varying gravity field, comprising:

[0007] Obtaining the observation data before the j-th day of the current month; the observation data includes: inter-satellite ranging data, precise orbit data, accelerometer data, and attitude data;

[0008] Performing data cutting on the observation data before the j-th day, and constructing an observation equation by using the cut observation data, and determining an observation vector, a coefficient matrix, and a weight matrix according to the observation equation;

[0009] Determining the initial gravity field model parameters based on the least squares criterion according to the observation vector, the coefficient matrix, and the weight matrix;

[0010] Constructing an observation equation for the j-th day by using the observation data of the j-th day, and determining the observation vector for the j-th day, the coefficient matrix for the j-th day, and the weight matrix for the j-th day according to the observation equation for the j-th day;

[0011] Based on the observation vector, coefficient matrix, and weight matrix on the j-th day, determine the updated gravity field model parameters according to the least squares criterion; then replace j with j + 1, and return the step of constructing the observation equation on the j-th day using the observation data on the j-th day, and determining the observation vector, coefficient matrix, and weight matrix on the j-th day according to the observation equation on the j-th day, until all days of the current month are traversed;

[0012] Traverse all months, determine the corresponding gravity field model parameters, and determine the time-varying gravity field according to all the gravity field model parameters.

[0013] Optionally, after obtaining the observation data before the j-th day of the current month, it further includes:

[0014] Preprocess the observation data; the preprocessing includes: unifying the time system and coordinate frame, interpolating the discontinuous accelerometer data and attitude data, and rejecting the gross errors in the inter-satellite ranging data, accelerometer data, and attitude data.

[0015] Optionally, the data cutting of the observation data before the j-th day, constructing the observation equation using the cut observation data, and determining the observation vector, coefficient matrix, and weight matrix specifically include:

[0016] Construct the first observation equation according to the cut precise orbit data, cut accelerometer data, and cut attitude data;

[0017] Determine the first coefficient matrix and the first observation vector according to the first observation equation;

[0018] Construct the second observation equation according to the cut inter-satellite ranging data;

[0019] Determine the second coefficient matrix and the second observation vector according to the second observation equation;

[0020] Determine the coefficient matrix according to the first coefficient matrix and the second coefficient matrix; and determine the observation vector according to the first observation vector and the second observation vector.

[0021] Optionally, the determination of the updated gravity field model parameters based on the observation vector, coefficient matrix, and weight matrix on the j-th day according to the least squares criterion specifically includes the following formula:

[0022]

[0023]

[0024] Where, and are the gravity field model parameters updated on the j-th day, and are the gravity field model parameters updated on the (j - 1)-th day, k is the current month, A j is the coefficient matrix on the j-th day, is the transpose of the coefficient matrix on the j-th day, P j is the weight matrix on the j-th day, is the reciprocal of the weight matrix on the j-th day, y j is the observation vector on the j-th day.

[0025] A time-varying gravity field determination system, comprising:

[0026] An observation data first acquisition module, configured to acquire the observation data before the j-th day in the current month; the observation data includes: inter-satellite ranging data, precise orbit data, accelerometer data, and attitude data;

[0027] An observation equation first construction module, configured to perform data cutting on the observation data before the j-th day, and construct an observation equation by using the cut observation data, and determine the observation vector, the coefficient matrix, and the weight matrix according to the observation equation;

[0028] An initial gravity field model parameter determination module, configured to determine the initial gravity field model parameters based on the least squares criterion according to the observation vector, the coefficient matrix, and the weight matrix;

[0029] An observation equation second construction module, configured to construct the observation equation on the j-th day by using the observation data on the j-th day, and determine the observation vector on the j-th day, the coefficient matrix on the j-th day, and the weight matrix on the j-th day according to the observation equation on the j-th day;

[0030] A gravity field model parameter update module, configured to determine the updated gravity field model parameters based on the least squares criterion according to the observation vector on the j-th day, the coefficient matrix on the j-th day, and the weight matrix on the j-th day; and then replace j with j + 1, and return to the steps of the observation equation second construction module until all days in the current month are traversed;

[0031] A time-varying gravity field determination module, configured to traverse all months, determine the corresponding gravity field model parameters, and determine the time-varying gravity field according to all the gravity field model parameters.

[0032] Optionally, it further includes:

[0033] A data preprocessing module, configured to preprocess the observation data; the preprocessing includes: unifying the time system and the coordinate frame, interpolating the discontinuous accelerometer data and attitude data, and removing the gross errors from the inter-satellite ranging data, accelerometer data, and attitude data.

[0034] Optionally, the first construction module of the observation equation specifically includes:

[0035] The first observation equation construction unit is used to construct the first observation equation according to the cut precise orbit data, the cut accelerometer data, and the cut attitude data;

[0036] The first coefficient matrix and first observation vector determination unit is used to determine the first coefficient matrix and the first observation vector according to the first observation equation;

[0037] The second observation equation construction unit is used to construct the second observation equation according to the cut inter-satellite ranging data;

[0038] The second coefficient matrix and second observation vector determination unit is used to determine the second coefficient matrix and the second observation vector according to the second observation equation;

[0039] The coefficient matrix and observation vector determination unit is used to determine the coefficient matrix according to the first coefficient matrix and the second coefficient matrix; and determine the observation vector according to the first observation vector and the second observation vector.

[0040] Optionally, the gravity field model parameter update module specifically includes the following formula:

[0041]

[0042]

[0043] Where and are the updated gravity field model parameters on the j-th day, and are the updated gravity field model parameters on the (j - 1)-th day, k is the current month, A j is the coefficient matrix on the j-th day, is the transpose of the coefficient matrix on the j-th day, P j is the weight matrix on the j-th day, is the reciprocal of the weight matrix on the j-th day, y j is the observation vector on the j-th day.

[0044] According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

[0045] A method and system for determining a time-varying gravity field provided by the present invention. First, observation equations are constructed using the observation data before the j-th day of the current month, and then the observation vector, coefficient matrix, and weight matrix are determined. Based on the observation vector, coefficient matrix, and weight matrix, the initial gravity field model parameters are determined according to the least squares criterion. Secondly, using the daily observation data, the continuous sequential adjustment method is adopted for dynamic update to determine the gravity field model parameters of the current month, and then the gravity field model parameters of all months are determined. The time-varying gravity field is determined based on all the gravity field model parameters. Compared with the traditional overall adjustment technology, the sequential adjustment solution proposed by the present invention greatly reduces the storage space required by the algorithm and significantly shortens the running time on the premise of ensuring that the estimated gravity field model parameters are equivalent to those of the traditional algorithm. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention, and those of ordinary skill in the art can also obtain other drawings based on these drawings without creative efforts.

[0047] Figure 1 It is a schematic flow chart of a method for determining a time-varying gravity field provided by the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0048] The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention. Obviously, the described embodiments are only some of the embodiments of the present invention, rather than all of them. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts belong to the scope of protection of the present invention.

[0049] The object of the present invention is to provide a method and system for determining a time-varying gravity field, which can improve the determination efficiency of the time-varying gravity field and shorten the running time.

[0050] In order to make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below with reference to the drawings and specific embodiments.

[0051] Figure 1 It is a schematic flow chart of a method for determining a time-varying gravity field provided by the present invention. As Figure 1 shown, a method for determining a time-varying gravity field provided by the present invention includes:

[0052] S101, obtaining the observation data before the j-th day of the current month; the observation data includes: inter-satellite ranging data, precise orbit data, accelerometer data, and attitude data.

[0053] As a specific embodiment, j = 6, and the observation data before the j-th day in the current month, that is, the observation data of the first 5 days in the current month.

[0054] After S101, it further includes:

[0055] Preprocessing the observation data; the preprocessing includes: unifying the time system and the coordinate frame, interpolating the accelerometer data and the attitude data discontinuously, and rejecting gross errors from the inter-satellite ranging data, accelerometer data, and attitude data.

[0056] S102, cutting the observation data before the j-th day, and constructing an observation equation using the cut observation data, and determining the observation vector, coefficient matrix, and weight matrix according to the observation equation;

[0057] As a specific embodiment, each arc segment is 2h for data cutting.

[0058] S102 specifically includes:

[0059] Constructing a first observation equation based on the cut precise orbit data, cut accelerometer data, and cut attitude data;

[0060] Constructing the first observation equation includes the following formula:

[0061]

[0062] Among them, r i is the geometric orbit observation vector at any position within the arc segment, is its correction; r0 and r N are the satellite boundary orbit parameters, and are their corrections respectively; τ i is the normalized epoch time, T is the arc segment length; K is the integral kernel function, τ′ is the integration time

[0063] At any time τ k The disturbing force per unit mass of the satellite is is the differential of the disturbing force, is the non-conservative force acceleration, which can be directly observed by the accelerometer, q = (q1, q2, q3, q4) is the attitude data, and u0 and p0 are the approximate initial values of the gravity field parameters and accelerometer parameters; δu and δp are the parameters to be estimated (corrections).

[0064] Determining the first coefficient matrix and the first observation vector according to the first observation equation;

[0065] Construct the first coefficient matrix and the first observation vector from the above formulas:

[0066]

[0067] Construct the second observation equation according to the inter-satellite ranging data after cutting;

[0068] The second observation equation is:

[0069]

[0070] In the formula, ρ i and ρ k are the inter-satellite distance observation values at times τ i and τ k respectively, and and are their corrections respectively.

[0071] Determine the second coefficient matrix and the second observation vector according to the second observation equation;

[0072] The second coefficient matrix and the second observation vector are respectively:

[0073]

[0074] Determine the coefficient matrix A according to the first coefficient matrix and the second coefficient matrix k =[A1 A2; and determine the observation vector y according to the first observation vector and the second observation vector k =[y1 y2].

[0075] S103. Determine the initial gravity field model parameters based on the least squares criterion according to the observation vector, the coefficient matrix and the weight matrix;

[0076] The initial gravity field model parameters are:

[0077]

[0078] S104. Construct the observation equation for the j-th day using the observation data for the j-th day, and determine the observation vector for the j-th day, the coefficient matrix for the j-th day and the weight matrix for the j-th day according to the observation equation for the j-th day;

[0079] S105. Determine the updated gravity field model parameters based on the least squares criterion according to the observation vector for the j-th day, the coefficient matrix for the j-th day and the weight matrix for the j-th day; then replace j with j + 1, and return to the step of constructing the observation equation for the j-th day using the observation data for the j-th day, and determining the observation vector for the j-th day, the coefficient matrix for the j-th day and the weight matrix for the j-th day, until all days of the current month are traversed;

[0080] S105 specifically includes the following formula:

[0081]

[0082]

[0083] Among them, and are the gravity field model parameters updated on the j-th day, and are the gravity field model parameters updated on the (j - 1)-th day. k is the current month, and A j is the coefficient matrix on the j-th day, is the transpose of the coefficient matrix on the j-th day, and P j is the weight matrix on the j-th day, is the reciprocal of the weight matrix on the j-th day, and y j is the observation vector on the j-th day.

[0084] S106. Traverse all months to determine the corresponding gravity field model parameters, and determine the time-varying gravity field based on all the gravity field model parameters.

[0085] A time-varying gravity field determination system provided by the present invention includes:

[0086] An observation data first acquisition module, configured to acquire the observation data before the j-th day in the current month; the observation data includes: inter-satellite ranging data, precise orbit data, accelerometer data, and attitude data;

[0087] An observation equation first construction module, configured to perform data cutting on the observation data before the j-th day, and construct an observation equation using the cut observation data, and determine the observation vector, coefficient matrix, and weight matrix according to the observation equation;

[0088] An initial gravity field model parameter determination module, configured to determine the initial gravity field model parameters based on the least squares criterion according to the observation vector, coefficient matrix, and weight matrix;

[0089] An observation equation second construction module, configured to construct the observation equation on the j-th day using the observation data on the j-th day, and determine the observation vector on the j-th day, the coefficient matrix on the j-th day, and the weight matrix on the j-th day according to the observation equation on the j-th day;

[0090] A gravity field model parameter update module, configured to determine the updated gravity field model parameters based on the least squares criterion according to the observation vector on the j-th day, the coefficient matrix on the j-th day, and the weight matrix on the j-th day; then replace j with j + 1, and return to the steps of the observation equation second construction module until all days in the current month are traversed;

[0091] A time-varying gravity field determination module, which is used to traverse all months, determine the corresponding gravity field model parameters, and determine the time-varying gravity field according to all the gravity field model parameters.

[0092] A time-varying gravity field determination system provided by the present invention further includes:

[0093] A data preprocessing module, which is used to preprocess the observation data; the preprocessing includes: unifying the time system and the coordinate frame, interpolating the discontinuous accelerometer data and attitude data, and rejecting the gross errors in the inter-satellite ranging data, accelerometer data, and attitude data.

[0094] The first observation equation construction module specifically includes:

[0095] A first observation equation construction unit, which is used to construct a first observation equation according to the cut precise orbit data, cut accelerometer data, and cut attitude data;

[0096] A first coefficient matrix and first observation vector determination unit, which is used to determine the first coefficient matrix and the first observation vector according to the first observation equation;

[0097] A second observation equation construction unit, which is used to construct a second observation equation according to the cut inter-satellite ranging data;

[0098] A second coefficient matrix and second observation vector determination unit, which is used to determine the second coefficient matrix and the second observation vector according to the second observation equation;

[0099] A coefficient matrix and observation vector determination unit, which is used to determine the coefficient matrix according to the first coefficient matrix and the second coefficient matrix; and determine the observation vector according to the first observation vector and the second observation vector.

[0100] The gravity field model parameter update module specifically includes the following formula:

[0101]

[0102]

[0103] Where and are the updated gravity field model parameters on the jth day, and are the updated gravity field model parameters on the (j - 1)th day, k is the current month, A j is the coefficient matrix on the jth day, is the transpose of the coefficient matrix on the jth day, P j is the weight matrix on the jth day, is the reciprocal of the weight matrix on the jth day, y j is the observation vector on the jth day.

[0104] In this specification, the various embodiments are described in a progressive manner. Each embodiment focuses on the differences from other embodiments, and the same or similar parts among the embodiments can be referred to each other. For the system disclosed in the embodiments, since it corresponds to the method disclosed in the embodiments, the description is relatively simple, and the relevant parts can be referred to the description in the method section.

[0105] In this article, specific examples are used to elaborate on the principles and implementation manners of the present invention. The description of the above embodiments is only used to help understand the method of the present invention and its core idea; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present invention.

Claims

1. A method for determining a time-varying gravity field, characterized in that Including: Obtaining the observation data before the j-th day in the current month; The observation data includes: inter-satellite ranging data, precise orbit data, accelerometer data, and attitude data; Performing data cutting on the observation data before the j-th day, constructing an observation equation using the cut observation data, and determining the observation vector, coefficient matrix, and weight matrix according to the observation equation; Determining the initial gravity field model parameters based on the least squares criterion according to the observation vector, coefficient matrix, and weight matrix; Constructing the observation equation for the j-th day using the observation data of the j-th day, and determining the observation vector for the j-th day, the coefficient matrix for the j-th day, and the weight matrix for the j-th day according to the observation equation for the j-th day; Determining the updated gravity field model parameters based on the least squares criterion according to the observation vector for the j-th day, the coefficient matrix for the j-th day, and the weight matrix for the j-th day; then replacing j with j + 1, and returning the step of constructing the observation equation for the j-th day using the observation data of the j-th day, and determining the observation vector for the j-th day, the coefficient matrix for the j-th day, and the weight matrix for the j-th day, until all days in the current month are traversed; Traversing all months, determining the corresponding gravity field model parameters, and determining the time-varying gravity field according to all the gravity field model parameters.

2. The method for determining a time-varying gravitational field according to claim 1, wherein After obtaining the observation data before the j-th day in the current month, it further includes: Preprocessing the observation data; the preprocessing includes: unifying the time system and coordinate frame, interpolating the discontinuous accelerometer data and attitude data, and rejecting the gross errors in the inter-satellite ranging data, accelerometer data, and attitude data.

3. The method for determining a time-varying gravitational field according to claim 1, wherein The performing data cutting on the observation data before the j-th day, constructing an observation equation using the cut observation data, and determining the observation vector, coefficient matrix, and weight matrix according to the observation equation specifically includes: Constructing the first observation equation according to the cut precise orbit data, cut accelerometer data, and cut attitude data; Determining the first coefficient matrix and the first observation vector according to the first observation equation; Constructing the second observation equation according to the cut inter-satellite ranging data; Determining the second coefficient matrix and the second observation vector according to the second observation equation; Determining the coefficient matrix according to the first coefficient matrix and the second coefficient matrix; and determining the observation vector according to the first observation vector and the second observation vector.

4. A method for determining a time-varying gravitational field according to claim 1, characterized in that, The determining the updated gravity field model parameters based on the least squares criterion according to the observation vector for the j-th day, the coefficient matrix for the j-th day, and the weight matrix for the j-th day specifically includes the following formula: Among them, and are the gravity field model parameters updated on the j-th day, and are the gravity field model parameters updated on the (j - 1)-th day, k is the current month, A j is the coefficient matrix on the j-th day, is the transpose of the coefficient matrix on the j-th day, P j is the weight matrix on the j-th day, is the reciprocal of the weight matrix on the j-th day, y j is the observation vector on the j-th day.

5. A time-varying gravity field determination system, characterized in that, Including: The first observation data acquisition module is used to obtain the observation data before the j-th day in the current month; The observation data includes: inter-satellite ranging data, precise orbit data, accelerometer data, and attitude data; The first observation equation construction module is used to perform data cutting on the observation data before the j-th day, construct an observation equation using the cut observation data, and determine the observation vector, coefficient matrix, and weight matrix according to the observation equation; The initial gravity field model parameter determination module is used to determine the initial gravity field model parameters based on the least squares criterion according to the observation vector, coefficient matrix, and weight matrix; The second construction module of the observation equation is used to construct the observation equation of the j-th day by using the observation data of the j-th day, and determine the observation vector, the coefficient matrix and the weight matrix of the j-th day according to the observation equation of the j-th day; The gravity field model parameter update module is used to determine the updated gravity field model parameters based on the least squares criterion according to the observation vector, the coefficient matrix and the weight matrix of the j-th day; then replace j with j + 1, and return to the steps of the second construction module of the observation equation until all days of the current month are traversed; The time-varying gravity field determination module is used to traverse all months, determine the corresponding gravity field model parameters, and determine the time-varying gravity field according to all the gravity field model parameters.

6. The time-varying gravity field determination system according to claim 5, characterized in that, It also includes: The data preprocessing module is used to preprocess the observation data; the preprocessing includes: unifying the time system and the coordinate frame, interpolating the discontinuous accelerometer data and attitude data, and rejecting the gross errors of the inter-satellite ranging data, accelerometer data and attitude data.

7. The time-varying gravity field determination system according to claim 5, wherein The first construction module of the observation equation specifically includes: The first observation equation construction unit is used to construct the first observation equation according to the cut precise orbit data, the cut accelerometer data and the cut attitude data; The first coefficient matrix and the first observation vector determination unit are used to determine the first coefficient matrix and the first observation vector according to the first observation equation; The second observation equation construction unit is used to construct the second observation equation according to the cut inter-satellite ranging data; The second coefficient matrix and the second observation vector determination unit are used to determine the second coefficient matrix and the second observation vector according to the second observation equation; The coefficient matrix and the observation vector determination unit are used to determine the coefficient matrix according to the first coefficient matrix and the second coefficient matrix; and determine the observation vector according to the first observation vector and the second observation vector.

8. A time-varying gravity field determination system according to claim 5, characterized in that The gravity field model parameter update module specifically includes the following formula: Among them, and are the gravity field model parameters updated on the j-th day, and are the gravity field model parameters updated on the (j - 1)-th day, k is the current month, A j is the coefficient matrix on the j-th day, is the transpose of the coefficient matrix on the j-th day, P j is the weight matrix on the j-th day, is the reciprocal of the weight matrix on the j-th day, y j is the observation vector on the j-th day.

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