Satellite gravitational gradient gross error detection method based on tensor invariance and Dixon statistical theory

Abstract

The invention discloses a satellite gravitational gradient gross error detection method based on tensor invariance and a Dixon statistical theory, and relates to the technical field of geodetic survey technologies. According to the method, firstly, a tensor invariant system of a satellite gravitational gradient observation value is established, a first invariant time sequence and Dixon statistics are calculated, and then the gross error of a main diagonal component of the satellite gravitational gradient observation tensor is detected integrally. Meanwhile, a prior gravity field model is introduced, residual error sequences of the second invariant and the third invariant are calculated, Dixon statistic calculation is carried out, and therefore gross errors of all six tensor components of the satellite gravitational gradient observation tensor are detected on the whole. According to the method, on the basis of the tensor invariance theory, the tensor invariance characteristic of the satellite gravitational gradient observation data is combined with the D * on statistical theory, reliable detection of the overall gross error of the satellite gravitational gradient observation tensor is achieved, the gross error detection efficiency and reliability are improved, and the method is suitable for large-scale popularization and application. And an effective means is provided for accurate measurement of a short-wave spectrum structure in an earth gravitational field.

Description

Technical Field

[0001] The invention belongs to the technical field of geodetic measurement, and in particular relates to a satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory. Background Art

[0002] As a high-precision earth observation satellite, the gravity gradient satellite is crucial for determining the fine structure of shortwave in the Earth's gravity field. Changes in the physical environment of the satellite in orbit cause unstable changes in the measurement state of the gravity gradiometer on board the satellite, which inevitably leads to certain gross errors in the satellite gravity gradient observation data. The existence of gross errors in observation values ​​affects the mathematical statistical characteristics of the observation values, resulting in the inapplicability of data processing methods such as least squares adjustment and the pathology of the solution process, which makes the availability of satellite gravity gradient observation data worse and restricts the improvement of the accuracy of the shortwave spectrum in the Earth's gravity field. For this reason, the satellite gravity gradient observation data needs to be detected and eliminated for gross errors.

[0003] The gross error detection methods of satellite gravity gradient observation data are mostly based on a certain component of the satellite gravity gradient observation tensor, using various mathematical statistics methods. This processing process does not take into account the mathematical relationship between the components of the satellite gravity gradient observation tensor. The detection process is cumbersome and has a certain degree of repetitiveness. It is impossible to detect the satellite gravity gradient tensor as a whole, and it is impossible to compare and verify the overall detection of the observation tensor with the gross error detection results of each component, resulting in poor gross error detection efficiency and reliability, which indirectly leads to poor performance of satellite data and affects the accurate determination of the short-wave spectrum structure in the Earth's gravity field. Summary of the invention

[0004] The purpose of the present invention is to provide a satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory. By combining Dixon statistical theory with the tensor invariance mathematical characteristics of the satellite gravity gradient tensor, the problem of poor quality or even unusable satellite gravity gradient observation data caused by the fact that most of the current satellite gravity gradient observation data are based on a certain observation component and the gross error detection efficiency is low is solved.

[0005] In order to solve the above technical problems, the present invention is achieved through the following technical solutions:

[0006] The present invention is a satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory, comprising the following steps:

[0007] Step 1: The gross error of the main diagonal component of the gravitational gradient observation tensor of the overall detection satellite;

[0008] Step 2: Detect gross errors of all six tensor components of the satellite gravity gradient observation tensor.

[0009] As a preferred technical solution of the present invention, the step 1 specifically includes:

[0010] Step 101 establishes a tensor invariant system {I1, I2, I3} of satellite gravity gradient observations;

[0011] Step 102 calculates the first invariant time series of satellite gravity gradient observations;

[0012] Step 103: Calculate the Dixon statistic of the first invariant sequence of satellite gravity gradient observations

[0013] Step 104: According to the Dixon statistic The comparison results with the critical value show the gross error of the main diagonal component of the gravitational gradient observation tensor of the overall detection satellite.

[0014] As a preferred technical solution of the present invention, the expression of the tensor invariant system {I1, I2, I3} in step 101 is:

[0015] I1=V 11 +V 22 +V 33 (1)

[0016]

[0017] As a preferred technical solution of the present invention, the step 104 specifically includes:

[0018] Given a significance level α and a window size K;

[0019] Selection Statistics;

[0020] If the Dixon statistic of the first invariant of the satellite gravitational gradient observation is One of them is greater than the critical value D of the Dixon test α , the observation epoch where the Kth element of the window length is located is considered to be abnormal data and a gross error mark is made;

[0021] If the Kth element is abnormal data, the detection step described in step 104 is performed on the first K-1 elements of the time series until no abnormal data is detected.

[0022] As a preferred technical solution of the present invention, the step 2 specifically includes:

[0023] Step 201 establishes the same tensor invariant system {I1, I2, I3} of satellite gravity gradient observations as step 101;

[0024] Step 202 calculates the residual sequence of the second invariant of the satellite gravity gradient and the third invariant of the satellite gravity gradient;

[0025] Step 203 is to detect the gross errors of all six tensor components of the satellite gravity gradient observation tensor as a whole. As a preferred technical solution of the present invention, the step 202 specifically includes:

[0026] Step 221 uses the prior gravity field model to calculate the prior model value of the gravity gradient tensor in the local north reference coordinate system, and converts it to the satellite gradiometer coordinate system, and then calculates the second invariant and the third invariant of the satellite gravity gradient prior model value;

[0027] Step 2022 calculates the second invariant and the third invariant of the satellite gravity gradient observation value in the satellite gradiometer coordinate system;

[0028] Step 2023 calculates the second invariant residual sequence and the third invariant residual sequence of the satellite gravity gradient observations.

[0029] As a preferred technical solution of the present invention, the step 203 specifically includes:

[0030] Step 2031 calculates the Dixon statistics of the second invariant residual sequence and the third invariant residual sequence of the satellite gravity gradient observation value and

[0031] Step 2032: Based on the Dixon statistic and Compared with the critical value, the overall detection satellite gravity gradient observation tensor of all six tensor components has coarse errors.

[0032] As a preferred technical solution of the present invention, the specific steps of step 2032 include:

[0033] Given a significance level α and a window size K, choose and Statistics;

[0034] If the Dixon statistics of the second invariant and the third variable of the satellite gravity gradient observation are and One of them is greater than the critical value D of the Dixon test α , then the observation epoch where the Kth element of the window length is located is considered to be abnormal data;

[0035] If the Kth element is abnormal data, the detection step of step 2031 is performed on the first K-1 elements of the time series after gross error marking until no abnormal data is detected.

[0036] The present invention has the following beneficial effects:

[0037] The present invention discloses a method for overall detection of gross errors of satellite gravity gradient based on tensor invariance and Dixon statistical theory. The method is based on the tensor invariance theory, combines the tensor invariance characteristics of satellite gravity gradient observation data with the Dixon statistical theory, and applies the method to overall detection of gross errors of satellite gravity gradient observation data, thereby realizing the reliability detection of overall gross errors of satellite gravity gradient observation tensors. By introducing a priori gravity field models, the overall detection of gross errors of the main diagonal components of the gravity gradient tensor and all six tensor components can be independently realized.

[0038] Of course, any product implementing the present invention does not necessarily need to achieve all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings required for describing the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other accompanying drawings can be obtained based on these accompanying drawings without paying creative work.

[0040] Figure 1 This is a flow chart of the satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory;

[0041] Figure 2 It is the overall detection flow chart of gross errors of the main diagonal components of the satellite gravity gradient observation tensor;

[0042] Figure 3 It is the overall detection flow chart of gross errors of all six tensor components of the satellite gravity gradient observation tensor. DETAILED DESCRIPTION

[0043] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0044] A specific application of the present invention is:

[0045] like Figure 1 As shown in the figure, the satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory includes:

[0046] Step 1: Gross error of the main diagonal component of the gravitational gradient observation tensor of the overall detection satellite;

[0047] Step 2: Detect gross errors in all six tensor components of the satellite gravity gradient observation tensor.

[0048] like Figure 2 As shown, the overall detection of gross errors of the main diagonal components of the satellite gravity gradient observation tensor in step 1 specifically includes the following steps:

[0049] Step 101 establishes a tensor invariant system {I1, I2, I3} of satellite gravity gradient observations;

[0050] The expression of the satellite gravitational gradient observation tensor invariant system {I1, I2, I3} is:

[0051] I1=V 11 +V 22 +V 33 (1)

[0052]

[0053] Where: I1 is the first invariant of the satellite gravity gradient tensor invariant system; I2 is the second invariant of the satellite gravity gradient tensor invariant system; I3 is the third invariant of the satellite gravity gradient tensor invariant system; V 11 V is the satellite gravitational gradient observation value component in the xx direction of the satellite gradiometer coordinate system or the XX direction of the local north coordinate system; 12 V is the satellite gravitational gradient observation value component in the xy direction of the satellite gradiometer coordinate system or the xy direction of the local north coordinate system; 13 V is the satellite gravitational gradient observation value component in the xz direction of the satellite gradiometer coordinate system or the XZ direction of the local north coordinate system; 22 V is the satellite gravity gradient observation value component in the yy direction of the satellite gradiometer coordinate system or the YY direction of the local north coordinate system; 23 V is the satellite gravitational gradient observation value component in the yz direction of the satellite gradiometer coordinate system or the YZ direction of the local north coordinate system; 33 It is the satellite gravity gradient observation value component in the zz direction of the satellite gradiometer coordinate system or the ZZ direction of the local north coordinate system.

[0054] It should be pointed out here that the gross error of the main diagonal component of the overall detection satellite gravity gradient observation tensor proposed in the present invention only involves the first invariant of the satellite gravity gradient.

[0055] Step 102 calculates a first invariant time series of satellite gravity gradient observations.

[0056] The main diagonal components of the satellite gravity gradient observations at different observation epochs k in the satellite gradiometer coordinate system are Where i = x, y, z, and substituting into the calculation formula (1) of the tensor invariant system, the first invariant of the satellite gravity gradient observation value at different observation epochs k is obtained:

[0057]

[0058] Select the satellite gravity gradient observation window length K for the Dixon test, and calculate the first invariant of the satellite gravity gradient observation at different observation epochs k. After taking the absolute value, sort them in ascending order to form a time series:

[0059]

[0060] Step 103 calculates the Dixon statistic of the first invariant sequence of satellite gravity gradient observations.

[0061] Introducing Dixon test theory, using quasi-range difference and To estimate the standard deviation of the time series, we can obtain the Dixon statistic of the first invariant of the satellite gravity gradient observations:

[0062]

[0063] Step 104 is to detect the gross errors of the main diagonal components of the satellite gravity gradient observation tensor as a whole.

[0064] Given a significance level α and a window size K, choose Statistics, if the Dixon statistics of the first invariant of the satellite gravitational gradient observations One of them is greater than the critical value D of the Dixon test α , then the observation epoch where the Kth element of the window length is located is considered to be abnormal data; if the Kth element is abnormal data, the same detection step operation is performed on the first K-1 elements of the time series after gross error marking (step 104) until no abnormal data is detected. D corresponding to different significance levels α α See Table 1 for values.

[0065] This completes the overall detection of gross errors in the principal diagonal component of the satellite gravity gradient observation tensor.

[0066] Table 1 Critical values ​​of Dixon test

[0067]

[0068] like Figure 3 As shown, the above step 2 specifically includes:

[0069] Step 201 establishes a tensor invariant system {I1, I2, I3} of satellite gravity gradient observations;

[0070] Step 202 calculates the residual sequence of the second invariant of the satellite gravity gradient and the third invariant of the satellite gravity gradient;

[0071] Step 203 detects the gross errors of all six tensor components of the satellite gravity gradient observation tensor as a whole.

[0072] The step 201 is the same as the step 101 .

[0073] The step 202 specifically includes:

[0074] Step 221 Prior model value of satellite gravity gradient tensor in local north coordinates Calculation.

[0075] Calculate the prior model value of the gravitational gradient tensor in the local north-pointing coordinate system using the prior gravity field model The calculation formula is:

[0076]

[0077] Where: GM is the gravitational constant, r, θ, λ are the geocentric radial, geocentric colatitude and geocentric longitude respectively, R is the average radius of the earth, n, m are the order and degree of the expansion of the spherical harmonic model of the earth's gravity field, and N is the highest order of the a priori gravity field model used. ij , is the gravitational gradient tensor coefficient, and its expression is shown in Table 2, where: are the fully normalized gravitational potential spherical harmonic coefficients of the prior gravity field model, and are the fully normalized associated Legendre function and its first and second order derivatives with respect to the geocentric colatitude θ, respectively.

[0078] Table 2 Expressions of gravity gradient components in the local north-pointing coordinate system

[0079]

[0080]

[0081] The geocentric radial, geocentric colatitude, geocentric longitude and prior gravity field model coefficients corresponding to a certain observation epoch k are Substituting into (6), we can obtain the prior model value of the satellite gravity gradient tensor in the local north coordinate at observation epoch k:

[0082] A priori model value of satellite gravity gradient tensor in satellite gradiometer coordinate system Calculation.

[0083] The satellite gravity gradient tensor prior model value in the local north-pointing coordinate system is converted to the satellite gradiometer coordinate system through the following conversion processes: local north-pointing coordinate system → earth-fixed coordinate system → inertial coordinate system → gradiometer coordinate system. The conversion formula is:

[0084]

[0085] Where: and are the satellite gravity gradient tensor before and after the coordinate system conversion, and R is the coordinate conversion matrix.

[0086] The prior model value of the satellite gravity gradient tensor in the local north coordinate of observation epoch k is And the coordinate transformation matrix R at that moment k Substituting into (7), we can obtain the prior model value of the satellite gravity gradient tensor in the satellite gradiometer coordinate system at observation epoch k:

[0087] Calculation of the second invariant of the satellite gravity gradient prior model value and the third invariant of the satellite gravity gradient prior model value in the satellite gradiometer coordinate system.

[0088] The prior model value of the satellite gravity gradient tensor in the satellite gradiometer coordinate system at different observation epochs k is Substituting into the calculation formulas (2) and (3) of the tensor invariant system, we can obtain the second invariant of the satellite gravity gradient prior model value at different observation epochs k and the third invariant of the satellite gravity gradient prior model value:

[0089]

[0090] Step 2022 calculates the second invariant of the satellite gravity gradient observation value and the third invariant of the satellite gravity gradient observation value in the satellite gradiometer coordinate system.

[0091] The satellite gravitational gradient observation value components at different observation epochs k in the satellite gradiometer coordinate system are Substituting into the calculation formulas (2) and (3) of the tensor invariant system, we can obtain the second invariant of the satellite gravity gradient observation value and the third invariant of the satellite gravity gradient observation value at different observation epochs k:

[0092]

[0093] Step 2023 calculates the second invariant residual sequence of the satellite gravity gradient observation value and the third invariant residual sequence of the satellite gravity gradient observation value in the satellite gradiometer coordinate system.

[0094] Subtract the second invariant of the satellite gravity gradient prior model value and the third invariant of the satellite gravity gradient prior model value at different observation epochs k, as well as the second invariant of the satellite gravity gradient observation value and the third invariant of the satellite gravity gradient observation value, to obtain the residual sequence of the second invariant of the satellite gravity gradient observation value and the residual sequence of the third invariant of the satellite gravity gradient observation value:

[0095]

[0096] The satellite gravity gradient observation window length K for the Dixon test is selected, and the residual sequence of the second invariant of the satellite gravity gradient observation at different observation epochs k is calculated. and the residual sequence of the third invariant of the satellite gravitational gradient observation After taking the absolute value, sort them in ascending order to form time series:

[0097]

[0098] The step 203 specifically includes:

[0099] Step 203 detects the gross errors of all six tensor components of the satellite gravity gradient observation tensor as a whole.

[0100] Step 2031 is to calculate the Dixon statistics of the second invariant residual sequence of the satellite gravity gradient observation value and the third invariant residual sequence of the satellite gravity gradient observation value.

[0101] Introducing Dixon test theory and using quasi-range and To estimate the standard deviation of the time series, we can obtain the Dixon statistic of the second invariant of the satellite gravity gradient observations:

[0102]

[0103] Pseudo-range and To estimate the standard deviation of the time series, we can obtain the Dixon statistic of the third invariant of the satellite gravity gradient observations:

[0104]

[0105] Step 2032 detects gross errors of all tensor components of the satellite gravity gradient observation tensor as a whole.

[0106] Given a significance level α and a window size K, choose Statistics, if the Dixon statistics of the second invariant of the satellite gravitational gradient observations One of them is greater than the critical value D of the Dixon test α, then the observation epoch where the Kth element of the window length is located is considered to be abnormal data. If the Kth element is abnormal data, the same detection step operation is performed on the first K-1 elements of the time series after gross error marking (step 2031) until no abnormal data is detected. Similarly, given the significance level α and the window size K, the selection Statistics, if the Dixon statistics of the third invariant of the satellite gravitational gradient observation One of them is greater than the critical value D of the Dixon test α , then the observation epoch where the Kth element of the window length is located is considered to be abnormal data. If the Kth element is abnormal data, the same detection step operation is performed on the first K-1 elements of the time series after gross error marking (step 2031) until no abnormal data is detected. D corresponding to different significance levels α α See Table 1 for values.

[0107] This completes the overall detection of gross errors in all six tensor components of the satellite gravity gradient observation tensor.

[0108] In the description of this specification, the description with reference to the terms "one embodiment", "example", "specific example", etc. means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are included in at least one embodiment or example of the present invention. In this specification, the schematic representation of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0109] The preferred embodiments of the present invention disclosed above are only used to help illustrate the present invention. The preferred embodiments do not describe all the details in detail, nor do they limit the invention to the specific implementation methods described. Obviously, many modifications and changes can be made according to the content of this specification. This specification selects and specifically describes these embodiments in order to better explain the principles and practical applications of the present invention, so that those skilled in the art can understand and use the present invention well. The present invention is limited only by the claims and their full scope and equivalents.

Claims

1. A satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory, characterized in that: The following steps are involved: Step 1: The gross error of the main diagonal component of the gravitational gradient observation tensor of the overall detection satellite; Step 2: Detect gross errors of all six tensor components of the satellite gravity gradient observation tensor.

2. The satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory according to claim 1 is characterized in that: The step 1 specifically includes: Step 101 establishes a tensor invariant system {I1, I2, I3} of satellite gravity gradient observations; Step 102 calculates the first invariant time series of satellite gravity gradient observations; Step 103: Calculate the Dixon statistic r1 of the first invariant sequence of satellite gravity gradient observations 1 , Step 104: According to the Dixon statistic r1 1 , The comparison results with the critical value show the gross error of the main diagonal component of the gravitational gradient observation tensor of the overall detection satellite.

3. The satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory according to claim 2 is characterized in that: The expression of the tensor invariant system {I1, I2, I3} in step 101 is: I1=V 11 +V 22 +V 33 (1) 4. The satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory according to claim 2 is characterized in that: The step 104 specifically includes: Given a significance level α and a window size K; Select r1 1 , Statistics; If the Dixon statistic of the first invariant of the satellite gravitational gradient observation is r1 1 , One of them is greater than the critical value D of the Dixon test α , the observation epoch where the Kth element of the window length is located is considered to be abnormal data and a gross error mark is made; If the Kth element is abnormal data, the detection step described in step 104 is performed on the first K-1 elements of the time series until no abnormal data is detected.

5. The satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory according to claim 3 is characterized in that: The step 2 specifically includes: Step 201 establishes the same tensor invariant system {I1, I2, I3} of satellite gravity gradient observations as step 101; Step 202 calculates the residual sequence of the second invariant of the satellite gravity gradient and the third invariant of the satellite gravity gradient; Step 203 detects the gross errors of all six tensor components of the satellite gravity gradient observation tensor as a whole.

6. The satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory according to claim 5 is characterized in that: The step 202 specifically includes: Step 221 uses the prior gravity field model to calculate the prior model value of the gravity gradient tensor in the local north reference coordinate system, and converts it to the satellite gradiometer coordinate system, and then calculates the second invariant and the third invariant of the satellite gravity gradient prior model value; Step 2022 calculates the second invariant and the third invariant of the satellite gravity gradient observation value in the satellite gradiometer coordinate system; Step 2023 calculates the second invariant residual sequence and the third invariant residual sequence of the satellite gravity gradient observations.

7. The satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory according to claim 6 is characterized in that: The step 203 specifically includes: Step 2031 calculates the Dixon statistic r1 of the second invariant residual sequence and the third invariant residual sequence of the satellite gravity gradient observation value 2 , and r1 3 , Step 2032: According to the Dixon statistic r1 2 , and r1 3 , Compared with the critical value, the overall detection satellite gravity gradient observation tensor of all six tensor components has coarse errors.

8. The satellite gravity gradient gross error detection method based on tensor invariance and Dixon statistical theory according to claim 7 is characterized in that: The specific steps of step 2032 include: Given the significance level α and window size K, choose r1 2 , and r1 3 , Statistics; If the Dixon statistics of the second invariant and the third variable of the satellite gravity gradient observation r1 2 , and r1 3 , One of them is greater than the critical value D of the Dixon test α , then the observation epoch where the Kth element of the window length is located is considered to be abnormal data; If the Kth element is abnormal data, the detection step of step 2031 is performed on the first K-1 elements of the time series after gross error marking until no abnormal data is detected.

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