A real-time joint filtering method for gravity and gravity gradient data

Abstract

The present invention discloses a real-time joint filtering method for gravity and gravity gradient data, belonging to the field of geophysics technology. The method comprises: combining gravity and gravity gradient data using gravity potential, incorporating the relationship between gravity and gravity gradient into the system equation and measurement equation of a standard Kalman filter using the Taylor formula; utilizing the difference between the predicted state and the actual state in the Kalman filter to adaptively update the filter parameters, thereby obtaining an adaptive update process equation for Kalman filter measurement noise; utilizing the system equation and the measurement equation to combine gravity and gravity gradient data, combined with the adaptive update process equation for Kalman filter measurement noise, to remove noise from the data in real time, thereby achieving real-time joint filtering of gravity and gravity gradient data. The present invention not only filters out noise but also ensures that the filtered data satisfies the constraints of the Laplace equation and meets the real-time data processing requirements, thereby achieving real-time joint filtering of gravity and gravity gradient data.

Description

Technical Field

[0001] The present invention relates to the field of geophysics technology, and in particular to a real-time joint filtering method for gravity and gravity gradient data. Background Art

[0002] Gravity and gravity gradient data reflect changes in subsurface density and structure and are widely used in geological exploration, plate tectonic research, climate and sea level change studies, and navigation aids. Due to instrument system errors, environmental conditions, and human factors, measured gravity and gravity gradient data contain significant high-frequency noise, which can contaminate the true signal. Removing the effects of noise from measured gravity and gravity gradient data is particularly important. Because the individual components of gravity and gravity gradient reflect the same geological information but have different effective frequency bandwidths, the filtered data must satisfy the constraints of the Laplace equation. In fields such as gravity and gravity gradient-aided navigation, real-time processing of the measured gravity and gravity gradient data is required. Therefore, removing noise from gravity and gravity gradient data is one of the most challenging tasks in measurement data processing. In processing gravity and gravity gradient data, joint processing of multiple components can fully utilize the information in the gravity field.

[0003] To eliminate noise from gravity and gravity gradient data, current filtering methods fall into two categories: digital low-pass filtering and inversion-based methods. Traditional digital low-pass filters convert each component of the data into the frequency domain, then use various window functions to filter out the high-frequency portion while retaining the low-frequency portion, thereby removing high-frequency noise. While these low-pass digital filters can process gravity and gravity gradient data in real time, they can only remove high-frequency noise from each gravity and gravity gradient component individually. Furthermore, these low-pass digital filters assume that the signal and noise have different energies, but in reality, the two are difficult to distinguish. Furthermore, the filtering results of traditional low-pass digital filters do not always meet the constraints of the Laplace equation. Therefore, traditional low-pass digital filters can only meet the requirements of real-time filtering.

[0004] Inversion-based methods use the derivative relationship between gravity and gravity gradient to construct the inversion equation. These methods use the optimal linear inversion method, combine gravity and gravity gradient data to calculate the equation coefficients, and use these coefficients to perform forward calculations on the filtered gravity and gravity gradient data. This inversion-based method uses the fitting results as the effective signal and the unfitted components as noise to weaken the influence of noise. It includes the equivalent source method, Fourier transform method, Fourier series method, constrained differential equation method, Kriging interpolation method, full tensor noise reduction (FTNR), etc. This inversion-based method can remove noise while ensuring that the filtering results meet the constraints of the Laplace equation. However, these methods can only process the measured gravity and gravity gradient data after all the data are obtained, and cannot realize real-time processing of the measured data during the measurement process.

[0005] It can be seen that the above-mentioned existing methods for filtering gravity and gravity gradient data still have inconveniences and defects, and are in urgent need of further improvement. Based on the existing methods, this application creates a new real-time joint filtering method for gravity and gravity gradient data, which uses an adaptive Kalman filter to filter out noise while ensuring that the filtered data meets the constraints of the Laplace equation, so as to achieve real-time joint filtering of gravity and gravity gradient data, thereby meeting the requirements of gravity and gravity gradient assisted navigation and other fields for real-time processing of gravity and gravity gradient data. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to provide a real-time joint filtering method for gravity and gravity gradient data, which uses an adaptive Kalman filter to filter out noise while ensuring that the filtered data meets the constraints of the Laplace equation, so as to realize real-time joint filtering processing of gravity and gravity gradient data, thereby meeting the requirements of fields such as gravity and gravity gradient assisted navigation for real-time processing of gravity and gravity gradient data, thereby overcoming the shortcomings of existing filtering processing methods for gravity and gravity gradient data.

[0007] To solve the above technical problems, the present invention provides a real-time joint filtering method for gravity and gravity gradient data, comprising the following steps:

[0008] (1) Combine gravity and gravity gradient data using gravity potential, and incorporate the relationship between gravity and gravity gradient into the system equation and measurement equation of the standard Kalman filter through Taylor formula;

[0009] The formula for combining gravity and gravity gradient using gravitational potential is:

[0010]

[0011] Where: g is the total gravity field vector; is the gravitational potential of the corresponding position;

[0012] The system equation for the standard Kalman filter is:

[0013] X k =F k-1 X k-1 +w k-1

[0014] Where: X k is the state vector at time k, F k-1 is the state transfer matrix of the kth moment before, X k-1 is the state vector at the moment before k, w k-1 is the system noise, which obeys the Gaussian normal distribution with mean 0 and covariance Q;

[0015] The measurement equation is:

[0016] Z k =H k X k +v k

[0017] Where: Z k is the observation vector, and X k The same form, H k is the measurement matrix, which is an 8-order unit matrix, v k is the measurement noise, which follows a Gaussian normal distribution with a mean of 0 and a covariance of R;

[0018] (2) Using the difference between the predicted state and the actual state in the Kalman filter, the filter parameters are adaptively updated, and the adaptive update process equation of the Kalman filter measurement noise covariance is obtained:

[0019]

[0020] Where: is the measurement noise covariance obtained after the Kalman filter adaptive update, α is the weight coefficient, R k-1 is the k-th moment before R k The noise estimate is N, the width of the sliding window; ξ j is the deviation between the predicted value and the actual value at time j; H k is the measurement matrix, which is an 8-order unit matrix; P k ′ is the estimation error covariance;

[0021] (3) Using the system equation and measurement equation of the standard Kalman filter obtained in step (1), combined with the gravity and gravity gradient data, and combined with the adaptive update process equation of the Kalman filter measurement noise obtained in step (2), the noise in the data is removed in real time, and the real-time joint filtering processing of the gravity and gravity gradient data is realized.

[0022] Further improvement, the system equation in step (1) is derived based on the relationship between the gravity and gravity gradient data between two points and the principle that the sum of all gravity gradient components satisfies the Laplace equation;

[0023] Among them, the Taylor expansion relationship of gravity and gravity gradient data between two points is:

[0024] T z (x2,y2,z2)=T z (x1,y1,z1)+[(x2-x1)T xz +(y2-y1)T yz +(z2-z1)T zz ]×10 -4 +Θ

[0025] Where: T z (x1, y1, z1) is the vertical gravity at the point (x1, y1, z1); T z (x2, y2, z2) is the vertical gravity at the point (x2, y2, z2); T xz is the gravity gradient T at point (x1, y1, z1) xz Quantity; T yz is the gravity gradient T at point (x1, y1, z1) yz Quantity; T zz is the gravity gradient T at point (x1, y1, z1) zz Component; Θ is a high-order infinitesimal quantity;

[0026] The sum of all gravity gradient components satisfies the Laplace equation, that is,

[0027] T xx +T yy +T zz =0

[0028] Where: T xx is the gravity gradient T xx Quantity; T yy is the gravity gradient T yy Quantity; T zz is the gravity gradient T zz Quantity.

[0029] Further improvement, in step (1) X k The specific form is:

[0030] X k =[T z ,T xx ,T xy ,T xz ,T yy ,Tyz ,T zz ,0] T

[0031] F k The specific form is:

[0032]

[0033] Among them: △x=x2-x1; △y=y2-y1; △z=z2-z1.

[0034] Further improvement, step (2) uses the difference between the predicted state and the actual state in the Kalman filter to include the deviation d between the estimated value and the actual value k and the deviation between the predicted value and the actual value ξ k ,

[0035] The deviation d between the estimated value and the actual value k For: d k =Z k -H k X k '

[0036] The deviation between the predicted value and the actual value ξ k for:

[0037] in,

[0038] X k ′=F k-1 X k-1 +w k-1

[0039]

[0040]

[0041]

[0042]

[0043] Where, X k ′ is the filter estimate; P k ′ is the estimated error covariance; P k-1 ′ is the estimated error covariance at the kth moment before; is the updated filter prediction value; K is the Kalman gain; is the updated estimated error covariance; I is the 8th-order unit matrix.

[0044] Further improvement, step (2) takes into account the deviation d between the estimated value and the actual value k and the deviation between the predicted value and the actual value ξk Based on this, we reuse the deviation ξ k Adaptively adjust the measurement error covariance R, the calculation process is:

[0045]

[0046]

[0047]

[0048] Where, for ξ k covariance of R k ′ is based on Q ξk The calculated measurement noise covariance;

[0049] Then calculate the covariance matrix by the sliding average method

[0050]

[0051] Where: is ξ obtained by sliding average k The covariance matrix of , N is the width of the sliding window; ξ j is the deviation between the predicted value and the actual value at time j;

[0052] Then introduce the weight coefficient α to balance the R k The estimate of , then:

[0053]

[0054] Where: R k-1 is the k-th moment before R k The estimated value of is the measurement noise covariance obtained after adaptive update;

[0055] Finally, the adaptive updating process equation of the Kalman filter measurement noise covariance is obtained.

[0056] Further improvement, step (3) realizes the real-time joint filtering of gravity and gravity gradient data. The updated filter prediction value calculation formula is:

[0057] After adopting such a design, the present invention has at least the following advantages:

[0058] The real-time joint filtering method for gravity and gravity gradient data of the present invention is based on an adaptive Kalman filtering method. While filtering out noise, it ensures that the filtered data satisfies the constraints of the Laplace equation, so as to realize real-time joint filtering processing of gravity and gravity gradient data, thereby meeting the requirements for real-time processing of gravity and gravity gradient data in fields such as gravity and gravity gradient assisted navigation. The method can overcome the drawback that traditional digital low-pass filters are difficult to realize joint processing of various components of gravity and gravity gradient, and the drawback that inversion-based methods cannot realize real-time processing of gravity and gravity gradient data. The method realizes real-time joint filtering processing of gravity and gravity gradient data while ensuring filtering accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0059] The above is only an overview of the technical solution of the present invention. In order to more clearly understand the technical means of the present invention, the present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0060] Figure 1 It is a flow chart of the real-time joint filtering method of gravity and gravity gradient data of the present invention.

[0061] Figure 2 : is the survey area location and map range selected in the embodiment of the present invention, wherein the black line is the cross-section location selected in this embodiment.

[0062] Figure 3 This is a comparison of the processing results of different filtering methods on the components Tz, Txx, Txy, Txz, Tyy, Tyz, and Tzz according to the embodiments of the present invention. The first column is the original measurement data, the second column is the FTNR filtering result, the third column is the AKF processing result, and the fourth column is the GLPF processing result.

[0063] Figure 4 This is a comparison of the processing results of the components Tz, Txx, Txy, Txz, Tyy, Tyz, and Tzz through different filtering methods for the selected profile in an embodiment of the present invention, where: (a) Tz; (b) Txx; (c) Txy; (d) Txz; (e) Tyy; (f) Tyz; and (g) Tzz.

[0064] Figure 5 The filtering results obtained by different filtering methods according to the embodiments of the present invention are displayed on the basis of satisfying the constraints of the Laplace equation, including: (a) FTNR filtering result; (b) AKF filtering result; and (c) GLPF filtering result. DETAILED DESCRIPTION

[0065] Refer to the attached Figure 1 As shown, the real-time joint processing method for gravity and gravity gradient data in this embodiment specifically includes the following steps:

[0066] Step 1: Construction of system equations and measurement equations

[0067] The gravity and gravity gradient data are linked by using the gravitational potential, and the relationship between gravity and gravity gradient is incorporated into the system equation and state equation through Taylor's formula;

[0068] The formula for analyzing the gravitational field information using gravitational potential is:

[0069]

[0070] Where: g is the total gravity field vector; is the gravitational potential of the corresponding position;

[0071] The total gravity field vector can be decomposed into gravity components in the x, y, and z directions. The first-order derivatives of these components in each coordinate direction can be used to obtain the corresponding gravity gradient components.

[0072] For the vertical gravity Tz, its total differential at the point (x, y, z) is:

[0073]

[0074] Therefore, the gravity and gravity gradient values ​​at point (x1, y1, z1) and point (x2, y2, z2) have the following relationship:

[0075] T z (x2,y2,z2)=T z (x1,y1,z1)+[(x2-x1)T xz +(y2-y1)T yz +(z2-z1)T zz ]×10 -4 +Θ (3)

[0076] Where: T z (x1, y1, z1) is the vertical gravity at the point (x1, y1, z1); T z (x2, y2, z2) is the vertical gravity at the point (x2, y2, z2); T xz is the gravity gradient T at point (x1, y1, z1) xz Quantity; T yz is the gravity gradient T at point (x1, y1, z1) yz Quantity; T zz is the gravity gradient T at point (x1, y1, z1) zz component; Θ is a high-order infinitesimal quantity.

[0077] Among all gravity gradient components, the sum of Txx, Tyy and Tzz components satisfies Laplace's equation:

[0078] T xx +T yy +T zz =0 (4)

[0079] Where: T xx is the gravity gradient T xx Quantity; T yy is the gravity gradient T yy Quantity; T zz is the gravity gradient T zz Quantity.

[0080] According to equations (3) and (4), the system equation of the discrete linear system constrained by the Laplace equation can be defined as:

[0081] X k =F k-1 X k-1 +w k-1 (5)

[0082] Where: X k is the state vector at time k, and its specific form is:

[0083] X k =[T z ,T xx ,T xy ,T xz ,T yy ,T yz ,T zz ,0] T (6)

[0084] F k is the state transfer matrix, and its specific form is:

[0085]

[0086] Among them: △x=x2-x1; △y=y2-y1; △z=z2-z1.

[0087] w k-1 is the system noise, which obeys the Gaussian normal distribution with mean 0 and covariance Q.

[0088] According to the system equation and state vector, the measurement equation of the standard Kalman filter can be defined as:

[0089] Z k =H k X k +v k (8)

[0090] Where: Z k is the observation vector, and X kThe same form; H k is the measurement matrix, which is an 8-order unit matrix; v k The noise is measured and has a Gaussian normal distribution with a mean of 0 and a covariance of R.

[0091] Step 2: Adaptive update of parameters

[0092] By utilizing the difference between the predicted state and the actual state in the Kalman filter and combining the established system equations and measurement equations, an adaptive Kalman filter is constructed to achieve real-time joint processing of gravity and gravity gradient data.

[0093] First, the classic Kalman filter includes two major processes: prediction and update. Formulas (9) to (10) represent the estimation prediction process in the classic Kalman filter, and formulas (11) to (13) represent the prediction update process based on the measurement value:

[0094] X k ′=F k-1 X k-1 +w k-1 (9)

[0095]

[0096]

[0097]

[0098]

[0099] Where: X k ′ is the filter estimate; P k ′ is the estimated error covariance; P k-1 ′ is the estimated error covariance at the kth moment before; is the updated filter prediction value; K is the Kalman gain; is the updated estimated error covariance; I is the 8th-order unit matrix;

[0100] Moreover, based on the classic Kalman filter, the deviation d between the estimated value and the actual value is considered. k and the deviation between the predicted value and the actual value ξ k :

[0101] d k =Z k -H k X k ′ (14)

[0102]

[0103] In the classic Kalman filter, it is necessary to pre-set the system error covariance Q and the measurement error covariance R. Using the deviation ξ k The value of the measurement error covariance R can be adaptively adjusted. In order to ensure the positive definiteness of R during the adaptive update process, the residual-based estimation method can be used to calculate it:

[0104]

[0105] For the deviation ξ k , the calculation process is as follows:

[0106]

[0107]

[0108] Where: for ξ k covariance of R k ' is based on The calculated measurement noise covariance;

[0109] In order to smooth the calculation results, the covariance matrix is ​​calculated by the sliding average method

[0110]

[0111] Where: is ξ obtained by sliding average k The covariance matrix of , N is the width of the sliding window;

[0112] ξ j is the deviation between the predicted value and the actual value at time j.

[0113] Then introduce the weight coefficient α to balance the R k The estimate of , then:

[0114]

[0115] Where: R k-1 is the k-th moment before R k The estimated value of is the measurement noise covariance obtained after adaptive update.

[0116] Therefore, the measurement noise covariance R k The adaptive update process can be summarized as:

[0117]

[0118] Step 3: Real-time joint filtering of gravity and gravity gradient data

[0119] By using the above system equations and measurement equations, combining gravity and gravity gradient data, and combining the adaptive update process equation of Kalman filter measurement noise, the noise in the data can be removed in real time, realizing real-time joint filtering processing of gravity and gravity gradient data.

[0120] The filter prediction value calculation formula after the real-time joint filtering and updating of gravity and gravity gradient data is the above formula (11).

[0121] Specific examples

[0122] In order to test the performance of the gravity and gravity gradient data filtering method (Adaptive Kalman Filter, AKF filter) implemented in this application based on the adaptive Kalman filter method under actual measurement environment, the applicant used the gravity and gravity gradient measurement data of St. George's Bay in Canada for verification.

[0123] In 2012, Bell Geospace was invited by the Canadian Department of Natural Resources to conduct airborne gravity surveys and full tensor gravity gradient surveys in St. George's Bay, Canada. The specific survey area and map range are shown in the attached figure. Figure 2 As shown in the figure, the black line indicates the profile location selected for the measurement. The measurement results include gravity anomaly data, gravity gradient data, and Full Tensor Noise Reduction (FTNR) processing results. The FTNR method is an inversion-based method that filters gravity and gravity gradient data, effectively reducing noise while preserving the valid signal in the gravity gradient data.

[0124] In this embodiment, the gravity and gravity gradient measurement data of St. George's Bay, Canada are filtered by an adaptive Kalman filter (AKF filter) and a Gaussian low-pass filter (GLPF filter), and the three filtering results are compared. The results are shown in the attached figure. Figure 3 、 4 、5.

[0125] Figure 3 The figure shows a comparison of the processing results of the three filtering methods on the components Tz, Txx, Txy, Txz, Tyy, Tyz, and Tzz, where the first column is the original measurement data, the second column is the FTNR filtering result, the third column is the AKF processing result, and the fourth column is the GLPF processing result.

[0126] Figure 3In the GLPF filter, the cutoff frequencies for the Tz, Txx, Txy, Txz, Tyy, Tyz, and Tzz components are set to 0.53Hz, 0.15Hz, 0.15Hz, 0.16Hz, 0.15Hz, 0.10Hz, and 0.13Hz, respectively. In the AKF filter, α = 0.89, N = 3000, the system noise parameter Q = 5, and the initial measurement noise parameter R = 0.09. Comparing the filtering results of FTNR, AKF, and GLPF, all filters effectively remove high-frequency noise while retaining the valid signal, particularly the components of the gravity gradient. However, for the same anomaly, the filtering results of different methods vary in details. The GLPF filter produces the smoothest result, the FTNR filter produces the least smooth, and the AKF filter results fall somewhere in between.

[0127] In order to conduct a more detailed comparative analysis, this measurement experiment selected a section whose location is as follows: Figure 2 As shown by the black line in . Figure 4 The figure shows the comparison of the processing results of the three filtering methods on the components Tz, Txx, Txy, Txz, Tyy, Tyz, and Tzz. Figure 4 In (a), for gravity anomaly data, there is no significant difference between the filtering results of GLPF and AKF. However, compared with the results after AKF and GLPF filtering, the FTNR results are significantly different and even deviate greatly from the original data. FTNR is an inversion-based method that uses the optimal linear inversion method to combine gravity and gravity gradient data to calculate the equation coefficients and forward calculate gravity. This method has a main control parameter, which is the cutoff frequency related to the line distance in the measurement. This may be the main reason for this difference. Figure 4 In (b)-(g), the FTNR, AKF, and GLPF filtering results show similar trends. However, the FTNR result exhibits significant residual noise. The AKF and GLPF results are smoother than the FTNR result. The smoothness of the AKF filtering result lies between the FTNR and GLPF filtering results.

[0128] Figure 5 The results of the three filtering methods are shown in Figure 1. The results of the three filtering methods are shown in Figure 1. The results of the three filtering methods are shown in Figure 1. Figure 5 It can be seen that the results of FTNR and AKF are both close to 0, while the results of GLPF deviate greatly from 0. This shows that the filtering results of FTNR and AKF meet the constraints of the Laplace equation, while the filtering results of GLPF contain a certain amount of residual noise.

[0129] In summary, the filtering processing method of gravity and gravity gradient data implemented in this application based on the adaptive Kalman filtering method can filter out noise while ensuring that the filtered data meets the constraints of the Laplace equation, and can also meet the real-time processing requirements of the data, realizing real-time joint filtering processing of gravity and gravity gradient data.

[0130] The above description is only a preferred embodiment of the present invention and does not limit the present invention in any form. Those skilled in the art can make some simple modifications, equivalent changes or modifications based on the technical content disclosed above, which all fall within the scope of protection of the present invention.

Claims

1. A real-time joint filtering method for gravity and gravity gradient data, characterized in that: The steps include: (1) Combine gravity and gravity gradient data using gravity potential, and incorporate the relationship between gravity and gravity gradient into the system equation and measurement equation of the standard Kalman filter through Taylor formula; The formula for combining gravity and gravity gradient using gravitational potential is: Where: g is the total gravity field vector; is the gravitational potential of the corresponding position; The system equation for the standard Kalman filter is: X k =F k-1 X k-1 +w k-1 Where: X k is the state vector at time k, F k-1 is the state transfer matrix of the kth moment before, X k-1 is the state vector at the moment before k, w k-1 is the system noise, which obeys the Gaussian normal distribution with mean 0 and covariance Q; The measurement equation is: Z k =H k X k +v k Where: Z k is the observation vector, and X k The same form, H k is the measurement matrix, which is an 8-order unit matrix, v k is the measurement noise, which follows a Gaussian normal distribution with a mean of 0 and a covariance of R; (2) Using the difference between the predicted state and the actual state in the Kalman filter, the filter parameters are adaptively updated, and the adaptive update process equation of the Kalman filter measurement noise covariance is obtained: Where: is the measurement noise covariance obtained after the Kalman filter adaptive update, α is the weight coefficient, R k-1 is the k-th moment before R k The noise estimate is N, the width of the sliding window; ξ j is the deviation between the predicted value and the actual value at time j; H k is the measurement matrix, which is an 8-order unit matrix; P k ′ is the estimation error covariance; (3) Using the system equation and measurement equation of the standard Kalman filter obtained in step (1), combined with the gravity and gravity gradient data, and combined with the adaptive update process equation of the Kalman filter measurement noise obtained in step (2), the noise in the data is removed in real time, and the real-time joint filtering processing of the gravity and gravity gradient data is realized.

2. The real-time joint filtering method of gravity and gravity gradient data according to claim 1, characterized in that: The system equation in step (1) is derived based on the relationship between the gravity and gravity gradient data between two points and the principle that the sum of all gravity gradient components satisfies the Laplace equation; Among them, the Taylor expansion relationship of gravity and gravity gradient data between two points is: T z (x2,y2,z2)=T z (x1,y1,z1)+[(x2-x1)T xz +(y2−y1)T yz +(z2-z1)T zz ]×10 -4 +Θ Where: T z (x1, y1, z1) is the vertical gravity at the point (x1, y1, z1); T z (x2, y2, z2) is the vertical gravity at the point (x2, y2, z2); T xz is the gravity gradient T at point (x1, y1, z1) xz Quantity; T yz is the gravity gradient T at point (x1, y1, z1) yz Quantity; T zz is the gravity gradient T at point (x1, y1, z1) zz Component; Θ is a high-order infinitesimal quantity; The sum of all gravity gradient components satisfies the Laplace equation, that is, T xx +T yy +T zz =0 Where: T xx is the gravity gradient T xx Quantity; T yy is the gravity gradient T yy Quantity; T zz is the gravity gradient T zz Quantity.

3. The real-time joint filtering method of gravity and gravity gradient data according to claim 2, characterized in that: In step (1), X k The specific form is: X k =[T z ,T xx ,T xy ,T xz ,T yy ,T yz ,T zz ,0] T F k The specific form is: Among them: △x=x2-x1; △y=y2-y1; △z=z2-z1.

4. The real-time joint filtering method for gravity and gravity gradient data according to claim 3, characterized in that: Step (2) uses the difference between the predicted state and the actual state in the Kalman filter, including the deviation d between the estimated value and the actual value k and the deviation between the predicted value and the actual value ξ k , The deviation d between the estimated value and the actual value k For: d k =Z k -H k X k ' The deviation between the predicted value and the actual value ξ k for: in, X k ′=F k-1 X k-1 +w k-1 Where, X k ′ is the filter estimate; P k ′ is the estimated error covariance; P k-1 ′ is the estimated error covariance at the kth moment before; is the updated filter prediction value; K is the Kalman gain; is the updated estimated error covariance; I is the 8th-order unit matrix.

5. The real-time joint filtering method for gravity and gravity gradient data according to claim 4, characterized in that: Step (2) considers the deviation d between the estimated value and the actual value k and the deviation between the predicted value and the actual value ξ k Based on this, we reuse the deviation ξ k Adaptively adjust the measurement error covariance R, the calculation process is: Where, for ξ k covariance of R k ' is based on The calculated measurement noise covariance; Then calculate the covariance matrix by the sliding average method Where: is ξ obtained by sliding average k The covariance matrix of , N is the width of the sliding window; ξ j is the deviation between the predicted value and the actual value at time j; Then introduce the weight coefficient α to balance the R k The estimate of , then: Where: R k-1 is the k-th moment before R k The estimated value of is the measurement noise covariance obtained after adaptive update; Finally, the adaptive updating process equation of the Kalman filter measurement noise covariance is obtained.

6. The real-time joint filtering method for gravity and gravity gradient data according to claim 5, characterized in that: Step (3) implements real-time joint filtering of gravity and gravity gradient data. The updated filter prediction value calculation formula is:

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