A method for compensating for attitude errors of a rotating accelerometer gravity gradiometer after processing
The attitude error of the rotating accelerometer gravity gradient meter is estimated and compensated offline using the RTS smoothing filtering method, which solves the problem of insufficient accuracy caused by attitude error in dynamic measurement and realizes high-precision gravity gradient measurement.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- CHINA STATE SHIPBUILDING CORP NO 707 RES INST
- Filing Date
- 2026-04-30
- Publication Date
- 2026-07-24
AI Technical Summary
In the prior art, the rotational accelerometer gravity gradiometer has attitude error during dynamic measurement, resulting in insufficient accuracy of gravity gradient measurement. Furthermore, the existing methods fail to fully utilize the accuracy potential of offline post-processing and lack deep model fusion.
The RTS smoothing filtering method is adopted, which combines inertial measurement unit and radio navigation data. The attitude error is optimally estimated by forward Kalman filtering and backward Kalman smoothing filtering, and error compensation is performed based on gravity gradient tensor coordinate transformation. A Kalman filter is constructed to perform high-precision estimation and offline compensation of attitude error.
It significantly improves the estimation accuracy of attitude error, reduces the impact of attitude error on gravity gradient measurement, enhances the dynamic measurement accuracy and environmental adaptability of the rotating accelerometer gravity gradiometer, and reduces the dependence on high-cost inertial measurement units.
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Figure CN122449643A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the field of dynamic gravity gradient measurement technology, and particularly relates to an offline post-processing compensation method for dynamic measurement attitude error of a rotating accelerometer full tensor gravity gradient meter. Background Technology
[0002] The gravity gradient, the second spatial derivative of the Earth's gravitational potential, is of great significance in mineral resource exploration and geophysical research. A gravity gradiometer is a precision instrument used to measure the gravity gradient. Although various gravity gradient measurement principles exist, such as cold atom interferometry and superconducting magnetic levitation, the rotating accelerometer gravity gradiometer is the only near-surface dynamic gravity gradiometer to date to achieve commercial application. The main instrument consists of a gravity gradient sensor and a stabilizing platform, along with corresponding shock absorbers, environmental control devices, and a display and control cabinet as auxiliary measurement equipment. The sensor and the inertial stabilizing platform, for example... Figure 1 As shown. The gravity gradient sensor is used to measure the full-tensor gravity gradient signal, while the stabilizing platform isolates the carrier from angular motion and provides a reliable pointing reference in dynamic environments.
[0003] In dynamic measurements, rotating accelerometer gravity gradiometers are typically mounted on mobile platforms such as aircraft. Because the gravity gradient tensor is direction-dependent, its measurement results are closely related to the attitude of the gravity gradient sensor (including the sensor's pitch, roll, and yaw angles). To obtain high-precision full-tensor gravity gradient information, it is essential to accurately obtain the real-time attitude of the gravity gradient sensor during dynamic measurements and, based on this, transform the gravity gradient measurements from the measurement coordinate system to the geographic coordinate system. Therefore, accurate estimation and compensation of sensor attitude errors are crucial for achieving high-precision dynamic gravity gradient measurements.
[0004] Currently, under dynamic conditions, the rotating accelerometer gravity gradiometer stabilizes the gravity gradient sensor in the geographic coordinate system using an inertial stabilization platform. However, due to factors such as gyroscope drift, accelerometer bias error, and motion interference under dynamic conditions inherent in the inertial measurement unit (IMU) fixed to the gravity gradient sensor, the IMU cannot strictly stabilize the gravity gradient sensor in the geographic coordinate system, resulting in a certain attitude error. In dynamic gravity gradient measurements, this attitude error is directly transmitted to the measurement results, severely affecting the accuracy of dynamic gravity gradient measurements.
[0005] To suppress the impact of sensor attitude errors on gravity gradient measurements, two approaches are taken: First, improve the precision of hardware such as the inertial measurement unit (IMU) to reduce attitude errors of the inertial stabilization platform caused by factors such as gyroscope drift or accelerometer bias error. However, high-precision IMUs are expensive and bulky, limiting their application in rotating accelerometer gravity gradient meters. Second, compensate for attitude errors in gravity gradient measurements through data processing. However, existing methods fail to jointly model and compensate for the carrier attitude with the gravity gradient measurement model and gravity gradient tensor coordinate transformation, thus failing to fully exploit the accuracy potential in offline post-processing.
[0006] In summary, at present, the estimation and compensation of attitude error caused by sensor attitude error in dynamic measurement still suffer from problems such as insufficient accuracy, failure to fully utilize the advantages of offline processing, and lack of deep integration with gradient measurement models.
[0007] Therefore, there is an urgent need for a method that can accurately estimate the attitude error of the gravity gradient sensor and achieve offline compensation, so as to further improve the dynamic measurement accuracy and environmental adaptability of the rotating accelerometer gravity gradient instrument.
[0008] A search revealed no publicly available literature of the same or similar prior art as this invention. Summary of the Invention
[0009] To address the shortcomings of existing technologies, this invention proposes an offline post-processing compensation method for dynamic measurement attitude error of a rotating accelerometer full-tensor gravity gradiometer. This method enables high-precision estimation and offline compensation of the attitude error of the gravity gradiometer component using measurement information of the carrier motion from gyroscopes and accelerometers in a dynamic measurement environment, thereby improving the dynamic measurement accuracy of the rotating accelerometer gravity gradiometer.
[0010] The above-mentioned objective of this invention is achieved through the following technical solution: A method for post-processing compensation of attitude error of a rotating accelerometer gravity gradient meter includes the following steps: Step 1: Collect raw motion data using an inertial measurement unit fixed to the gravity gradient sensor, and combine it with positioning and velocity information provided by radio navigation to complete the raw data acquisition. Step 2: Based on the raw data collected in Step 1, the attitude error of the gravity gradient sensor during the measurement process is optimally estimated by using the RTS smoothing filtering method, which integrates forward Kalman filtering and backward Kalman smoothing filtering. Step 3: Combine the attitude error estimated in Step 2 with the gravity gradient measurement information collected synchronously in Step 1. Based on the coordinate transformation matrix of the gravity gradient tensor in different coordinate systems, perform error compensation on the gravity gradient measurement value to finally obtain the gravity gradient measurement data after attitude error compensation.
[0011] Furthermore, the specific steps of step 1 include: (1) Install the rotating accelerometer gravity gradiometer on a dynamic carrier (such as an aircraft) and start the gravity gradiometer data acquisition system, the inertial measurement unit data acquisition system and the radio navigation data acquisition system; (2) During the dynamic measurement process, the following data shall be recorded synchronously using a unified time base: ① The raw measurement data output by the gravity gradient sensor is the measured value of the gravity gradient tensor in the sensor coordinate system after demodulation, denoted as Γ. s ( t ); ② The raw measurement data of the three-axis angular velocity and linear acceleration output by the inertial measurement unit are denoted as follows: ω x ( t ), ω y ( t )and ω z ( t ),as well as f x ( t ), f y ( t )and f z ( t ); ③ The latitude, longitude, and altitude data of the carrier output by radio navigation are respectively denoted as... L ( t ), λ ( t )and h ( t ).
[0012] Data acquisition covers the entire dynamic measurement process, ensuring that subsequent offline processing has complete original observation information.
[0013] Furthermore, the specific method for step 2 is as follows: The raw measurement data and radio navigation position information collected by the inertial measurement unit are subjected to RTS smoothing filtering. This process is divided into three stages: forward filtering, backward filtering, and smoothing filtering. A Kalman filter is constructed using the error equation of the inertial stabilized platform as the system state equation and the difference between the radio navigation and the state variables of the inertial stabilized platform as the observation equation. (1) Wherein, the system state vector is (2) The system measurement vector is: (3) In the formula, X It is a 15-dimensional state vector, with each state representing, in order: three-directional attitude error, three-directional velocity error, latitude, longitude, and altitude position error, three-directional gyroscope drift, and three-directional additive zero bias. Z It is a 6-dimensional measurement vector, consisting of three-directional velocity errors and latitude, longitude, and altitude position errors, respectively. F , G and H These are known structural parameters of an inertial / radio integrated navigation system, referred to as the state one-step transition matrix, system noise allocation matrix, and measurement matrix, respectively. Their specific expressions are common in the field of integrated navigation and will not be elaborated upon in this invention. W It is the system noise vector. V It is a measurement noise vector, and its specific parameters are determined by the inertial stabilization platform and radio navigation information, respectively.
[0014] Discretizing equation (1), we get: (4) The zero bias of the gyroscope and accelerometer in the state variables can be modeled as random constant errors, the differential of which is zero. Therefore, the forward filtering of the Kalman filter can be expressed as: (5) In the formula, the subscript " f " indicates forward filtering. When k = j At that time, the state can be obtained from equation (6). X j positive optimal estimate and its mean square error matrix P f,k .
[0015] In inverse filtering, the state-space model equation (4) can be rewritten as: (6) remember: , (7) Then we have the inverse filter state-space model: (8) The rotating accelerometer-gravity gradient meter isolates the carrier's angular motion through a stable platform, and can be approximated as follows when the system is discretized: (9) For the system state model space in equation (8), we can utilize j Inverse filtering is applied to measurements taken after a certain time. X j+1 Perform optimal estimation, and then... X j The algorithm for performing a reverse one-step prediction is as follows: (10) In the formula, the subscript " b " indicates forward filtering. When k = j At that time, the state can be obtained from equation (10). X j The reverse optimal one-step prediction and its mean square error matrix P b,j / j+1 ; Combining the results of forward and reverse filtering, the following model is established: (11) For radio navigation systems, j The errors in the first and second halves of the time measurement are independent of each other, and since the Kalman filter state estimation is a linear combination of the measurements, therefore... and They are also independent of each other. The RTS smoothing filter algorithm can be used to... X j The optimal estimate is calculated using the following formula: ( k = M -1, M -2, ..., 1) (12) The initial value for the inverse smoothing filter is selected as follows: and ; The state can be obtained from this. X j The bidirectional optimal estimate, where the state vector X The first three components represent the attitude error of the gravity gradient sensor.
[0016] Furthermore, the specific method for step 3 is as follows: Construct the direction cosine matrix from the measurement coordinate system of the gravity gradient sensor to the geographic coordinate system based on the attitude error estimation results: (13) In the formula, This is the direction cosine matrix from the measurement coordinate system to the geographic coordinate system. It is used to compensate for attitude errors in gravity gradient measurement data; the specific calculation formula is as follows: (14) In the formula, Γ g These are gravity gradient measurement data after attitude error compensation, Γ m These are gravity gradient measurement data before compensation; The above calculation is repeated for each moment to obtain the full tensor gravity gradient data Γ in the geographic coordinate system after attitude error compensation for the entire measurement period. g It includes five independent components (Γ) xx ,Γ xy ,Γ xz ,Γ yy and Γ yz This serves as the final dynamic measurement result of the gravity gradient, which is then output.
[0017] The advantages and beneficial effects of this invention are as follows: 1. This invention proposes an offline post-processing compensation method for dynamic attitude measurement errors using a rotating accelerometer full tensor gravity gradient meter. Firstly, it utilizes RTS smoothing filtering, which, compared to real-time filtering, can smoothly estimate attitude errors using forward and backward vector measurement information during the measurement process, significantly improving the estimation accuracy. Secondly, it integrates attitude error estimation with the gravity gradient measurement model and coordinate transformation process for unified modeling and joint compensation. This allows attitude error correction to directly affect the compensation stage of gravity gradient measurement data, avoiding the additional errors introduced by separating attitude processing and gravity gradient measurement in traditional methods. Thirdly, it does not rely on high-cost, high-precision inertial measurement units, achieving high-precision attitude error compensation at low cost, demonstrating good engineering applicability and economy.
[0018] 2. This invention is specifically designed for a rotating accelerometer gravity gradiometer. It uses RTS bidirectional smoothing filtering to estimate the sensor attitude error in dynamic measurement offline, and directly compensates the estimation result to the dynamic measurement signal of gravity gradient based on tensor coordinate transformation. This can effectively suppress gravity gradient measurement error caused by attitude error and improve the dynamic measurement accuracy of gravity gradiometer. Attached Figure Description
[0019] Figure 1 This is a diagram showing the components of a rotating accelerometer-gravity gradient meter system. Figure 2This is a diagram showing the gravity gradient measurement results before attitude error compensation. Figure 3 This is a diagram showing the attitude error estimation results of the gravity gradient sensor. Figure 4 This is a graph showing the gravity gradient measurement results after attitude error compensation; Explanation of reference numerals in the attached figures: 1-Inertial stabilization platform; 2-Inertial measurement unit; 3-Gravity gradient sensor. Detailed Implementation
[0020] The structure of the present invention will be further described below with reference to the accompanying drawings and embodiments. It should be noted that these embodiments are descriptive and not limiting.
[0021] A method for post-processing compensation of attitude error of a rotating accelerometer gravity gradient meter includes the following steps: Step 1: Collect raw motion data using an inertial measurement unit fixed to the gravity gradient sensor, and combine it with positioning and velocity information provided by radio navigation to complete the raw data acquisition. The specific steps of step 1 include: (1) Install the rotating accelerometer gravity gradiometer on a dynamic carrier (such as an aircraft) and start the gravity gradiometer data acquisition system, the inertial measurement unit data acquisition system and the radio navigation data acquisition system; (2) During the dynamic measurement process, the following data shall be recorded synchronously using a unified time base: ① The raw measurement data output by the gravity gradient sensor is the measured value of the gravity gradient tensor in the sensor coordinate system after demodulation, denoted as Γ. s ( t ); ② The raw measurement data of the three-axis angular velocity and linear acceleration output by the inertial measurement unit are denoted as follows: ω x ( t ), ω y ( t )and ω z ( t ),as well as f x ( t ), f y ( t )and f z ( t ); ③ The latitude, longitude, and altitude data output by radio navigation are respectively denoted as... L ( t ), λ ( t )and h ( t ).
[0022] Data acquisition covers the entire dynamic measurement process, ensuring that subsequent offline processing has complete original observation information.
[0023] Step 2: Based on the raw data collected in Step 1, the attitude error of the gravity gradient sensor during the measurement process is optimally estimated by using the RTS smoothing filtering method, which integrates forward Kalman filtering and backward Kalman smoothing filtering. The specific method for step 2 is as follows: The raw measurement data and radio navigation position information collected by the inertial measurement unit are subjected to RTS smoothing filtering. This process is divided into three stages: forward filtering, backward filtering, and smoothing filtering. A Kalman filter is constructed using the error equation of the inertial stabilized platform as the system state equation and the difference between the radio navigation and the state variables of the inertial stabilized platform as the observation equation. (1) Wherein, the system state vector is (2) The system measurement vector is: (3) In the formula, X It is a 15-dimensional state vector, with each state representing, in order: three-directional attitude error, three-directional velocity error, latitude, longitude, and altitude position error, three-directional gyroscope drift, and three-directional additive zero bias. Z It is a 6-dimensional measurement vector, consisting of three-directional velocity errors and latitude, longitude, and altitude position errors, respectively. F , G and H These are known structural parameters of an inertial / radio integrated navigation system, referred to as the state one-step transition matrix, system noise allocation matrix, and measurement matrix, respectively. Their specific expressions are common in the field of integrated navigation and will not be elaborated upon in this invention. W It is the system noise vector. V It is a measurement noise vector, and its specific parameters are determined by the inertial stabilization platform and radio navigation information, respectively.
[0024] Discretizing equation (1), we get: (4) The zero bias of the gyroscope and accelerometer in the state variables can be modeled as random constant errors, the differential of which is zero. Therefore, the forward filtering of the Kalman filter can be expressed as: (5) In the formula, the subscript " f " indicates forward filtering. When k = j At that time, the state can be obtained from equation (6). X j positive optimal estimate and its mean square error matrix P f,k .
[0025] In inverse filtering, the state-space model equation (4) can be rewritten as: (6) remember: , (7) Then we have the inverse filter state-space model: (8) The rotating accelerometer-gravity gradient meter isolates the carrier's angular motion through a stable platform, and can be approximated as follows when the system is discretized: (9) For the system state model space in equation (8), we can utilize j Inverse filtering is applied to measurements taken after a certain time. X j+1 Perform optimal estimation, and then... X j The algorithm for performing a reverse one-step prediction is as follows: (10) In the formula, the subscript " b "Indicates forward filtering. When k = j At that time, the state can be obtained from equation (10). X j The reverse optimal one-step prediction and its mean square error matrix P b,j / j+1 ; Combining the results of forward and reverse filtering, the following model is established: (11) For radio navigation systems, j The errors in the first and second halves of the time measurement are independent of each other, and since the Kalman filter state estimation is a linear combination of the measurements, therefore... and They are also independent of each other. The RTS smoothing filter algorithm can be used to... X j The optimal estimate is calculated using the following formula: ( k = M -1, M -2, ..., 1) (12) The initial value for the inverse smoothing filter is selected as follows: and ; The state can be obtained from this. X j The bidirectional optimal estimate, where the state vector X The first three components represent the attitude error of the gravity gradient sensor.
[0026] Step 3: Combine the attitude error estimated in Step 2 with the gravity gradient measurement information collected synchronously in Step 1. Based on the coordinate transformation matrix of the gravity gradient tensor in different coordinate systems, perform error compensation on the gravity gradient measurement value to finally obtain the gravity gradient measurement data after attitude error compensation.
[0027] The specific method for step 3 is as follows: Construct the direction cosine matrix from the measurement coordinate system of the gravity gradient sensor to the geographic coordinate system based on the attitude error estimation results: (13) In the formula, This is the direction cosine matrix from the measurement coordinate system to the geographic coordinate system. It is used to compensate for attitude errors in gravity gradient measurement data; the specific calculation formula is as follows: (14) In the formula, Γ g These are gravity gradient measurement data after attitude error compensation, Γ m These are gravity gradient measurement data before compensation; The above calculation is repeated for each moment to obtain the full tensor gravity gradient data Γ in the geographic coordinate system after attitude error compensation for the entire measurement period. g It includes five independent components (Γ) xx ,Γ xy ,Γ xz ,Γ yy and Γ yz This serves as the final dynamic measurement result of the gravity gradient, which is then output.
[0028] Example 1: To verify the effectiveness of the offline compensation method for dynamic measurement attitude error of the rotating accelerometer gravity gradient meter proposed in this invention, a specific implementation is described using a shipborne measurement experiment as an example.
[0029] 1. Experimental Platform and Data Acquisition The rotating accelerometer full-tensor gravity gradiometer system was installed inside the cabin of the experimental measurement vessel. After system startup, following the method described in step 1, using a unified high-precision radio navigation time as the synchronization reference, the following three types of data were collected throughout the entire navigation mission, with a total duration of approximately 4 hours. The route included various maneuvers such as uniform straight-line travel, variable speed travel, and turns: (1) Gravity gradient data: The original measurement signal output by the gravity gradient sensor is demodulated online to obtain the full tensor gravity gradient measurement value Γ in the sensor coordinate system. s (t), with a sampling rate of 1 Hz; (2) Inertial measurement data: The inertial measurement unit (fiber optic gyroscope zero bias stability is 0.01° / h, accelerometer zero bias stability is 50 μg) fixed to the sensor synchronously outputs triaxial angular velocity ω(t) and specific force f(t), with a sampling rate of 200 Hz; (3) Radio navigation measurement data: The radio navigation system (horizontal positioning accuracy 1 m, velocity measurement accuracy 0.5 m / s) outputs the latitude L(t), longitude λ(t), altitude h(t) and north, east and ground velocities of the carrier. The sampling rate is 1 Hz, and it is subsequently aligned to 200 Hz by interpolation.
[0030] 2. RTS smoothing estimation of attitude error Based on step 2, using the raw IMU data and radio navigation measurement data collected above, a 15-dimensional state-variable inertial / radio integrated navigation system is constructed, and RTS smoothing filtering is implemented. The specific implementation is as follows: Forward Kalman filtering: from start time t0 to end time t N The system noise covariance matrix Q and the measurement noise covariance matrix R are recursively derived using formula (5). The system noise covariance matrix Q and the measurement noise covariance matrix R are initialized based on the nominal accuracy of the inertial measurement unit and the radio navigation, where the gyroscope angle random walk noise density is set to 0.002° / h. 1 / 2 The accelerometer velocity random walk noise density was set to 10 μg / Hz. 1 / 2 Radio navigation speed observation noise is set to 0.2 m / s, and position observation noise is set to 0.2 m.
[0031] Backward Kalman filtering: from the end time t N Reverse the process back to the starting time t0 and process it using formula (10).
[0032] RTS Smoothing: Using formulas (11) and (12), the results of forward filtering and backward filtering are fused to obtain the optimal state estimate for each time step k. The first three components of the state vector X are the attitude error estimates δ of the gravity gradient sensor in pitch, roll, and yaw directions. , δθ, δψ.
[0033] Figure 3 The results show the attitude error estimation along a typical survey line (approximately 30 minutes) obtained using the RTS smoothing filtering method described above. It can be seen that the peak value of the heading angle error is approximately 1.5°, while the pitch and roll angle errors are within 0.2°, indicating that this method can effectively separate and estimate attitude drift under dynamic conditions.
[0034] 3. Attitude error compensation for gravity gradient data Based on step 3, the attitude error (δ) estimated in step 2 at each moment is... Substituting δθ, δψ) into formula (13), we construct the direction cosine matrix from the measurement coordinate system (m system) to the geographic coordinate system (g system, i.e., the northeast-sky coordinate system). .
[0035] Then, the original gravity gradient measurement data Γ acquired synchronously is processed using formula (14). m (t) Perform point-by-point compensation to obtain Γ g (t).
[0036] 4. Compensation Effect Analysis and Result Output Results before compensation: such as Figure 2 As shown, uncompensated attitude errors result in significant low-frequency drift and perturbation noise related to carrier maneuvering in the gravity gradient measurement results.
[0037] Result after compensation: Figure 3 After substituting the attitude error estimate into the compensation, the resulting gravity gradient data is as follows: Figure 4 As shown. Comparison Figure 2 It is evident that disturbances caused by low-frequency drift and maneuvering have been significantly suppressed.
[0038] Final output: Repeat the above compensation calculation for all 4 hours of measurement data, and finally output the full tensor gravity gradient data Γ in the geographic coordinate system for the entire measurement period. g , including Γ xx The five independent components Γxy, Γxz, Γyy, and Γyz, as well as the non-independent component Γzz (Γzz = -Γxx-Γyy), are used as the final results of this shipborne dynamic gravity gradient measurement. This is compared with the full tensor gravity gradient dynamic measurement data before compensation (…). Figure 2 Compared to the attitude error-compensated dynamic measurement data of the full tensor gravity gradient, Figure 4 The overall smoothness has been significantly improved, and the short-term fluctuations that are significantly related to the dynamics of the carrier have been suppressed.
[0039] This embodiment fully demonstrates that the method proposed in this invention can effectively suppress the influence of attitude error in dynamic measurement by using the joint processing of RTS smoothing filtering and gravity gradient measurement model without relying on high-precision and high-cost inertial measurement units, and significantly improve the dynamic measurement accuracy and environmental adaptability of the rotating accelerometer gravity gradient instrument.
[0040] Among them, the gravity gradient measurement results before attitude error compensation are as follows: Figure 2 As shown, the attitude error estimation results of the gravity gradient sensor obtained using the RTS smoothing algorithm are as follows: Figure 3 As shown, attitude error compensation is performed using equation (14), and the compensated gravity gradient measurement results are as follows. Figure 4 As shown.
[0041] Although embodiments and drawings of the present invention have been disclosed for illustrative purposes, those skilled in the art will understand that various substitutions, variations and modifications are possible without departing from the spirit and scope of the present invention and the appended claims. Therefore, the scope of the present invention is not limited to the contents disclosed in the embodiments and drawings.
Claims
1. A method for post-processing compensation of attitude error of a rotating accelerometer gravity gradient meter, characterized in that: Includes the following steps: Step 1: Collect raw motion data using an inertial measurement unit fixed to the gravity gradient sensor, and combine it with positioning and velocity information provided by radio navigation to complete the raw data acquisition. Step 2: Based on the raw data collected in Step 1, the attitude error of the gravity gradient sensor during the measurement process is optimally estimated by using the RTS smoothing filtering method, which integrates forward Kalman filtering and backward Kalman smoothing filtering. Step 3: Combine the attitude error estimated in Step 2 with the gravity gradient measurement information collected synchronously in Step 1. Based on the coordinate transformation matrix of the gravity gradient tensor in different coordinate systems, perform error compensation on the gravity gradient measurement value to finally obtain the gravity gradient measurement data after attitude error compensation.
2. The method for post-processing compensation of attitude error of a rotating accelerometer gravity gradient instrument according to claim 1, characterized in that: The specific steps of step 1 include: (1) Install the rotating accelerometer gravity gradiometer on a dynamic carrier (such as an aircraft) and start the gravity gradiometer data acquisition system, the inertial measurement unit data acquisition system and the radio navigation data acquisition system; (2) During the dynamic measurement process, the following data shall be recorded synchronously using a unified time base: ① The raw measurement data output by the gravity gradient sensor is the measured value of the gravity gradient tensor in the sensor coordinate system after demodulation, denoted as Γ. s ( t ); ② The raw measurement data of the three-axis angular velocity and linear acceleration output by the inertial measurement unit are denoted as follows: ω x ( t ), ω y ( t )and ω z ( t ),as well as f x ( t ), f y ( t )and f z ( t ); ③ The latitude, longitude, and altitude data output by radio navigation are respectively denoted as... L ( t ), λ ( t )and h ( t ); Data acquisition covers the entire dynamic measurement process, ensuring that subsequent offline processing has complete original observation information.
3. The method for post-processing compensation of attitude error of a rotating accelerometer gravity gradient instrument according to claim 1, characterized in that: The specific method for step 2 is as follows: The raw measurement data and radio navigation position information collected by the inertial measurement unit are subjected to RTS smoothing filtering. This process is divided into three stages: forward filtering, backward filtering, and smoothing filtering. A Kalman filter is constructed using the error equation of the inertial stabilized platform as the system state equation and the difference between the radio navigation and the state variables of the inertial stabilized platform as the observation equation. （1） Wherein, the system state vector is （2） The system measurement vector is: （3） In the formula, X It is a 15-dimensional state vector, with each state representing, in order: three-directional attitude error, three-directional velocity error, latitude, longitude, and altitude position error, three-directional gyroscope drift, and three-directional additive zero bias. Z It is a 6-dimensional measurement vector, consisting of three-directional velocity errors and latitude, longitude, and altitude position errors, respectively. F , G and H These are known structural parameters of an inertial / radio integrated navigation system, referred to as the state one-step transition matrix, system noise allocation matrix, and measurement matrix, respectively. Their specific expressions are common in the field of integrated navigation and will not be elaborated upon in this invention. W It is the system noise vector. V It is a measurement noise vector, and its specific parameters are determined by the inertial stabilization platform and radio navigation information, respectively. Discretizing equation (1), we get: （4） The zero bias of the gyroscope and accelerometer in the state variables can be modeled as random constant errors, the differential of which is zero. Therefore, the forward filtering of the Kalman filter can be expressed as: （5） In the formula, the subscript " f " indicates forward filtering; when k = j At that time, the state can be obtained from equation (6). X j positive optimal estimate and its mean square error matrix P f,k ; In inverse filtering, the state-space model equation (4) can be rewritten as: （6） remember: ， （7） Then we have the inverse filter state-space model: （8） The rotating accelerometer-gravity gradient meter isolates the carrier's angular motion through a stable platform, and can be approximated as follows when the system is discretized: （9） For the system state model space in equation (8), we can utilize j Inverse filtering is applied to measurements taken after a certain time. X j+1 Perform optimal estimation, and then... X j The algorithm for performing a reverse one-step prediction is as follows: （10） In the formula, the subscript " b " indicates forward filtering; when k = j At that time, the state can be obtained from equation (10). X j The reverse optimal one-step prediction and its mean square error matrix P b,j / j+1 ; Combining the results of forward and reverse filtering, the following model is established: （11） For radio navigation systems, j The errors in the first and second halves of the time measurement are independent of each other, and since the Kalman filter state estimation is a linear combination of the measurements, therefore... and They are also uncorrelated; the RTS smoothing filter algorithm can be used to... X j The optimal estimate is calculated using the following formula: （ k = M -1， M -2，…，1） （12） The initial value for the inverse smoothing filter is selected as follows: and ; The state can be obtained from this. X j The bidirectional optimal estimate, where the state vector X The first three components represent the attitude error of the gravity gradient sensor.
4. The method for post-processing compensation of attitude error of a rotating accelerometer gravity gradient instrument according to claim 1, characterized in that: The specific method for step 3 is as follows: Construct the direction cosine matrix from the measurement coordinate system of the gravity gradient sensor to the geographic coordinate system based on the attitude error estimation results: （13） In the formula, This is the direction cosine matrix from the measurement coordinate system to the geographic coordinate system; it is used to compensate for attitude errors in gravity gradient measurement data. The specific calculation formula is as follows: （14） In the formula, Γ g These are gravity gradient measurement data after attitude error compensation, Γ m These are gravity gradient measurement data before compensation; The above calculation is repeated for each moment to obtain the full tensor gravity gradient data Γ in the geographic coordinate system after attitude error compensation for the entire measurement period. g It includes five independent components (Γ) xx ,Γ xy ,Γ xz ,Γ yy and Γ yz This serves as the final dynamic measurement result of the gravity gradient, which is then output.