Shipborne measurement zero position calibration method for a rotating accelerometer gravity gradiometer

Abstract

The present application relates to a kind of rotation accelerometer gravity gradiometer shipborne measurement zero calibration method, comprising the following steps: step 1, obtain measured gravity gradient sequence, and pre-process, obtain pre-processed measured gravity gradient sequence;Step 2, extract model-based gravity gradient long wavelength reference;Step 3, establish Kalman filter fusion model, pre-process measured gravity gradient sequence and track based on model long wavelength reference sequence of gravity gradient, complete Kalman filter construction;Step 4, based on the Kalman filter of step 3 construction, output Kalman filter recursion and fusion signal, complete shipborne long time gravity gradient measurement signal zero drift calibration.The present application can realize the adaptive estimation of zero drift and the optimal recovery of gravity gradient signal under the condition of not needing to stop ship calibration and drift model assumption, calibrate the measurement zero of gravity gradiometer by gravity field model under dynamic condition, to improve instrument dynamic measurement precision.

Description

Technical Field

[0001] This invention belongs to the field of dynamic gravity gradient measurement technology, and relates to a method for zero-point drift calibration and signal fusion of measurement data of a rotating accelerometer gravity gradiometer on a ship for long-term navigation, especially a method for zero-point calibration of a rotating accelerometer gravity gradiometer on a ship. Background Technology

[0002] The rotating accelerometer gravity gradiometer obtains partial or complete components of the gravity gradient tensor through differential measurements using four high-resolution accelerometers deployed on a rotating disk. It is widely used in resource exploration, geoid refinement, and gravity-assisted navigation. During long-duration shipboard measurements, the gravity gradiometer needs to continuously measure for dozens of days, with survey lines reaching tens of thousands of kilometers in length. Due to factors such as the accelerometer's zero-bias temperature sensitivity, electronic component reference drift, and changes in the marine environment, the gravity gradiometer's output signal inevitably contains a slowly accumulating zero-point drift over time. This drift changes very little within hours, but can accumulate to tens of Eötvöss (E, 1 E = 10⁻⁶) over the entire measurement cycle. -9 s -2 In severe cases, gravity gradient errors can submerge the long-wavelength components in the true gravity gradient signal, leading to excessive gravity gradient closure error and regional gravity field distortion, which restricts the application of gravity gradient measurement data in geological surveys and geophysics.

[0003] Existing methods for zero-point drift correction of geophysical instruments mainly include: periodically stopping the ship at known benchmark points for zeroing calibration, using survey line intersections or repeated survey lines for network adjustment, and hardware suppression through high-precision temperature control and a stable platform.

[0004] Currently, there are no known benchmarks for the marine gravity gradient, making calibration impossible; network adjustment requires dense cross-line surveys and prior assumptions about the drift model, while the actual drift pattern is often complex, resulting in poor polynomial fitting; hardware improvements cannot eliminate residual drift and increase instrument costs.

[0005] In recent years, high-resolution Earth gravity field models (such as EGM2008 and EIGEN-6C4) and ocean gravity field models (such as the SIO and DTU series) have been able to provide global coverage gravity field information with a spatial resolution of up to 10 km half-wavelength. These models possess extremely high absolute accuracy and naturally drift-free characteristics at wavelengths greater than 100 km, making them ideal as long-wavelength references for shipborne gravity gradient measurements. However, the models have limited accuracy in the short-wavelength band and cannot directly replace the high-resolution signals measured by instruments. The key to solving the null drift problem lies in how to optimally integrate the stability of the model in the long-wavelength band with the details measured by instruments in the short-wavelength band. Existing simple difference or piecewise averaging methods fail to allocate frequency domain weights reasonably from a statistically optimal perspective, resulting in residual drift in calibration results or contamination by model errors.

[0006] Therefore, there is an urgent need to propose a zero-point calibration method for shipborne measurement of a rotating accelerometer gravity gradiometer that can integrate the long-wavelength drift-free characteristics of the gravity field model and the short-wavelength high-precision characteristics of the gravity gradiometer, so as to improve the accuracy of gravity gradient measurement.

[0007] A search revealed no publicly available literature of the same or similar prior art as this invention. Summary of the Invention

[0008] This invention addresses the shortcomings of existing calibration methods, which rely on difficult-to-obtain reference points, strongly assumed drift models, or inability to optimally integrate external long-wavelength references, due to the severe accumulation of zero-point drift during long-term measurements of shipborne gravity gradiometers. It provides a zero-point calibration method for shipborne measurement signals of rotating accelerometer gravity gradiometers based on Kalman filtering. This method enables adaptive estimation of zero-point drift and optimal recovery of the gravity gradient signal without requiring ship-stop calibration or drift model assumptions. Under dynamic conditions, it calibrates the measurement zero point of the gravity gradiometer using a gravity field model, thereby improving the instrument's dynamic measurement accuracy.

[0009] The above-mentioned objective of this invention is achieved through the following technical solution: A method for zero-point calibration of a shipborne rotary accelerometer gravity gradient meter includes the following steps: Step 1: Obtain the measured gravity gradient sequence and perform preprocessing to obtain the preprocessed measured gravity gradient sequence; Step 2: Based on the preprocessed measured gravity gradient sequence obtained in Step 1, extract the long-wavelength reference of gravity gradient based on the model. Step 3: Establish a Kalman filter fusion model. Combine the preprocessed measured gravity gradient sequence obtained in Step 1 with the model-based long-wavelength gravity gradient reference sequence on the track obtained in Step 2 to complete the construction of the Kalman filter. Step 4: Based on the Kalman filter constructed in Step 3, output the Kalman filter recursive and fused signal to complete the zero-point drift calibration of the shipborne long-duration gravity gradient measurement signal.

[0010] Furthermore, the specific method of step 1 is as follows: The raw sensor measurement signal output from the shipborne rotating accelerometer gravity gradiometer is acquired, demodulated, and a component of the gravity gradient tensor is obtained, denoted as . C ( t (Simultaneously record sampling time) t The measurement point location information and carrier motion information are collected and preprocessed, including instrument parameter correction, motion error compensation, low-pass filtering, and spatial resampling, to obtain the preprocessed measured gravity gradient sequence. C ( k ), k =1, …,N； Furthermore, the specific method for step 2 is as follows: Based on the measurement point location information obtained in step 1, select either a global gravity field model or a global ocean gravity field model, and obtain the long-wavelength reference of the gravity gradient on the carrier track according to the following steps: If a gravity field model based on ellipsoidal harmonic series expansion, such as EGM2008 or XGM2019e, is selected, the geodetic coordinates of the carrier location ( L , l , h Convert to geocentric coordinates ( r , i , l ),in r It is the distance from the location of the carrier to the center of the Earth. i The covariance is then used to calculate the gravitational potential of the carrier position using the spherical harmonic expansion formula. The specific formula is as follows: (1) In the formula, T It is the potential function of gravitational perturbation. GM It is the gravitational constant. N It is the maximum expansion order. R e It is the semi-major axis of the reference ellipsoid. C nm and S nm These are fully normalized bit coefficients. P nm It is a fully normalized associated Legendre function. n and m These are the order and degree of the spherical harmonic function expansion; taking the second-order partial derivative with respect to the perturbation potential yields the components of the gravity gradient tensor, specifically: (2) If a gravity field model based on discrete digital grids, such as SIO or DTU series, is selected, the grid data of gravity anomalies and vertical deviations must first be converted into grid data of each component of the gravity gradient using frequency domain or spatial domain methods. Then, interpolation is used to obtain each component of the gravity gradient on the carrier track.

[0011] Furthermore, the specific method for step 3 is as follows: The true gravity gradient signal at each measurement location on the carrier's trajectory s k and instrument measurement zero point b k As state variables, they constitute a two-dimensional state vector x k ,Right now: (3) There is a strong spatial correlation between adjacent measurement positions on the carrier track, which can be modeled as a random walk process; the drift of the instrument measurement zero point is recorded as slow, which can also be described by a random walk. Therefore, the state transition equation is: , (4) In the formula, w is the system noise during the update process, which has a mean of 0 and a standard deviation of . Q The system noise covariance matrix follows a normal distribution, where the system noise covariance matrix is... Q It can be represented as: (5) In the formula, q s These are the noise propagation parameters of the actual gravity gradient signal. q b It is a rotating accelerometer gravity gradient meter that measures the drift change of the zero point over time. q b The value is much smaller than q s ; The equation for the observation of the gravity gradient is established as follows: , (6) In the formula, Γ k It is the output value of the rotating accelerometer-gravimetric gradiometer at the k-th position. The gravity gradient value is obtained from the gravity field model, and v is the measurement noise matrix, which follows a mean of 0 and a standard deviation of . R The normal distribution, where the measurement noise covariance matrix is... R It can be represented as: (7) In the formula, s i This refers to the short-wavelength noise level of the measured gravity gradient value. s m It is the long-wavelength noise level of the gravity gradient obtained from the gravity field model; The measurement equation (6) can be simplified as follows: (8) This leads to the state transition equation and measurement equation of the Kalman filter, thus completing the design of the Kalman filter.

[0012] Furthermore, the specific method for step 4 is as follows: Kalman filtering is performed based on the state transition equation (4) and measurement equation (8) obtained from step 3. The specific filtering method is as follows: (9) In the formula, K is the correction coefficient matrix, P is the co-mean square error matrix of the state vector x, and the initial value x0 of the state vector is: (10) The initial value P0 of the comean square error matrix can be set as follows: (11) This setting indicates that the initial uncertainty is relatively large, which enables the filter to converge quickly.

[0013] State estimation of the filtered output In, the first component This is the calibrated and fused gravity gradient signal. For real-time estimation of zero-point drift measured by gravity gradiometer, This is the final gravity gradient measurement result. Thus, the shipborne long-duration gravity gradient measurement signal after zero-drift calibration is obtained. .

[0014] The advantages and beneficial effects of this invention are as follows: 1. This invention requires no offshore reference point, features adaptive calibration, and directly utilizes the long-wavelength components of a global or oceanic gravity field model as an absolute reference. It eliminates the need for ship-based calibration and automatically tracks drift changes through Kalman filtering, without relying on any functional form assumptions. This invention employs adaptive zero-point calibration, eliminating the need for external reference points and drift model assumptions: by using the long-wavelength components of the Earth's gravity field model as the external absolute observation and modeling the instrument's zero-point drift as a state variable for Kalman filtering recursion (steps 2 to 4), the filter can adaptively track the slow changes in drift. This method completely eliminates dependence on known offshore reference points, ship-based calibration, and prior drift function forms (such as polynomials), achieving fully data-driven, assumption-free online zero-point calibration.

[0015] 2. This invention achieves optimal frequency domain fusion, balancing long-wave stability with short-wave high resolution and high fidelity. By setting observation noise parameters, filtering automatically separates the frequency domain functions of "short-wave signal to instrument, long-wave signal to model," thus fully preserving the high-resolution information of instrument measurements while completely eliminating long-wave drift. This invention utilizes differentiated settings of the dual-observation noise covariance to minimize long-wave error in the model and clearly define the short-wave noise characteristics of the instrument (step 3). During filtering recursion, the frequency domain function is automatically separated: long-wave gain is biased towards the model to forcibly eliminate cumulative drift; short-wave gain is biased towards the instrument to fully preserve geological details. The fusion result not only eradicates long-haul zero-point drift but also preserves the instrument's inherent high-resolution measurement capabilities, significantly improving data fidelity.

[0016] 3. This invention is simple to calculate and easy to implement in real time. It only requires standard Kalman filter recursion and does not involve large-scale matrix inversion. It is suitable for shipborne real-time processing and can be flexibly adapted to different gravity field models. Attached Figure Description

[0017] Figure 1 This is a graph showing the original measured values ​​of the gravity gradient meter on the measuring line of the present invention. Figure 2 This is a graph showing the gravity gradient values ​​obtained from the Earth's gravity field model on the survey line of this invention. Figure 3 This is a graph showing the calibrated gravity gradient measurements of the present invention. Figure 4 This is a graph showing the real-time estimation results of the zero-point drift measured by the gravity gradient meter of the present invention. Detailed Implementation

[0018] 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.

[0019] A method for zero-point calibration of a shipborne rotary accelerometer gravity gradient meter includes the following steps: Step 1: Obtain the measured gravity gradient sequence and perform preprocessing to obtain the preprocessed measured gravity gradient sequence; The specific method for step 1 is as follows: The raw sensor measurement signal output from the shipborne rotating accelerometer gravity gradiometer is acquired, demodulated, and a component of the gravity gradient tensor is obtained, denoted as . C ( t (Simultaneously record sampling time) t Measurement point location information (longitude) l ,latitude L ellipsoidal height h ) and carrier motion information (including carrier linear motion information, angular motion information and attitude, etc.).

[0020] Preprocessing includes: (1) Instrument parameter calibration: The scale factor, zero offset and cross-coupling coefficient of the gravity gradient measurement signal are compensated using laboratory calibration parameters; (2) Motion error compensation: Compensate for motion errors caused by the movement of the carrier, such as vertical line motion error, horizontal angle motion error and self-gradient error in the gravity gradient measurement signal; (3) Low-pass filtering and spatial resampling: To suppress high-frequency noise caused by factors such as carrier motion and instrument electronic noise, a digital low-pass filter (such as an FIR low-pass filter with a cutoff frequency of 0.01 Hz, corresponding to a spatial resolution of about 250 m at a ship speed of 10 knots) is used. After filtering, the gravity gradient measurement information with time as the independent variable is converted into gravity gradient measurement information with spatial position as the independent variable according to the carrier position information, and the measurement is performed at fixed spatial intervals. d Perform cubic spline interpolation resampling to obtain the preprocessed measured gravity gradient sequence. C ( k ), k =1, …, N . d Typically, a depth of 30 m to 50 m is used to ensure that short-wavelength anomalies in the actual gravity gradient signal are fully captured.

[0021] Step 2: Based on the preprocessed measured gravity gradient sequence obtained in Step 1, extract the long-wavelength reference of gravity gradient based on the model. The specific method for step 2 is as follows: Using the location information (longitude, latitude, and altitude) of the measurement points obtained in step 1, and selecting a global gravity field model (such as EGM2008 or XGM2019e) or a global ocean gravity field model (such as SIO or DTU series), the long-wavelength reference of the gravity gradient on the carrier track can be obtained by following the steps below: If a gravity field model based on ellipsoidal harmonic series expansion, such as EGM2008 or XGM2019e, is selected, the geodetic coordinates of the carrier's location need to be used. L , l , h Convert to geocentric coordinates ( r , i , l ),in r It is the distance from the location of the carrier to the center of the Earth. i The covariance is then used to calculate the gravitational potential of the carrier position using the spherical harmonic expansion formula. The specific formula is as follows: (1) In the formula T It is the potential function of gravitational perturbation. GM It is the gravitational constant. N It is the maximum expansion order. R e It is the semi-major axis of the reference ellipsoid. C nm and S nm These are fully normalized bit coefficients. P nm It is a fully normalized associated Legendre function. nand m These are the order and degree of the spherical harmonic function expansion. Taking the second-order partial derivative with respect to the perturbation potential yields the components of the gravity gradient tensor, as shown in the following formula: (2) If a gravity field model based on discrete digital grids, such as the SIO or DTU series, is selected, the grid data of gravity anomalies and vertical deviations must first be converted into grid data of each component of the gravity gradient using frequency domain or spatial domain methods. Then, interpolation is used to obtain each component of the gravity gradient on the carrier track. Since frequency domain or spatial domain gravity gradient tensor conversion methods are common in the field of gravity gradient data processing, they will not be elaborated upon in this invention.

[0022] Step 3: Establish a Kalman filter fusion model. Combine the preprocessed measured gravity gradient sequence Γ(k) obtained in Step 1 with the model-based long-wavelength gravity gradient reference sequence on the track obtained in Step 2 to complete the construction of the Kalman filter. The specific method for step 3 is as follows: The true gravity gradient signal at each measurement location on the carrier's trajectory s k and instrument measurement zero point b k As state variables, they constitute a two-dimensional state vector x k ,Right now: (3) There is a strong spatial correlation between adjacent measurement positions on the carrier track, which can be modeled as a random walk process; the drift of the instrument's measurement zero point is denoted as slow and can also be described by a random walk. Therefore, the state transition equation is: , (4) In the formula, w is the system noise during the update process, which has a mean of 0 and a standard deviation of . Q The system noise covariance matrix follows a normal distribution, where the system noise covariance matrix is... Q It can be represented as: (5) In the formula q s These are the noise propagation parameters of the actual gravity gradient signal, determined based on the spatial rate of change of the regional gravity gradient and the carrier's velocity. Specifically, they can be determined through analysis of historical high-precision measurement data or simulation. q b The rotary accelerometer gravity gradient meter measures the drift change of the zero point over time. This can be determined based on the instrument's output signal under static conditions. q b The value is much smaller than qs .

[0023] The equation for the observation of the gravity gradient is established as follows: , (6) In the formula, Γ k It is the output value of the rotating accelerometer-gravimetric gradiometer at the k-th position. The gravity gradient value is obtained from the gravity field model, and v is the measurement noise matrix, which follows a mean of 0 and a standard deviation of . R The normal distribution, where the measurement noise covariance matrix is... R It can be represented as: (7) In the formula s i This refers to the short-wavelength noise level of the measured gravity gradient value, which can be determined by the instrument's measurement accuracy. s m This is the long-wavelength noise level of the gravity gradient obtained from the gravity field model. Since the absolute error of the model at long wavelengths is usually less than 1 E, a minimum value can be set, reflecting the high reliability of the gravity gradient values ​​obtained from the gravity field model at long wavelengths during the fusion process. This R-array setting strategy ensures that in the long-wavelength band, the filter gain automatically biases towards the model observations, thereby forcing the drift to zero; while in the short-wavelength band, the model observations contain almost no information, and the gain naturally shifts towards the instrument's measured values, preserving the short-wavelength details in the instrument measurements.

[0024] The measurement equation (6) can be simplified as follows: (8) This leads to the state transition equation and measurement equation of the Kalman filter, thus completing the design of the Kalman filter.

[0025] Step 4: Based on the Kalman filter constructed in Step 3, output the Kalman filter recursive and fused signal to complete the zero-point drift calibration of the shipborne long-duration gravity gradient measurement signal. The specific method for step 4 is as follows: Kalman filtering is performed based on the state transition equation (4) and measurement equation (8) obtained from step 3. The specific filtering method is as follows: (9) In the formula, K is the correction coefficient matrix, P is the co-mean square error matrix of the state vector x, and the initial value x0 of the state vector is: (10) The initial value P0 of the comean square error matrix can be set as follows: (11) This setting indicates that the initial uncertainty is relatively large, which enables the filter to converge quickly.

[0026] State estimation of the filtered output In, the first component This is the calibrated and fused gravity gradient signal. For real-time estimation of zero-point drift measured by gravity gradiometer, This yields the final gravity gradient measurement result, thus obtaining the shipborne long-duration gravity gradient measurement signal after zero-point drift calibration. .

[0027] The present invention will be further illustrated below through specific embodiments: To verify the effectiveness of the shipborne measurement zero-point calibration method for the rotating accelerometer gravity gradient meter proposed in this invention, the data from a single shipborne gravity gradient measurement was analyzed. xy The processing of components fully demonstrates the implementation process of this invention.

[0028] The gravity gradient meter measurement results on one of the measuring lines are as follows: Figure 1 As shown, the long-wavelength reference of the gravity gradient obtained from the gravity field model on this survey line is as follows: Figure 2 As shown, the sampling interval was set to 50 m, and a total of 2001 measuring points were obtained under the condition that the survey line was 100 km long. Q Zhenhe R The formation is as follows: (12) (13) Therefore, using Equation (9) for Kalman filtering, the calibrated gravity gradient signal and the real-time estimation results of the zero-point drift measured by the gravity gradiometer are as follows: Figure 3 and Figure 4 As shown, it can be seen that after the Kalman filter converges, the gravity gradient measurement results output by the filter can not only completely retain the high-resolution information of the instrument measurement, but also completely eliminate the influence of long-wavelength drift.

[0029] The working principle of this invention is: This invention provides a method for zero-point calibration of a shipborne rotary accelerometer gravity gradient meter, comprising the following steps: (1) Obtain the measured gravity gradient sequence along the measurement line by the gravity gradiometer and perform preprocessing to suppress high-frequency noise and the influence of dynamic environment; (2) Calculate the model gravity gradient value along the survey line using the Earth gravity field model or the ocean gravity field model, and extract long-wave components with wavelengths greater than 100km through spatial domain low-pass filtering to form a drift-free long-wave reference sequence. (3) Establish the state equation with the real gravity gradient signal and zero drift as state variables, establish the observation equation with the preprocessed measured sequence and the long-wave reference sequence as dual observations, and set the observation noise covariance according to the instrument noise level and the long-wave accuracy of the model to construct the Kalman filter fusion model. (4) Perform Kalman filtering recursive estimation along the survey line to simultaneously obtain the zero drift estimate and the fused gravity gradient signal after calibration. The fused signal is faithful to the instrument measurement details in the short wave band and consistent with the gravity field model reference in the long wave band.

[0030] First, the measured signals from the shipborne rotating accelerometer gravity gradiometer are calibrated for instrument parameters, compensated for motion errors, and subjected to low-pass filtering and spatial resampling to obtain a preprocessed measured gravity gradient sequence. Simultaneously, the gravity gradient along the survey line is calculated using a global or oceanic gravity field model, and a drift-free long-wave reference sequence with wavelengths greater than 100 km is extracted through spatial domain low-pass filtering. Second, the actual gravity gradient signal and instrument zero-point drift are modeled as random walk processes, and a state equation is established. The preprocessed measured sequence and the model long-wave reference sequence constitute a dual-observation system. Based on the instrument's short-wave noise level and the model's high-precision long-wave characteristics, the observation noise covariance is set separately, and a Kalman filter fusion model is constructed. During recursive filtering along the survey line, the filter automatically performs frequency domain division based on noise characteristics: in the long-wave band, the model's observation noise is minimal, and the filter gain automatically biases towards the model, forcing the drift to zero; in the short-wave band, the model has almost no information, and the gain naturally shifts towards the instrument's measured values, fully preserving high-resolution details. Finally, the system synchronously outputs the real-time estimate of zero-point drift and the fused gravity gradient signal after calibration. The innovation lies in using the long-wavelength component of the gravity field model as an external absolute reference. Through statistical optimal fusion, it completely eliminates the dependence on the assumptions of the sea reference point and drift model, and achieves adaptive, high-fidelity long-duration zero-point calibration.

[0031] 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 zero-point calibration of a shipborne rotary accelerometer gravity gradient meter, characterized in that: Includes the following steps: Step 1: Obtain the measured gravity gradient sequence and perform preprocessing to obtain the preprocessed measured gravity gradient sequence; Step 2: Based on the preprocessed measured gravity gradient sequence obtained in Step 1, extract the long-wavelength reference of gravity gradient based on the model. Step 3: Establish a Kalman filter fusion model. Combine the preprocessed measured gravity gradient sequence obtained in Step 1 with the model-based long-wavelength gravity gradient reference sequence on the track obtained in Step 2 to complete the construction of the Kalman filter. Step 4: Based on the Kalman filter constructed in Step 3, output the Kalman filter recursive and fused signal to complete the zero-point drift calibration of the shipborne long-duration gravity gradient measurement signal.

2. The method for zero-point calibration of a shipborne rotary accelerometer gravity gradient meter according to claim 1, characterized in that: The specific method for step 1 is as follows: The raw sensor measurement signal output from the shipborne rotating accelerometer gravity gradiometer is acquired, demodulated, and a component of the gravity gradient tensor is obtained, denoted as . Γ ( t (Simultaneously record sampling time) t The measurement point location information and carrier motion information are collected and preprocessed, including instrument parameter correction, motion error compensation, low-pass filtering, and spatial resampling, to obtain the preprocessed measured gravity gradient sequence. Γ ( k ), k =1, …, N .

3. The zero-point calibration method for a shipborne rotating accelerometer gravity gradient meter according to claim 1, characterized in that: The specific method for step 2 is as follows: Based on the measurement point location information obtained in step 1, select either a global gravity field model or a global ocean gravity field model, and obtain the long-wavelength reference of the gravity gradient on the carrier track according to the following steps: If a gravity field model based on ellipsoidal harmonic series expansion, such as EGM2008 or XGM2019e, is selected, the geodetic coordinates of the carrier location ( L , λ , h Convert to geocentric coordinates ( r , θ , λ ),in r It is the distance from the location of the carrier to the center of the Earth. θ The covariance is then used to calculate the gravitational potential of the carrier position using the spherical harmonic expansion formula. The specific formula is as follows: （1） In the formula, T It is the potential function of gravitational perturbation. GM It is the gravitational constant. N It is the maximum expansion order. R e It is the semi-major axis of the reference ellipsoid. C nm and S nm These are fully normalized bit coefficients. P nm It is a fully normalized associated Legendre function. n and m These are the order and degree of the spherical harmonic function expansion; taking the second-order partial derivative with respect to the perturbation potential yields the components of the gravity gradient tensor, specifically: （2） If a gravity field model based on discrete digital grids, such as SIO or DTU series, is selected, the grid data of gravity anomalies and vertical deviations must first be converted into grid data of each component of the gravity gradient using frequency domain or spatial domain methods. Then, interpolation is used to obtain each component of the gravity gradient on the carrier track.

4. The zero-point calibration method for a shipborne measurement of a rotating accelerometer gravity gradient meter according to claim 1, characterized in that: The specific method for step 3 is as follows: The true gravity gradient signal at each measurement location on the carrier's trajectory s k and instrument measurement zero point b k As state variables, they constitute a two-dimensional state vector x k ,Right now: （3） There is a strong spatial correlation between adjacent measurement positions on the carrier track, which can be modeled as a random walk process; the drift of the instrument measurement zero point is recorded as slow, which can also be described by a random walk. Therefore, the state transition equation is: ， （4） In the formula, w is the system noise during the update process, which has a mean of 0 and a standard deviation of . Q The system noise covariance matrix follows a normal distribution, where the system noise covariance matrix is... Q It can be represented as: （5） In the formula, q s These are the noise propagation parameters of the actual gravity gradient signal. q b It is a rotating accelerometer gravity gradient meter that measures the drift change of the zero point over time. q b The value is much smaller than q s ; The equation for the observation of the gravity gradient is established as follows: ， （6） In the formula, Γ k It is the output value of the rotating accelerometer-gravimetric gradiometer at the k-th position. The gravity gradient value is obtained from the gravity field model, and v is the measurement noise matrix, which follows a mean of 0 and a standard deviation of . R The normal distribution, where the measurement noise covariance matrix is... R It can be represented as: （7） In the formula, σ i This refers to the short-wavelength noise level of the measured gravity gradient value. σ m It is the long-wavelength noise level of the gravity gradient obtained from the gravity field model; The measurement equation (6) can be simplified as follows: （8） This leads to the state transition equation and measurement equation of the Kalman filter, thus completing the design of the Kalman filter.

5. The zero-point calibration method for a shipborne measurement of a rotating accelerometer gravity gradient instrument according to claim 1, characterized in that: The specific method for step 4 is as follows: Kalman filtering is performed based on the state transition equation (4) and measurement equation (8) obtained from step 3. The specific filtering method is as follows: （9） In the formula, K is the correction coefficient matrix, P is the co-mean square error matrix of the state vector x, and the initial value x0 of the state vector is: （10） The initial value P0 of the comean square error matrix can be set as follows: （11） This setting indicates that the initial uncertainty is relatively large, which enables the filter to converge quickly; State estimation of the filtered output In, the first component This is the calibrated and fused gravity gradient signal. For real-time estimation of zero-point drift measured by gravity gradiometer, This yields the final gravity gradient measurement result, thus obtaining the shipborne long-duration gravity gradient measurement signal after zero-point drift calibration. .

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