A gravity gradient decoupling method based on markov estimation

Abstract

The application relates to a gravity gradient decoupling method based on Markov estimation, which comprises the following steps: step 1, three gravity gradient sensors acquire original output signals in a real-time measurement coordinate system; step 2, based on the numerical values of the original output signals of the three gravity gradient sensors in the real-time measurement coordinate system collected in step 1, a measurement equation of a gravity gradient coaxial component is established in combination with a Laplace equation, and decoupling of the coaxial component is completed through Markov estimation. The application can fully consider the differences in the measurement capabilities of various sensors in the gravity gradient decoupling process, and further realize higher-precision decoupling of the gravity gradient coaxial component.

Description

Technical Field

[0001] This invention belongs to the technical field of gravity gradiometer measurement accuracy, and relates to a coaxial component decoupling method for gravity gradiometers based on the principle of rotational accelerometer, especially a gravity gradient decoupling method based on Markov estimation. Background Technology

[0002] The gravity gradient is the spatial rate of change of the gravity vector, and it is of great significance in mineral resource exploration, earth science research, and inertial navigation. A gravity gradiometer is a precision device used to measure the gravity gradient. The gravity gradiometer based on the rotational accelerometer measurement principle proposed by Bell Aerospace is, to date, the only practical near-surface dynamic gravity gradiometer.

[0003] like Figure 1 As shown, the gravity gradient measurement component, which serves as the core sensor, is based on the accelerometer position differential measurement principle. It modulates the gravity gradient tensor component to twice the system's rotation frequency through mechanical rotation. The relationship between the gravity gradient sensor output and the gravity gradient tensor component can be expressed as:

[0004] (a1+a3)-(a2+a4)=4R(Γ uv sin2ωt+Γ xy cos2ωt) (1)

[0005] In the formula, a1, a2, a3, and a4 are the measurement output signals of the four accelerometers, R is the distance from the center of mass detected by the accelerometer to the center of rotation, and Γ is the distance from the center of mass to the center of rotation. uv and Γ xy These are the gravitational gradient tensor components in the corresponding direction, where ω is the rotational angular velocity of the rotating mechanism. The final gravity gradient tensor signal Γ is obtained by synchronously demodulating the combined accelerometer signal output from the sensor at a frequency of 2ω. uv and Γ xy .

[0006] In full-tensor gravity gradient measurement, the rotation axes of three gravity gradient sensors are orthogonally arranged in space, and a right-handed coordinate system is constructed from the rotation axes of the three sensors, becoming the measurement coordinate system. At this time, the three sensors can measure Γ in this coordinate system in real time. uv With Γ xy ,Γ vw With Γ yz and Γ nw With Γ xz Components (of which) From this, we can obtain all the cross components Γ of the gravity gradient in the measurement coordinate system. xy ,Γ yz and Γ xz However, the coaxial component of the gravity gradient Γyz ,Γ yy and Γ zz Further decoupling is still needed to achieve full tensor gravity gradient measurement.

[0007] Existing decoupling methods do not fully consider the differences in measurement capabilities of the three sensors, assuming that the measurement capabilities of the three sensors are equivalent in isolation, which reduces the decoupling accuracy of the gravity gradiometer signal.

[0008] A search revealed no patent documents of the same or similar prior art as this invention. Summary of the Invention

[0009] The purpose of this invention is to overcome the shortcomings of the prior art and propose a gravity gradient decoupling method based on Markov estimation, which can fully consider the different measurement capabilities of each sensor in the gravity gradient decoupling process, thereby achieving higher precision coaxial component decoupling of gravity gradient.

[0010] The present invention solves its practical problem by adopting the following technical solution:

[0011] A gravity gradient decoupling method based on Markov estimation includes the following steps:

[0012] Step 1: The three gravity gradient sensors acquire the raw output signal in the measurement coordinate system in real time.

[0013] Step 2: Based on the three gravity gradient sensors collected in Step 1, the values ​​of the original output signals in the measurement coordinate system are obtained in real time. Combined with the Laplace equation, the measurement equation of the coaxial component of the gravity gradient is established, and then the coaxial component is decoupled by Markov estimation.

[0014] Furthermore, the specific method of step 1 is as follows:

[0015] Three gravity gradient sensors can acquire the Γ value in the measurement coordinate system in real time. uv ,Γ vw ,Γ uw ,Γ yz ,Γ xz and Γ xy Signal, where the cross component Γ xy ,Γ yz and Γ xz It can be obtained directly through demodulation, while the coaxial component Γ xx ,Γ yy and Γ zz The decoupling requires combining the Laplace equation and obtaining it through Markov estimation.

[0016] Furthermore, the specific steps of step 2 include:

[0017] (1) Establish the measurement equation for the coaxial component of the gravity gradient by combining the outputs of three gravity gradient sensors in real time with the Laplace equation:

[0018] Z = HX + V (1)

[0019] In the formula, Z: the observation vector combining the outputs of the three synchronously output gravity gradient sensors with the Laplace equation, its scalar form is Z = [Γ vw Γ uw Γ uv 0] T ;

[0020] H: The coefficient matrix of the 4×3 order state variables, in scalar form as follows

[0021]

[0022] X: The state variable to be estimated, its scalar form is X = [Γ] xx Γ yy Γ zz ] T ;

[0023] V: 3D interference noise vector.

[0024] (2) To ensure observation estimation The weighted sum of squared errors between them is minimized. Decoupling of the coaxial components is achieved through Markov estimation, and the estimation result is as follows:

[0025]

[0026] In the formula, R represents the estimated value of the state variable, and R is the error matrix of the measurement information, which is in scalar form as R = diag(R1 R2 R3 R4); where R1, R2 and R3 are the error variance values ​​of the output signals of the corresponding numbered gravity gradient sensors, and R4 is the error variance of the Laplace equation. Since this is a theoretical formula, R4 is assumed to be (0.01E). 2 .

[0027] Advantages and beneficial effects of the present invention:

[0028] This invention proposes a gravity gradient decoupling method based on Markov estimation. When performing full-tensor gravity gradient measurements using a full-tensor gravity gradiometer based on the rotational accelerometer principle, it is necessary to obtain the Γ values ​​output in real time from three gravity gradient sensors. uv ,Γ vw and Γ uwThis invention employs component decoupling to fully consider the varying measurement noise levels of different sensors during gravity gradient decoupling. By combining the measurement components of the three sensors with the Laplace equation to establish a linear regression equation, and constructing a variance matrix for the measurement noise of the three sensors, the coaxial component of the gravity gradient is decoupled using Markov estimation. This invention achieves optimal decoupling while fully considering the different measurement capabilities of each sensor. The decoupling method of this invention yields a lower-noise coaxial component of the gravity gradient, thereby improving the accuracy of gravity gradient measurement. Attached Figure Description

[0029] Figure 1 The figure shows the measurement principle of the rotating accelerometer-type gravity gradient meter of the present invention. Detailed Implementation

[0030] The embodiments of the present invention will be further described in detail below with reference to the accompanying drawings:

[0031] A gravity gradient decoupling method based on Markov estimation includes the following steps:

[0032] Step 1: The three gravity gradient sensors acquire the raw output signal in the measurement coordinate system in real time.

[0033] The specific method for step 1 is as follows:

[0034] Three gravity gradient sensors can acquire the Γ value in the measurement coordinate system in real time. uw ,Γ vw ,Γ vw ,Γ yz ,Γ xz and Γ xy Signal, where the cross component Γ xy ,Γ yz and Γ xz It can be obtained directly through demodulation, while the coaxial component Γ xx ,Γ yy and Γ zz The decoupling requires combining the Laplace equation and obtaining it through Markov estimation.

[0035] Step 2: Based on the three gravity gradient sensors collected in Step 1, the values ​​of the original output signals in the measurement coordinate system are obtained in real time. Combined with the Laplace equation, the measurement equation of the coaxial component of the gravity gradient is established, and then the coaxial component is decoupled by Markov estimation.

[0036] The specific steps of step 2 include:

[0037] (1) Establish the measurement equation for the coaxial component of the gravity gradient by combining the outputs of three gravity gradient sensors in real time with the Laplace equation:

[0038] Z = HX + V (1)

[0039] In the formula, Z: the observation vector combining the outputs of the three synchronously output gravity gradient sensors with the Laplace equation, its scalar form is Z = [Γ vw Γ uw Γ uv 0] T ;

[0040] H: The coefficient matrix of the 4×3 order state variables, in scalar form as follows

[0041]

[0042] X: The state variable to be estimated, its scalar form is X = [Γ] xx Γ yy Γ zz ] T ;

[0043] V: 3D interference noise vector.

[0044] (2) To ensure observation estimation The weighted sum of squared errors between them is minimized. Decoupling of the coaxial components is achieved through Markov estimation, and the estimation result is as follows:

[0045]

[0046] In the formula, R is the estimated value of the state variable, and R is the error matrix of the measurement information. Its scalar form is R = diag(R1 R2 R3); where R1, R2 and R3 are the error variance values ​​of the output signals of the corresponding numbered gravity gradient sensors, and R4 is the error variance of the Laplace equation. Since this is a theoretical formula, R4 is assumed to be (0.01E). 2 .

[0047] In this embodiment, the coaxial component of the gravity gradient Γ is thus obtained. xx ,Γ yy and Γ zz Then, combined with the gravity gradient cross component Γ obtained in step 1 xy ,Γ yz and Γ xz This enables the extraction of the full tensor gravity gradient information in the measurement coordinate system.

[0048] In this embodiment, we compare Markov estimation with the conventional least squares method. Markov estimation, based on the least squares method, considers the potential mismatch in output signal noise levels among the three gravity gradient sensors. It obtains the minimum variance optimal estimate of the state variables by adjusting the weights. Since the mean square error matrix of Markov estimation has no theoretical solution, the advantages of the Markov estimation method are illustrated below through numerical simulation:

[0049] Define the coefficient matrix of the estimator and the observation as B, i.e.

[0050] =B(HTR) -1 H) -1 H T R -1 (3)

[0051] And assume that the data noise intensities of the three gravity gradient sensors are respectively and Right now

[0052]

[0053] Then the coefficient matrix B obtained by the Markov estimation method M for:

[0054]

[0055] The coefficient matrix B obtained by the conventional least squares method LS for:

[0056]

[0057] Comparing the two coefficient matrices reveals that the Markov estimation method assigns greater weight to observations with lower noise levels to minimize the sum of squared weighted errors. Of course, if the output signals of the three gravity gradient sensors have the same noise level, the estimation results from both methods will be identical. In this case, the mean square error matrix of the estimated state variables is:

[0058]

[0059] In the formula C V —The variance matrix of noise V|.

[0060] If the power spectral density of the output signal noise of the three gravity gradient sensors is P GGI (unit is) Under the same filtering scale, we have:

[0061]

[0062] Substituting equation (8) into equation (7), we obtain the approximate numerical solution of the mean square error matrix of the state variables as follows:

[0063]

[0064] All elements on the diagonal are and The results show that by combining the Laplace equation with Markov estimation, the noise of the coaxial gradient estimator can be reduced by 5.7% compared to the output noise of the gravity gradient sensor.

[0065] It should be emphasized that the embodiments described in this invention are illustrative rather than limiting. Therefore, this invention includes, but is not limited to, the embodiments described in the specific implementation. Any other implementations derived by those skilled in the art based on the technical solutions of this invention are also within the scope of protection of this invention.

Claims

1. A gravity gradient decoupling method based on Markov estimation, characterized in that: Includes the following steps: Step 1: The three gravity gradient sensors acquire the raw output signal in the measurement coordinate system in real time. Step 2: Based on the three gravity gradient sensors collected in Step 1, the values ​​of the original output signals in the measurement coordinate system are obtained in real time. Combined with the Laplace equation, the measurement equation of the coaxial component of the gravity gradient is established, and then the coaxial component is decoupled by Markov estimation. The specific steps of step 2 include: (1) Establish the measurement equation for the coaxial component of the gravity gradient by combining the outputs of three gravity gradient sensors in real time with the Laplace equation: Z = HX + V (1) In the formula, Z: the observation vector combining the outputs of the three synchronously output gravity gradient sensors with the Laplace equation, its scalar form is Z = [Γ vw Γ uw Γ uv 0] T ; H: The coefficient matrix of the 4×3 order state variables, in scalar form as follows X: The state variable to be estimated, its scalar form is X = [Γ] xx Γ yy Γ zz ] T ; V: 3D interference noise vector; (2) To ensure observation estimation The weighted sum of squared errors between them is minimized. Decoupling of the coaxial components is achieved through Markov estimation, and the estimation result is as follows: In the formula, R represents the estimated value of the state variable, and R is the error matrix of the measurement information, which is in scalar form as R = diag(R1 R2 R3 R4); where R1, R2 and R3 are the error variance values ​​of the output signals of the corresponding numbered gravity gradient sensors, and R4 is the error variance of the Laplace equation. Since this is a theoretical formula, R4 is assumed to be (0.01E). 2 .

2. The gravity gradient decoupling method based on Markov estimation according to claim 1, characterized in that: The specific method for step 1 is as follows: Three gravity gradient sensors can acquire the Γ value in the measurement coordinate system in real time. uv ,Γ vw ,Γ uw ,Γ yz ,Γ xz and Γ xy Signal, where the cross component Γ xy ,Γ yz and Γ xz It can be obtained directly through demodulation, while the coaxial component Γ xx ,Γ yy and Γ zz The decoupling requires combining the Laplace equation and obtaining it through Markov estimation.

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