Gradiometer error estimation and compensation method and system based on physical attribute constraint

Abstract

The invention discloses a gradiometer error estimation and compensation method and a gradiometer error estimation and compensation system based on physical attribute constraint, which are used for solving the problem that an existing motion error model parameter is usually determined by minimizing a standard deviation or a variance of a difference value between model output and instrument output, so that overfitting is easily caused. According to the technical scheme, constraint conditions are generated on the basis of physical attributes of an instrument and fused into a target function, so that estimated motion error model parameters approach actual error parameters of the instrument, and the over-fitting phenomenon is effectively relieved or eliminated. In addition, according to the technical scheme, the input and output of the motion error model are multiplied by the carrier waves at the same time, and the demodulated motion error model is obtained. Motion error deduction can be carried out before orthogonal demodulation and can also be completed after demodulation, so that an instrument system can dynamically adjust an error compensation strategy in different application scenes, and more flexible and accurate error compensation is realized.

Description

Technical Field

[0001] This invention belongs to the field of gradient meter technology, specifically relating to a gradient meter error estimation and compensation method and system based on physical property constraints. Background Technology

[0002] The parameters of a motion error model are typically determined by the physical properties of the instrument, such as the accelerometer's mounting parameters and input / output model parameters. These physical property parameters can be measured or their ranges determined during instrument manufacturing and testing.

[0003] Currently, the parameters of motion error models are typically estimated by minimizing the standard deviation or variance of the difference between the model output and the instrument output. This method, lacking external constraints, makes it difficult for the estimated model parameters to converge to the actual error parameters of the instrument, leading to overfitting. The severity of this overfitting is closely related to the inherent constraints of the motion error model itself. Specifically, the higher the degrees of freedom and the lower the constraints, the more prone the model is to overfitting. For example, the high-degree-of-freedom 541-parameter motion error model (CN118501978A) is more prone to overfitting than the 54-parameter analytical model (patents CN117805936A, CN112363247A, CN109766812A and the paper Posterror Compensation of Moving-Base Rotating Accelerometer Gravity Gradiometer). This is because the motion term of the 54-parameter model is constrained by the physical properties of the gradient instrument, resulting in low degrees of freedom. Summary of the Invention

[0004] The purpose of this invention is to address the overfitting problem in motion error model parameter estimation in existing technologies. Traditional parameter estimation methods determine model parameters by minimizing the standard deviation or variance of the difference between the model output and the instrument output. However, this method is prone to overfitting, especially in models with high degrees of freedom and low constraints. This invention proposes a gradient instrument error estimation and compensation method and system based on physical property constraints. This method generates constraints based on the instrument's physical properties and integrates them into the gradient instrument's motion error objective function. This makes the estimated motion error model parameters approximate the actual instrument error parameters, effectively mitigating or eliminating overfitting and significantly reducing the search space of the objective function, thus reducing the solution time for model parameters. Furthermore, this invention provides two feasible compensation methods: by multiplying both the input and output of the motion error model by a carrier wave to obtain the demodulated motion error model, motion error subtraction can be performed either before or after orthogonal demodulation. This allows the instrument system to dynamically adjust the error compensation strategy in different application scenarios, achieving more flexible and accurate error compensation.

[0005] Therefore, the present invention provides the following technical solution:

[0006] On the one hand, the present invention provides a gradient meter error estimation method based on physical property constraints, comprising the following steps:

[0007] S1: Acquire the output sampling signal G of the gradient meter out (t) and the sampling signal from the gradient meter motion monitoring sensor, and then the motion vector M at each sampling time is obtained based on the sampling signal from the gradient meter motion monitoring sensor. G (t), where t is the sampling time;

[0008] The sampling signal of the gradient meter motion monitoring sensor consists of the specific force vector, angular velocity vector, and angular acceleration vector at the sampling time;

[0009] S2: Based on the physical properties of the gradient meter, determine the boundary of the motion error model parameter vector P of the gradient meter. The motion error model of the gradient meter is represented as G. merr (t)=M G (t)P,G merr (t) represents the motion error of the gradient instrument at time t;

[0010] Among them, based on the physical properties of the gradient meter, the minimum and maximum values ​​of the motion error model parameter vector P are determined by using the motion error propagation mechanism or by using the gradient meter motion error analytical model;

[0011] S3: Introduce the boundary of the motion error model parameter vector P into the gradient meter's motion error objective function, and utilize the output sampling signal G of the gradient meter. out (t), the motion vector M G (t) Determine the motion error model parameter vector P, and then determine the motion error of the gradient instrument.

[0012] Preferably, the process of determining the minimum and maximum values ​​of the motion error model parameter vector P based on the physical properties of the gradient meter and utilizing the motion error propagation mechanism in step S2 is as follows:

[0013] Define the motion vector M at time t. G (t)=[m1(t),...,m i (t),…,m N (t)],m1(t),m i (t),m N (t) is the motion vector M G The first, i-th, and N-th elements of (t), the motion error propagation mechanism is based on the motion vector M. G The element m of (t) i (t) contains motion terms that determine the motion error coefficient p.i The limit, motion error coefficient p i Let i be the value of the i-th element in the parameter vector P of the motion error model;

[0014] Specifically:

[0015]

[0016] In the formula, p imin and p imax These are the motion error coefficients p i The lower and upper limits, k 1max K represents the maximum linear scaling coefficient of the accelerometer group that senses gravitational acceleration in the gradient instrument. 2max It is the maximum value of the second-order nonlinear coefficient of the accelerometer group that senses gravitational acceleration in the gradient instrument, k 0max It is the maximum value of the zero bias of the accelerometer group that senses gravitational acceleration in the gradient instrument, n. acc R is the number of accelerometers in the accelerometer group that senses gravitational acceleration in the gradient meter; R is the distance from the accelerometer mounting point to the origin of the gradient meter's measurement coordinate system; q1, q2, q3, q4, q5, q6 are m i (t) contains the number of terms in the six categories of motion error terms, corresponding to motion terms containing quadratic terms of centripetal acceleration, quadratic terms of angular acceleration, and coupled terms of angular and centripetal acceleration; motion terms containing coupled terms of centripetal and linear acceleration, and coupled terms of angular and linear acceleration; motion terms containing quadratic terms of linear motion; motion terms containing linear and linear acceleration; motion terms containing linear acceleration; and motion error terms with a unit of 1.

[0017] Preferably, the process of determining the minimum and maximum values ​​of the motion error model parameter vector P based on the physical properties of the gradient meter and using the gradient meter motion error analytical model in step S2 is as follows:

[0018] Based on the range of values ​​for the physical property parameters of the gradient meter, the parameter vector P of the analytical model of the gradient meter's motion error is calculated. Analytical maximum value and minimum value

[0019]

[0020] In the formula, g(k1,K2,R,θ) is the parameter vector P of the analytical model of the gradient instrument's motion error. Analytical The analytical expression for (which can be derived using existing technology and will not be elaborated further); k1 is the linear scaling coefficient of the gradient meter accelerometer group, k 1min and k 1maxK1 represents the minimum and maximum values ​​of k1; K2 represents the second-order nonlinear coefficients of the gradient meter accelerometer assembly. 2min and K 2max These are the minimum and maximum values ​​of K2; R is the radial installation distance of the gradient meter accelerometer assembly, i.e., the distance from the accelerometer installation point to the origin of the gradient meter measurement coordinate system. min and R max These are the minimum and maximum values ​​of R; θ is the installation angle parameter of the gradient meter accelerometer assembly, including the elevation angle, initial phase angle, attitude angle, and θ. min and θ max These are the minimum and maximum values ​​of θ; max() calculates the maximum value, and min() calculates the minimum value.

[0021] Based on the maximum value Minimum value And the motion error model parameter vector P and the motion error analytical model parameter vector P of the gradient instrument. Analytical Given the relationship, calculate the bounds of P:

[0022]

[0023] In the formula, f() represents the derived motion error model parameter vector P and the motion error analytical model parameter vector P. Analytical The relationship is derived as follows: M is the motion vector M at the sampling time of the gradient meter. G The motion vector sequence M is composed of (t) Analytical It is the motion vector of the gradient meter analytical model; max() represents calculating the maximum value, and min() represents calculating the minimum value; P max P min These are the maximum and minimum values ​​of the motion error model parameter vector P, respectively.

[0024] Preferably, in step S3, the boundary of the motion error model parameter vector P is introduced into the gradient meter motion error objective function, specifically expressed as:

[0025]

[0026] Constraints:

[0027] P min ≤P≤P max

[0028] M0·P>G0

[0029] M1·P>G1

[0030] M2·P=G2

[0031] In the formula, The square of the 2-norm is represented; λ1~λ4 are the coefficients of the penalty term, f1~f4 are the penalty functions; P=[p1,…,p i …,p N ] T It is the motion error model parameter vector, which is an N×1 vector, and the i-th element is p. i It is the motion error coefficient; It is an estimate of P;

[0032] In the formula, the first type of constraint is the limit of the motion error model parameter vector P determined based on the physical properties of the gradient meter: P min ≤P≤P max P max =[p 1max ,…p imax ,…,p Nmax ] T It is the maximum value of the motion error model parameter vector, P. min =[p 1min ,…p imin ,…,p Nmin ] T It is the minimum value of the motion error model parameter vector, p imin and p imax They are p i The lower and upper limits;

[0033] The second type of constraint is that the output sequence M*P of the motion error model and the output sequence G of the instrument are different. out There are three types of relationships: greater than, less than, and equal to. M0, M1, and M2 correspond to the motion vector sequences generated by the gravimeter's motion excitation under the three working conditions of greater than, less than, and equal to, respectively. G0, G1, and G2 correspond to the output sampling signal sequences of the gravimeter under the three working conditions of greater than, less than, and equal to, respectively. out This is the output sampled signal sequence of the gradient meter.

[0034] It should be understood that the second type of constraint is formed by utilizing the relationship between the output of the motion error model and the output of the gradient meter. The relationships of greater than, less than, and equal to encompass all possible constraints. These constraints are consistent with reality; for example, applying only linear motion excitations ax, ay, and az and observing the gradient meter's output can constitute a constraint. These three operating conditions are common and known conditions in the assembly and testing process of the gradient meter.

[0035] Preferably, in step S1, the output sampling signal G of the gradient meter out (t) and motion vector M G (t) is processed as follows:

[0036] S11: The original output analog signal of the gradient meter and the original analog signal of the gradient meter motion monitoring sensor are both subjected to anti-aliasing filtering 1 and high-frequency sampling;

[0037] S12: Then, perform anti-aliasing filtering, downsampling, and bandpass filtering on the output of S11 to obtain the result as the input of step S2;

[0038] The parameters of the filters and samplers corresponding to the two types of data are the same.

[0039] Anti-aliasing filter 1 is an operation performed before analog signal sampling; anti-aliasing filter 2 reduces the frequency of the discrete signal sampled at high frequencies; the parameters for anti-aliasing and filtering must be consistent for the output signal of the gradient meter and the output signal of the motion monitoring sensor, ensuring the use of the same anti-aliasing filtering and sampling circuits. It should be understood that anti-aliasing filtering, high-frequency sampling, low-frequency sampling, and bandpass filtering are all existing technologies, and no specific limitations are imposed on them.

[0040] Secondly, the present invention also provides a gradient meter error compensation method based on the above-mentioned error estimation method, comprising:

[0041] Step 1: Determine the motion error of the gradient meter according to the process of steps S1-S3;

[0042] Step 2: Using the motion error of the gradient meter, subtract the motion error from the output sampled signal of the gradient meter:

[0043]

[0044] In the formula, G out To output the sampled signal G out The data sequence consisting of (t) is M, where M is the motion vector M. G The motion vector sequence composed of (t), The gradient instrument's motion error parameter vector is determined by S3. It is the result of subtracting motion error from the data sequence output by the gradient meter;

[0045] Step 3: Output data after deducting motion errors Multiplying by a sine carrier and a cosine carrier respectively, and then performing a low-pass filter, quadrature amplitude demodulation is achieved to obtain the sinusoidal channel output Γ. sin Cosine channel output Γ cos .

[0046] Thirdly, the present invention also provides a gradient meter error compensation method based on the above-mentioned error estimation method, comprising:

[0047] Step 1: Determine the boundary of the motion error model parameter vector P of the gradient instrument according to the process of steps S1-S2;

[0048] Step 2: Introduce the boundary of the motion error model parameter vector P into the gradient meter motion error objective function to construct the objective functions of the sine channel and cosine channel;

[0049] Specifically, the output sampling signal sequence and motion vector sequence of the gradient meter are multiplied by a sine carrier wave, respectively, and used as the input of the objective function of the sine channel to calculate the motion error model parameter vector corresponding to the sine channel; the output sampling signal sequence and motion vector sequence of the gradient meter are multiplied by a cosine carrier wave, respectively, and used as the input of the objective function of the cosine channel to calculate the motion error model parameter vector corresponding to the cosine channel.

[0050] Step 3: Subtract the corresponding motion error from the sine and cosine channels of the gradient meter's output sampled signal sequence to obtain the sine channel output Γ. sin Cosine channel output Γ cos :

[0051]

[0052] In the formula, Γ sin For sinusoidal channel output, Γ cos For cosine channel output; G out To output the sampled signal G out The data sequence consisting of (t) is M, where M is the motion vector M. G The motion vector sequence composed of (t), f c Let t be the carrier frequency and t be the time. The gradient instrument's motion error parameter vector is determined by S3.

[0053] Fourthly, the present invention also provides a system for the above-mentioned error estimation method, comprising at least:

[0054] The signal processing module is used to acquire the output sampling signal G of the gradient meter. out (t) and the sampling signal of the motion monitoring sensor inside the gradient meter, and then the motion vector M at each sampling time is obtained based on the sampling signal of the motion monitoring sensor. G (t), where t is the sampling time;

[0055] The sampling signal of the motion monitoring sensor consists of the specific force vector, angular velocity vector, and angular acceleration vector at the sampling time.

[0056] The motion error boundary determination module is used to determine the boundary of the motion error model parameter vector P of the gradient meter based on the physical properties of the gradient meter. The motion error model of the gradient meter is represented as G. merr (t)=M G (t)P,G merr (t) represents the motion error of the gradient instrument at time t;

[0057] Among them, based on the physical properties of the gradient meter, the minimum and maximum values ​​of the motion error model parameter vector P are determined by using the motion error propagation mechanism or by using the gradient meter motion error analytical model;

[0058] The motion error calculation module is used to introduce the boundary of the motion error model parameter vector P into the motion error objective function of the gradient meter, and utilize the output sampling signal G of the gradient meter. out (t), the motion vector M G (t) Determine the motion error model parameter vector P, and then determine the motion error of the gradient meter; or introduce the boundary of the motion error model parameter vector P into the objective function of the gradient meter motion error to construct the objective functions of the sine channel and the cosine channel; then multiply the output sampling signal sequence and the motion vector sequence of the gradient meter by a sine carrier, respectively, as the input of the objective function of the sine channel, and calculate the motion error model parameter vector corresponding to the sine channel; multiply the output sampling signal sequence and the motion vector sequence of the gradient meter by a cosine carrier, respectively, as the input of the objective function of the cosine channel, and calculate the motion error model parameter vector corresponding to the cosine channel.

[0059] Preferably, the system further includes a compensation module, which is used to adjust the output data after deducting motion errors. Multiplying by a sine carrier and a cosine carrier respectively, and then performing a low-pass filter, quadrature amplitude demodulation is achieved to obtain the sinusoidal channel output Γ. sin Cosine channel output Γ cos ;

[0060] Alternatively, the compensation module is used to subtract the corresponding motion error from the sine and cosine channels of the gradient meter's output sampled signal sequence to obtain the sine channel output Γ. sin Cosine channel output Γ cos .

[0061] In addition, the present invention provides a computer terminal, comprising at least:

[0062] One or more processors;

[0063] A memory that stores one or more computer programs;

[0064] The processor calls the computer program to implement:

[0065] A method for estimating gradient meter error based on physical property constraints or a method for compensating gradient meter error based on physical property constraints.

[0066] In six aspects, the present invention also provides a computer-readable storage medium storing a computer program that is invoked by a processor to implement:

[0067] A method for estimating gradient meter error based on physical property constraints or a method for compensating gradient meter error based on physical property constraints.

[0068] Beneficial effects

[0069] Compared with existing methods, the advantages of the present invention are:

[0070] 1. The parameters of the motion error model are usually determined by the physical properties of the instrument, such as the installation parameters of the accelerometer and the input-output model parameters. These physical property parameters can be measured or their range determined during the instrument manufacturing and testing process. The technical solution of this invention generates constraints based on the physical properties of the instrument and incorporates them into the objective function, so that the estimated motion error model parameters are closer to the actual physical error parameters of the instrument, thereby effectively reducing or eliminating overfitting.

[0071] 2. Unlike traditional methods that separate error compensation and demodulation, the present invention constructs a motion error model after orthogonal demodulation by multiplying both the input and output of the motion error model by the carrier wave. This allows the motion error model parameters to be estimated and motion errors to be subtracted even after orthogonal demodulation. As a result, motion error compensation can be performed both before and after demodulation. This integrated approach enables the instrument system to flexibly adjust the error compensation strategy in different application scenarios, ensuring its wide applicability and adaptability. Attached Figure Description

[0072] Figure 1 This is a flowchart of Example 2;

[0073] Figure 2 This is a flowchart of Example 3;

[0074] Figure 3 This is a parameter range diagram of the analytical model of motion error of the gradient meter calculated based on the physical parameter properties of the gradient meter;

[0075] Figure 4 This is a parameter range diagram of the 541-parameter motion error model calculated using the analytical motion error model;

[0076] Figure 5 This is a schematic diagram comparing the estimated motion error model parameters with theoretical values ​​under constrained conditions.

[0077] Figure 6 This is a schematic diagram comparing the estimated motion error model parameters with the theoretical values ​​under unconstrained conditions.

[0078] Figure 7 This is a schematic diagram comparing motion error deduction between unconstrained and constrained estimations, where Figure a corresponds to unconstrained estimation and Figure b corresponds to constrained estimation. Detailed Implementation

[0079] This invention proposes a method to generate constraints based on the physical properties of the instrument and integrate them into the motion error objective function of a gradiometer (gravity gradiometer). This reduces the solution time for model parameters and allows the estimated motion error model parameters to approximate the actual error parameters of the instrument, thereby effectively mitigating or eliminating overfitting. Two feasible methods are provided to generate constraints based on the instrument's physical properties: utilizing the motion error propagation mechanism or using the gradiometer's motion error analytical model to determine the boundaries of the motion error model parameter vector. Furthermore, this invention fully considers the limitation of traditional methods that separate error compensation and demodulation to ensure time synchronization between motion monitoring data and instrument output, which restricts their application space. By multiplying both the input and output of the motion error model by a carrier wave, an orthogonally demodulated motion error model is constructed. This allows the motion error model parameters to still be estimated and motion errors to be subtracted after orthogonal demodulation, enabling motion error compensation to be performed both before and after demodulation. This allows the instrument system to flexibly adjust its error compensation strategy in different application scenarios.

[0080] The present invention will be further described below with reference to embodiments.

[0081] Example 1:

[0082] This embodiment provides a gradient meter error estimation method based on physical property constraints, including the following steps:

[0083] S1: Acquire the output sampling signal G of the gradient meter out (t) and the sampling signals from the motion monitoring sensors inside the gradient meter, and then the motion vector M at each sampling time is obtained based on the sampling signals from the motion monitoring sensors. G (t), where t is the sampling time; the sampling signal of the motion monitoring sensor consists of the specific force vector a(t), angular velocity vector ω(t), and angular acceleration vector at the sampling time. constitute.

[0084] In this embodiment, the original output analog signal of the gradient meter and the original analog signal of the motion monitoring sensor are preferably obtained and then subjected to anti-aliasing filtering 1 and high-frequency sampling; then anti-aliasing filtering 2, downsampling and bandpass filtering are performed.

[0085] For example, the high-frequency sampling frequency is set to 1000Hz, and the downsampling frequency is set to 10Hz. The specific sampling frequency is an empirical value set according to the actual application requirements and accuracy.

[0086] The resulting output sampled signal sequence G out Represented as:

[0087] Gout =[G out (t0),G out (t0+T s ),…G out (t end )] T

[0088] In the formula, t0 represents the start time, t end Indicates the end time, T s G represents the sampling period. out (t0),G out (t0+T s ),G out (t end ) represent time t0, time t0+T, and time t, respectively. end Gradient meter output data at time 1.

[0089] The motion vector M is calculated based on the sampling signal from the motion monitoring sensor. G (t)=[m1(t),m2(t),m3(t),…,m N [t] is a 1×N row vector, where each element m i (t) are all a(t), ω(t) and The function. It should be noted that m i (t) is the i-th element at time t. Its calculation and dimension N are determined by the specific construction of the motion error model, which is already public technology in this field and will not be described in detail. The motion vectors calculated at each time point are used to construct the motion vector sequence M as follows:

[0090] M = [M G (t0),M G (t0+T s ),…M G (t end )] T

[0091] With motion vector M G The element m of (t) i (t) will be used as an example to illustrate the six categories of sports included in the sports:

[0092] The first type of motion error term is a motion term containing quadratic terms of centripetal acceleration, quadratic terms of angular acceleration, and coupled terms of angular acceleration and centripetal acceleration. Typical examples of this type of motion term include... Etc., q1 equals m i(t) The number of such motion terms; the second type of motion error term, which is a motion term containing coupled terms of centripetal acceleration and linear acceleration, and coupled terms of angular acceleration and linear acceleration. Typical examples of this type of motion term include... Etc., q² equals m i (t) The number of such motion terms included; the third type of motion error term, which is a motion term containing a quadratic linear motion term. Typical examples of this type of motion term include... a x a y sin4ωt、a x a z sin3ωt, q3 equals m i (t) The number of terms of this type; the fourth type of motion, which contains a first-order term of centripetal acceleration and a first-order term of angular acceleration. Typical examples of this type of motion include... Etc., q4 equals m i (t) The number of such motion items included; the fifth type of motion item, which is a motion item containing linear acceleration. Typical examples of this type of motion item include a. x sin4ωt、a y sinωt, etc., q5 equals m i (t) is the number of such motion terms; the sixth type of motion error term, with a unit of 1, q6 equals m. i (t) is the number of such motion terms included.

[0093] It should be understood that this invention is limited to element m. i (t) includes six types of sports, without limiting the specific calculation formula for each type of sports. It can be selected or tested according to application needs.

[0094] S2: Based on the physical properties of the gradient meter, determine the boundary of the parameter vector P of the gradient meter's motion error model. The motion error model of the gradient meter is represented as G. merr (t)=M G (t)P,G merr (t) represents the motion error of the gradient instrument at time t. This embodiment of the invention provides two feasible methods for determining the boundary of the motion error model parameter vector P, which are illustrated using these examples. Other feasible embodiments may also select other feasible methods to determine the boundary of the motion error model parameter vector P.

[0095] 1. Based on the physical properties of the gradient meter, the minimum and maximum values ​​of the motion error model parameter vector P are determined using the motion error propagation mechanism. That is, the minimum value P of the motion error model parameter vector P is roughly determined. min and maximum value P maxThis method is relatively fast, but the range it determines is relatively large. The general expression for the motion error model of a gradient meter is:

[0096] G merr (t)=M G (t)P

[0097] From the above equation, it can be seen that the motion vector element m of the gradient meter... i (t), the corresponding motion error coefficient is the element p of the motion error model parameter vector P. i Based on the motion error propagation mechanism, it can be determined based on the motion vector M. G The element m of (t) i (t) contains motion terms; calculate the motion error coefficient p. i The boundary is defined, therefore, the execution process is as follows:

[0098] First, calculate element m i The error coefficient p corresponding to (t) i Boundaries:

[0099]

[0100] In the formula, p imin and p imax They are p i The lower and upper limits, k 1max K represents the maximum linear scaling coefficient of the accelerometer group that senses gravitational acceleration in the gradient instrument. 2max It is the maximum value of the second-order nonlinear coefficient of the accelerometer group that senses gravitational acceleration in the gradient instrument, k 0max It is the maximum value of the zero bias of the accelerometer group that senses gravitational acceleration in the gradient instrument, n. acc This refers to the number of accelerometers in the accelerometer group that senses gravitational acceleration within the gradient meter. For a 4-accelerometer gradient meter, n... acc =4, R is the distance from the accelerometer mounting point to the origin of the gradient meter measurement coordinate system; q1~q6 is m i (t) represents the number of terms in the six categories of motion error. It should be understood that the error coefficient p... i The value of is independent of time; it is determined by the physical properties of the instrument.

[0101] 2. Based on the physical properties of the gradient meter, the minimum and maximum values ​​of the motion error model parameter vector P are determined using the gradient meter motion error analytical model, as follows:

[0102] First, based on the following equations, establish the motion error model parameter vector P and the gradient meter's motion error analytical model parameter vector P. Analytical Relationship:

[0103]

[0104] In the formula, M is the gradient meter motion vector, P is the gradient meter error model parameter vector, and M Analytical It is the motion vector of the gradient meter analytical model (which can be determined by existing technology), P Analytical It is the parameter vector of the motion error analytical model of the gradient instrument; f() is derived from the equation using P Analytical P represents the symbol.

[0105] Then, based on the range of values ​​for the physical property parameters of the gradient meter and the analytical expression of the parameter vector of the gradient meter's motion error analytical model, the parameter vector P of the gradient meter's motion error analytical model is calculated. Analytical maximum value and minimum value

[0106]

[0107] In the formula, g(k1,K2,R,θ) is the analytical expression of the parameter vector of the gradient meter's motion error analytical model; k1 is the linear scaling coefficient of the gradient meter accelerometer group, k 1min and k 1max K represents the minimum and maximum values ​​of k1; k2 is the second-order nonlinear coefficient of the gradient meter accelerometer group. 2min and K 2max These are the minimum and maximum values ​​of K2; R is the radial installation distance of the gradient meter accelerometer assembly. min and R max These are the minimum and maximum values ​​of R; θ is the installation angle parameter of the gradient meter accelerometer assembly, including the elevation angle, initial phase angle, attitude angle, and θ. min and θ max These are the minimum and maximum values ​​of θ; max() calculates the maximum value, and min() calculates the minimum value.

[0108] Finally, based on the analytical model parameter vector P of the gradient meter's motion error... Analytical The range of values ​​for , and the motion error model parameter vector P and the gradient meter's motion error analytical model parameter vector P Analytical Given the relationship, calculate the bounds of P:

[0109]

[0110] In the above formula, and It is P determined in the previous step. Analytical The maximum value of f() is the parameter vector P of the motion error model derived in the first step and the parameter vector P of the analytical motion error model. AnalyticalThe relationship is as follows: max() calculates the maximum value, and min() calculates the minimum value.

[0111] S3: Introduce the boundary of the motion error model parameter vector P into the gradient meter's motion error objective function, and utilize the gradient meter's output sampling signal G. out (t), motion vector M G (t) Determine the motion error model parameter vector P, and then determine the motion error of the gradient meter. Specifically, it is expressed as:

[0112]

[0113] Constraints:

[0114] P min ≤P≤P max

[0115] M0·P>G0

[0116] M1·P<G1

[0117] M2·P=G2

[0118] In the formula, The square of the 2-norm is represented; λ1~λ4 are the coefficients of the penalty term, f1~f4 are the penalty functions; P=[p1,…,p i …,p N ] T It is the motion error model parameter vector, which is an NΔ1 vector, and the i-th element is p. i It is the motion error coefficient; It is an estimate of P;

[0119] In the formula, the first type of constraint is the limit of the motion error model parameter vector P determined based on the physical properties of the gradient meter: P min ≤P≤P max P max =[p 1max ,…p imax ,…,p Nmax ] T It is the maximum value of the motion error model parameter vector, P. min =[p 1min ,…p imin ,…,p Nmin ] T It is the minimum value of the motion error model parameter vector, p imin and p imax They are p iThe lower and upper limits; the second type of constraint condition, the output sequence of the motion error model and the output sequence of the instrument have three types of relationships: greater than, less than, and equal to. M0~M2 correspond to the motion vector sequences generated by the motion excitation of the gravimeter under the three working conditions of greater than, less than, and equal to, respectively. G0~G2 correspond to the output sampling signal sequences of the gravimeter under the three working conditions of greater than, less than, and equal to, respectively. out This is the output sampled signal sequence of the gradient meter.

[0120] In summary, this embodiment obtains the estimated value of the motion error model parameter vector P by solving the above objective function. It should be understood that This represents the error term in the output sampling signal of the gradient meter. This embodiment, through constraints based on physical properties, reduces the solution time for model parameters and enables the estimated motion error model parameters to approximate the actual error parameters of the instrument, thereby effectively mitigating or eliminating overfitting problems.

[0121] Example 2:

[0122] like Figure 1 As shown, the present invention also provides a gradient meter error compensation method based on the above-described error estimation method, comprising:

[0123] Step 1: Determine the motion error of the gradient meter according to the process of steps S1-S3 in Example 1;

[0124] Step 2: Utilize the motion error of the gradient meter to subtract motion error from the output sampled signal of the gradient meter:

[0125]

[0126] In the formula, G out To output the sampled signal G out The data sequence consisting of (t) is M, where M is the motion vector M. G The motion vector sequence composed of (t), The gradient instrument's motion error parameter vector is determined in step S3. It is the result of subtracting motion error from the data sequence output by the gradient meter;

[0127] Step 3: Output data after deducting motion errors Multiplying by a sine carrier and a cosine carrier respectively, and then performing a low-pass filter, quadrature amplitude demodulation is achieved to obtain the sinusoidal channel output Γ. sin Cosine channel output Γ cos .

[0128] It should be understood that in this embodiment, motion error compensation is performed first and then demodulation is performed. In the following embodiment 3, demodulation is performed first and then motion error compensation is performed.

[0129] Example 3:

[0130] like Figure 2 As shown, the present invention also provides a gradient meter error compensation method based on the above-described error estimation method, comprising:

[0131] Step 1: Determine the boundary of the motion error model parameter vector P of the gradient meter according to the process of steps S1-S2 in Example 1.

[0132] Step 2: Introduce the boundary of the motion error model parameter vector P into the gradient meter motion error objective function to construct the objective functions of the sine channel and cosine channel;

[0133] Step 3: Subtract the corresponding motion error from the sine and cosine channels of the gradient meter's output sampled signal sequence to obtain the sine channel output Γ. sin Cosine channel output Γ cos .

[0134] Specifically, the output sampled signal sequence of the gradient meter and the motion vector sequence are multiplied by a sine carrier wave, respectively, and used as inputs to the objective function of the sine channel to calculate the motion error model parameter vector corresponding to the sine channel; the output sampled signal sequence of the gradient meter and the motion vector sequence are multiplied by a cosine carrier wave, respectively, and used as inputs to the objective function of the cosine channel to calculate the motion error model parameter vector corresponding to the cosine channel. The details are as follows:

[0135] Sine wave channel: Motion vector data sequence M and gradient meter output data sequence G out Multiplying each component by a sinusoidal carrier wave, the motion error model parameters are estimated according to the objective function below, and the motion error is subtracted to obtain the demodulated sinusoidal channel output Γ after subtracting the motion error. sin :

[0136]

[0137] Constraints:

[0138] P min ≤P≤P max

[0139] M0·P>G0

[0140] M1·P<G1

[0141] M2·P=G2

[0142]

[0143] In the above formula, Γ sin This is the demodulated sine channel output after deducting motion errors, sin2πf ct represents a sinusoidal carrier wave, and the other physical quantities in the above formula are the same as in Example 1.

[0144] Cosine channel:

[0145] Motion vector data sequence M and gradient meter output data sequence G out Multiply by the cosine carrier wave respectively, estimate the motion error model parameters according to the objective function below, and subtract the motion error to obtain the motion error-subtracted and demodulated cosine channel output Γ. cos :

[0146]

[0147] Constraints:

[0148] P min ≤P≤P max

[0149] M0·P>G0

[0150] M1·P<G1

[0151] M2·P=G2

[0152]

[0153] In the above formula, Γ cos This is the demodulated cosine channel output after subtracting motion errors, cos2πf c t represents a cosine carrier wave, and the other physical quantities in the above formula are the same as those in Method 1.

[0154] To verify the scheme in the embodiments of this application, a rotational accelerometer gradiometer is used as an example for simulation analysis. The test mass is 480 kg, the initial position of the gradiometer measurement coordinate system is (1.5,0,0), and the rotational angular velocity around the gradiometer is ω(t) = 3600 + 260sin(0.0628t) deg / h, generating a gravitational gradient excitation.

[0155] The simulated gradient meter has a disk radius R = 0.1 m and a disk rotation angular frequency Ω = 1.57 rad / s. The gradient meter accelerometer installation parameters, linear scaling coefficients, and second-order nonlinear coefficients of the accelerometer are shown in Table 1.

[0156] Table 1

[0157]

[0158] A Gaussian-distributed swept-frequency linear vibration was applied to the gradiometer. The mean linear vibration acceleration in the vertical direction was 1g, with a standard deviation of 15mg; the mean linear vibration acceleration in the horizontal direction was 1mg, with a standard deviation of 0.03g. Simultaneously, Gaussian angular vibrations of equal intensity were applied to the gradiometer in all three directions, with a mean angular vibration rate of 50deg / h and a standard deviation of 50deg / h. The motion parameters of the gradiometer are shown in Table 2.

[0159] Table 2

[0160] Gradient meter motion parameters mean Standard deviation <![CDATA[a x / a y ]]> 3mg 15mg <![CDATA[a z ]]> 1g 30mg <![CDATA[ω x / h y / h z ]]> 50deg / h 50deg / h

[0161] In this simulation, the three installation misalignment angles of the motion monitoring sensor are [10deg, 10deg, 10deg]. Data processing is performed using the method described in Example 2, and the gradient meter motion error model used is the 541-parameter motion error model disclosed in Chinese Patent No. CN118501978A.

[0162] First, based on the physical property parameters of the gradient meter, and following the method in Example 3, the constraints of the motion error model parameters are obtained relatively accurately. The K2 accelerometer used in the simulation has a mean of 60 μg and a standard deviation of 105 μg, and a K4 mean of 89 μg and a standard deviation of 76 μg; these are not listed here individually. Based on the statistical characteristics of the physical and installation parameters of the accelerometer used in the gradient meter, substituting them into the gradient meter motion error analytical model, the parameter range of the gradient meter motion error analytical model can be obtained. Figure 3 This is the error parameter range of the 54-parameter motion error analytical model calculated in this simulation. The horizontal axis x corresponds to the 54 parameters (p1~p...). 54 The subscript of ) corresponds to the parameter value of the y-axis, i.e., p1 to p2. 54 By utilizing the relationship between the analytical model and the motion error model of the gradient meter, the range of parameters in the motion error model can be calculated. Figure 4 This is the parameter range of the calculated 541-parameter motion error model, with the x-axis corresponding to the 541 parameters (p1~p...). 541 The subscript of ) corresponds to the parameter value of the y-axis, i.e., p1 to p2. 541 After substituting the calculated range of the 541-parameter motion error model parameters into the objective function for constraint, the model parameters can be estimated by minimizing the objective function. Figure 5 Under constraints, the estimated motion error model parameters are compared with the theoretical values. It can be seen that the estimated motion error model parameters approximate the actual motion error parameters. The horizontal axis x corresponds to the 541 parameters (p1~p). 541 The subscript of ) corresponds to the parameter value on the y-axis. A comparative analysis is presented here. Figure 6This is a comparison between the estimated 541-parameter motion error model parameters and the theoretical values ​​under unconstrained conditions. The horizontal axis x corresponds to the 541 parameters (p1~p...). 541 The subscripts of the equations () correspond to the parameter values ​​on the y-axis. It can be seen that under unconstrained conditions, the estimated motion error model parameters differ significantly from the actual motion error model parameters. The following section will further examine the motion error subtraction effect under constrained estimation. Figure 7 This figure compares the motion error subtraction effects of constrained and unconstrained estimation. The theoretical gradient response in the figure is the multi-frequency gravitational gradient signal generated by a mass block rotating around a gradiometer. Figure a compares the gradient response extracted after subtracting motion errors from the unconstrained motion error model parameters with the theoretical gradient response. Figure a shows that the peak values ​​differ significantly at various frequencies, indicating overfitting in the unconstrained estimation, causing the gradient signal to be subtracted as motion error. This is because the 541-parameter model has excessive freedom and lacks constraints. Figure b shows the gradient response extracted after subtracting motion errors from the constrained motion error model parameters. As can be seen, the gradient response extracted under constrained conditions almost perfectly matches the theoretical gradient response at various frequencies, effectively eliminating the overfitting problem.

[0163] Example 4:

[0164] This invention also provides a system for the above-described error estimation method, comprising at least: a signal processing module, a motion error boundary determination module, and a motion error calculation module.

[0165] The signal processing module is used to acquire the output sampling signal G of the gradient meter. out (t) and the sampling signals from the motion monitoring sensors inside the gradient meter, and then the motion vector M at each sampling time is obtained based on the sampling signals from the motion monitoring sensors. G (t), where t is the sampling time; the sampling signal of this motion monitoring sensor consists of the specific force vector, angular velocity vector, and angular acceleration vector at the sampling time.

[0166] The motion error boundary determination module is used to determine the boundary of the motion error model parameter vector P of the gradient meter based on the physical properties of the gradient meter. The motion error model of the gradient meter is represented as G. merr (t)=M G (t)P,G merr (t) represents the motion error of the gradient instrument at time t;

[0167] Among them, based on the physical properties of the gradient meter, the minimum and maximum values ​​of the motion error model parameter vector P are determined by using the motion error propagation mechanism or by using the gradient meter motion error analytical model;

[0168] The motion error calculation module is used to introduce the boundary of the motion error model parameter vector P into the motion error objective function of the gradient meter, and utilize the output sampling signal G of the gradient meter. out (t), motion vector M G (t) Determine the motion error model parameter vector P, and then determine the motion error of the gradient meter; or introduce the boundary of the motion error model parameter vector P into the objective function of the gradient meter motion error to construct the objective functions of the sine channel and the cosine channel; then multiply the output sampling signal sequence and the motion vector sequence of the gradient meter by a sine carrier, respectively, as the input of the objective function of the sine channel, and calculate the motion error model parameter vector corresponding to the sine channel; multiply the output sampling signal sequence and the motion vector sequence of the gradient meter by a cosine carrier, respectively, as the input of the objective function of the cosine channel, and calculate the motion error model parameter vector corresponding to the cosine channel.

[0169] It should be understood that while the above system implements error estimation, in some embodiments, error compensation is also required. That is, the system further includes a compensation module, which is used to adjust the output data after deducting motion errors. Multiplying by a sine carrier and a cosine carrier respectively, and then performing a low-pass filter, quadrature amplitude demodulation is achieved to obtain the sinusoidal channel output Γ. sin Cosine channel output Γ cos ;

[0170] In some implementations, the compensation module is used to subtract the corresponding motion error from the sine and cosine channels of the gradient meter's output sampled signal sequence to obtain the sine channel output and cosine channel output, respectively.

[0171] It should be noted that this system can be understood as a system built with software modules, a system built with hardware and software modules, or a gradient meter with the above-mentioned functional modules.

[0172] It should also be understood that the specific implementation process of each module is described in the above method. This invention will not repeat it here. The above division of functional modules is only for illustrative purposes. In some embodiments, some functional modules can be combined and some functional modules can be separated. Each functional module can be implemented in software, hardware, or a combination of software and hardware. The software and hardware devices include, but are not limited to, general-purpose computer equipment, programmable gate arrays, digital signal processors, microprocessors and their corresponding programming or burning software.

[0173] Example 5:

[0174] This invention also provides a computer terminal, comprising at least: one or more processors; and a memory storing one or more computer programs;

[0175] The processor calls the computer program to achieve the following:

[0176] A method for estimating gradient meter errors based on physical property constraints or a method for compensating gradient meter errors based on physical property constraints. Refer to the implementation process of Examples 1-3 above for details.

[0177] Please refer to the explanation of the method above for the specific implementation process of each step.

[0178] It should be understood that, in the embodiments of the present invention, the processor may be a Central Processing Unit (CPU), or it may be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or any conventional processor. The memory may include read-only memory and random access memory, and provides instructions and data to the processor. A portion of the memory may also include non-volatile random access memory. For example, the memory may also store device type information.

[0179] Example 6:

[0180] This invention also provides a computer-readable storage medium storing a computer program that is invoked by a processor to implement:

[0181] A method for estimating gradient meter errors based on physical property constraints or a method for compensating gradient meter errors based on physical property constraints. Refer to the implementation process of Examples 1-3 above for details.

[0182] Please refer to the explanation of the method above for the specific implementation process of each step.

[0183] The readable storage medium is a computer-readable storage medium, which can be an internal storage unit of the hardware and software device described in any of the foregoing embodiments, such as the hard drive or memory of the controller. The readable storage medium can also be an external storage device of the controller, such as a plug-in hard drive, Smart MediaCard (SMC), Secure Digital (SD) card, or Flash Card equipped on the controller. Further, the readable storage medium can include both internal storage units and external storage devices of the controller. The readable storage medium is used to store the computer program and other programs and data required by the controller. The readable storage medium can also be used to temporarily store data that has been output or will be output.

[0184] Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned readable storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0185] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-readable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code. This application refers to flowchart illustrations and / or instructions executed by a processor of a method, apparatus (system), and computer program product according to embodiments of this application to create means for implementing the functions specified in one or more flowchart illustrations and / or one or more block diagrams. These computer program instructions may also be stored in a computer-readable storage medium capable of directing a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means that implement the functions specified in one or more flowchart illustrations and / or one or more block diagrams. These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer-implemented process, such that the instructions, which execute on the computer or other programmable apparatus, provide steps for implementing the functions specified in one or more flowcharts and / or one or more blocks of a block diagram.

[0186] It should be emphasized that the examples described in this invention are illustrative rather than limiting. Therefore, this invention is not limited to the examples described in the specific embodiments. Any other embodiments derived by those skilled in the art based on the technical solutions of this invention, without departing from the spirit and scope of this invention, whether modifications or substitutions, are also within the protection scope of this invention.

Claims

1. A gradient meter error estimation method based on physical property constraints, characterized in that: Includes the following steps: S1: Acquire the output sampling signal G of the gradient meter out (t) and the sampling signal from the gradient meter motion monitoring sensor, and then the motion vector M at each sampling time is obtained based on the sampling signal from the gradient meter motion monitoring sensor. G (t), where t is the sampling time; The sampling signal of the gradient meter motion monitoring sensor consists of the specific force vector, angular velocity vector, and angular acceleration vector at the sampling time. S2: Based on the physical properties of the gradient meter, determine the boundary of the motion error model parameter vector P of the gradient meter. The motion error model of the gradient meter is represented as G. merr (t)=M G (t)P,G merr (t) represents the motion error of the gradient instrument at time t; Among them, based on the physical properties of the gradient meter, the minimum and maximum values ​​of the motion error model parameter vector P are determined by using the motion error propagation mechanism or by using the gradient meter motion error analytical model; S3: Introduce the boundary of the motion error model parameter vector P into the gradient meter's motion error objective function, and utilize the output sampling signal G of the gradient meter. out (t), the motion vector M G (t) Determine the motion error model parameter vector P, and then determine the motion error of the gradient instrument.

2. The method according to claim 1, characterized in that: In step S2, the process of determining the minimum and maximum values ​​of the motion error model parameter vector P based on the physical properties of the gradient meter and using the motion error propagation mechanism is as follows: Define the motion vector M at time t. G (t)=[m1(t),...,m i (t),…,m N (t)],m1(t),m i (t),m N (t) is the motion vector M G The first, i-th, and N-th elements of (t), the motion error propagation mechanism is based on the motion vector M. G The element m of (t) i (t) contains motion terms that determine the motion error coefficient p. i The limit, motion error coefficient p i Let i be the value of the i-th element in the parameter vector P of the motion error model; Specifically: In the formula, p imin and p imax These are the motion error coefficients p i The lower and upper limits, k 1max K represents the maximum linear scaling coefficient of the accelerometer group that senses gravitational acceleration in the gradient instrument. 2max It is the maximum value of the second-order nonlinear coefficient of the accelerometer group that senses gravitational acceleration in the gradient instrument, k 0max It is the maximum value of the zero bias of the accelerometer group that senses gravitational acceleration in the gradient instrument, n. acc R is the number of accelerometers in the accelerometer group that senses gravitational acceleration in the gradient meter; R is the distance from the accelerometer mounting point to the origin of the gradient meter's measurement coordinate system; q1, q2, q3, q4, q5, q6 are m i (t) contains the number of terms in the six categories of motion error terms, corresponding to motion terms containing quadratic terms of centripetal acceleration, quadratic terms of angular acceleration, and coupled terms of angular and centripetal acceleration; motion terms containing coupled terms of centripetal and linear acceleration, and coupled terms of angular and linear acceleration; motion terms containing quadratic terms of linear motion; motion terms containing linear and linear acceleration; motion terms containing linear acceleration; and motion error terms with a unit of 1.

3. The method according to claim 1, characterized in that: In step S2, based on the physical properties of the gradient meter, the process of determining the minimum and maximum values ​​of the motion error model parameter vector P using the gradient meter motion error analytical model is as follows: Based on the range of values ​​for the physical property parameters of the gradient meter, the parameter vector P of the analytical model of the gradient meter's motion error is calculated. Analytical maximum value and minimum value In the formula, g(k1,K2,R,θ) is the parameter vector P of the analytical model of the gradient instrument's motion error. Analytical The analytical expression; k1 is the linear scaling coefficient of the gradient meter accelerometer group, k 1min and k 1max K1 represents the minimum and maximum values ​​of k1; K2 represents the second-order nonlinear coefficients of the gradient meter accelerometer assembly. 2min and K 2max These are the minimum and maximum values ​​of K2; R is the radial installation distance of the gradient meter accelerometer assembly, which is the distance from the accelerometer installation point to the origin of the gradient meter measurement coordinate system. min and R max These are the minimum and maximum values ​​of R; θ is the installation angle parameter of the gradient meter accelerometer assembly, including the elevation angle, initial phase angle, and attitude angle. min and θ max These are the minimum and maximum values ​​of θ; max() calculates the maximum value, and min() calculates the minimum value. Based on the maximum value Minimum value And the motion error model parameter vector P and the motion error analytical model parameter vector P of the gradient instrument. Analytical Given the relationship, calculate the bounds of P: In the formula, f() represents the derived motion error model parameter vector P and the motion error analytical model parameter vector P. Analytical The relationship is derived as follows: M is the motion vector M at the sampling time of the gradient meter. G The motion vector sequence M is composed of (t) Analytical These are the motion vectors of the gradient meter's analytical model; max() calculates the maximum value, and min() calculates the minimum value; P max P min These are the maximum and minimum values ​​of the motion error model parameter vector P, respectively.

4. The method according to claim 1, characterized in that: In step S3, the boundary of the motion error model parameter vector P is introduced into the gradient meter motion error objective function, specifically expressed as: Constraints: P min ≤P≤P max M0·P>G0 M1·PλG1 M2·P=G2 In the formula, The square of the 2-norm is represented; λ1~λ4 are the coefficients of the penalty term, f1~f4 are the penalty functions; P=[p1,…,p i …,p N ] T It is the motion error model parameter vector, which is an N×1 vector, and the i-th element is p. i It is the motion error coefficient; It is an estimate of P; In the formula, the first type of constraint is the limit of the motion error model parameter vector P determined based on the physical properties of the gradient meter: P min ≤P≤P max P max =[p 1max ,…p imax ,…,p Nmax ] T It is the maximum value of the motion error model parameter vector, P. min =[p 1min ,…p imin ,…,p Nmin ] T It is the minimum value of the motion error model parameter vector, p imin and p imax They are p i The lower and upper limits; The second type of constraint condition stipulates that the output sequence of the motion error model and the output sequence of the instrument have three relationships: greater than, less than, and equal to. M0, M1, and M2 correspond to the motion vector sequences generated by the motion excitation of the gravimeter under the three conditions of being greater than, less than, and equal to, respectively. G0, G1, and G2 correspond to the output sampling signal sequences of the gravimeter under the three conditions of being greater than, less than, and equal to, respectively. out This is the output sampled signal sequence of the gradient meter.

5. The method according to claim 1, characterized in that: In step S1, the output sampling signal G of the gradient meter out (t) and motion vector M G (t) is processed as follows: S11: The original output analog signal of the gradient meter and the original analog signal of the gradient meter motion monitoring sensor are both subjected to anti-aliasing filtering 1 and high-frequency sampling; S12: Then, perform anti-aliasing filtering, downsampling, and bandpass filtering on the output of S11 to obtain the result as the input of step S2; The parameters of the filters and samplers corresponding to the two types of data are the same.

6. A gradient meter error compensation method based on the method of any one of claims 1-5, characterized in that: include: Step 1: Determine the motion error of the gradient meter according to the process of steps S1-S3; Step 2: Using the motion error of the gradient meter, subtract the motion error from the output sampled signal of the gradient meter: In the formula, G out To output the sampled signal G out The data sequence consisting of (t) is M, where M is the motion vector M. G The motion vector sequence composed of (t), The gradient instrument's motion error parameter vector is determined in step S3. It is the result of subtracting motion error from the data sequence output by the gradient meter; Step 3: Output data after deducting motion errors Multiplying by a sine carrier and a cosine carrier respectively, and then performing a low-pass filter, quadrature amplitude demodulation is achieved to obtain the sinusoidal channel output Γ. sin Cosine channel output Γ cos .

7. A gradient meter error compensation method based on the method of any one of claims 1-5, characterized in that: include: Step 1: Determine the boundary of the motion error model parameter vector P of the gradient instrument according to the process of steps S1-S2; Step 2: Introduce the boundary of the motion error model parameter vector P into the gradient meter motion error objective function to construct the objective functions of the sine channel and cosine channel; Specifically, the output sampling signal sequence and motion vector sequence of the gradient meter are multiplied by a sine carrier wave, respectively, and used as the input of the objective function of the sine channel to calculate the motion error model parameter vector corresponding to the sine channel; the output sampling signal sequence and motion vector sequence of the gradient meter are multiplied by a cosine carrier wave, respectively, and used as the input of the objective function of the cosine channel to calculate the motion error model parameter vector corresponding to the cosine channel. Step 3: Subtract the corresponding motion error from the sine and cosine channels of the gradient meter's output sampled signal sequence to obtain the sine channel output Γ. sin Cosine channel output Γ cos : In the formula, Γ sin For sinusoidal channel output, Γ cos For cosine channel output; G out To output the sampled signal G out The data sequence consisting of (t) is M, where M is the motion vector M. G The motion vector sequence composed of (t), f c Let t be the carrier frequency and t be the time. The gradient instrument's motion error parameter vector is determined by S3.

8. A system based on the method of any one of claims 1-5, characterized in that: At least include: The signal processing module is used to acquire the output sampling signal G of the gradient meter. out (t) and the sampling signal of the motion monitoring sensor inside the gradient meter, and then the motion vector M at each sampling time is obtained based on the sampling signal of the motion monitoring sensor. G (t), where t is the sampling time; The sampling signal of the motion monitoring sensor consists of the specific force vector, angular velocity vector, and angular acceleration vector at the sampling time. The motion error boundary determination module is used to determine the boundary of the motion error model parameter vector P of the gradient meter based on the physical properties of the gradient meter. The motion error model of the gradient meter is represented as G. merr (t)=M G (t)P,G merr (t) represents the motion error of the gradient instrument at time t; Among them, based on the physical properties of the gradient meter, the minimum and maximum values ​​of the motion error model parameter vector P are determined by using the motion error propagation mechanism or by using the gradient meter motion error analytical model; The motion error calculation module is used to introduce the boundary of the motion error model parameter vector P into the motion error objective function of the gradient meter, and utilize the output sampling signal G of the gradient meter. out (t), the motion vector M G (t) Determine the motion error model parameter vector P, and then determine the motion error of the gradient meter; or introduce the boundary of the motion error model parameter vector P into the objective function of the gradient meter motion error to construct the objective functions of the sine channel and the cosine channel; then multiply the output sampling signal sequence and the motion vector sequence of the gradient meter by a sine carrier, respectively, as the input of the objective function of the sine channel, and calculate the motion error model parameter vector corresponding to the sine channel; multiply the output sampling signal sequence and the motion vector sequence of the gradient meter by a cosine carrier, respectively, as the input of the objective function of the cosine channel, and calculate the motion error model parameter vector corresponding to the cosine channel.

9. A computer terminal, characterized in that: At least including: One or more processors; A memory that stores one or more computer programs; The processor calls the computer program to implement: The gradient meter error estimation method according to any one of claims 1-5 or the gradient meter error compensation method according to claim 6 or 7.

10. A computer-readable storage medium, characterized in that: The computer program is stored and is invoked by the processor to implement: The gradient meter error estimation method according to any one of claims 1-5 or the gradient meter error compensation method according to claim 6 or 7.

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