CN-122018038-A - Gradiometer error estimation and compensation method and system based on physical attribute constraint

CN122018038ACN 122018038 ACN122018038 ACN 122018038ACN-122018038-A

Abstract

The invention discloses a gradiometer error estimation and compensation method and system based on physical attribute constraint, which are used for solving the problem that the existing motion error model parameters are usually determined by minimizing the standard deviation or variance of the difference between the model output and the instrument output, and are easy to cause over fitting. In addition, the technical scheme of the invention obtains the demodulated motion error model by multiplying the carrier wave at the same time of the input and the output of the motion error model. The motion error subtraction can be performed before quadrature demodulation or after demodulation, so that an instrument system can dynamically adjust error compensation strategies in different application scenes, and more flexible and accurate error compensation is realized.

Inventors

YU MINGBIAO
LIU HUAFENG
ZHAO WEI
ZHANG LIANG
HU CHENYUAN
FAN JI
YU LI

Assignees

贵州大学

Dates

Publication Date: 20260512
Application Date: 20250114

Claims (10)

1. A gradiometer error estimation method based on physical attribute constraint is characterized by comprising the following steps: S1, acquiring an output sampling signal G out (t) of a gradiometer and a sampling signal of a gradiometer motion monitoring sensor, and further acquiring a motion vector M G (t) at each sampling moment based on the sampling signal of the gradiometer motion monitoring sensor, wherein t is the sampling moment; the sampling signal of the gradiometer motion monitoring sensor consists of a specific force vector, an angular velocity vector and an angular acceleration vector at the sampling moment; s2, determining the boundary of a motion error model parameter vector P of the gradiometer according to the physical attribute of the gradiometer, wherein the motion error model of the gradiometer is represented as G merr (t)＝M G (t)P,G merr (t) which is the motion error of the gradiometer at the time t; The motion error analysis method comprises the steps of determining the minimum value and the maximum value of a motion error model parameter vector P by utilizing a motion error transfer mechanism or a motion error analysis model of a gradiometer based on the physical attribute of the gradiometer; And S3, introducing the boundary of the motion error model parameter vector P into a motion error objective function of the gradiometer, and determining the motion error model parameter vector P by utilizing an output sampling signal G out (t) of the gradiometer and the motion vector M G (t), thereby determining the motion error of the gradiometer.
2. The method according to claim 1, wherein the step S2 is based on the physical properties of the gradiometer, and the process of determining the minimum and maximum values of the motion error model parameter vector P by using the motion error transfer mechanism is as follows: Defining that a motion vector M G (t)＝[m 1 (t),...,m i (t),…,m N (t)],m 1 (t),m i (t),m N (t) at a sampling time t is the 1 st, i th and N th element of a motion vector M G (t), wherein the motion error transfer mechanism is used for determining a limit of a motion error coefficient P i based on a motion item contained in an element M i (t) of the motion vector M G (t), and the motion error coefficient P i is the i th element value in a motion error model parameter vector P; The method comprises the following steps: Where p imin and p imax are the lower and upper limits of the motion error coefficient p i , respectively, K 1max is the maximum value of the linear scale coefficient of the accelerometer group of the gravitational acceleration in the gradiometer, K 2max is the maximum value of the second order nonlinear coefficient of the accelerometer group of the gravitational acceleration in the gradiometer, K 0max is the maximum value of the zero bias of the accelerometer group of the gravitational acceleration in the gradiometer, n acc is the number of accelerometers contained in the accelerometer group of the gravitational acceleration in the gradiometer, R is the distance from the point of the accelerometer mounting position to the origin of the measurement coordinate system of the gradiometer, q 1 ,q 2 ,q 3 ,q 4 ,q 5 ,q 6 is the number of items of six motion error items contained in m i (t), and corresponds to the second item of the centripetal acceleration, the second item of the angular acceleration, the motion item of the coupling item of the angular acceleration and the centripetal acceleration, the motion item of the coupling item of the angular acceleration and the linear acceleration, the motion second item of the motion item of the centripetal acceleration, the motion item of the first item of the angular acceleration and the linear acceleration, the motion item of the first item of the centripetal acceleration, the motion item of the linear acceleration, and the motion item of the motion unit of 1.
3. The method according to claim 1, wherein the step S2 is characterized in that the process of determining the minimum value and the maximum value of the motion error model parameter vector P by using the motion error analysis model of the gradiometer based on the physical attribute of the gradiometer is as follows: Calculating the maximum value of a motion error analysis model parameter vector P Analytical of the gradiometer based on the value range of the physical attribute parameter of the gradiometer And minimum value Where g (K 1 ,K 2 , R, θ) is the analytical expression of the motion error analytical model parameter vector P Analytical of the gradiometer, K 1 is the linear scale coefficient of the gradiometer set, K 1min and K 1max are the minimum and maximum values of K 1 , K 2 is the second order nonlinear coefficient of the gradiometer set, K 2min and K 2max are the minimum and maximum values of K 2 , R is the radial mounting distance of the gradiometer set, expressed as the distance from the accelerometer mounting position point to the origin of the gradiometer measurement coordinate system, R min and R max are the minimum and maximum values of R, θ is the mounting angle parameter of the gradiometer set, including the altitude angle, initial phase angle, attitude angle, θ min and θ max are the minimum and maximum values of θ, max () represents the calculated maximum value, and min () represents the calculated minimum value; Based on the maximum value Minimum value And calculating the boundary of P according to the relation between the motion error model parameter vector P and the motion error analysis model parameter vector P Analytical of the gradiometer: In the formula, f () is the relationship between the derived motion error model parameter vector P and the motion error analysis model parameter vector P Analytical , and the derivation process is as follows: M is a motion vector sequence formed by motion vectors M G (t) at the sampling moment of the gradiometer, M Analytical is a motion vector of a gradiometer analysis model, max () represents a calculated maximum value, min () represents a calculated minimum value, and P max 、P min is a maximum value and a minimum value of a motion error model parameter vector P respectively.
4. The method according to claim 1, wherein the boundary of the motion error model parameter vector P is introduced into the gradiometer motion error objective function in step S3, specifically expressed as: constraint conditions: P min ≤P≤P max M 0 ·P＞G 0 M 1 ·PλG 1 M 2 ·P＝G 2 In the formula, Lambda 1 ～λ 4 is a penalty term coefficient, f 1 ～f 4 is a penalty function, P= [ P 1 ,…,p i …,p N ] T is a motion error model parameter vector, which is an Nx 1 vector, and the ith element P i is a motion error coefficient; is an estimate of P; Wherein, the first constraint condition is the limit of the motion error model parameter vector P determined based on the physical attribute of the gradiometer, P min ≤P≤P max ,P max ＝[p 1max ,…p imax ,…,p Nmax ] T is the maximum value of the motion error model parameter vector, P min ＝[p 1min ,…p imin ,…,p Nmin ] T is the minimum value of the motion error model parameter vector, and P imin and P imax are the lower limit and the upper limit of P i respectively; And under the second constraint condition, the output sequence of the motion error model and the output sequence of the instrument have three relations of more than, less than and equal to each other, M 0 ,M 1 ,M 2 corresponds to a motion vector sequence generated by gravity meter motion excitation under three working conditions of more than, less than and equal to each other, G 0 ,G 1 ,G 2 corresponds to an output sampling signal sequence of the gravity meter under three working conditions of more than, less than and equal to each other, and G out is an output sampling signal sequence of the gradiometer.
5. The method according to claim 1, wherein the output sample signal G out (t) of the gradiometer and the motion vector M G (t) are processed as follows: s11, performing anti-aliasing filtering 1 and high-frequency sampling on an original output analog signal of a gradiometer and an original analog signal of a gradiometer motion monitoring sensor; S12, performing anti-aliasing filtering 2, downsampling and band-pass filtering treatment on the output result of the step S11 to obtain a result as the input of the step S2; The parameters of the filters and the samplers corresponding to the two types of data are respectively the same.
6. A gradiometer error compensation method based on the method of any one of claims 1 to 5, comprising: step 1, determining the motion error of the gradiometer according to the process of the steps S1-S3; Step 2, subtracting the motion error of the output sampling signal of the gradiometer by utilizing the motion error of the gradiometer: Wherein G out is a data sequence composed of output sampling signals G out (t), M is a motion vector sequence composed of motion vectors M G (t), The motion error parameter vector of the gradiometer determined for step S3, The result is obtained by subtracting the motion error from the data sequence output by the gradiometer; Step 3, deducting the output data of the motion error And multiplying the sine carrier and the cosine carrier respectively, and then performing low-pass filtering to realize quadrature amplitude demodulation to obtain sine channel output gamma sin and cosine channel output gamma cos .
7. A gradiometer error compensation method based on the method of any one of claims 1 to 5, comprising: step 1, determining the boundary of a motion error model parameter vector P of the gradiometer according to the process of the steps 1-S2; Step 2, introducing the boundary of the motion error model parameter vector P into a motion error objective function of a gradiometer to construct objective functions of a sine channel and a cosine channel; the motion error model parameter vector corresponding to the sine channel is calculated by multiplying the output sampling signal sequence and the motion vector sequence of the gradiometer by a sine carrier respectively as the input of the sine channel objective function; step 3, subtracting corresponding motion errors in a sine channel and a cosine channel respectively from an output sampling signal sequence of the gradiometer to obtain sine channel output gamma sin and cosine channel output gamma cos : Wherein Γ sin is sine channel output, Γ cos is cosine channel output, G out is data sequence composed of output sampling signal G out (t), M is motion vector sequence composed of motion vector M G (t), f c is carrier frequency, t is time, Motion error parameter vector of gradiometer determined for S3.
8. A system based on the method according to any one of claims 1 to 5, characterized in that it comprises at least: The signal processing module is used for obtaining an output sampling signal G out (t) of the gradiometer and a sampling signal of a motion monitoring sensor in the gradiometer, and further obtaining a motion vector M G (t) at each sampling moment based on the sampling signal of the motion monitoring sensor, wherein t is the sampling moment; the sampling signal of the motion monitoring sensor consists of a specific force vector, an angular velocity vector and an angular acceleration vector at the sampling moment; The motion error boundary determining module is used for determining the boundary of a motion error model parameter vector P of the gradiometer according to the physical attribute of the gradiometer, and the motion error model of the gradiometer is represented as the motion error of the gradiometer with G merr (t)＝M G (t)P,G merr (t) being the moment t; The motion error analysis method comprises the steps of determining the minimum value and the maximum value of a motion error model parameter vector P by utilizing a motion error transfer mechanism or a motion error analysis model of a gradiometer based on the physical attribute of the gradiometer; the motion error calculation module is used for introducing the boundary of the motion error model parameter vector P into a motion error objective function of a gradiometer, determining the motion error model parameter vector P by utilizing an output sampling signal G out (t) of the gradiometer and the motion vector M G (t), further determining the motion error of the gradiometer, or introducing the boundary of the motion error model parameter vector P into the motion error objective function of the gradiometer, constructing objective functions of a sine channel and a cosine channel, further multiplying the output sampling signal sequence and the motion vector sequence of the gradiometer by sine carriers respectively to serve as inputs of the sine channel objective function, calculating the motion error model parameter vector corresponding to the sine channel, and multiplying the output sampling signal sequence and the motion vector sequence of the gradiometer by cosine carriers respectively to serve as inputs of the cosine channel objective function, and calculating the motion error model parameter vector corresponding to the cosine channel.
9. A computer terminal is characterized by comprising at least: one or more processors; A memory storing one or more computer programs; Wherein the processor invokes the computer program to implement: a gradiometer error estimation method as claimed in any one of claims 1 to 5 or a gradiometer error compensation method as claimed in claim 6 or 7.
10. A computer-readable storage medium storing a computer program, the computer program being invoked by a processor to implement: a gradiometer error estimation method as claimed in any one of claims 1 to 5 or a gradiometer error compensation method as claimed in claim 6 or 7.

Description

Gradiometer error estimation and compensation method and system based on physical attribute constraint Technical Field The invention belongs to the technical field of gradiometers, and particularly relates to a gradiometer error estimation and compensation method and system based on physical attribute constraint. Background The parameters of the motion error model are typically determined by physical properties of the instrument, such as the accelerometer mounting parameters and input-output model parameters. These physical property parameters may be measured or their ranges determined during instrument manufacturing and testing. Currently, parameters of a motion error model are typically estimated by minimizing the standard deviation or variance of the difference between the model output and the instrument output. This approach, due to the lack of external constraints, makes it difficult for the estimated model parameters to converge to the actual error parameter values of the instrument, resulting in an overfitting, the severity of which is closely related to the constraints of the motion error model itself. Specifically, the higher the degree of freedom of the model, the lower the constraint, the more likely the overfitting will occur. For example, the 541-parameter motion error model with high degrees of freedom (CN 118501978A) is more prone to overfitting than the 54-parameter analytical model (patents CN117805936a, CN112363247a, CN109766812a and papers Posterror Compensation of Moving-Base Rotating Accelerometer Gravity Gradiometer) because the motion term of the 54-parameter model is constrained by the physical properties of the gradiometer, the degrees of freedom are low. Disclosure of Invention The invention aims to solve the problem of overfitting of motion error model parameter estimation in the prior art, namely a traditional parameter estimation method determines model parameters by minimizing the standard deviation or variance of a difference value between model output and instrument output, but the method is easy to cause overfitting, especially in a model with high degree of freedom and low constraint. The technical scheme of the invention provides a gradiometer error estimation and compensation method and system based on physical attribute constraint, and the method provides a gradiometer motion error objective function based on the generation constraint condition of the physical attribute of the instrument and fused the constraint condition, so that the estimated motion error model parameter approximates to the actual error parameter of the instrument, thereby effectively reducing or eliminating the over-fitting phenomenon, greatly reducing the search space of the objective function and reducing the solving time of the model parameter. On the other hand, the invention also provides two feasible modes for the compensation method, namely, the motion error model after demodulation is obtained by multiplying the carrier waves at the same time of the input and the output of the motion error model, so that the motion error subtraction can be performed before quadrature demodulation or after demodulation, and an instrument system can dynamically adjust an error compensation strategy in different application scenes, thereby realizing more flexible and accurate error compensation. For this purpose, the invention provides the following technical scheme: on one hand, the gradiometer error estimation method based on physical attribute constraint provided by the invention comprises the following steps: S1, acquiring an output sampling signal G out (t) of a gradiometer and a sampling signal of a gradiometer motion monitoring sensor, and further acquiring a motion vector M G (t) at each sampling moment based on the sampling signal of the gradiometer motion monitoring sensor, wherein t is the sampling moment; the sampling signal of the gradiometer motion monitoring sensor consists of a specific force vector, an angular velocity vector and an angular acceleration vector at the sampling moment; s2, determining the boundary of a motion error model parameter vector P of the gradiometer according to the physical attribute of the gradiometer, wherein the motion error model of the gradiometer is represented as G merr(t)＝MG(t)P,Gmerr (t) which is the motion error of the gradiometer at the time t; The motion error analysis method comprises the steps of determining the minimum value and the maximum value of a motion error model parameter vector P by utilizing a motion error transfer mechanism or a motion error analysis model of a gradiometer based on the physical attribute of the gradiometer; And S3, introducing the boundary of the motion error model parameter vector P into a motion error objective function of the gradiometer, and determining the motion error model parameter vector P by utilizing an output sampling signal G out (t) of the gradiometer and the motion vector M G (t), thereby determining the motion err