CN112052600A - Underwater gravity measurement error compensation method based on correlation analysis - Google Patents
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Abstract
The invention belongs to the field of gravity measurement, and discloses an underwater gravity measurement error compensation method based on correlation analysis. The method mainly comprises the following steps: firstly, performing empirical mode analysis on a gravity measurement result on a measurement line to obtain a group of intrinsic mode functions and residual signals; secondly, removing intrinsic mode functions which have no correlation with influence factors such as a gravity measurement result and the like, and performing signal reconstruction on the rest intrinsic mode functions and the rest signals; thirdly, subtracting the reconstructed gravity measurement result from a fitting curve of the gravity measurement result, and establishing an error model between the difference value and the sky direction specific force, the sky direction specific force derivative, the sky direction speed, the sky direction acceleration and the pitch angle according to a least square fitting method; and finally, carrying out error compensation on the reconstructed gravity measurement result according to the error model. The method is used for compensating errors related to the dynamics of the gravimeter, and has high theoretical value and practical significance.
Description
The technical field is as follows:
the invention belongs to the field of gravity measurement, relates to an underwater gravity measurement error compensation method, and particularly relates to an error compensation method related to carrier dynamics.
Background art:
the underwater dynamic gravity measurement can be used for large-area coverage measurement and can be close to a submarine gravity field signal source, and the advantages of the two measurement modes are integrated. The short wavelength gravity information obtained by underwater dynamic gravity measurement can be used for small-scale ore deposit detection and seawater intrusion monitoring, and the development and utilization of ocean resources are of great significance for guaranteeing national resource safety at present when land resources are increasingly exhausted. The underwater dynamic gravity measurement can also be used for underwater gravity assisted navigation, which is an autonomous navigation mode without sound, light and electricity interaction with the outside, and can greatly improve the concealment and the viability of the submarine.
The carrier dynamics is a main factor influencing the measurement accuracy of the strapdown gravimeter. Generally, the poorer the dynamic property of the carrier, the lower the accuracy of the gravity measurement. The carrier dynamics is mainly reflected in the depth change, and the more drastic the depth change and the larger the fluctuation, the worse the carrier dynamics. In the towed underwater gravity measurement scheme, the attitude and depth changes of the carrier cannot be well controlled, so that the carrier has poor dynamic property, and errors are brought to underwater gravity measurement. Errors caused by the dynamic property cannot be eliminated through low-pass filtering, so that adverse effects of the dynamic property of the carrier on measurement are overcome, and the research on related error compensation methods is of great significance in improving the gravity measurement precision and the gravity data quality.
The invention content is as follows:
the invention provides an underwater gravity measurement error compensation method based on correlation analysis, aiming at the problems of poor carrier dynamic property and low measurement precision in underwater gravity measurement, and the main technical scheme is as follows:
the underwater gravity measurement error compensation method based on correlation analysis comprises the following steps:
step one, a depth curve of each measuring line in a measuring area is obtained, and a standard deviation is obtained for the depth value of each measuring line; the larger the standard deviation is, the more severe the depth change of the measuring line is, and the worse the dynamic property of the carrier on the measuring line is; selecting the measuring line with the maximum standard deviation of the depth curve as a target measuring line;
calculating the specific force, depth, pitch angle and gravity measurement result of the gravity meter on the target measuring line; differentiating the specific force in the sky to obtain a derivative of the specific force in the sky; differentiating the depth to obtain a space velocity; differentiating the speed in the sky to obtain acceleration in the sky; taking the gravity measurement result, the specific force in the sky direction, the derivative of the specific force in the sky direction, the speed in the sky direction, the acceleration in the sky direction and the pitch angle as influence factors;
performing empirical mode decomposition on the gravity measurement result of the target measuring line to obtain a group of intrinsic mode functions from high frequency to low frequency and a residual signal;
performing correlation analysis on each intrinsic mode function and gravity measurement results, the space direction specific force derivative, the space direction speed, the space direction acceleration and the pitch angle influence factor to obtain a correlation coefficient r; when the absolute value r is more than or equal to 0.7, the correlation between the intrinsic mode function and the influence factor is strong; when the absolute r is more than or equal to 0.2 and less than 0.7, the correlation between the intrinsic mode function and the influence factor is weak; when the absolute value of r is less than 0.2, the intrinsic mode function has no correlation with the influence factor; according to the value range of r, determining an intrinsic mode function with strong correlation and an intrinsic mode function with weak correlation;
removing intrinsic mode functions which are not related to the gravity measurement result, the space direction specific force derivative, the space direction speed, the space direction acceleration and the pitch angle, and accumulating the rest intrinsic mode functions and the rest signals to obtain a reconstructed gravity measurement result;
step six, performing curve fitting on the reconstructed gravity measurement result to obtain a fitted gravity measurement result curve; taking the fitted curve as a standard value, and solving a difference value between the reconstructed gravity measurement result and the fitted curve, namely the gravity measurement error of the target measurement line;
step seven, establishing a model among the gravity measurement error, the space direction specific force derivative, the space direction speed, the space direction acceleration and the pitch angle, and according to the formula (1):
in the formula, gfittingThe fitted gravity measurement result is obtained; g1The reconstructed gravity measurement result is obtained; f is the specific force in the natural direction;
is the acceleration in the sky direction; df is the derivative of the specific force in the day direction; dp is a pitch angle; dh is the speed in the direction of the sky; k is a radical ofnIs an error model parameter, and n is 1,2, …, 20;
estimating each model parameter in the formula (1) by using a least square fitting method to obtain a specific form of an error equation;
and step nine, performing error compensation on the reconstructed gravity measurement result according to the error model to obtain a compensated gravity measurement result, wherein an error compensation equation is shown as a formula (2):
in the formula, gcompensateIs the gravity measurement result after compensation.
Step ten, selecting other measuring lines in the measuring area, wherein the type of the fitting curve of the gravity measurement result of the target measuring line is the same as that of the fitting curve of the gravity measurement result of the target measuring line, and if the fitting curve of the gravity measurement result of the target measuring line is a secondary curve, the fitting curve of the gravity measurement result of the selected other measuring lines is also a secondary curve; and obtaining the gravity measurement results of other measuring lines according to the third step to the fifth step after reconstruction, and carrying out error compensation according to the ninth step to obtain the compensated gravity measurement results.
In the invention, the underwater gravity measurement error compensation based on the correlation analysis can be realized through the ten steps.
Compared with the prior art, the invention has the following advantages:
(1) errors caused by carrier dynamics can be compensated, and gravity measurement accuracy is improved;
(2) the method is suitable for an underwater gravity measurement environment and can be applied to aviation and shipborne gravity measurement;
(3) the invention has simple operation, easy execution and strong universality.
Description of the drawings:
FIG. 1 is a flow chart of a method for compensating errors in underwater gravity measurement based on correlation analysis;
FIG. 2 is a plot of a plot profile;
FIG. 3 is a depth profile on the inline ML 2;
FIG. 4 is a diagram of the eigenmodes of the gravity measurements taken at line ML 2-1;
FIG. 5 is a reconstructed gravity measurement result and a fitted gravity measurement result of the line ML 2-1;
FIG. 6 is a gravity measurement compensated for line ML 2-1;
FIG. 7 is a gravity measurement compensated for line ML 2-2;
FIG. 8 is a gravity measurement compensated for line ML 2-3;
FIG. 9 is a gravity measurement compensated for line ML 2-4.
The specific implementation mode is as follows:
FIG. 1 is a flow chart of an underwater gravity measurement error compensation method based on correlation analysis according to the present invention. The method of the present invention will be further described in detail with reference to the accompanying drawings and a certain actual underwater gravity measurement test, the measurement conditions of which are shown in table 1.
TABLE 1
Step one, in this test, the profile of the test area is shown in fig. 2, and the statistical results of the test area are shown in table 2. Taking four repeated measuring lines ML2 in the measuring area as an example, the depth curves of the four repeated lines ML2 are shown in FIG. 3, and the standard deviation of the depth curve of each repeated line of the measuring line ML2 is calculated; the larger the standard deviation is, the more severe the depth change of the measuring line is, and the worse the dynamic property of the carrier on the measuring line is; the standard deviation of the depth profile of the four repeated lines is shown in table 3. As can be seen from Table 3, the standard deviation of the depth curve of line ML2-1 is the greatest, so line ML2-1 is selected as the target line.
TABLE 2
TABLE 3
Step two, calculating the specific force, the depth, the pitch angle and the gravity measurement result of the gravity meter on a measurement line ML 2-1; differentiating the specific gravity of the measuring line ML2-1 to obtain a specific gravity derivative, deeply differentiating to obtain a specific gravity speed, and differentiating the specific gravity speed to obtain a specific gravity acceleration; taking the gravity measurement result, the specific force in the sky direction, the derivative of the specific force in the sky direction, the speed in the sky direction, the acceleration in the sky direction and the pitch angle as influence factors;
and thirdly, performing empirical mode decomposition on the gravity measurement result of the line ML2-1 to obtain a group of eigenmode functions imf-imf6 from high frequency to low frequency and a residual signal, as shown in FIG. 4.
Performing correlation analysis on each intrinsic mode function and gravity measurement results, the space direction specific force derivative, the space direction speed, the space direction acceleration and the pitch angle influence factor to obtain a correlation coefficient r shown in a table 4; when the absolute value r is more than or equal to 0.7, the correlation between the intrinsic mode function and the influence factor is strong; when the absolute r is more than or equal to 0.2 and less than 0.7, the correlation between the intrinsic mode function and the influence factor is weak; when the absolute value of r is less than 0.2, the intrinsic mode function has no correlation with the influence factor; according to the value range of r, the combination of the value range of r and the table 4 shows that imf2 has weak correlation with the derivative of the specific force in the sky direction; imf3 have a weak correlation with the specific force derivative in the sky; imf4 have weak correlation with both the specific force in the sky and the acceleration in the sky; imf5 have a weak correlation with gravity anomalies; imf6 have a strong correlation with gravity anomalies. Therefore, imf6 is an eigenmode function with strong correlation, and imf2-imf5 are eigenmode functions with weak correlation.
TABLE 4
Step five, as seen from table 4, the eigenmode function imf1 has no correlation with the gravity measurement result, the specific force in the sky, the specific force derivative in the sky, the speed in the sky, the acceleration in the sky, and the pitch angle, and mainly includes noise, which needs to be removed during reconstruction. The reconstructed signal is accumulated from the remaining eigenmode functions imf2-imf6 and the remaining signals, so that the reconstructed signal contains the effective gravity signal and the dynamically related error terms.
Step six, fitting the gravity measurement result reconstructed by the measuring line ML2-1 into a quadratic curve to obtain a fitted gravity measurement result curve shown in FIG. 5; and taking the fitted curve as a standard value, and solving the difference between the reconstructed gravity measurement result and the fitted curve, namely the gravity measurement error of the measurement line ML 2-1.
And step seven, establishing a model among the gravity measurement error, the space-direction specific force derivative, the space-direction speed, the space-direction acceleration and the pitch angle, wherein the model is shown as the formula (1).
Step eight, estimating each model parameter in the formula (1) by using a least square fitting method to obtain a specific form of an error equation, wherein the specific form is shown in the formula (3)
And step nine, performing error compensation on the reconstructed gravity measurement result according to the error model and the formula (4), and obtaining a compensated gravity measurement result as shown in fig. 6. As can be seen from the figure, the curve of the gravity measurement result before the compensation of the line ML2-1 has local large fluctuation, which is caused by large depth change; the gravity measurement result curve after compensation becomes smoother, the fluctuation becomes smaller, and the further verification that the gravity measurement result can effectively inhibit the error influence caused by the dynamic property by carrying out error compensation according to the method disclosed by the invention is further verified.
Step ten, because the measuring line ML2-2, the measuring line ML2-3, the measuring line ML2-4 and the measuring line ML2-1 are repeated measuring lines, the gravity measurement results of the measuring line ML2-2, the measuring line ML2-3 and the measuring line ML2-4 and the measuring line ML2-1 are the same in fitting curve type and are all quadratic curves. And (4) obtaining the reconstructed gravity measurement results of the measuring line ML2-2, the measuring line ML2-3 and the measuring line ML2-4 according to the steps three to five, and performing error compensation according to the step nine to obtain the gravity measurement results shown in the figures 7-9. As can be seen from fig. 6, the remaining repeated lines, error compensated, gave a slightly improved but not very obvious curve of the gravimetric measurement results, since the remaining repeated lines had better dynamics than the line ML 2-1. It follows that the poorer the dynamics, the better the error compensation.
The above description is only a preferred embodiment of the present invention, and the protection scope of the present invention is not limited to the above embodiments, and all technical solutions belonging to the idea of the present invention belong to the protection scope of the present invention. It should be noted that modifications and embellishments within the scope of the invention may occur to those skilled in the art without departing from the principle of the invention, and are considered to be within the scope of the invention.
Claims (1)
1. The underwater gravity measurement error compensation method based on correlation analysis is characterized by comprising the following steps of:
step one, a depth curve of each measuring line in a measuring area is obtained, and a standard deviation is obtained for the depth value of each measuring line; the larger the standard deviation is, the more severe the depth change of the measuring line is, and the worse the dynamic property of the carrier on the measuring line is; selecting the measuring line with the maximum standard deviation of the depth curve as a target measuring line;
calculating the specific force, depth, pitch angle and gravity measurement result of the gravity meter on the target measuring line; differentiating the specific force in the sky to obtain a derivative of the specific force in the sky; differentiating the depth to obtain a space velocity; differentiating the speed in the sky to obtain acceleration in the sky; taking the gravity measurement result, the specific force in the sky direction, the derivative of the specific force in the sky direction, the speed in the sky direction, the acceleration in the sky direction and the pitch angle as influence factors;
performing empirical mode decomposition on the gravity measurement result of the target measuring line to obtain a group of intrinsic mode functions from high frequency to low frequency and a residual signal;
performing correlation analysis on each intrinsic mode function and gravity measurement results, the space direction specific force derivative, the space direction speed, the space direction acceleration and the pitch angle influence factor to obtain a correlation coefficient r; when the absolute value r is more than or equal to 0.7, the correlation between the intrinsic mode function and the influence factor is strong; when the absolute r is more than or equal to 0.2 and less than 0.7, the correlation between the intrinsic mode function and the influence factor is weak; when the absolute value of r is less than 0.2, the intrinsic mode function has no correlation with the influence factor; according to the value range of r, determining an intrinsic mode function with strong correlation and an intrinsic mode function with weak correlation;
removing intrinsic mode functions which are not related to the gravity measurement result, the space direction specific force derivative, the space direction speed, the space direction acceleration and the pitch angle, and accumulating the rest intrinsic mode functions and the rest signals to obtain a reconstructed gravity measurement result;
step six, performing curve fitting on the reconstructed gravity measurement result to obtain a fitted gravity measurement result curve; taking the fitted curve as a standard value, and solving a difference value between the reconstructed gravity measurement result and the fitted curve, namely the gravity measurement error of the target measurement line;
step seven, establishing a model among the gravity measurement error, the space direction specific force derivative, the space direction speed, the space direction acceleration and the pitch angle, and according to the formula (1):
in the formula, gfittingThe fitted gravity measurement result is obtained; g1The reconstructed gravity measurement result is obtained; f is the specific force in the natural direction;
is the acceleration in the sky direction; df is the derivative of the specific force in the day direction; dp is a pitch angle; dh is the speed in the direction of the sky; k is a radical ofnIs an error model parameter, and n is 1,2, …, 20;
estimating each model parameter in the formula (1) by using a least square fitting method to obtain a specific form of an error equation;
and step nine, performing error compensation on the reconstructed gravity measurement result according to the error model to obtain a compensated gravity measurement result, wherein an error compensation equation is shown as a formula (2):
in the formula, gcompensateIs the gravity measurement result after compensation;
step ten, selecting other measuring lines in the measuring area, wherein the type of the fitting curve of the gravity measurement result of the target measuring line is the same as that of the fitting curve of the gravity measurement result of the target measuring line, and if the fitting curve of the gravity measurement result of the target measuring line is a secondary curve, the fitting curve of the gravity measurement result of the selected other measuring lines is also a secondary curve; and obtaining the gravity measurement results of other measuring lines according to the third step to the fifth step after reconstruction, and carrying out error compensation according to the ninth step to obtain the compensated gravity measurement results.
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