CN110632674B - Weak information extraction method for aviation gravity measurement data - Google Patents

Weak information extraction method for aviation gravity measurement data Download PDF

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CN110632674B
CN110632674B CN201911034180.4A CN201911034180A CN110632674B CN 110632674 B CN110632674 B CN 110632674B CN 201911034180 A CN201911034180 A CN 201911034180A CN 110632674 B CN110632674 B CN 110632674B
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王冠鑫
罗锋
周锡华
熊盛青
王林飞
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China Aero Geophysical Survey and Remote Sensing Center for Natural Resources
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    • G01—MEASURING; TESTING
    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
    • G01V7/00—Measuring gravitational fields or waves; Gravimetric prospecting or detecting
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Abstract

A weak information extraction method of aviation gravity measurement data comprises the following steps: (S1) correcting the DGPS data and the acceleration data; (S2) performing kalman filtering processing on the corrected DGPS data and acceleration data; (S3) kalman smoothing is performed on the result obtained in the step (S2) to obtain gravity anomaly data. The invention firstly converts the traditional frequency domain filtering into time domain filtering, thus avoiding the selection of cut-off frequency and the loss of signals; and secondly, the real state is estimated from the angle of the aircraft motion, so that the gravity anomaly signal can be directly obtained, the aviation gravity data processing flow is simplified, and the operation efficiency is improved. And thirdly, a brand-new mathematical model for extracting the aviation gravity anomaly is provided, the DGPS data and the acceleration data are prevented from being staggered, and even if the fluctuating flight data are targeted, the gravity anomaly signal can be accurately extracted.

Description

Weak information extraction method for aviation gravity measurement data
Technical Field
The invention belongs to the technical field of aviation gravity exploration, and relates to a weak information extraction method of aviation gravity measurement data.
Background
Gravity exploration is an important geophysical exploration means, mainly comprises ground gravity measurement and aviation gravity measurement, and is usually adopted to acquire gravity field data when the conditions that workers cannot pass through complicated mountainous regions, marshes, oceans and the like or rapid scanning measurement is required. The aviation gravity measurement takes an airplane as a carrying platform, and utilizes a gravity and positioning sensor combined system to measure and obtain aviation gravity original measurement data of a free space; then, resolving the obtained original measurement data to obtain space gravity anomaly data (namely weak information); finally, based on the information, useful geophysical information is deduced. In the actual flight measurement process, because the aircraft is simultaneously influenced by multiple aspects such as self vibration, fluctuation, turning flight, airflow action and the like, no matter the aircraft is subjected to flight measurement by adopting a strapdown gravimeter, a vector gravimeter or a platform gravimeter, the obtained original gravity signal contains a large amount of noise, and the noise-signal ratio is up to thousands or even tens of thousands. For an aviation gravity measurement result, the in-line coincidence accuracy of the engineering exploration work requirement is 0.8mGal, and for a newly developed domestic gravimeter, the in-line coincidence accuracy of the newly developed domestic gravimeter requirement is 0.6mGal, so that a data resolving technology is required to reach a very high level. On the other hand, the vertical acceleration information measured by the gravimeter contains gravity field information, the vertical acceleration of the airplane and high-frequency noise. The method is characterized in that a traditional frequency domain filter (such as fir100s filtering which is commonly adopted at present) is adopted, firstly, the vertical acceleration of the airplane contained in original measurement data cannot be removed, the vertical acceleration needs to be processed independently in the resolving process, secondly, the accurate cut-off frequency cannot be determined, only the low-frequency component of the original measurement data can be extracted approximately, and effective information contained in the high-frequency component is filtered out together, so that the later-stage data resolving and application effects are poor. Therefore, how to obtain the gravity anomaly data meeting the available precision from the original measurement data still remains a key technical problem restricting the deep development of the aviation gravity exploration field.
Disclosure of Invention
The invention aims to overcome the technical defects in the prior art and provides the method for extracting the weak information of the aviation gravity measurement data, which has the advantages of concise data processing process, high information extraction accuracy and precision and less hardware resources occupied in the calculation process.
In order to achieve the purpose, the invention adopts the following technical scheme:
a weak information extraction method of aviation gravity measurement data comprises the following steps:
(S1) correcting the DGPS data and the acceleration data;
(S2) performing kalman filtering processing on the corrected DGPS data and acceleration data;
(S3) kalman smoothing is performed on the result obtained in the step (S2) to obtain gravity anomaly data.
The method for correcting the DGPS data and the acceleration data in step (S1) includes the following steps: eccentricity correction, ertvows correction, normal field correction, null shift correction, horizontal acceleration correction.
Further, the method of the kalman filter process in step (S2) is as follows:
(S2.1) constructing a mathematical model of the aviation gravity anomaly:
Figure BDA0002249837260000021
wherein Δ g is an abnormal value of gravity, fΣFor each corrected vertical gravity value, including normal field correction, height correction, horizontal acceleration correction, Ergo correction, null shift correction, base point correction, etc., vuIs the vertical acceleration of the aircraft, qΣIs the sum of various types of noise;
(S2.2) constructing a Kalman filtering state equation:
Figure BDA0002249837260000022
in the formula (f)1'、f2'、f3' are two measurements of horizontal and vertical acceleration; the error of vertical acceleration measured by gravimeter can be divided into low-frequency components delta fTAnd a high frequency component δ f, where δ fTDue to low frequency disturbances, such as angular acceleration caused by aircraft pitch, roll motion; KF1、KF2The variable quantity of the platform installation error angle caused by material fatigue and temperature change;
(S2.3) constructing a Kalman filtering measurement equation:
h'＝h+δh (3)
in the formula, h' is the actual measurement height, h is the real height, and δ h is the error of the actual measurement height;
(S2.4) substituting the state equation established in the step (S2.2) and the measurement equation established in the step (S2.3) into kalman filter equations (4) and (5) to solve:
Xk＝Φk,k-1Xk-1+Bk-1uk-1+Γk-1Wk-1 (4)
Zk＝HkXk+Vk (5)
in the formula phik,k-1、Bk-1Is a constant matrix; u. ofk-1Is a control item; gamma-shapedk-1Driving the array for system noise; wkExciting a noise sequence for the system; vkFor measuring noise sequences, HkIs a measuring array; wherein the input value of Kalman filtering is f1'、f2'、f3'、fΣH', output values h, vu、KF1、KF2、Δg、
Figure BDA0002249837260000023
Δ g is a gravity abnormal value (namely weak information) which needs to be extracted in aviation gravity exploration;
further, the Kalman filter state equation adopted in the step (S2.4) is calculated by
Xk＝Φk,k-1Xk-1+Bk-1uk-1+Γk-1Wk-1 (4)
Replacing the steps as follows:
Xk＝Φk,k-1Xk-1+Bkuk+ΓW (6)
in the formula, XkIs an estimated state; phik,k-1、Bk-1、BkIs a constant matrix; u. ofk-1、ukIs a control item; gamma-shapedk-1Gamma is a system noise driving array; wkAnd W is a system excitation noise sequence.
The invention discloses a method for extracting weak information of aviation gravity measurement data, which has the following beneficial effects: one is to convert the conventional frequency domain filtering into time domain filtering. The aviation gravity data belongs to the bit field data, the frequency of the gravity abnormal signal is distributed in the whole frequency band, the traditional frequency domain frequency filtering (such as the fir100s filtering commonly used in the current stage engineering) only extracts the low-frequency component of the signal, the high-frequency part is abandoned, and the loss of useful information is caused. The Kalman filtering selected in the technical scheme estimates the real state of the gravity sensor in flight according to the stress and motion conditions of the gravity sensor in flight, so that a gravity abnormal signal is extracted, and the selection of a cut-off frequency and the loss of the signal are avoided. And secondly, the aviation gravity data processing flow is simplified, and the operation efficiency is improved. The vertical acceleration generated by the movement of the airplane cannot be removed by adopting the traditional frequency domain filtering, and the vertical acceleration of the airplane needs to be processed independently. The Kalman filter adopted by the technical scheme carries out estimation on the real state from the angle of airplane motion, so that the gravity anomaly signal can be directly obtained without other processing. Thirdly, a general Kalman filtering equation with control items (see Kalman filtering and integrated navigation principle (3 rd edition), page 49, formula (2.2.35)) is improved, the invention provides a mathematical model for aviation gravity anomaly extraction, and the control item at the previous moment is modified into the control item at the current moment according to actual characteristics, so that the DGPS data and the acceleration data are prevented from being misplaced. The improved algorithm can accurately extract the gravity anomaly signal even aiming at the measurement data acquired in the fluctuating flight.
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FIG. 1 is a schematic flow chart of a weak information extraction method of airborne gravity measurement data according to embodiment 1;
fig. 2 is a processing result in embodiment 2 using a conventional fir100s filter;
FIG. 3 is the result of the treatment in example 2 using the method described in example 1;
FIG. 4 is the results of processing the pre and post heave flight data in example 2 using the band control term equation described in example 1.
Detailed Description
The following further describes a specific embodiment of the method for extracting weak information of airborne gravity measurement data according to the present invention with reference to the accompanying drawings. The weak information extraction method of the aviation gravity measurement data is not limited to the description of the following embodiments.
Example 1:
the embodiment provides the principle and the steps of a weak information extraction method of aviation gravity measurement data.
As shown in fig. 1, the weak information extraction method of the aviation gravity measurement data mainly includes three steps of various gravity corrections, kalman filtering, and kalman smoothing.
(S1) gravity correction of items: the method adopted in this step is a method existing in the field of aviation gravity, for example, described in "theory and application of aviation gravity exploration" (bear bloom, etc., chapter seventh), and is not described herein again.
(S2) kalman filtering: the principle of the method proposed by the step is as follows:
let the estimated state XkAt tkTime instant receiving system noise sequence Wk-1And uncertain entry uk-1The equation of state of the driving mechanism is:
Xk＝Φk,k-1Xk-1+Bk-1uk-1+Γk-1Wk-1 (4)
in the formula phik,k-1、Bk-1Is a constant matrix; u. ofk-1Is a control item; gamma-shapedk-1Driving the array for system noise; wkFor system excitation noise sequence with variance Qk；VkFor measuring noise sequences, the variance is Rk. And WkAnd VkSatisfies the following conditions:
Figure BDA0002249837260000041
Figure BDA0002249837260000042
Figure BDA0002249837260000043
wherein Q is assumedkIs not negatively determined, RkIs positive. ZkAnd XkThe linear relation is satisfied, and the measurement equation is as follows:
Zk＝HkXk+Vk (5)
in the formula, HkIs a measurement array.
In the actual measurement of the aviation gravity, the stress and the flight state of a measurement carrier are analyzed according to a Newton second law, and a mathematical model of the aviation gravity anomaly can be constructed as follows:
Figure BDA0002249837260000044
wherein Δ g is an abnormal value of gravity, fΣFor each corrected vertical gravity value (including normal field correction, height correction, horizontal acceleration correction, erturb correction, null shift correction),
Figure BDA0002249837260000045
is the vertical acceleration of the aircraft, qΣIs the sum of various types of noise.
From the formula (1), it can be seen that the gravity anomaly Δ g at each moment needs to be corrected by the corrected vertical gravity value f at that momentΣVertical acceleration
Figure BDA0002249837260000046
And noise qΣIt is determined that, in the case of an airborne gravimetric measurement, the control term u from the previous time in equation (4) is still usedk-1And noise Wk-1Driving the state at the present moment is obviously not suitable. To solve this problem, the sub-topic is to correct the expression (4), i.e. the control item u at the current timekAnd noise WkDriving the current state:
Xk＝Φk,k-1Xk-1+Bkuk+ΓkWk (8)
in fact, gravity anomaly is similar to a steady and uniform random process, and the systematic error of the state equation constructed according to (1) can be considered as a constant state, and there are:
Xk＝Φk,k-1Xk-1+Bkuk+ΓW (5)
where k is 1, 2.
After the formula (4) is changed into the formula (5), the data calculation result is slightly improved when the airplane flies smoothly, and the data calculation result is obviously improved when the airplane flies in an undulating manner.
One of the differences between airborne and ground gravity measurements is that the latter is calibrated before the measurement area is made, whereas the former is calibrated only in the laboratory. In actual measurement, the aviation gravity sensor is influenced by a series of external factors such as temperature, humidity and material fatigue, and the calibrated parameters in a laboratory may have deviation. Therefore, additional considerations need to be added to equation (1). Equation (9) is an equation established using the measurement error relationship:
Figure BDA0002249837260000051
in the formula (f)1'、f2'、f3' are two measurements of horizontal and vertical acceleration; f. ofz1、fz2、fz3The real values of the two horizontal acceleration and the vertical acceleration are obtained; KF3Is the variation of the scale factor of the gravimeter; δ f1、δf2Measuring error for horizontal acceleration; the error of vertical acceleration measured by gravimeter can be divided into low-frequency components delta fTAnd high frequency components δ f, δ fTDue to low frequency disturbances (e.g., angular acceleration due to aircraft pitch, roll motion), and the portion δ f is due to vibration, noise, and external disturbances.
For the convenience of solution, the unknown value f in the formula (9) needs to be subjected to the mechanical relationship (10)z1、fz2、fz3And (3) replacement:
fz3＝f3-(α1+KF1)fz2+(α2+KF2)fz1 (10)
in the formula, alpha1、α2The error angles of the platform are inclined around the x axis and the y axis respectively; KF1、KF2The variable quantity of the platform installation error angle caused by material fatigue and temperature change is basically unchanged in one flight and can be treated as a constant. The equations (1), (9) and (10) are combined to obtain the equation of state:
Figure BDA0002249837260000052
gravity anomaly is a random process that can be filtered using a shaping filter:
Figure BDA0002249837260000053
this is modeled, and equation (2) is supplemented, and the gravity anomaly Δ g is taken as the estimated state. Here, the
Figure BDA0002249837260000054
As a filter state vector, Fg、ΓgIs a constant matrix, qgTo generate an intensity of QgWhite noise of (2).
Get
Figure BDA0002249837260000055
Two-dimensional, then:
Figure BDA0002249837260000056
combining equations (2), (12), the equation of state can be obtained:
Figure BDA0002249837260000061
obtaining estimated state after discrete processing
Figure BDA0002249837260000062
The Kalman filtering equation of state given in this embodiment fully considers the influence of factors such as the flight state of the aircraft and the fatigue of materials, and the traditional frequency domain filtering only processes data from the perspective of signal frequency bands.
(S3) kalman smoothing: since a certain time is required for kalman filtering to reach convergence, a small segment of unconverged value appears before the algorithm reaches a steady state, and this embodiment uses an RTS smoothing technique to process the small segment of unconverged value, as described in the kalman filtering and integrated navigation principle (3 rd edition), page 189. I.e. re-estimating the non-converged estimated value by using the already converged estimated value.
The weak information extraction method of the aviation gravity measurement data provided by the embodiment can better remove noise interference and cope with more complex flight conditions while keeping more useful information.
Example 2:
the embodiment provides a specific result of processing aviation gravity measurement data acquired by actual flight in a certain sea area by using the method in embodiment 1.
As shown in fig. 2 and 3, the results of the conventional fir100s filter and the kalman filter processing described in example 1 are shown. The aircraft performed 4 measurements on the same survey line, resulting in 4 replicate line data. Compared with the internal coincidence precision of 4 repeated line data, the processing result of Kalman filtering is smoother than that of a traditional fir100s filter, the coincidence precision in the repeated line is 0.471mGal, the coincidence precision in the repeated line of the traditional fir100s processing result is 0.719mGal, and the requirements of actual exploration and new development of a domestic gravimeter can be met by obviously using the Kalman filtering. Therefore, the Kalman filtering has better effect in processing the aviation gravity measurement data compared with the traditional fir100 s.
As shown in fig. 4, the results of processing the data of the flat flight and the heave flight before and after the improvement with the control term formula are shown. Through comparison, the processing effect is slightly improved in the stable flight stage of the airplane after the Kalman filtering formula is modified, and the processing effect is obviously improved in the fluctuating flight stage of the airplane. As can be seen, the use of equation (5) has a superior effect in the case of performing a complicated flight as compared to equation (4).
The foregoing is a more detailed description of the invention in connection with specific preferred embodiments and it is not intended that the invention be limited to these specific details. For those skilled in the art to which the invention pertains, several simple deductions or substitutions can be made without departing from the spirit of the invention, and all shall be considered as belonging to the protection scope of the invention.

Claims (2)

1. A weak information extraction method of aviation gravity measurement data is characterized by comprising the following steps: the method comprises the following steps:
(S1) correcting the synchronized DGPS data and acceleration data;
(S2) performing kalman filtering processing on the corrected DGPS data and acceleration data;
(S3) performing kalman smoothing processing on the result obtained in the step (S2) to obtain gravity anomaly data;
wherein the method of the kalman filtering process in the step (S2) is as follows:
(S2.1) constructing a mathematical model of the aviation gravity anomaly:
Figure FDA0002898273810000011
wherein Δ g is an abnormal value of gravity, f∑The corrected vertical gravities include normal field correction, height correction, horizontal acceleration correction, crock correction, null shift correction, base point correction, vuIs the vertical acceleration of the aircraft, q∑As a sum of various types of noise；
(S2.2) constructing a Kalman filtering state equation:
Figure FDA0002898273810000012
Figure FDA0002898273810000013
Figure FDA0002898273810000014
Figure FDA0002898273810000015
Figure FDA0002898273810000016
Figure FDA0002898273810000017
Figure FDA0002898273810000018
of formula (II) to'1、f′2、f′3Two horizontal acceleration and vertical acceleration measurement values are obtained; the error of vertical acceleration measured by gravimeter can be divided into low-frequency components delta fTAnd a high frequency component δ f, where δ fTDue to low frequency disturbances, including angular accelerations caused by pitching and rolling movements of the aircraft; KF1、KF2The variable quantity of the platform installation error angle caused by material fatigue and temperature change;
(S2.3) constructing a Kalman filtering measurement equation:
h′＝h+δh (3)
in the formula, h' is the actual measurement height, h is the real height, and δ h is the error of the actual measurement height;
(S2.4) substituting the state equation established in the step (S2.2) and the measurement equation established in the step (S2.3) into kalman filter equations (6) and (5) to solve:
Xk＝Φk，k-1Xk-1+Bkuk+ΓW (6)
Zk＝HkXk+Vk (5)
in the formula, XkIs an estimated state; phik，k-1、BK-1、BkIs a constant matrix; u. ofk-1、ukIs a control item; gamma-shapedk-1Gamma is a system noise driving array; wkW is a system excitation noise sequence; vkFor measuring noise sequences, HkIs a measuring array; wherein the input value of Kalman filtering is f'1、f′2、f′3、f∑H', output values h, vu、KF1、KF2、Δg、
Figure FDA0002898273810000019
And deltag is a gravity abnormal value required to be extracted in aviation gravity exploration.
2. The weak information extraction method of the airborne gravity measurement data according to claim 1, characterized in that: the method for correcting the synchronized DGPS data and acceleration data in step (S1) includes the following steps: eccentricity correction, ertvows correction, normal field correction, null shift correction, horizontal acceleration correction.
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